TSTP Solution File: ITP072^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP072^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:17:59 EDT 2023
% Result : Theorem 0.95s 1.20s
% Output : Proof 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.19 % Problem : ITP072^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.19 % Command : do_cvc5 %s %d
% 0.17/0.40 % Computer : n018.cluster.edu
% 0.17/0.40 % Model : x86_64 x86_64
% 0.17/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.40 % Memory : 8042.1875MB
% 0.17/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.40 % CPULimit : 300
% 0.17/0.40 % WCLimit : 300
% 0.17/0.40 % DateTime : Sun Aug 27 16:18:01 EDT 2023
% 0.17/0.40 % CPUTime :
% 0.23/0.56 %----Proving TH0
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.57 % File : ITP072^1 : TPTP v8.1.2. Released v7.5.0.
% 0.23/0.57 % Domain : Interactive Theorem Proving
% 0.23/0.57 % Problem : Sledgehammer HF problem prob_113__5324706_1
% 0.23/0.57 % Version : Especial.
% 0.23/0.57 % English :
% 0.23/0.57
% 0.23/0.57 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.23/0.57 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.23/0.57 % Source : [Des21]
% 0.23/0.57 % Names : HF/prob_113__5324706_1 [Des21]
% 0.23/0.57
% 0.23/0.57 % Status : Theorem
% 0.23/0.57 % Rating : 0.31 v8.1.0, 0.27 v7.5.0
% 0.23/0.57 % Syntax : Number of formulae : 415 ( 154 unt; 63 typ; 0 def)
% 0.23/0.57 % Number of atoms : 1084 ( 383 equ; 0 cnn)
% 0.23/0.57 % Maximal formula atoms : 12 ( 3 avg)
% 0.23/0.57 % Number of connectives : 2828 ( 164 ~; 16 |; 87 &;2035 @)
% 0.23/0.57 % ( 0 <=>; 526 =>; 0 <=; 0 <~>)
% 0.23/0.57 % Maximal formula depth : 18 ( 6 avg)
% 0.23/0.57 % Number of types : 6 ( 5 usr)
% 0.23/0.57 % Number of type conns : 221 ( 221 >; 0 *; 0 +; 0 <<)
% 0.23/0.57 % Number of symbols : 59 ( 58 usr; 9 con; 0-2 aty)
% 0.23/0.57 % Number of variables : 898 ( 41 ^; 811 !; 46 ?; 898 :)
% 0.23/0.57 % SPC : TH0_THM_EQU_NAR
% 0.23/0.57
% 0.23/0.57 % Comments : This file was generated by Sledgehammer 2021-02-23 15:36:17.372
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.57 % Could-be-implicit typings (5)
% 0.23/0.57 thf(ty_n_t__Set__Oset_It__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_J,type,
% 0.23/0.57 set_se933006839lle_hf: $tType ).
% 0.23/0.57
% 0.23/0.57 thf(ty_n_t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 set_HF_Mirabelle_hf: $tType ).
% 0.23/0.57
% 0.23/0.57 thf(ty_n_t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 hF_Mirabelle_hf: $tType ).
% 0.23/0.57
% 0.23/0.57 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.23/0.57 set_nat: $tType ).
% 0.23/0.57
% 0.23/0.57 thf(ty_n_t__Nat__Onat,type,
% 0.23/0.57 nat: $tType ).
% 0.23/0.57
% 0.23/0.57 % Explicit typings (58)
% 0.23/0.57 thf(sy_c_Finite__Set_Ocard_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 finite1213132899lle_hf: set_HF_Mirabelle_hf > nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 0.23/0.57 finite_card_nat: set_nat > nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 finite90088345lle_hf: set_se933006839lle_hf > nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Finite__Set_Ofinite_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 finite586181922lle_hf: set_HF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 0.23/0.57 finite_finite_nat: set_nat > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 finite1450550360lle_hf: set_se933006839lle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Fun_Oinj__on_001t__HF____Mirabelle____glliljednj__Ohf_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 inj_on755450110lle_hf: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > set_HF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Fun_Oinj__on_001t__HF____Mirabelle____glliljednj__Ohf_001t__Nat__Onat,type,
% 0.23/0.57 inj_on1874279374hf_nat: ( hF_Mirabelle_hf > nat ) > set_HF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 inj_on1988990670lle_hf: ( nat > hF_Mirabelle_hf ) > set_nat > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.23/0.57 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Fun_Oinj__on_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 inj_on811196232lle_hf: ( set_HF_Mirabelle_hf > hF_Mirabelle_hf ) > set_se933006839lle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.23/0.57 minus_minus_nat: nat > nat > nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 minus_1450406810lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.23/0.57 minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_J,type,
% 0.23/0.57 minus_500612048lle_hf: set_se933006839lle_hf > set_se933006839lle_hf > set_se933006839lle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Groups_Ozero__class_Ozero_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 zero_z189798548lle_hf: hF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.23/0.57 zero_zero_nat: nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_HF__Mirabelle__glliljednj_OHF,type,
% 0.23/0.57 hF_Mirabelle_HF: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohf_OAbs__hf,type,
% 0.23/0.57 hF_Mirabelle_Abs_hf: nat > hF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohfset,type,
% 0.23/0.57 hF_Mirabelle_hfset: hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohinsert,type,
% 0.23/0.57 hF_Mirabelle_hinsert: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohmem,type,
% 0.23/0.57 hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__HF____Mirabelle____glliljednj__Ohf_001t__Nat__Onat,type,
% 0.23/0.57 lattic710307446hf_nat: ( hF_Mirabelle_hf > nat ) > set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.23/0.57 lattic1974000059at_nat: ( nat > nat ) > set_nat > nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Nat__Onat,type,
% 0.23/0.57 semiring_1_Nats_nat: set_nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__HF____Mirabelle____glliljednj__Ohf_M_Eo_J,type,
% 0.23/0.57 bot_bo1263054448e_hf_o: hF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.23/0.57 bot_bot_nat_o: nat > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_M_Eo_J,type,
% 0.23/0.57 bot_bo554042810e_hf_o: set_HF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 0.23/0.57 bot_bot_o: $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 0.23/0.57 bot_bot_nat: nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 bot_bo53200981lle_hf: set_HF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.23/0.57 bot_bot_set_nat: set_nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_J,type,
% 0.23/0.57 bot_bo2093393035lle_hf: set_se933006839lle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.23/0.57 ord_less_eq_nat: nat > nat > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 ord_le432112161lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.23/0.57 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_J,type,
% 0.23/0.57 ord_le2016357975lle_hf: set_se933006839lle_hf > set_se933006839lle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Parity_Osemiring__bit__shifts__class_Odrop__bit_001t__Nat__Onat,type,
% 0.23/0.57 semiri2115134414it_nat: nat > nat > nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Parity_Osemiring__bit__shifts__class_Opush__bit_001t__Nat__Onat,type,
% 0.23/0.57 semiri2013084963it_nat: nat > nat > nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_OCollect_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 collec2046588256lle_hf: ( hF_Mirabelle_hf > $o ) > set_HF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.23/0.57 collect_nat: ( nat > $o ) > set_nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_OCollect_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 collec1758573718lle_hf: ( set_HF_Mirabelle_hf > $o ) > set_se933006839lle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Oimage_001t__HF____Mirabelle____glliljednj__Ohf_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 image_1743964010lle_hf: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Oimage_001t__HF____Mirabelle____glliljednj__Ohf_001t__Nat__Onat,type,
% 0.23/0.57 image_131453538hf_nat: ( hF_Mirabelle_hf > nat ) > set_HF_Mirabelle_hf > set_nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 image_246164834lle_hf: ( nat > hF_Mirabelle_hf ) > set_nat > set_HF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.23/0.57 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Oimage_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 image_899003828lle_hf: ( set_HF_Mirabelle_hf > hF_Mirabelle_hf ) > set_se933006839lle_hf > set_HF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Oimage_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 image_1514960916lle_hf: ( set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ) > set_se933006839lle_hf > set_se933006839lle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Oinsert_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 insert9649339lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 0.23/0.57 insert_nat: nat > set_nat > set_nat ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 insert1636143089lle_hf: set_HF_Mirabelle_hf > set_se933006839lle_hf > set_se933006839lle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Ois__empty_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 is_emp566801209lle_hf: set_HF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Ois__singleton_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 is_sin1448700567lle_hf: set_HF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_Set_Othe__elem_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 the_el1104322134lle_hf: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_member_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.23/0.57 member1367349282lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_member_001t__Nat__Onat,type,
% 0.23/0.57 member_nat: nat > set_nat > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_c_member_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.23/0.57 member1490636632lle_hf: set_HF_Mirabelle_hf > set_se933006839lle_hf > $o ).
% 0.23/0.57
% 0.23/0.57 thf(sy_v_z,type,
% 0.23/0.57 z: hF_Mirabelle_hf ).
% 0.23/0.57
% 0.23/0.57 % Relevant facts (351)
% 0.23/0.57 thf(fact_0_hf__ext,axiom,
% 0.23/0.57 ( ( ^ [Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] : ( Y = Z ) )
% 0.23/0.57 = ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.23/0.57 ! [X: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( hF_Mirabelle_hmem @ X @ A )
% 0.23/0.57 = ( hF_Mirabelle_hmem @ X @ B ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % hf_ext
% 0.23/0.57 thf(fact_1_hemptyE,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % hemptyE
% 0.23/0.57 thf(fact_2_hmem__hempty,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % hmem_hempty
% 0.23/0.57 thf(fact_3_hf__cases,axiom,
% 0.23/0.57 ! [Y2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( Y2 != zero_z189798548lle_hf )
% 0.23/0.57 => ~ ! [A3: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( Y2
% 0.23/0.57 = ( hF_Mirabelle_hinsert @ A3 @ B2 ) )
% 0.23/0.57 => ( hF_Mirabelle_hmem @ A3 @ B2 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % hf_cases
% 0.23/0.57 thf(fact_4_hmem__hinsert,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,B3: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( hF_Mirabelle_hmem @ A2 @ ( hF_Mirabelle_hinsert @ B3 @ C ) )
% 0.23/0.57 = ( ( A2 = B3 )
% 0.23/0.57 | ( hF_Mirabelle_hmem @ A2 @ C ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % hmem_hinsert
% 0.23/0.57 thf(fact_5_hmem__def,axiom,
% 0.23/0.57 ( hF_Mirabelle_hmem
% 0.23/0.57 = ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % hmem_def
% 0.23/0.57 thf(fact_6_zero__reorient,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( zero_z189798548lle_hf = X2 )
% 0.23/0.57 = ( X2 = zero_z189798548lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % zero_reorient
% 0.23/0.57 thf(fact_7_zero__reorient,axiom,
% 0.23/0.57 ! [X2: nat] :
% 0.23/0.57 ( ( zero_zero_nat = X2 )
% 0.23/0.57 = ( X2 = zero_zero_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % zero_reorient
% 0.23/0.57 thf(fact_8_Abs__hf__0,axiom,
% 0.23/0.57 ( ( hF_Mirabelle_Abs_hf @ zero_zero_nat )
% 0.23/0.57 = zero_z189798548lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % Abs_hf_0
% 0.23/0.57 thf(fact_9_Zero__hf__def,axiom,
% 0.23/0.57 ( zero_z189798548lle_hf
% 0.23/0.57 = ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % Zero_hf_def
% 0.23/0.57 thf(fact_10_push__bit__of__0,axiom,
% 0.23/0.57 ! [N: nat] :
% 0.23/0.57 ( ( semiri2013084963it_nat @ N @ zero_zero_nat )
% 0.23/0.57 = zero_zero_nat ) ).
% 0.23/0.57
% 0.23/0.57 % push_bit_of_0
% 0.23/0.57 thf(fact_11_push__bit__eq__0__iff,axiom,
% 0.23/0.57 ! [N: nat,A2: nat] :
% 0.23/0.57 ( ( ( semiri2013084963it_nat @ N @ A2 )
% 0.23/0.57 = zero_zero_nat )
% 0.23/0.57 = ( A2 = zero_zero_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % push_bit_eq_0_iff
% 0.23/0.57 thf(fact_12_drop__bit__of__0,axiom,
% 0.23/0.57 ! [N: nat] :
% 0.23/0.57 ( ( semiri2115134414it_nat @ N @ zero_zero_nat )
% 0.23/0.57 = zero_zero_nat ) ).
% 0.23/0.57
% 0.23/0.57 % drop_bit_of_0
% 0.23/0.57 thf(fact_13_Nats__0,axiom,
% 0.23/0.57 member_nat @ zero_zero_nat @ semiring_1_Nats_nat ).
% 0.23/0.57
% 0.23/0.57 % Nats_0
% 0.23/0.57 thf(fact_14_HF__hfset,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A2 ) )
% 0.23/0.57 = A2 ) ).
% 0.23/0.57
% 0.23/0.57 % HF_hfset
% 0.23/0.57 thf(fact_15_empty__iff,axiom,
% 0.23/0.57 ! [C: set_HF_Mirabelle_hf] :
% 0.23/0.57 ~ ( member1490636632lle_hf @ C @ bot_bo2093393035lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % empty_iff
% 0.23/0.57 thf(fact_16_empty__iff,axiom,
% 0.23/0.57 ! [C: nat] :
% 0.23/0.57 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 0.23/0.57
% 0.23/0.57 % empty_iff
% 0.23/0.57 thf(fact_17_empty__iff,axiom,
% 0.23/0.57 ! [C: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( member1367349282lle_hf @ C @ bot_bo53200981lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % empty_iff
% 0.23/0.57 thf(fact_18_all__not__in__conv,axiom,
% 0.23/0.57 ! [A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( ! [X: set_HF_Mirabelle_hf] :
% 0.23/0.57 ~ ( member1490636632lle_hf @ X @ A4 ) )
% 0.23/0.57 = ( A4 = bot_bo2093393035lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % all_not_in_conv
% 0.23/0.57 thf(fact_19_all__not__in__conv,axiom,
% 0.23/0.57 ! [A4: set_nat] :
% 0.23/0.57 ( ( ! [X: nat] :
% 0.23/0.57 ~ ( member_nat @ X @ A4 ) )
% 0.23/0.57 = ( A4 = bot_bot_set_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % all_not_in_conv
% 0.23/0.57 thf(fact_20_all__not__in__conv,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ! [X: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( member1367349282lle_hf @ X @ A4 ) )
% 0.23/0.57 = ( A4 = bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % all_not_in_conv
% 0.23/0.57 thf(fact_21_Collect__empty__eq,axiom,
% 0.23/0.57 ! [P: nat > $o] :
% 0.23/0.57 ( ( ( collect_nat @ P )
% 0.23/0.57 = bot_bot_set_nat )
% 0.23/0.57 = ( ! [X: nat] :
% 0.23/0.57 ~ ( P @ X ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_empty_eq
% 0.23/0.57 thf(fact_22_Collect__empty__eq,axiom,
% 0.23/0.57 ! [P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( ( collec1758573718lle_hf @ P )
% 0.23/0.57 = bot_bo2093393035lle_hf )
% 0.23/0.57 = ( ! [X: set_HF_Mirabelle_hf] :
% 0.23/0.57 ~ ( P @ X ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_empty_eq
% 0.23/0.57 thf(fact_23_Collect__empty__eq,axiom,
% 0.23/0.57 ! [P: hF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( ( collec2046588256lle_hf @ P )
% 0.23/0.57 = bot_bo53200981lle_hf )
% 0.23/0.57 = ( ! [X: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( P @ X ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_empty_eq
% 0.23/0.57 thf(fact_24_empty__Collect__eq,axiom,
% 0.23/0.57 ! [P: nat > $o] :
% 0.23/0.57 ( ( bot_bot_set_nat
% 0.23/0.57 = ( collect_nat @ P ) )
% 0.23/0.57 = ( ! [X: nat] :
% 0.23/0.57 ~ ( P @ X ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % empty_Collect_eq
% 0.23/0.57 thf(fact_25_empty__Collect__eq,axiom,
% 0.23/0.57 ! [P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( bot_bo2093393035lle_hf
% 0.23/0.57 = ( collec1758573718lle_hf @ P ) )
% 0.23/0.57 = ( ! [X: set_HF_Mirabelle_hf] :
% 0.23/0.57 ~ ( P @ X ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % empty_Collect_eq
% 0.23/0.57 thf(fact_26_empty__Collect__eq,axiom,
% 0.23/0.57 ! [P: hF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( bot_bo53200981lle_hf
% 0.23/0.57 = ( collec2046588256lle_hf @ P ) )
% 0.23/0.57 = ( ! [X: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( P @ X ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % empty_Collect_eq
% 0.23/0.57 thf(fact_27_bot__apply,axiom,
% 0.23/0.57 ( bot_bo1263054448e_hf_o
% 0.23/0.57 = ( ^ [X: hF_Mirabelle_hf] : bot_bot_o ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_apply
% 0.23/0.57 thf(fact_28_bot__apply,axiom,
% 0.23/0.57 ( bot_bo554042810e_hf_o
% 0.23/0.57 = ( ^ [X: set_HF_Mirabelle_hf] : bot_bot_o ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_apply
% 0.23/0.57 thf(fact_29_hinsert__def,axiom,
% 0.23/0.57 ( hF_Mirabelle_hinsert
% 0.23/0.57 = ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % hinsert_def
% 0.23/0.57 thf(fact_30_hfset__HF,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ A4 ) )
% 0.23/0.57 = A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % hfset_HF
% 0.23/0.57 thf(fact_31_zero__natural_Orsp,axiom,
% 0.23/0.57 zero_zero_nat = zero_zero_nat ).
% 0.23/0.57
% 0.23/0.57 % zero_natural.rsp
% 0.23/0.57 thf(fact_32_emptyE,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ~ ( member1490636632lle_hf @ A2 @ bot_bo2093393035lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % emptyE
% 0.23/0.57 thf(fact_33_emptyE,axiom,
% 0.23/0.57 ! [A2: nat] :
% 0.23/0.57 ~ ( member_nat @ A2 @ bot_bot_set_nat ) ).
% 0.23/0.57
% 0.23/0.57 % emptyE
% 0.23/0.57 thf(fact_34_emptyE,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( member1367349282lle_hf @ A2 @ bot_bo53200981lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % emptyE
% 0.23/0.57 thf(fact_35_equals0D,axiom,
% 0.23/0.57 ! [A4: set_se933006839lle_hf,A2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( A4 = bot_bo2093393035lle_hf )
% 0.23/0.57 => ~ ( member1490636632lle_hf @ A2 @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % equals0D
% 0.23/0.57 thf(fact_36_equals0D,axiom,
% 0.23/0.57 ! [A4: set_nat,A2: nat] :
% 0.23/0.57 ( ( A4 = bot_bot_set_nat )
% 0.23/0.57 => ~ ( member_nat @ A2 @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % equals0D
% 0.23/0.57 thf(fact_37_equals0D,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( A4 = bot_bo53200981lle_hf )
% 0.23/0.57 => ~ ( member1367349282lle_hf @ A2 @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % equals0D
% 0.23/0.57 thf(fact_38_insert__absorb2,axiom,
% 0.23/0.57 ! [X2: nat,A4: set_nat] :
% 0.23/0.57 ( ( insert_nat @ X2 @ ( insert_nat @ X2 @ A4 ) )
% 0.23/0.57 = ( insert_nat @ X2 @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_absorb2
% 0.23/0.57 thf(fact_39_insert__absorb2,axiom,
% 0.23/0.57 ! [X2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( insert1636143089lle_hf @ X2 @ ( insert1636143089lle_hf @ X2 @ A4 ) )
% 0.23/0.57 = ( insert1636143089lle_hf @ X2 @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_absorb2
% 0.23/0.57 thf(fact_40_insert__absorb2,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( insert9649339lle_hf @ X2 @ ( insert9649339lle_hf @ X2 @ A4 ) )
% 0.23/0.57 = ( insert9649339lle_hf @ X2 @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_absorb2
% 0.23/0.57 thf(fact_41_insert__iff,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat,A4: set_nat] :
% 0.23/0.57 ( ( member_nat @ A2 @ ( insert_nat @ B3 @ A4 ) )
% 0.23/0.57 = ( ( A2 = B3 )
% 0.23/0.57 | ( member_nat @ A2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_iff
% 0.23/0.57 thf(fact_42_insert__iff,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,B3: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ A2 @ ( insert1636143089lle_hf @ B3 @ A4 ) )
% 0.23/0.57 = ( ( A2 = B3 )
% 0.23/0.57 | ( member1490636632lle_hf @ A2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_iff
% 0.23/0.57 thf(fact_43_insert__iff,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,B3: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ B3 @ A4 ) )
% 0.23/0.57 = ( ( A2 = B3 )
% 0.23/0.57 | ( member1367349282lle_hf @ A2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_iff
% 0.23/0.57 thf(fact_44_insertCI,axiom,
% 0.23/0.57 ! [A2: nat,B4: set_nat,B3: nat] :
% 0.23/0.57 ( ( ~ ( member_nat @ A2 @ B4 )
% 0.23/0.57 => ( A2 = B3 ) )
% 0.23/0.57 => ( member_nat @ A2 @ ( insert_nat @ B3 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertCI
% 0.23/0.57 thf(fact_45_insertCI,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,B4: set_se933006839lle_hf,B3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ~ ( member1490636632lle_hf @ A2 @ B4 )
% 0.23/0.57 => ( A2 = B3 ) )
% 0.23/0.57 => ( member1490636632lle_hf @ A2 @ ( insert1636143089lle_hf @ B3 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertCI
% 0.23/0.57 thf(fact_46_insertCI,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ~ ( member1367349282lle_hf @ A2 @ B4 )
% 0.23/0.57 => ( A2 = B3 ) )
% 0.23/0.57 => ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ B3 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertCI
% 0.23/0.57 thf(fact_47_singletonI,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf] : ( member1490636632lle_hf @ A2 @ ( insert1636143089lle_hf @ A2 @ bot_bo2093393035lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % singletonI
% 0.23/0.57 thf(fact_48_singletonI,axiom,
% 0.23/0.57 ! [A2: nat] : ( member_nat @ A2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % singletonI
% 0.23/0.57 thf(fact_49_singletonI,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % singletonI
% 0.23/0.57 thf(fact_50_mk__disjoint__insert,axiom,
% 0.23/0.57 ! [A2: nat,A4: set_nat] :
% 0.23/0.57 ( ( member_nat @ A2 @ A4 )
% 0.23/0.57 => ? [B5: set_nat] :
% 0.23/0.57 ( ( A4
% 0.23/0.57 = ( insert_nat @ A2 @ B5 ) )
% 0.23/0.57 & ~ ( member_nat @ A2 @ B5 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % mk_disjoint_insert
% 0.23/0.57 thf(fact_51_mk__disjoint__insert,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ A2 @ A4 )
% 0.23/0.57 => ? [B5: set_se933006839lle_hf] :
% 0.23/0.57 ( ( A4
% 0.23/0.57 = ( insert1636143089lle_hf @ A2 @ B5 ) )
% 0.23/0.57 & ~ ( member1490636632lle_hf @ A2 @ B5 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % mk_disjoint_insert
% 0.23/0.57 thf(fact_52_mk__disjoint__insert,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A2 @ A4 )
% 0.23/0.57 => ? [B5: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( A4
% 0.23/0.57 = ( insert9649339lle_hf @ A2 @ B5 ) )
% 0.23/0.57 & ~ ( member1367349282lle_hf @ A2 @ B5 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % mk_disjoint_insert
% 0.23/0.57 thf(fact_53_insert__commute,axiom,
% 0.23/0.57 ! [X2: nat,Y2: nat,A4: set_nat] :
% 0.23/0.57 ( ( insert_nat @ X2 @ ( insert_nat @ Y2 @ A4 ) )
% 0.23/0.57 = ( insert_nat @ Y2 @ ( insert_nat @ X2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_commute
% 0.23/0.57 thf(fact_54_insert__commute,axiom,
% 0.23/0.57 ! [X2: set_HF_Mirabelle_hf,Y2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( insert1636143089lle_hf @ X2 @ ( insert1636143089lle_hf @ Y2 @ A4 ) )
% 0.23/0.57 = ( insert1636143089lle_hf @ Y2 @ ( insert1636143089lle_hf @ X2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_commute
% 0.23/0.57 thf(fact_55_insert__commute,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( insert9649339lle_hf @ X2 @ ( insert9649339lle_hf @ Y2 @ A4 ) )
% 0.23/0.57 = ( insert9649339lle_hf @ Y2 @ ( insert9649339lle_hf @ X2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_commute
% 0.23/0.57 thf(fact_56_insert__eq__iff,axiom,
% 0.23/0.57 ! [A2: nat,A4: set_nat,B3: nat,B4: set_nat] :
% 0.23/0.57 ( ~ ( member_nat @ A2 @ A4 )
% 0.23/0.57 => ( ~ ( member_nat @ B3 @ B4 )
% 0.23/0.57 => ( ( ( insert_nat @ A2 @ A4 )
% 0.23/0.57 = ( insert_nat @ B3 @ B4 ) )
% 0.23/0.57 = ( ( ( A2 = B3 )
% 0.23/0.57 => ( A4 = B4 ) )
% 0.23/0.57 & ( ( A2 != B3 )
% 0.23/0.57 => ? [C2: set_nat] :
% 0.23/0.57 ( ( A4
% 0.23/0.57 = ( insert_nat @ B3 @ C2 ) )
% 0.23/0.57 & ~ ( member_nat @ B3 @ C2 )
% 0.23/0.57 & ( B4
% 0.23/0.57 = ( insert_nat @ A2 @ C2 ) )
% 0.23/0.57 & ~ ( member_nat @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_eq_iff
% 0.23/0.57 thf(fact_57_insert__eq__iff,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf,B3: set_HF_Mirabelle_hf,B4: set_se933006839lle_hf] :
% 0.23/0.57 ( ~ ( member1490636632lle_hf @ A2 @ A4 )
% 0.23/0.57 => ( ~ ( member1490636632lle_hf @ B3 @ B4 )
% 0.23/0.57 => ( ( ( insert1636143089lle_hf @ A2 @ A4 )
% 0.23/0.57 = ( insert1636143089lle_hf @ B3 @ B4 ) )
% 0.23/0.57 = ( ( ( A2 = B3 )
% 0.23/0.57 => ( A4 = B4 ) )
% 0.23/0.57 & ( ( A2 != B3 )
% 0.23/0.57 => ? [C2: set_se933006839lle_hf] :
% 0.23/0.57 ( ( A4
% 0.23/0.57 = ( insert1636143089lle_hf @ B3 @ C2 ) )
% 0.23/0.57 & ~ ( member1490636632lle_hf @ B3 @ C2 )
% 0.23/0.57 & ( B4
% 0.23/0.57 = ( insert1636143089lle_hf @ A2 @ C2 ) )
% 0.23/0.57 & ~ ( member1490636632lle_hf @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_eq_iff
% 0.23/0.57 thf(fact_58_insert__eq__iff,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B3: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ~ ( member1367349282lle_hf @ A2 @ A4 )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ B3 @ B4 )
% 0.23/0.57 => ( ( ( insert9649339lle_hf @ A2 @ A4 )
% 0.23/0.57 = ( insert9649339lle_hf @ B3 @ B4 ) )
% 0.23/0.57 = ( ( ( A2 = B3 )
% 0.23/0.57 => ( A4 = B4 ) )
% 0.23/0.57 & ( ( A2 != B3 )
% 0.23/0.57 => ? [C2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( A4
% 0.23/0.57 = ( insert9649339lle_hf @ B3 @ C2 ) )
% 0.23/0.57 & ~ ( member1367349282lle_hf @ B3 @ C2 )
% 0.23/0.57 & ( B4
% 0.23/0.57 = ( insert9649339lle_hf @ A2 @ C2 ) )
% 0.23/0.57 & ~ ( member1367349282lle_hf @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_eq_iff
% 0.23/0.57 thf(fact_59_insert__absorb,axiom,
% 0.23/0.57 ! [A2: nat,A4: set_nat] :
% 0.23/0.57 ( ( member_nat @ A2 @ A4 )
% 0.23/0.57 => ( ( insert_nat @ A2 @ A4 )
% 0.23/0.57 = A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_absorb
% 0.23/0.57 thf(fact_60_insert__absorb,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ A2 @ A4 )
% 0.23/0.57 => ( ( insert1636143089lle_hf @ A2 @ A4 )
% 0.23/0.57 = A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_absorb
% 0.23/0.57 thf(fact_61_insert__absorb,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A2 @ A4 )
% 0.23/0.57 => ( ( insert9649339lle_hf @ A2 @ A4 )
% 0.23/0.57 = A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_absorb
% 0.23/0.57 thf(fact_62_insert__ident,axiom,
% 0.23/0.57 ! [X2: nat,A4: set_nat,B4: set_nat] :
% 0.23/0.57 ( ~ ( member_nat @ X2 @ A4 )
% 0.23/0.57 => ( ~ ( member_nat @ X2 @ B4 )
% 0.23/0.57 => ( ( ( insert_nat @ X2 @ A4 )
% 0.23/0.57 = ( insert_nat @ X2 @ B4 ) )
% 0.23/0.57 = ( A4 = B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_ident
% 0.23/0.57 thf(fact_63_insert__ident,axiom,
% 0.23/0.57 ! [X2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf,B4: set_se933006839lle_hf] :
% 0.23/0.57 ( ~ ( member1490636632lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ~ ( member1490636632lle_hf @ X2 @ B4 )
% 0.23/0.57 => ( ( ( insert1636143089lle_hf @ X2 @ A4 )
% 0.23/0.57 = ( insert1636143089lle_hf @ X2 @ B4 ) )
% 0.23/0.57 = ( A4 = B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_ident
% 0.23/0.57 thf(fact_64_insert__ident,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ~ ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ X2 @ B4 )
% 0.23/0.57 => ( ( ( insert9649339lle_hf @ X2 @ A4 )
% 0.23/0.57 = ( insert9649339lle_hf @ X2 @ B4 ) )
% 0.23/0.57 = ( A4 = B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_ident
% 0.23/0.57 thf(fact_65_Set_Oset__insert,axiom,
% 0.23/0.57 ! [X2: nat,A4: set_nat] :
% 0.23/0.57 ( ( member_nat @ X2 @ A4 )
% 0.23/0.57 => ~ ! [B5: set_nat] :
% 0.23/0.57 ( ( A4
% 0.23/0.57 = ( insert_nat @ X2 @ B5 ) )
% 0.23/0.57 => ( member_nat @ X2 @ B5 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Set.set_insert
% 0.23/0.57 thf(fact_66_Set_Oset__insert,axiom,
% 0.23/0.57 ! [X2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ X2 @ A4 )
% 0.23/0.57 => ~ ! [B5: set_se933006839lle_hf] :
% 0.23/0.57 ( ( A4
% 0.23/0.57 = ( insert1636143089lle_hf @ X2 @ B5 ) )
% 0.23/0.57 => ( member1490636632lle_hf @ X2 @ B5 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Set.set_insert
% 0.23/0.57 thf(fact_67_Set_Oset__insert,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 => ~ ! [B5: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( A4
% 0.23/0.57 = ( insert9649339lle_hf @ X2 @ B5 ) )
% 0.23/0.57 => ( member1367349282lle_hf @ X2 @ B5 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Set.set_insert
% 0.23/0.57 thf(fact_68_insertI2,axiom,
% 0.23/0.57 ! [A2: nat,B4: set_nat,B3: nat] :
% 0.23/0.57 ( ( member_nat @ A2 @ B4 )
% 0.23/0.57 => ( member_nat @ A2 @ ( insert_nat @ B3 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertI2
% 0.23/0.57 thf(fact_69_insertI2,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,B4: set_se933006839lle_hf,B3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ A2 @ B4 )
% 0.23/0.57 => ( member1490636632lle_hf @ A2 @ ( insert1636143089lle_hf @ B3 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertI2
% 0.23/0.57 thf(fact_70_insertI2,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A2 @ B4 )
% 0.23/0.57 => ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ B3 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertI2
% 0.23/0.57 thf(fact_71_insertI1,axiom,
% 0.23/0.57 ! [A2: nat,B4: set_nat] : ( member_nat @ A2 @ ( insert_nat @ A2 @ B4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertI1
% 0.23/0.57 thf(fact_72_insertI1,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,B4: set_se933006839lle_hf] : ( member1490636632lle_hf @ A2 @ ( insert1636143089lle_hf @ A2 @ B4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertI1
% 0.23/0.57 thf(fact_73_insertI1,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] : ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ A2 @ B4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertI1
% 0.23/0.57 thf(fact_74_insertE,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat,A4: set_nat] :
% 0.23/0.57 ( ( member_nat @ A2 @ ( insert_nat @ B3 @ A4 ) )
% 0.23/0.57 => ( ( A2 != B3 )
% 0.23/0.57 => ( member_nat @ A2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertE
% 0.23/0.57 thf(fact_75_insertE,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,B3: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ A2 @ ( insert1636143089lle_hf @ B3 @ A4 ) )
% 0.23/0.57 => ( ( A2 != B3 )
% 0.23/0.57 => ( member1490636632lle_hf @ A2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertE
% 0.23/0.57 thf(fact_76_insertE,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,B3: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ B3 @ A4 ) )
% 0.23/0.57 => ( ( A2 != B3 )
% 0.23/0.57 => ( member1367349282lle_hf @ A2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insertE
% 0.23/0.57 thf(fact_77_finite__cases,axiom,
% 0.23/0.57 ! [F: set_se933006839lle_hf] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ F )
% 0.23/0.57 => ( ( F != bot_bo2093393035lle_hf )
% 0.23/0.57 => ~ ! [A5: set_se933006839lle_hf,X3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( F
% 0.23/0.57 = ( insert1636143089lle_hf @ X3 @ A5 ) )
% 0.23/0.57 => ( ~ ( member1490636632lle_hf @ X3 @ A5 )
% 0.23/0.57 => ~ ( finite1450550360lle_hf @ A5 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_cases
% 0.23/0.57 thf(fact_78_finite__cases,axiom,
% 0.23/0.57 ! [F: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ F )
% 0.23/0.57 => ( ( F != bot_bot_set_nat )
% 0.23/0.57 => ~ ! [A5: set_nat,X3: nat] :
% 0.23/0.57 ( ( F
% 0.23/0.57 = ( insert_nat @ X3 @ A5 ) )
% 0.23/0.57 => ( ~ ( member_nat @ X3 @ A5 )
% 0.23/0.57 => ~ ( finite_finite_nat @ A5 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_cases
% 0.23/0.57 thf(fact_79_finite__cases,axiom,
% 0.23/0.57 ! [F: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F )
% 0.23/0.57 => ( ( F != bot_bo53200981lle_hf )
% 0.23/0.57 => ~ ! [A5: set_HF_Mirabelle_hf,X3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( F
% 0.23/0.57 = ( insert9649339lle_hf @ X3 @ A5 ) )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ X3 @ A5 )
% 0.23/0.57 => ~ ( finite586181922lle_hf @ A5 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_cases
% 0.23/0.57 thf(fact_80_bot__set__def,axiom,
% 0.23/0.57 ( bot_bot_set_nat
% 0.23/0.57 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_set_def
% 0.23/0.57 thf(fact_81_bot__set__def,axiom,
% 0.23/0.57 ( bot_bo2093393035lle_hf
% 0.23/0.57 = ( collec1758573718lle_hf @ bot_bo554042810e_hf_o ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_set_def
% 0.23/0.57 thf(fact_82_bot__set__def,axiom,
% 0.23/0.57 ( bot_bo53200981lle_hf
% 0.23/0.57 = ( collec2046588256lle_hf @ bot_bo1263054448e_hf_o ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_set_def
% 0.23/0.57 thf(fact_83_singleton__inject,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,B3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( insert1636143089lle_hf @ A2 @ bot_bo2093393035lle_hf )
% 0.23/0.57 = ( insert1636143089lle_hf @ B3 @ bot_bo2093393035lle_hf ) )
% 0.23/0.57 => ( A2 = B3 ) ) ).
% 0.23/0.57
% 0.23/0.57 % singleton_inject
% 0.23/0.57 thf(fact_84_singleton__inject,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat] :
% 0.23/0.57 ( ( ( insert_nat @ A2 @ bot_bot_set_nat )
% 0.23/0.57 = ( insert_nat @ B3 @ bot_bot_set_nat ) )
% 0.23/0.57 => ( A2 = B3 ) ) ).
% 0.23/0.57
% 0.23/0.57 % singleton_inject
% 0.23/0.57 thf(fact_85_singleton__inject,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf )
% 0.23/0.57 = ( insert9649339lle_hf @ B3 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 => ( A2 = B3 ) ) ).
% 0.23/0.57
% 0.23/0.57 % singleton_inject
% 0.23/0.57 thf(fact_86_insert__not__empty,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( insert1636143089lle_hf @ A2 @ A4 )
% 0.23/0.57 != bot_bo2093393035lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % insert_not_empty
% 0.23/0.57 thf(fact_87_insert__not__empty,axiom,
% 0.23/0.57 ! [A2: nat,A4: set_nat] :
% 0.23/0.57 ( ( insert_nat @ A2 @ A4 )
% 0.23/0.57 != bot_bot_set_nat ) ).
% 0.23/0.57
% 0.23/0.57 % insert_not_empty
% 0.23/0.57 thf(fact_88_insert__not__empty,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( insert9649339lle_hf @ A2 @ A4 )
% 0.23/0.57 != bot_bo53200981lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % insert_not_empty
% 0.23/0.57 thf(fact_89_doubleton__eq__iff,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,B3: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf,D: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( insert1636143089lle_hf @ A2 @ ( insert1636143089lle_hf @ B3 @ bot_bo2093393035lle_hf ) )
% 0.23/0.57 = ( insert1636143089lle_hf @ C @ ( insert1636143089lle_hf @ D @ bot_bo2093393035lle_hf ) ) )
% 0.23/0.57 = ( ( ( A2 = C )
% 0.23/0.57 & ( B3 = D ) )
% 0.23/0.57 | ( ( A2 = D )
% 0.23/0.57 & ( B3 = C ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % doubleton_eq_iff
% 0.23/0.57 thf(fact_90_doubleton__eq__iff,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 0.23/0.57 ( ( ( insert_nat @ A2 @ ( insert_nat @ B3 @ bot_bot_set_nat ) )
% 0.23/0.57 = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 0.23/0.57 = ( ( ( A2 = C )
% 0.23/0.57 & ( B3 = D ) )
% 0.23/0.57 | ( ( A2 = D )
% 0.23/0.57 & ( B3 = C ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % doubleton_eq_iff
% 0.23/0.57 thf(fact_91_doubleton__eq__iff,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,B3: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( insert9649339lle_hf @ A2 @ ( insert9649339lle_hf @ B3 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 = ( insert9649339lle_hf @ C @ ( insert9649339lle_hf @ D @ bot_bo53200981lle_hf ) ) )
% 0.23/0.57 = ( ( ( A2 = C )
% 0.23/0.57 & ( B3 = D ) )
% 0.23/0.57 | ( ( A2 = D )
% 0.23/0.57 & ( B3 = C ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % doubleton_eq_iff
% 0.23/0.57 thf(fact_92_mem__Collect__eq,axiom,
% 0.23/0.57 ! [A2: nat,P: nat > $o] :
% 0.23/0.57 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 0.23/0.57 = ( P @ A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % mem_Collect_eq
% 0.23/0.57 thf(fact_93_mem__Collect__eq,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A2 @ ( collec2046588256lle_hf @ P ) )
% 0.23/0.57 = ( P @ A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % mem_Collect_eq
% 0.23/0.57 thf(fact_94_mem__Collect__eq,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( member1490636632lle_hf @ A2 @ ( collec1758573718lle_hf @ P ) )
% 0.23/0.57 = ( P @ A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % mem_Collect_eq
% 0.23/0.57 thf(fact_95_Collect__mem__eq,axiom,
% 0.23/0.57 ! [A4: set_nat] :
% 0.23/0.57 ( ( collect_nat
% 0.23/0.57 @ ^ [X: nat] : ( member_nat @ X @ A4 ) )
% 0.23/0.57 = A4 ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_mem_eq
% 0.23/0.57 thf(fact_96_Collect__mem__eq,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( collec2046588256lle_hf
% 0.23/0.57 @ ^ [X: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X @ A4 ) )
% 0.23/0.57 = A4 ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_mem_eq
% 0.23/0.57 thf(fact_97_Collect__mem__eq,axiom,
% 0.23/0.57 ! [A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( collec1758573718lle_hf
% 0.23/0.57 @ ^ [X: set_HF_Mirabelle_hf] : ( member1490636632lle_hf @ X @ A4 ) )
% 0.23/0.57 = A4 ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_mem_eq
% 0.23/0.57 thf(fact_98_Collect__cong,axiom,
% 0.23/0.57 ! [P: hF_Mirabelle_hf > $o,Q: hF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ! [X3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( P @ X3 )
% 0.23/0.57 = ( Q @ X3 ) )
% 0.23/0.57 => ( ( collec2046588256lle_hf @ P )
% 0.23/0.57 = ( collec2046588256lle_hf @ Q ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_cong
% 0.23/0.57 thf(fact_99_Collect__cong,axiom,
% 0.23/0.57 ! [P: set_HF_Mirabelle_hf > $o,Q: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ! [X3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( P @ X3 )
% 0.23/0.57 = ( Q @ X3 ) )
% 0.23/0.57 => ( ( collec1758573718lle_hf @ P )
% 0.23/0.57 = ( collec1758573718lle_hf @ Q ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_cong
% 0.23/0.57 thf(fact_100_singleton__iff,axiom,
% 0.23/0.57 ! [B3: set_HF_Mirabelle_hf,A2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ B3 @ ( insert1636143089lle_hf @ A2 @ bot_bo2093393035lle_hf ) )
% 0.23/0.57 = ( B3 = A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % singleton_iff
% 0.23/0.57 thf(fact_101_singleton__iff,axiom,
% 0.23/0.57 ! [B3: nat,A2: nat] :
% 0.23/0.57 ( ( member_nat @ B3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 0.23/0.57 = ( B3 = A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % singleton_iff
% 0.23/0.57 thf(fact_102_singleton__iff,axiom,
% 0.23/0.57 ! [B3: hF_Mirabelle_hf,A2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ B3 @ ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 = ( B3 = A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % singleton_iff
% 0.23/0.57 thf(fact_103_singletonD,axiom,
% 0.23/0.57 ! [B3: set_HF_Mirabelle_hf,A2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ B3 @ ( insert1636143089lle_hf @ A2 @ bot_bo2093393035lle_hf ) )
% 0.23/0.57 => ( B3 = A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % singletonD
% 0.23/0.57 thf(fact_104_singletonD,axiom,
% 0.23/0.57 ! [B3: nat,A2: nat] :
% 0.23/0.57 ( ( member_nat @ B3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 0.23/0.57 => ( B3 = A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % singletonD
% 0.23/0.57 thf(fact_105_singletonD,axiom,
% 0.23/0.57 ! [B3: hF_Mirabelle_hf,A2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ B3 @ ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 => ( B3 = A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % singletonD
% 0.23/0.57 thf(fact_106_bot__nat__def,axiom,
% 0.23/0.57 bot_bot_nat = zero_zero_nat ).
% 0.23/0.57
% 0.23/0.57 % bot_nat_def
% 0.23/0.57 thf(fact_107_finite__hfset,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_hfset
% 0.23/0.57 thf(fact_108_bot__fun__def,axiom,
% 0.23/0.57 ( bot_bo1263054448e_hf_o
% 0.23/0.57 = ( ^ [X: hF_Mirabelle_hf] : bot_bot_o ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_fun_def
% 0.23/0.57 thf(fact_109_bot__fun__def,axiom,
% 0.23/0.57 ( bot_bo554042810e_hf_o
% 0.23/0.57 = ( ^ [X: set_HF_Mirabelle_hf] : bot_bot_o ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_fun_def
% 0.23/0.57 thf(fact_110_ex__in__conv,axiom,
% 0.23/0.57 ! [A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( ? [X: set_HF_Mirabelle_hf] : ( member1490636632lle_hf @ X @ A4 ) )
% 0.23/0.57 = ( A4 != bot_bo2093393035lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % ex_in_conv
% 0.23/0.57 thf(fact_111_ex__in__conv,axiom,
% 0.23/0.57 ! [A4: set_nat] :
% 0.23/0.57 ( ( ? [X: nat] : ( member_nat @ X @ A4 ) )
% 0.23/0.57 = ( A4 != bot_bot_set_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % ex_in_conv
% 0.23/0.57 thf(fact_112_ex__in__conv,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ? [X: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X @ A4 ) )
% 0.23/0.57 = ( A4 != bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % ex_in_conv
% 0.23/0.57 thf(fact_113_equals0I,axiom,
% 0.23/0.57 ! [A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ! [Y3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ~ ( member1490636632lle_hf @ Y3 @ A4 )
% 0.23/0.57 => ( A4 = bot_bo2093393035lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % equals0I
% 0.23/0.57 thf(fact_114_equals0I,axiom,
% 0.23/0.57 ! [A4: set_nat] :
% 0.23/0.57 ( ! [Y3: nat] :
% 0.23/0.57 ~ ( member_nat @ Y3 @ A4 )
% 0.23/0.57 => ( A4 = bot_bot_set_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % equals0I
% 0.23/0.57 thf(fact_115_equals0I,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ! [Y3: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( member1367349282lle_hf @ Y3 @ A4 )
% 0.23/0.57 => ( A4 = bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % equals0I
% 0.23/0.57 thf(fact_116_finite__insert,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ ( insert1636143089lle_hf @ A2 @ A4 ) )
% 0.23/0.57 = ( finite1450550360lle_hf @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_insert
% 0.23/0.57 thf(fact_117_finite__insert,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ ( insert9649339lle_hf @ A2 @ A4 ) )
% 0.23/0.57 = ( finite586181922lle_hf @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_insert
% 0.23/0.57 thf(fact_118_finite__insert,axiom,
% 0.23/0.57 ! [A2: nat,A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ ( insert_nat @ A2 @ A4 ) )
% 0.23/0.57 = ( finite_finite_nat @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_insert
% 0.23/0.57 thf(fact_119_finite_Ocases,axiom,
% 0.23/0.57 ! [A2: set_se933006839lle_hf] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ A2 )
% 0.23/0.57 => ( ( A2 != bot_bo2093393035lle_hf )
% 0.23/0.57 => ~ ! [A5: set_se933006839lle_hf] :
% 0.23/0.57 ( ? [A3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( A2
% 0.23/0.57 = ( insert1636143089lle_hf @ A3 @ A5 ) )
% 0.23/0.57 => ~ ( finite1450550360lle_hf @ A5 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.cases
% 0.23/0.57 thf(fact_120_finite_Ocases,axiom,
% 0.23/0.57 ! [A2: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A2 )
% 0.23/0.57 => ( ( A2 != bot_bot_set_nat )
% 0.23/0.57 => ~ ! [A5: set_nat] :
% 0.23/0.57 ( ? [A3: nat] :
% 0.23/0.57 ( A2
% 0.23/0.57 = ( insert_nat @ A3 @ A5 ) )
% 0.23/0.57 => ~ ( finite_finite_nat @ A5 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.cases
% 0.23/0.57 thf(fact_121_finite_Ocases,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A2 )
% 0.23/0.57 => ( ( A2 != bot_bo53200981lle_hf )
% 0.23/0.57 => ~ ! [A5: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ? [A3: hF_Mirabelle_hf] :
% 0.23/0.57 ( A2
% 0.23/0.57 = ( insert9649339lle_hf @ A3 @ A5 ) )
% 0.23/0.57 => ~ ( finite586181922lle_hf @ A5 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.cases
% 0.23/0.57 thf(fact_122_finite_Osimps,axiom,
% 0.23/0.57 ( finite1450550360lle_hf
% 0.23/0.57 = ( ^ [A: set_se933006839lle_hf] :
% 0.23/0.57 ( ( A = bot_bo2093393035lle_hf )
% 0.23/0.57 | ? [A6: set_se933006839lle_hf,B: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( A
% 0.23/0.57 = ( insert1636143089lle_hf @ B @ A6 ) )
% 0.23/0.57 & ( finite1450550360lle_hf @ A6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.simps
% 0.23/0.57 thf(fact_123_finite_Osimps,axiom,
% 0.23/0.57 ( finite_finite_nat
% 0.23/0.57 = ( ^ [A: set_nat] :
% 0.23/0.57 ( ( A = bot_bot_set_nat )
% 0.23/0.57 | ? [A6: set_nat,B: nat] :
% 0.23/0.57 ( ( A
% 0.23/0.57 = ( insert_nat @ B @ A6 ) )
% 0.23/0.57 & ( finite_finite_nat @ A6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.simps
% 0.23/0.57 thf(fact_124_finite_Osimps,axiom,
% 0.23/0.57 ( finite586181922lle_hf
% 0.23/0.57 = ( ^ [A: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( A = bot_bo53200981lle_hf )
% 0.23/0.57 | ? [A6: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( A
% 0.23/0.57 = ( insert9649339lle_hf @ B @ A6 ) )
% 0.23/0.57 & ( finite586181922lle_hf @ A6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.simps
% 0.23/0.57 thf(fact_125_finite__induct,axiom,
% 0.23/0.57 ! [F: set_se933006839lle_hf,P: set_se933006839lle_hf > $o] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ F )
% 0.23/0.57 => ( ( P @ bot_bo2093393035lle_hf )
% 0.23/0.57 => ( ! [X3: set_HF_Mirabelle_hf,F2: set_se933006839lle_hf] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ F2 )
% 0.23/0.57 => ( ~ ( member1490636632lle_hf @ X3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert1636143089lle_hf @ X3 @ F2 ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_induct
% 0.23/0.57 thf(fact_126_finite__induct,axiom,
% 0.23/0.57 ! [F: set_nat,P: set_nat > $o] :
% 0.23/0.57 ( ( finite_finite_nat @ F )
% 0.23/0.57 => ( ( P @ bot_bot_set_nat )
% 0.23/0.57 => ( ! [X3: nat,F2: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ F2 )
% 0.23/0.57 => ( ~ ( member_nat @ X3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert_nat @ X3 @ F2 ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_induct
% 0.23/0.57 thf(fact_127_finite__induct,axiom,
% 0.23/0.57 ! [F: set_HF_Mirabelle_hf,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F )
% 0.23/0.57 => ( ( P @ bot_bo53200981lle_hf )
% 0.23/0.57 => ( ! [X3: hF_Mirabelle_hf,F2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F2 )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ X3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert9649339lle_hf @ X3 @ F2 ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_induct
% 0.23/0.57 thf(fact_128_finite_Oinducts,axiom,
% 0.23/0.57 ! [X2: set_se933006839lle_hf,P: set_se933006839lle_hf > $o] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ X2 )
% 0.23/0.57 => ( ( P @ bot_bo2093393035lle_hf )
% 0.23/0.57 => ( ! [A5: set_se933006839lle_hf,A3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ A5 )
% 0.23/0.57 => ( ( P @ A5 )
% 0.23/0.57 => ( P @ ( insert1636143089lle_hf @ A3 @ A5 ) ) ) )
% 0.23/0.57 => ( P @ X2 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.inducts
% 0.23/0.57 thf(fact_129_finite_Oinducts,axiom,
% 0.23/0.57 ! [X2: set_nat,P: set_nat > $o] :
% 0.23/0.57 ( ( finite_finite_nat @ X2 )
% 0.23/0.57 => ( ( P @ bot_bot_set_nat )
% 0.23/0.57 => ( ! [A5: set_nat,A3: nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A5 )
% 0.23/0.57 => ( ( P @ A5 )
% 0.23/0.57 => ( P @ ( insert_nat @ A3 @ A5 ) ) ) )
% 0.23/0.57 => ( P @ X2 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.inducts
% 0.23/0.57 thf(fact_130_finite_Oinducts,axiom,
% 0.23/0.57 ! [X2: set_HF_Mirabelle_hf,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( finite586181922lle_hf @ X2 )
% 0.23/0.57 => ( ( P @ bot_bo53200981lle_hf )
% 0.23/0.57 => ( ! [A5: set_HF_Mirabelle_hf,A3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A5 )
% 0.23/0.57 => ( ( P @ A5 )
% 0.23/0.57 => ( P @ ( insert9649339lle_hf @ A3 @ A5 ) ) ) )
% 0.23/0.57 => ( P @ X2 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.inducts
% 0.23/0.57 thf(fact_131_finite__ne__induct,axiom,
% 0.23/0.57 ! [F: set_se933006839lle_hf,P: set_se933006839lle_hf > $o] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ F )
% 0.23/0.57 => ( ( F != bot_bo2093393035lle_hf )
% 0.23/0.57 => ( ! [X3: set_HF_Mirabelle_hf] : ( P @ ( insert1636143089lle_hf @ X3 @ bot_bo2093393035lle_hf ) )
% 0.23/0.57 => ( ! [X3: set_HF_Mirabelle_hf,F2: set_se933006839lle_hf] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ F2 )
% 0.23/0.57 => ( ( F2 != bot_bo2093393035lle_hf )
% 0.23/0.57 => ( ~ ( member1490636632lle_hf @ X3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert1636143089lle_hf @ X3 @ F2 ) ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_ne_induct
% 0.23/0.57 thf(fact_132_finite__ne__induct,axiom,
% 0.23/0.57 ! [F: set_nat,P: set_nat > $o] :
% 0.23/0.57 ( ( finite_finite_nat @ F )
% 0.23/0.57 => ( ( F != bot_bot_set_nat )
% 0.23/0.57 => ( ! [X3: nat] : ( P @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.23/0.57 => ( ! [X3: nat,F2: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ F2 )
% 0.23/0.57 => ( ( F2 != bot_bot_set_nat )
% 0.23/0.57 => ( ~ ( member_nat @ X3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert_nat @ X3 @ F2 ) ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_ne_induct
% 0.23/0.57 thf(fact_133_finite__ne__induct,axiom,
% 0.23/0.57 ! [F: set_HF_Mirabelle_hf,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F )
% 0.23/0.57 => ( ( F != bot_bo53200981lle_hf )
% 0.23/0.57 => ( ! [X3: hF_Mirabelle_hf] : ( P @ ( insert9649339lle_hf @ X3 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 => ( ! [X3: hF_Mirabelle_hf,F2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F2 )
% 0.23/0.57 => ( ( F2 != bot_bo53200981lle_hf )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ X3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert9649339lle_hf @ X3 @ F2 ) ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_ne_induct
% 0.23/0.57 thf(fact_134_infinite__finite__induct,axiom,
% 0.23/0.57 ! [P: set_se933006839lle_hf > $o,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ! [A5: set_se933006839lle_hf] :
% 0.23/0.57 ( ~ ( finite1450550360lle_hf @ A5 )
% 0.23/0.57 => ( P @ A5 ) )
% 0.23/0.57 => ( ( P @ bot_bo2093393035lle_hf )
% 0.23/0.57 => ( ! [X3: set_HF_Mirabelle_hf,F2: set_se933006839lle_hf] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ F2 )
% 0.23/0.57 => ( ~ ( member1490636632lle_hf @ X3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert1636143089lle_hf @ X3 @ F2 ) ) ) ) )
% 0.23/0.57 => ( P @ A4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % infinite_finite_induct
% 0.23/0.57 thf(fact_135_infinite__finite__induct,axiom,
% 0.23/0.57 ! [P: set_nat > $o,A4: set_nat] :
% 0.23/0.57 ( ! [A5: set_nat] :
% 0.23/0.57 ( ~ ( finite_finite_nat @ A5 )
% 0.23/0.57 => ( P @ A5 ) )
% 0.23/0.57 => ( ( P @ bot_bot_set_nat )
% 0.23/0.57 => ( ! [X3: nat,F2: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ F2 )
% 0.23/0.57 => ( ~ ( member_nat @ X3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert_nat @ X3 @ F2 ) ) ) ) )
% 0.23/0.57 => ( P @ A4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % infinite_finite_induct
% 0.23/0.57 thf(fact_136_infinite__finite__induct,axiom,
% 0.23/0.57 ! [P: set_HF_Mirabelle_hf > $o,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ! [A5: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ~ ( finite586181922lle_hf @ A5 )
% 0.23/0.57 => ( P @ A5 ) )
% 0.23/0.57 => ( ( P @ bot_bo53200981lle_hf )
% 0.23/0.57 => ( ! [X3: hF_Mirabelle_hf,F2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F2 )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ X3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert9649339lle_hf @ X3 @ F2 ) ) ) ) )
% 0.23/0.57 => ( P @ A4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % infinite_finite_induct
% 0.23/0.57 thf(fact_137_the__elem__eq,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( the_el1104322134lle_hf @ ( insert9649339lle_hf @ X2 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 = X2 ) ).
% 0.23/0.57
% 0.23/0.57 % the_elem_eq
% 0.23/0.57 thf(fact_138_finite_OemptyI,axiom,
% 0.23/0.57 finite_finite_nat @ bot_bot_set_nat ).
% 0.23/0.57
% 0.23/0.57 % finite.emptyI
% 0.23/0.57 thf(fact_139_finite_OemptyI,axiom,
% 0.23/0.57 finite586181922lle_hf @ bot_bo53200981lle_hf ).
% 0.23/0.57
% 0.23/0.57 % finite.emptyI
% 0.23/0.57 thf(fact_140_infinite__imp__nonempty,axiom,
% 0.23/0.57 ! [S: set_nat] :
% 0.23/0.57 ( ~ ( finite_finite_nat @ S )
% 0.23/0.57 => ( S != bot_bot_set_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % infinite_imp_nonempty
% 0.23/0.57 thf(fact_141_infinite__imp__nonempty,axiom,
% 0.23/0.57 ! [S: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ~ ( finite586181922lle_hf @ S )
% 0.23/0.57 => ( S != bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % infinite_imp_nonempty
% 0.23/0.57 thf(fact_142_finite_OinsertI,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( finite586181922lle_hf @ ( insert9649339lle_hf @ A2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.insertI
% 0.23/0.57 thf(fact_143_finite_OinsertI,axiom,
% 0.23/0.57 ! [A4: set_nat,A2: nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( finite_finite_nat @ ( insert_nat @ A2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite.insertI
% 0.23/0.57 thf(fact_144_bot__empty__eq,axiom,
% 0.23/0.57 ( bot_bo1263054448e_hf_o
% 0.23/0.57 = ( ^ [X: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X @ bot_bo53200981lle_hf ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_empty_eq
% 0.23/0.57 thf(fact_145_Collect__empty__eq__bot,axiom,
% 0.23/0.57 ! [P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( ( collec1758573718lle_hf @ P )
% 0.23/0.57 = bot_bo2093393035lle_hf )
% 0.23/0.57 = ( P = bot_bo554042810e_hf_o ) ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_empty_eq_bot
% 0.23/0.57 thf(fact_146_Collect__empty__eq__bot,axiom,
% 0.23/0.57 ! [P: hF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( ( collec2046588256lle_hf @ P )
% 0.23/0.57 = bot_bo53200981lle_hf )
% 0.23/0.57 = ( P = bot_bo1263054448e_hf_o ) ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_empty_eq_bot
% 0.23/0.57 thf(fact_147_is__singleton__the__elem,axiom,
% 0.23/0.57 ( is_sin1448700567lle_hf
% 0.23/0.57 = ( ^ [A6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( A6
% 0.23/0.57 = ( insert9649339lle_hf @ ( the_el1104322134lle_hf @ A6 ) @ bot_bo53200981lle_hf ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % is_singleton_the_elem
% 0.23/0.57 thf(fact_148_is__singletonI,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf] : ( is_sin1448700567lle_hf @ ( insert9649339lle_hf @ X2 @ bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % is_singletonI
% 0.23/0.57 thf(fact_149_Set_Ois__empty__def,axiom,
% 0.23/0.57 ( is_emp566801209lle_hf
% 0.23/0.57 = ( ^ [A6: set_HF_Mirabelle_hf] : ( A6 = bot_bo53200981lle_hf ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Set.is_empty_def
% 0.23/0.57 thf(fact_150_is__singleton__def,axiom,
% 0.23/0.57 ( is_sin1448700567lle_hf
% 0.23/0.57 = ( ^ [A6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ? [X: hF_Mirabelle_hf] :
% 0.23/0.57 ( A6
% 0.23/0.57 = ( insert9649339lle_hf @ X @ bot_bo53200981lle_hf ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % is_singleton_def
% 0.23/0.57 thf(fact_151_is__singletonE,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( is_sin1448700567lle_hf @ A4 )
% 0.23/0.57 => ~ ! [X3: hF_Mirabelle_hf] :
% 0.23/0.57 ( A4
% 0.23/0.57 != ( insert9649339lle_hf @ X3 @ bot_bo53200981lle_hf ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % is_singletonE
% 0.23/0.57 thf(fact_152_is__singletonI_H,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( A4 != bot_bo53200981lle_hf )
% 0.23/0.57 => ( ! [X3: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ X3 @ A4 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ Y3 @ A4 )
% 0.23/0.57 => ( X3 = Y3 ) ) )
% 0.23/0.57 => ( is_sin1448700567lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % is_singletonI'
% 0.23/0.57 thf(fact_153_card__0__eq,axiom,
% 0.23/0.57 ! [A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( ( finite_card_nat @ A4 )
% 0.23/0.57 = zero_zero_nat )
% 0.23/0.57 = ( A4 = bot_bot_set_nat ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_0_eq
% 0.23/0.57 thf(fact_154_card__0__eq,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( ( ( finite1213132899lle_hf @ A4 )
% 0.23/0.57 = zero_zero_nat )
% 0.23/0.57 = ( A4 = bot_bo53200981lle_hf ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_0_eq
% 0.23/0.57 thf(fact_155_finite__subset__induct,axiom,
% 0.23/0.57 ! [F: set_nat,A4: set_nat,P: set_nat > $o] :
% 0.23/0.57 ( ( finite_finite_nat @ F )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ F @ A4 )
% 0.23/0.57 => ( ( P @ bot_bot_set_nat )
% 0.23/0.57 => ( ! [A3: nat,F2: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ F2 )
% 0.23/0.57 => ( ( member_nat @ A3 @ A4 )
% 0.23/0.57 => ( ~ ( member_nat @ A3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert_nat @ A3 @ F2 ) ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset_induct
% 0.23/0.57 thf(fact_156_finite__subset__induct,axiom,
% 0.23/0.57 ! [F: set_HF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ F @ A4 )
% 0.23/0.57 => ( ( P @ bot_bo53200981lle_hf )
% 0.23/0.57 => ( ! [A3: hF_Mirabelle_hf,F2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F2 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ A3 @ A4 )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ A3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert9649339lle_hf @ A3 @ F2 ) ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset_induct
% 0.23/0.57 thf(fact_157_finite__subset__induct_H,axiom,
% 0.23/0.57 ! [F: set_nat,A4: set_nat,P: set_nat > $o] :
% 0.23/0.57 ( ( finite_finite_nat @ F )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ F @ A4 )
% 0.23/0.57 => ( ( P @ bot_bot_set_nat )
% 0.23/0.57 => ( ! [A3: nat,F2: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ F2 )
% 0.23/0.57 => ( ( member_nat @ A3 @ A4 )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ F2 @ A4 )
% 0.23/0.57 => ( ~ ( member_nat @ A3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert_nat @ A3 @ F2 ) ) ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset_induct'
% 0.23/0.57 thf(fact_158_finite__subset__induct_H,axiom,
% 0.23/0.57 ! [F: set_HF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ F @ A4 )
% 0.23/0.57 => ( ( P @ bot_bo53200981lle_hf )
% 0.23/0.57 => ( ! [A3: hF_Mirabelle_hf,F2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F2 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ A3 @ A4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ F2 @ A4 )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ A3 @ F2 )
% 0.23/0.57 => ( ( P @ F2 )
% 0.23/0.57 => ( P @ ( insert9649339lle_hf @ A3 @ F2 ) ) ) ) ) ) )
% 0.23/0.57 => ( P @ F ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset_induct'
% 0.23/0.57 thf(fact_159_inj__on__HF,axiom,
% 0.23/0.57 inj_on811196232lle_hf @ hF_Mirabelle_HF @ ( collec1758573718lle_hf @ finite586181922lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_HF
% 0.23/0.57 thf(fact_160_order__refl,axiom,
% 0.23/0.57 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.23/0.57
% 0.23/0.57 % order_refl
% 0.23/0.57 thf(fact_161_subsetI,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ! [X3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ X3 @ A4 )
% 0.23/0.57 => ( member1367349282lle_hf @ X3 @ B4 ) )
% 0.23/0.57 => ( ord_le432112161lle_hf @ A4 @ B4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % subsetI
% 0.23/0.57 thf(fact_162_le__zero__eq,axiom,
% 0.23/0.57 ! [N: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.23/0.57 = ( N = zero_zero_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % le_zero_eq
% 0.23/0.57 thf(fact_163_subset__empty,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ A4 @ bot_bo53200981lle_hf )
% 0.23/0.57 = ( A4 = bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_empty
% 0.23/0.57 thf(fact_164_empty__subsetI,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] : ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A4 ) ).
% 0.23/0.57
% 0.23/0.57 % empty_subsetI
% 0.23/0.57 thf(fact_165_insert__subset,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ ( insert9649339lle_hf @ X2 @ A4 ) @ B4 )
% 0.23/0.57 = ( ( member1367349282lle_hf @ X2 @ B4 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ A4 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_subset
% 0.23/0.57 thf(fact_166_singleton__insert__inj__eq_H,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( insert9649339lle_hf @ A2 @ A4 )
% 0.23/0.57 = ( insert9649339lle_hf @ B3 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 = ( ( A2 = B3 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ A4 @ ( insert9649339lle_hf @ B3 @ bot_bo53200981lle_hf ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % singleton_insert_inj_eq'
% 0.23/0.57 thf(fact_167_singleton__insert__inj__eq,axiom,
% 0.23/0.57 ! [B3: hF_Mirabelle_hf,A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( insert9649339lle_hf @ B3 @ bot_bo53200981lle_hf )
% 0.23/0.57 = ( insert9649339lle_hf @ A2 @ A4 ) )
% 0.23/0.57 = ( ( A2 = B3 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ A4 @ ( insert9649339lle_hf @ B3 @ bot_bo53200981lle_hf ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % singleton_insert_inj_eq
% 0.23/0.57 thf(fact_168_card_Oempty,axiom,
% 0.23/0.57 ( ( finite1213132899lle_hf @ bot_bo53200981lle_hf )
% 0.23/0.57 = zero_zero_nat ) ).
% 0.23/0.57
% 0.23/0.57 % card.empty
% 0.23/0.57 thf(fact_169_card_Oinfinite,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ~ ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( ( finite1213132899lle_hf @ A4 )
% 0.23/0.57 = zero_zero_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % card.infinite
% 0.23/0.57 thf(fact_170_card_Oinfinite,axiom,
% 0.23/0.57 ! [A4: set_nat] :
% 0.23/0.57 ( ~ ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( finite_card_nat @ A4 )
% 0.23/0.57 = zero_zero_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % card.infinite
% 0.23/0.57 thf(fact_171_dual__order_Oantisym,axiom,
% 0.23/0.57 ! [B3: nat,A2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ B3 @ A2 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.23/0.57 => ( A2 = B3 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % dual_order.antisym
% 0.23/0.57 thf(fact_172_dual__order_Oeq__iff,axiom,
% 0.23/0.57 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.23/0.57 = ( ^ [A: nat,B: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ B @ A )
% 0.23/0.57 & ( ord_less_eq_nat @ A @ B ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % dual_order.eq_iff
% 0.23/0.57 thf(fact_173_dual__order_Otrans,axiom,
% 0.23/0.57 ! [B3: nat,A2: nat,C: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ B3 @ A2 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ C @ B3 )
% 0.23/0.57 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % dual_order.trans
% 0.23/0.57 thf(fact_174_linorder__wlog,axiom,
% 0.23/0.57 ! [P: nat > nat > $o,A2: nat,B3: nat] :
% 0.23/0.57 ( ! [A3: nat,B2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.23/0.57 => ( P @ A3 @ B2 ) )
% 0.23/0.57 => ( ! [A3: nat,B2: nat] :
% 0.23/0.57 ( ( P @ B2 @ A3 )
% 0.23/0.57 => ( P @ A3 @ B2 ) )
% 0.23/0.57 => ( P @ A2 @ B3 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % linorder_wlog
% 0.23/0.57 thf(fact_175_dual__order_Orefl,axiom,
% 0.23/0.57 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 0.23/0.57
% 0.23/0.57 % dual_order.refl
% 0.23/0.57 thf(fact_176_order__trans,axiom,
% 0.23/0.57 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.23/0.57 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % order_trans
% 0.23/0.57 thf(fact_177_order__class_Oorder_Oantisym,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ B3 @ A2 )
% 0.23/0.57 => ( A2 = B3 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % order_class.order.antisym
% 0.23/0.57 thf(fact_178_ord__le__eq__trans,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat,C: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.23/0.57 => ( ( B3 = C )
% 0.23/0.57 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % ord_le_eq_trans
% 0.23/0.57 thf(fact_179_ord__eq__le__trans,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat,C: nat] :
% 0.23/0.57 ( ( A2 = B3 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.23/0.57 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % ord_eq_le_trans
% 0.23/0.57 thf(fact_180_order__class_Oorder_Oeq__iff,axiom,
% 0.23/0.57 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.23/0.57 = ( ^ [A: nat,B: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.57 & ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % order_class.order.eq_iff
% 0.23/0.57 thf(fact_181_antisym__conv,axiom,
% 0.23/0.57 ! [Y2: nat,X2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.23/0.57 = ( X2 = Y2 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % antisym_conv
% 0.23/0.57 thf(fact_182_le__cases3,axiom,
% 0.23/0.57 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.23/0.57 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.23/0.57 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 0.23/0.57 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.23/0.57 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 0.23/0.57 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.23/0.57 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 0.23/0.57 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 0.23/0.57 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 0.23/0.57 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.23/0.57 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 0.23/0.57 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 0.23/0.57 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % le_cases3
% 0.23/0.57 thf(fact_183_order_Otrans,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat,C: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.23/0.57 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % order.trans
% 0.23/0.57 thf(fact_184_le__cases,axiom,
% 0.23/0.57 ! [X2: nat,Y2: nat] :
% 0.23/0.57 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 0.23/0.57 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % le_cases
% 0.23/0.57 thf(fact_185_eq__refl,axiom,
% 0.23/0.57 ! [X2: nat,Y2: nat] :
% 0.23/0.57 ( ( X2 = Y2 )
% 0.23/0.57 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % eq_refl
% 0.23/0.57 thf(fact_186_linear,axiom,
% 0.23/0.57 ! [X2: nat,Y2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.23/0.57 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.23/0.57
% 0.23/0.57 % linear
% 0.23/0.57 thf(fact_187_antisym,axiom,
% 0.23/0.57 ! [X2: nat,Y2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.23/0.57 => ( X2 = Y2 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % antisym
% 0.23/0.57 thf(fact_188_eq__iff,axiom,
% 0.23/0.57 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.23/0.57 = ( ^ [X: nat,Y4: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.23/0.57 & ( ord_less_eq_nat @ Y4 @ X ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % eq_iff
% 0.23/0.57 thf(fact_189_ord__le__eq__subst,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat,F3: nat > nat,C: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.23/0.57 => ( ( ( F3 @ B3 )
% 0.23/0.57 = C )
% 0.23/0.57 => ( ! [X3: nat,Y3: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ X3 ) @ ( F3 @ Y3 ) ) )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ A2 ) @ C ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % ord_le_eq_subst
% 0.23/0.57 thf(fact_190_ord__eq__le__subst,axiom,
% 0.23/0.57 ! [A2: nat,F3: nat > nat,B3: nat,C: nat] :
% 0.23/0.57 ( ( A2
% 0.23/0.57 = ( F3 @ B3 ) )
% 0.23/0.57 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.23/0.57 => ( ! [X3: nat,Y3: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ X3 ) @ ( F3 @ Y3 ) ) )
% 0.23/0.57 => ( ord_less_eq_nat @ A2 @ ( F3 @ C ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % ord_eq_le_subst
% 0.23/0.57 thf(fact_191_order__subst2,axiom,
% 0.23/0.57 ! [A2: nat,B3: nat,F3: nat > nat,C: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ ( F3 @ B3 ) @ C )
% 0.23/0.57 => ( ! [X3: nat,Y3: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ X3 ) @ ( F3 @ Y3 ) ) )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ A2 ) @ C ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % order_subst2
% 0.23/0.57 thf(fact_192_order__subst1,axiom,
% 0.23/0.57 ! [A2: nat,F3: nat > nat,B3: nat,C: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ ( F3 @ B3 ) )
% 0.23/0.57 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.23/0.57 => ( ! [X3: nat,Y3: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ X3 ) @ ( F3 @ Y3 ) ) )
% 0.23/0.57 => ( ord_less_eq_nat @ A2 @ ( F3 @ C ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % order_subst1
% 0.23/0.57 thf(fact_193_Collect__mono__iff,axiom,
% 0.23/0.57 ! [P: set_HF_Mirabelle_hf > $o,Q: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( ord_le2016357975lle_hf @ ( collec1758573718lle_hf @ P ) @ ( collec1758573718lle_hf @ Q ) )
% 0.23/0.57 = ( ! [X: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( P @ X )
% 0.23/0.57 => ( Q @ X ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_mono_iff
% 0.23/0.57 thf(fact_194_Collect__mono,axiom,
% 0.23/0.57 ! [P: set_HF_Mirabelle_hf > $o,Q: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ! [X3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( P @ X3 )
% 0.23/0.57 => ( Q @ X3 ) )
% 0.23/0.57 => ( ord_le2016357975lle_hf @ ( collec1758573718lle_hf @ P ) @ ( collec1758573718lle_hf @ Q ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Collect_mono
% 0.23/0.57 thf(fact_195_subset__iff,axiom,
% 0.23/0.57 ( ord_le432112161lle_hf
% 0.23/0.57 = ( ^ [A6: set_HF_Mirabelle_hf,B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ! [T: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ T @ A6 )
% 0.23/0.57 => ( member1367349282lle_hf @ T @ B6 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_iff
% 0.23/0.57 thf(fact_196_subset__eq,axiom,
% 0.23/0.57 ( ord_le432112161lle_hf
% 0.23/0.57 = ( ^ [A6: set_HF_Mirabelle_hf,B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ! [X: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ X @ A6 )
% 0.23/0.57 => ( member1367349282lle_hf @ X @ B6 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_eq
% 0.23/0.57 thf(fact_197_subsetD,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ C @ A4 )
% 0.23/0.57 => ( member1367349282lle_hf @ C @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % subsetD
% 0.23/0.57 thf(fact_198_in__mono,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( member1367349282lle_hf @ X2 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % in_mono
% 0.23/0.57 thf(fact_199_card__subset__eq,axiom,
% 0.23/0.57 ! [B4: set_HF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( ( ( finite1213132899lle_hf @ A4 )
% 0.23/0.57 = ( finite1213132899lle_hf @ B4 ) )
% 0.23/0.57 => ( A4 = B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_subset_eq
% 0.23/0.57 thf(fact_200_card__subset__eq,axiom,
% 0.23/0.57 ! [B4: set_nat,A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.23/0.57 => ( ( ( finite_card_nat @ A4 )
% 0.23/0.57 = ( finite_card_nat @ B4 ) )
% 0.23/0.57 => ( A4 = B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_subset_eq
% 0.23/0.57 thf(fact_201_infinite__arbitrarily__large,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,N: nat] :
% 0.23/0.57 ( ~ ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ? [B5: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B5 )
% 0.23/0.57 & ( ( finite1213132899lle_hf @ B5 )
% 0.23/0.57 = N )
% 0.23/0.57 & ( ord_le432112161lle_hf @ B5 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % infinite_arbitrarily_large
% 0.23/0.57 thf(fact_202_infinite__arbitrarily__large,axiom,
% 0.23/0.57 ! [A4: set_nat,N: nat] :
% 0.23/0.57 ( ~ ( finite_finite_nat @ A4 )
% 0.23/0.57 => ? [B5: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B5 )
% 0.23/0.57 & ( ( finite_card_nat @ B5 )
% 0.23/0.57 = N )
% 0.23/0.57 & ( ord_less_eq_set_nat @ B5 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % infinite_arbitrarily_large
% 0.23/0.57 thf(fact_203_zero__le,axiom,
% 0.23/0.57 ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 0.23/0.57
% 0.23/0.57 % zero_le
% 0.23/0.57 thf(fact_204_le__numeral__extra_I3_J,axiom,
% 0.23/0.57 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.23/0.57
% 0.23/0.57 % le_numeral_extra(3)
% 0.23/0.57 thf(fact_205_bot_Oextremum,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf] : ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A2 ) ).
% 0.23/0.57
% 0.23/0.57 % bot.extremum
% 0.23/0.57 thf(fact_206_bot_Oextremum,axiom,
% 0.23/0.57 ! [A2: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A2 ) ).
% 0.23/0.57
% 0.23/0.57 % bot.extremum
% 0.23/0.57 thf(fact_207_bot_Oextremum__unique,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ A2 @ bot_bo53200981lle_hf )
% 0.23/0.57 = ( A2 = bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot.extremum_unique
% 0.23/0.57 thf(fact_208_bot_Oextremum__unique,axiom,
% 0.23/0.57 ! [A2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 0.23/0.57 = ( A2 = bot_bot_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot.extremum_unique
% 0.23/0.57 thf(fact_209_bot_Oextremum__uniqueI,axiom,
% 0.23/0.57 ! [A2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ A2 @ bot_bo53200981lle_hf )
% 0.23/0.57 => ( A2 = bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot.extremum_uniqueI
% 0.23/0.57 thf(fact_210_bot_Oextremum__uniqueI,axiom,
% 0.23/0.57 ! [A2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 0.23/0.57 => ( A2 = bot_bot_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot.extremum_uniqueI
% 0.23/0.57 thf(fact_211_finite__has__maximal2,axiom,
% 0.23/0.57 ! [A4: set_nat,A2: nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( member_nat @ A2 @ A4 )
% 0.23/0.57 => ? [X3: nat] :
% 0.23/0.57 ( ( member_nat @ X3 @ A4 )
% 0.23/0.57 & ( ord_less_eq_nat @ A2 @ X3 )
% 0.23/0.57 & ! [Xa: nat] :
% 0.23/0.57 ( ( member_nat @ Xa @ A4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 0.23/0.57 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_has_maximal2
% 0.23/0.57 thf(fact_212_finite__has__minimal2,axiom,
% 0.23/0.57 ! [A4: set_nat,A2: nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( member_nat @ A2 @ A4 )
% 0.23/0.57 => ? [X3: nat] :
% 0.23/0.57 ( ( member_nat @ X3 @ A4 )
% 0.23/0.57 & ( ord_less_eq_nat @ X3 @ A2 )
% 0.23/0.57 & ! [Xa: nat] :
% 0.23/0.57 ( ( member_nat @ Xa @ A4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.23/0.57 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_has_minimal2
% 0.23/0.57 thf(fact_213_finite__subset,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( finite586181922lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset
% 0.23/0.57 thf(fact_214_finite__subset,axiom,
% 0.23/0.57 ! [A4: set_nat,B4: set_nat] :
% 0.23/0.57 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.23/0.57 => ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset
% 0.23/0.57 thf(fact_215_infinite__super,axiom,
% 0.23/0.57 ! [S: set_HF_Mirabelle_hf,T2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ S @ T2 )
% 0.23/0.57 => ( ~ ( finite586181922lle_hf @ S )
% 0.23/0.57 => ~ ( finite586181922lle_hf @ T2 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % infinite_super
% 0.23/0.57 thf(fact_216_infinite__super,axiom,
% 0.23/0.57 ! [S: set_nat,T2: set_nat] :
% 0.23/0.57 ( ( ord_less_eq_set_nat @ S @ T2 )
% 0.23/0.57 => ( ~ ( finite_finite_nat @ S )
% 0.23/0.57 => ~ ( finite_finite_nat @ T2 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % infinite_super
% 0.23/0.57 thf(fact_217_rev__finite__subset,axiom,
% 0.23/0.57 ! [B4: set_HF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( finite586181922lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % rev_finite_subset
% 0.23/0.57 thf(fact_218_rev__finite__subset,axiom,
% 0.23/0.57 ! [B4: set_nat,A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.23/0.57 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % rev_finite_subset
% 0.23/0.57 thf(fact_219_insert__mono,axiom,
% 0.23/0.57 ! [C3: set_HF_Mirabelle_hf,D2: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ C3 @ D2 )
% 0.23/0.57 => ( ord_le432112161lle_hf @ ( insert9649339lle_hf @ A2 @ C3 ) @ ( insert9649339lle_hf @ A2 @ D2 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_mono
% 0.23/0.57 thf(fact_220_subset__insert,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ~ ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ A4 @ ( insert9649339lle_hf @ X2 @ B4 ) )
% 0.23/0.57 = ( ord_le432112161lle_hf @ A4 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_insert
% 0.23/0.57 thf(fact_221_subset__insertI,axiom,
% 0.23/0.57 ! [B4: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf] : ( ord_le432112161lle_hf @ B4 @ ( insert9649339lle_hf @ A2 @ B4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_insertI
% 0.23/0.57 thf(fact_222_subset__insertI2,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( ord_le432112161lle_hf @ A4 @ ( insert9649339lle_hf @ B3 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_insertI2
% 0.23/0.57 thf(fact_223_finite__has__minimal,axiom,
% 0.23/0.57 ! [A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.23/0.57 => ? [X3: nat] :
% 0.23/0.57 ( ( member_nat @ X3 @ A4 )
% 0.23/0.57 & ! [Xa: nat] :
% 0.23/0.57 ( ( member_nat @ Xa @ A4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.23/0.57 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_has_minimal
% 0.23/0.57 thf(fact_224_finite__has__maximal,axiom,
% 0.23/0.57 ! [A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.23/0.57 => ? [X3: nat] :
% 0.23/0.57 ( ( member_nat @ X3 @ A4 )
% 0.23/0.57 & ! [Xa: nat] :
% 0.23/0.57 ( ( member_nat @ Xa @ A4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 0.23/0.57 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_has_maximal
% 0.23/0.57 thf(fact_225_subset__singleton__iff,axiom,
% 0.23/0.57 ! [X4: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ X4 @ ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 = ( ( X4 = bot_bo53200981lle_hf )
% 0.23/0.57 | ( X4
% 0.23/0.57 = ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_singleton_iff
% 0.23/0.57 thf(fact_226_subset__singletonD,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ A4 @ ( insert9649339lle_hf @ X2 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 => ( ( A4 = bot_bo53200981lle_hf )
% 0.23/0.57 | ( A4
% 0.23/0.57 = ( insert9649339lle_hf @ X2 @ bot_bo53200981lle_hf ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_singletonD
% 0.23/0.57 thf(fact_227_card__eq__0__iff,axiom,
% 0.23/0.57 ! [A4: set_nat] :
% 0.23/0.57 ( ( ( finite_card_nat @ A4 )
% 0.23/0.57 = zero_zero_nat )
% 0.23/0.57 = ( ( A4 = bot_bot_set_nat )
% 0.23/0.57 | ~ ( finite_finite_nat @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_eq_0_iff
% 0.23/0.57 thf(fact_228_card__eq__0__iff,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( finite1213132899lle_hf @ A4 )
% 0.23/0.57 = zero_zero_nat )
% 0.23/0.57 = ( ( A4 = bot_bo53200981lle_hf )
% 0.23/0.57 | ~ ( finite586181922lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_eq_0_iff
% 0.23/0.57 thf(fact_229_inj__on__empty,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf] : ( inj_on811196232lle_hf @ F3 @ bot_bo2093393035lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_empty
% 0.23/0.57 thf(fact_230_finite__ranking__induct,axiom,
% 0.23/0.57 ! [S: set_nat,P: set_nat > $o,F3: nat > nat] :
% 0.23/0.57 ( ( finite_finite_nat @ S )
% 0.23/0.57 => ( ( P @ bot_bot_set_nat )
% 0.23/0.57 => ( ! [X3: nat,S2: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ S2 )
% 0.23/0.57 => ( ! [Y5: nat] :
% 0.23/0.57 ( ( member_nat @ Y5 @ S2 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ Y5 ) @ ( F3 @ X3 ) ) )
% 0.23/0.57 => ( ( P @ S2 )
% 0.23/0.57 => ( P @ ( insert_nat @ X3 @ S2 ) ) ) ) )
% 0.23/0.57 => ( P @ S ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_ranking_induct
% 0.23/0.57 thf(fact_231_finite__ranking__induct,axiom,
% 0.23/0.57 ! [S: set_HF_Mirabelle_hf,P: set_HF_Mirabelle_hf > $o,F3: hF_Mirabelle_hf > nat] :
% 0.23/0.57 ( ( finite586181922lle_hf @ S )
% 0.23/0.57 => ( ( P @ bot_bo53200981lle_hf )
% 0.23/0.57 => ( ! [X3: hF_Mirabelle_hf,S2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ S2 )
% 0.23/0.57 => ( ! [Y5: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ Y5 @ S2 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ Y5 ) @ ( F3 @ X3 ) ) )
% 0.23/0.57 => ( ( P @ S2 )
% 0.23/0.57 => ( P @ ( insert9649339lle_hf @ X3 @ S2 ) ) ) ) )
% 0.23/0.57 => ( P @ S ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_ranking_induct
% 0.23/0.57 thf(fact_232_inj__on__subset,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_se933006839lle_hf,B4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ( ord_le2016357975lle_hf @ B4 @ A4 )
% 0.23/0.57 => ( inj_on811196232lle_hf @ F3 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_subset
% 0.23/0.57 thf(fact_233_subset__inj__on,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,B4: set_se933006839lle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ B4 )
% 0.23/0.57 => ( ( ord_le2016357975lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( inj_on811196232lle_hf @ F3 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_inj_on
% 0.23/0.57 thf(fact_234_insert__subsetI,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,X4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ X4 @ A4 )
% 0.23/0.57 => ( ord_le432112161lle_hf @ ( insert9649339lle_hf @ X2 @ X4 ) @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_subsetI
% 0.23/0.57 thf(fact_235_subset__emptyI,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ! [X3: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( member1367349282lle_hf @ X3 @ A4 )
% 0.23/0.57 => ( ord_le432112161lle_hf @ A4 @ bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_emptyI
% 0.23/0.57 thf(fact_236_bot__nat__0_Oextremum,axiom,
% 0.23/0.57 ! [A2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A2 ) ).
% 0.23/0.57
% 0.23/0.57 % bot_nat_0.extremum
% 0.23/0.57 thf(fact_237_le0,axiom,
% 0.23/0.57 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.23/0.57
% 0.23/0.57 % le0
% 0.23/0.57 thf(fact_238_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.23/0.57 ! [A2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 0.23/0.57 => ( A2 = zero_zero_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_nat_0.extremum_uniqueI
% 0.23/0.57 thf(fact_239_bot__nat__0_Oextremum__unique,axiom,
% 0.23/0.57 ! [A2: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 0.23/0.57 = ( A2 = zero_zero_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % bot_nat_0.extremum_unique
% 0.23/0.57 thf(fact_240_le__0__eq,axiom,
% 0.23/0.57 ! [N: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.23/0.57 = ( N = zero_zero_nat ) ) ).
% 0.23/0.57
% 0.23/0.57 % le_0_eq
% 0.23/0.57 thf(fact_241_less__eq__nat_Osimps_I1_J,axiom,
% 0.23/0.57 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.23/0.57
% 0.23/0.57 % less_eq_nat.simps(1)
% 0.23/0.57 thf(fact_242_finite__if__finite__subsets__card__bdd,axiom,
% 0.23/0.57 ! [F: set_HF_Mirabelle_hf,C3: nat] :
% 0.23/0.57 ( ! [G: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ G @ F )
% 0.23/0.57 => ( ( finite586181922lle_hf @ G )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite1213132899lle_hf @ G ) @ C3 ) ) )
% 0.23/0.57 => ( ( finite586181922lle_hf @ F )
% 0.23/0.57 & ( ord_less_eq_nat @ ( finite1213132899lle_hf @ F ) @ C3 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_if_finite_subsets_card_bdd
% 0.23/0.57 thf(fact_243_finite__if__finite__subsets__card__bdd,axiom,
% 0.23/0.57 ! [F: set_nat,C3: nat] :
% 0.23/0.57 ( ! [G: set_nat] :
% 0.23/0.57 ( ( ord_less_eq_set_nat @ G @ F )
% 0.23/0.57 => ( ( finite_finite_nat @ G )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ G ) @ C3 ) ) )
% 0.23/0.57 => ( ( finite_finite_nat @ F )
% 0.23/0.57 & ( ord_less_eq_nat @ ( finite_card_nat @ F ) @ C3 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_if_finite_subsets_card_bdd
% 0.23/0.57 thf(fact_244_card__seteq,axiom,
% 0.23/0.57 ! [B4: set_HF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ B4 ) @ ( finite1213132899lle_hf @ A4 ) )
% 0.23/0.57 => ( A4 = B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_seteq
% 0.23/0.57 thf(fact_245_card__seteq,axiom,
% 0.23/0.57 ! [B4: set_nat,A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B4 ) @ ( finite_card_nat @ A4 ) )
% 0.23/0.57 => ( A4 = B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_seteq
% 0.23/0.57 thf(fact_246_card__mono,axiom,
% 0.23/0.57 ! [B4: set_HF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A4 ) @ ( finite1213132899lle_hf @ B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_mono
% 0.23/0.57 thf(fact_247_card__mono,axiom,
% 0.23/0.57 ! [B4: set_nat,A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_mono
% 0.23/0.57 thf(fact_248_card__insert__le,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A4 ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ X2 @ A4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_insert_le
% 0.23/0.57 thf(fact_249_card__insert__le,axiom,
% 0.23/0.57 ! [A4: set_nat,X2: nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ ( insert_nat @ X2 @ A4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_insert_le
% 0.23/0.57 thf(fact_250_inj__on__inverseI,axiom,
% 0.23/0.57 ! [A4: set_se933006839lle_hf,G2: hF_Mirabelle_hf > set_HF_Mirabelle_hf,F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.23/0.57 ( ! [X3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ X3 @ A4 )
% 0.23/0.57 => ( ( G2 @ ( F3 @ X3 ) )
% 0.23/0.57 = X3 ) )
% 0.23/0.57 => ( inj_on811196232lle_hf @ F3 @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_inverseI
% 0.23/0.57 thf(fact_251_inj__on__contraD,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_se933006839lle_hf,X2: set_HF_Mirabelle_hf,Y2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ( X2 != Y2 )
% 0.23/0.57 => ( ( member1490636632lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ( member1490636632lle_hf @ Y2 @ A4 )
% 0.23/0.57 => ( ( F3 @ X2 )
% 0.23/0.57 != ( F3 @ Y2 ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_contraD
% 0.23/0.57 thf(fact_252_inj__on__eq__iff,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_se933006839lle_hf,X2: set_HF_Mirabelle_hf,Y2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ( member1490636632lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ( member1490636632lle_hf @ Y2 @ A4 )
% 0.23/0.57 => ( ( ( F3 @ X2 )
% 0.23/0.57 = ( F3 @ Y2 ) )
% 0.23/0.57 = ( X2 = Y2 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_eq_iff
% 0.23/0.57 thf(fact_253_inj__on__cong,axiom,
% 0.23/0.57 ! [A4: set_se933006839lle_hf,F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,G2: set_HF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.23/0.57 ( ! [A3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ A3 @ A4 )
% 0.23/0.57 => ( ( F3 @ A3 )
% 0.23/0.57 = ( G2 @ A3 ) ) )
% 0.23/0.57 => ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 = ( inj_on811196232lle_hf @ G2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_cong
% 0.23/0.57 thf(fact_254_inj__on__def,axiom,
% 0.23/0.57 ( inj_on811196232lle_hf
% 0.23/0.57 = ( ^ [F4: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A6: set_se933006839lle_hf] :
% 0.23/0.57 ! [X: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ X @ A6 )
% 0.23/0.57 => ! [Y4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ Y4 @ A6 )
% 0.23/0.57 => ( ( ( F4 @ X )
% 0.23/0.57 = ( F4 @ Y4 ) )
% 0.23/0.57 => ( X = Y4 ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_def
% 0.23/0.57 thf(fact_255_inj__onI,axiom,
% 0.23/0.57 ! [A4: set_se933006839lle_hf,F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.23/0.57 ( ! [X3: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ X3 @ A4 )
% 0.23/0.57 => ( ( member1490636632lle_hf @ Y3 @ A4 )
% 0.23/0.57 => ( ( ( F3 @ X3 )
% 0.23/0.57 = ( F3 @ Y3 ) )
% 0.23/0.57 => ( X3 = Y3 ) ) ) )
% 0.23/0.57 => ( inj_on811196232lle_hf @ F3 @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_onI
% 0.23/0.57 thf(fact_256_inj__onD,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_se933006839lle_hf,X2: set_HF_Mirabelle_hf,Y2: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ( ( F3 @ X2 )
% 0.23/0.57 = ( F3 @ Y2 ) )
% 0.23/0.57 => ( ( member1490636632lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ( member1490636632lle_hf @ Y2 @ A4 )
% 0.23/0.57 => ( X2 = Y2 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_onD
% 0.23/0.57 thf(fact_257_obtain__subset__with__card__n,axiom,
% 0.23/0.57 ! [N: nat,S: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_less_eq_nat @ N @ ( finite1213132899lle_hf @ S ) )
% 0.23/0.57 => ~ ! [T3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ T3 @ S )
% 0.23/0.57 => ( ( ( finite1213132899lle_hf @ T3 )
% 0.23/0.57 = N )
% 0.23/0.57 => ~ ( finite586181922lle_hf @ T3 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % obtain_subset_with_card_n
% 0.23/0.57 thf(fact_258_obtain__subset__with__card__n,axiom,
% 0.23/0.57 ! [N: nat,S: set_nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S ) )
% 0.23/0.57 => ~ ! [T3: set_nat] :
% 0.23/0.57 ( ( ord_less_eq_set_nat @ T3 @ S )
% 0.23/0.57 => ( ( ( finite_card_nat @ T3 )
% 0.23/0.57 = N )
% 0.23/0.57 => ~ ( finite_finite_nat @ T3 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % obtain_subset_with_card_n
% 0.23/0.57 thf(fact_259_card__le__if__inj__on__rel,axiom,
% 0.23/0.57 ! [B4: set_HF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ! [A3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A3 @ A4 )
% 0.23/0.57 => ? [B7: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ B7 @ B4 )
% 0.23/0.57 & ( R @ A3 @ B7 ) ) )
% 0.23/0.57 => ( ! [A1: hF_Mirabelle_hf,A22: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A1 @ A4 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ A22 @ A4 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ B2 @ B4 )
% 0.23/0.57 => ( ( R @ A1 @ B2 )
% 0.23/0.57 => ( ( R @ A22 @ B2 )
% 0.23/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A4 ) @ ( finite1213132899lle_hf @ B4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_le_if_inj_on_rel
% 0.23/0.57 thf(fact_260_card__le__if__inj__on__rel,axiom,
% 0.23/0.57 ! [B4: set_nat,A4: set_HF_Mirabelle_hf,R: hF_Mirabelle_hf > nat > $o] :
% 0.23/0.57 ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ! [A3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A3 @ A4 )
% 0.23/0.57 => ? [B7: nat] :
% 0.23/0.57 ( ( member_nat @ B7 @ B4 )
% 0.23/0.57 & ( R @ A3 @ B7 ) ) )
% 0.23/0.57 => ( ! [A1: hF_Mirabelle_hf,A22: hF_Mirabelle_hf,B2: nat] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A1 @ A4 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ A22 @ A4 )
% 0.23/0.57 => ( ( member_nat @ B2 @ B4 )
% 0.23/0.57 => ( ( R @ A1 @ B2 )
% 0.23/0.57 => ( ( R @ A22 @ B2 )
% 0.23/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A4 ) @ ( finite_card_nat @ B4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_le_if_inj_on_rel
% 0.23/0.57 thf(fact_261_arg__min__least,axiom,
% 0.23/0.57 ! [S: set_nat,Y2: nat,F3: nat > nat] :
% 0.23/0.57 ( ( finite_finite_nat @ S )
% 0.23/0.57 => ( ( S != bot_bot_set_nat )
% 0.23/0.57 => ( ( member_nat @ Y2 @ S )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ ( lattic1974000059at_nat @ F3 @ S ) ) @ ( F3 @ Y2 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % arg_min_least
% 0.23/0.57 thf(fact_262_arg__min__least,axiom,
% 0.23/0.57 ! [S: set_HF_Mirabelle_hf,Y2: hF_Mirabelle_hf,F3: hF_Mirabelle_hf > nat] :
% 0.23/0.57 ( ( finite586181922lle_hf @ S )
% 0.23/0.57 => ( ( S != bot_bo53200981lle_hf )
% 0.23/0.57 => ( ( member1367349282lle_hf @ Y2 @ S )
% 0.23/0.57 => ( ord_less_eq_nat @ ( F3 @ ( lattic710307446hf_nat @ F3 @ S ) ) @ ( F3 @ Y2 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % arg_min_least
% 0.23/0.57 thf(fact_263_bounded__Max__nat,axiom,
% 0.23/0.57 ! [P: nat > $o,X2: nat,M: nat] :
% 0.23/0.57 ( ( P @ X2 )
% 0.23/0.57 => ( ! [X3: nat] :
% 0.23/0.57 ( ( P @ X3 )
% 0.23/0.57 => ( ord_less_eq_nat @ X3 @ M ) )
% 0.23/0.57 => ~ ! [M2: nat] :
% 0.23/0.57 ( ( P @ M2 )
% 0.23/0.57 => ~ ! [X5: nat] :
% 0.23/0.57 ( ( P @ X5 )
% 0.23/0.57 => ( ord_less_eq_nat @ X5 @ M2 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % bounded_Max_nat
% 0.23/0.57 thf(fact_264_Nat_Oex__has__greatest__nat,axiom,
% 0.23/0.57 ! [P: nat > $o,K: nat,B3: nat] :
% 0.23/0.57 ( ( P @ K )
% 0.23/0.57 => ( ! [Y3: nat] :
% 0.23/0.57 ( ( P @ Y3 )
% 0.23/0.57 => ( ord_less_eq_nat @ Y3 @ B3 ) )
% 0.23/0.57 => ? [X3: nat] :
% 0.23/0.57 ( ( P @ X3 )
% 0.23/0.57 & ! [Y5: nat] :
% 0.23/0.57 ( ( P @ Y5 )
% 0.23/0.57 => ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Nat.ex_has_greatest_nat
% 0.23/0.57 thf(fact_265_nat__le__linear,axiom,
% 0.23/0.57 ! [M3: nat,N: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ M3 @ N )
% 0.23/0.57 | ( ord_less_eq_nat @ N @ M3 ) ) ).
% 0.23/0.57
% 0.23/0.57 % nat_le_linear
% 0.23/0.57 thf(fact_266_le__antisym,axiom,
% 0.23/0.57 ! [M3: nat,N: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ M3 @ N )
% 0.23/0.57 => ( ( ord_less_eq_nat @ N @ M3 )
% 0.23/0.57 => ( M3 = N ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % le_antisym
% 0.23/0.57 thf(fact_267_eq__imp__le,axiom,
% 0.23/0.57 ! [M3: nat,N: nat] :
% 0.23/0.57 ( ( M3 = N )
% 0.23/0.57 => ( ord_less_eq_nat @ M3 @ N ) ) ).
% 0.23/0.57
% 0.23/0.57 % eq_imp_le
% 0.23/0.57 thf(fact_268_le__trans,axiom,
% 0.23/0.57 ! [I: nat,J: nat,K: nat] :
% 0.23/0.57 ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.57 => ( ( ord_less_eq_nat @ J @ K )
% 0.23/0.57 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % le_trans
% 0.23/0.57 thf(fact_269_le__refl,axiom,
% 0.23/0.57 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.23/0.57
% 0.23/0.57 % le_refl
% 0.23/0.57 thf(fact_270_finite__nat__set__iff__bounded__le,axiom,
% 0.23/0.57 ( finite_finite_nat
% 0.23/0.57 = ( ^ [N2: set_nat] :
% 0.23/0.57 ? [M4: nat] :
% 0.23/0.57 ! [X: nat] :
% 0.23/0.57 ( ( member_nat @ X @ N2 )
% 0.23/0.57 => ( ord_less_eq_nat @ X @ M4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_nat_set_iff_bounded_le
% 0.23/0.57 thf(fact_271_card__Diff1__le,axiom,
% 0.23/0.57 ! [A4: set_nat,X2: nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_Diff1_le
% 0.23/0.57 thf(fact_272_card__Diff1__le,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ X2 @ bot_bo53200981lle_hf ) ) ) @ ( finite1213132899lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_Diff1_le
% 0.23/0.57 thf(fact_273_card__le__inj,axiom,
% 0.23/0.57 ! [A4: set_se933006839lle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite1450550360lle_hf @ A4 )
% 0.23/0.57 => ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ ( finite90088345lle_hf @ A4 ) @ ( finite1213132899lle_hf @ B4 ) )
% 0.23/0.57 => ? [F5: set_HF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ ( image_899003828lle_hf @ F5 @ A4 ) @ B4 )
% 0.23/0.57 & ( inj_on811196232lle_hf @ F5 @ A4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_le_inj
% 0.23/0.57 thf(fact_274_card__le__inj,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A4 ) @ ( finite1213132899lle_hf @ B4 ) )
% 0.23/0.57 => ? [F5: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ ( image_1743964010lle_hf @ F5 @ A4 ) @ B4 )
% 0.23/0.57 & ( inj_on755450110lle_hf @ F5 @ A4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_le_inj
% 0.23/0.57 thf(fact_275_card__le__inj,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_nat] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A4 ) @ ( finite_card_nat @ B4 ) )
% 0.23/0.57 => ? [F5: hF_Mirabelle_hf > nat] :
% 0.23/0.57 ( ( ord_less_eq_set_nat @ ( image_131453538hf_nat @ F5 @ A4 ) @ B4 )
% 0.23/0.57 & ( inj_on1874279374hf_nat @ F5 @ A4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_le_inj
% 0.23/0.57 thf(fact_276_card__le__inj,axiom,
% 0.23/0.57 ! [A4: set_nat,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite1213132899lle_hf @ B4 ) )
% 0.23/0.57 => ? [F5: nat > hF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ ( image_246164834lle_hf @ F5 @ A4 ) @ B4 )
% 0.23/0.57 & ( inj_on1988990670lle_hf @ F5 @ A4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_le_inj
% 0.23/0.57 thf(fact_277_card__le__inj,axiom,
% 0.23/0.57 ! [A4: set_nat,B4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) )
% 0.23/0.57 => ? [F5: nat > nat] :
% 0.23/0.57 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F5 @ A4 ) @ B4 )
% 0.23/0.57 & ( inj_on_nat_nat @ F5 @ A4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_le_inj
% 0.23/0.57 thf(fact_278_card__inj__on__le,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_se933006839lle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ ( image_899003828lle_hf @ F3 @ A4 ) @ B4 )
% 0.23/0.57 => ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ord_less_eq_nat @ ( finite90088345lle_hf @ A4 ) @ ( finite1213132899lle_hf @ B4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_inj_on_le
% 0.23/0.57 thf(fact_279_image__eqI,axiom,
% 0.23/0.57 ! [B3: hF_Mirabelle_hf,F3: hF_Mirabelle_hf > hF_Mirabelle_hf,X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( B3
% 0.23/0.57 = ( F3 @ X2 ) )
% 0.23/0.57 => ( ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( member1367349282lle_hf @ B3 @ ( image_1743964010lle_hf @ F3 @ A4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % image_eqI
% 0.23/0.57 thf(fact_280_DiffI,axiom,
% 0.23/0.57 ! [C: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ C @ A4 )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ C @ B4 )
% 0.23/0.57 => ( member1367349282lle_hf @ C @ ( minus_1450406810lle_hf @ A4 @ B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % DiffI
% 0.23/0.57 thf(fact_281_Diff__iff,axiom,
% 0.23/0.57 ! [C: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ C @ ( minus_1450406810lle_hf @ A4 @ B4 ) )
% 0.23/0.57 = ( ( member1367349282lle_hf @ C @ A4 )
% 0.23/0.57 & ~ ( member1367349282lle_hf @ C @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Diff_iff
% 0.23/0.57 thf(fact_282_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.23/0.57 ! [A2: nat] :
% 0.23/0.57 ( ( minus_minus_nat @ A2 @ A2 )
% 0.23/0.57 = zero_zero_nat ) ).
% 0.23/0.57
% 0.23/0.57 % cancel_comm_monoid_add_class.diff_cancel
% 0.23/0.57 thf(fact_283_diff__zero,axiom,
% 0.23/0.57 ! [A2: nat] :
% 0.23/0.57 ( ( minus_minus_nat @ A2 @ zero_zero_nat )
% 0.23/0.57 = A2 ) ).
% 0.23/0.57
% 0.23/0.57 % diff_zero
% 0.23/0.57 thf(fact_284_zero__diff,axiom,
% 0.23/0.57 ! [A2: nat] :
% 0.23/0.57 ( ( minus_minus_nat @ zero_zero_nat @ A2 )
% 0.23/0.57 = zero_zero_nat ) ).
% 0.23/0.57
% 0.23/0.57 % zero_diff
% 0.23/0.57 thf(fact_285_image__empty,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.23/0.57 ( ( image_1743964010lle_hf @ F3 @ bot_bo53200981lle_hf )
% 0.23/0.57 = bot_bo53200981lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % image_empty
% 0.23/0.57 thf(fact_286_empty__is__image,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( bot_bo53200981lle_hf
% 0.23/0.57 = ( image_1743964010lle_hf @ F3 @ A4 ) )
% 0.23/0.57 = ( A4 = bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % empty_is_image
% 0.23/0.57 thf(fact_287_image__is__empty,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( image_1743964010lle_hf @ F3 @ A4 )
% 0.23/0.57 = bot_bo53200981lle_hf )
% 0.23/0.57 = ( A4 = bot_bo53200981lle_hf ) ) ).
% 0.23/0.57
% 0.23/0.57 % image_is_empty
% 0.23/0.57 thf(fact_288_finite__imageI,axiom,
% 0.23/0.57 ! [F: set_HF_Mirabelle_hf,H: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F )
% 0.23/0.57 => ( finite586181922lle_hf @ ( image_1743964010lle_hf @ H @ F ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_imageI
% 0.23/0.57 thf(fact_289_finite__imageI,axiom,
% 0.23/0.57 ! [F: set_HF_Mirabelle_hf,H: hF_Mirabelle_hf > nat] :
% 0.23/0.57 ( ( finite586181922lle_hf @ F )
% 0.23/0.57 => ( finite_finite_nat @ ( image_131453538hf_nat @ H @ F ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_imageI
% 0.23/0.57 thf(fact_290_finite__imageI,axiom,
% 0.23/0.57 ! [F: set_nat,H: nat > hF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite_finite_nat @ F )
% 0.23/0.57 => ( finite586181922lle_hf @ ( image_246164834lle_hf @ H @ F ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_imageI
% 0.23/0.57 thf(fact_291_finite__imageI,axiom,
% 0.23/0.57 ! [F: set_nat,H: nat > nat] :
% 0.23/0.57 ( ( finite_finite_nat @ F )
% 0.23/0.57 => ( finite_finite_nat @ ( image_nat_nat @ H @ F ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_imageI
% 0.23/0.57 thf(fact_292_image__insert,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( image_1743964010lle_hf @ F3 @ ( insert9649339lle_hf @ A2 @ B4 ) )
% 0.23/0.57 = ( insert9649339lle_hf @ ( F3 @ A2 ) @ ( image_1743964010lle_hf @ F3 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % image_insert
% 0.23/0.57 thf(fact_293_insert__image,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,F3: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ( insert9649339lle_hf @ ( F3 @ X2 ) @ ( image_1743964010lle_hf @ F3 @ A4 ) )
% 0.23/0.57 = ( image_1743964010lle_hf @ F3 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_image
% 0.23/0.57 thf(fact_294_Diff__empty,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( minus_1450406810lle_hf @ A4 @ bot_bo53200981lle_hf )
% 0.23/0.57 = A4 ) ).
% 0.23/0.57
% 0.23/0.57 % Diff_empty
% 0.23/0.57 thf(fact_295_empty__Diff,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( minus_1450406810lle_hf @ bot_bo53200981lle_hf @ A4 )
% 0.23/0.57 = bot_bo53200981lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % empty_Diff
% 0.23/0.57 thf(fact_296_Diff__cancel,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( minus_1450406810lle_hf @ A4 @ A4 )
% 0.23/0.57 = bot_bo53200981lle_hf ) ).
% 0.23/0.57
% 0.23/0.57 % Diff_cancel
% 0.23/0.57 thf(fact_297_finite__Diff,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( finite586181922lle_hf @ ( minus_1450406810lle_hf @ A4 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_Diff
% 0.23/0.57 thf(fact_298_finite__Diff,axiom,
% 0.23/0.57 ! [A4: set_nat,B4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_Diff
% 0.23/0.57 thf(fact_299_finite__Diff2,axiom,
% 0.23/0.57 ! [B4: set_HF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( finite586181922lle_hf @ ( minus_1450406810lle_hf @ A4 @ B4 ) )
% 0.23/0.57 = ( finite586181922lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_Diff2
% 0.23/0.57 thf(fact_300_finite__Diff2,axiom,
% 0.23/0.57 ! [B4: set_nat,A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.23/0.57 = ( finite_finite_nat @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_Diff2
% 0.23/0.57 thf(fact_301_Diff__insert0,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ~ ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ X2 @ B4 ) )
% 0.23/0.57 = ( minus_1450406810lle_hf @ A4 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Diff_insert0
% 0.23/0.57 thf(fact_302_insert__Diff1,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ X2 @ B4 )
% 0.23/0.57 => ( ( minus_1450406810lle_hf @ ( insert9649339lle_hf @ X2 @ A4 ) @ B4 )
% 0.23/0.57 = ( minus_1450406810lle_hf @ A4 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_Diff1
% 0.23/0.57 thf(fact_303_Diff__eq__empty__iff,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( minus_1450406810lle_hf @ A4 @ B4 )
% 0.23/0.57 = bot_bo53200981lle_hf )
% 0.23/0.57 = ( ord_le432112161lle_hf @ A4 @ B4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % Diff_eq_empty_iff
% 0.23/0.57 thf(fact_304_insert__Diff__single,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( insert9649339lle_hf @ A2 @ ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) ) )
% 0.23/0.57 = ( insert9649339lle_hf @ A2 @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_Diff_single
% 0.23/0.57 thf(fact_305_finite__Diff__insert,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ A2 @ B4 ) ) )
% 0.23/0.57 = ( finite586181922lle_hf @ ( minus_1450406810lle_hf @ A4 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_Diff_insert
% 0.23/0.57 thf(fact_306_finite__Diff__insert,axiom,
% 0.23/0.57 ! [A4: set_nat,A2: nat,B4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A2 @ B4 ) ) )
% 0.23/0.57 = ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_Diff_insert
% 0.23/0.57 thf(fact_307_inj__on__insert,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ ( insert1636143089lle_hf @ A2 @ A4 ) )
% 0.23/0.57 = ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 & ~ ( member1367349282lle_hf @ ( F3 @ A2 ) @ ( image_899003828lle_hf @ F3 @ ( minus_500612048lle_hf @ A4 @ ( insert1636143089lle_hf @ A2 @ bot_bo2093393035lle_hf ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_insert
% 0.23/0.57 thf(fact_308_inj__on__insert,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on755450110lle_hf @ F3 @ ( insert9649339lle_hf @ A2 @ A4 ) )
% 0.23/0.57 = ( ( inj_on755450110lle_hf @ F3 @ A4 )
% 0.23/0.57 & ~ ( member1367349282lle_hf @ ( F3 @ A2 ) @ ( image_1743964010lle_hf @ F3 @ ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_insert
% 0.23/0.57 thf(fact_309_inj__on__image__set__diff,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,C3: set_se933006839lle_hf,A4: set_se933006839lle_hf,B4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ C3 )
% 0.23/0.57 => ( ( ord_le2016357975lle_hf @ ( minus_500612048lle_hf @ A4 @ B4 ) @ C3 )
% 0.23/0.57 => ( ( ord_le2016357975lle_hf @ B4 @ C3 )
% 0.23/0.57 => ( ( image_899003828lle_hf @ F3 @ ( minus_500612048lle_hf @ A4 @ B4 ) )
% 0.23/0.57 = ( minus_1450406810lle_hf @ ( image_899003828lle_hf @ F3 @ A4 ) @ ( image_899003828lle_hf @ F3 @ B4 ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_image_set_diff
% 0.23/0.57 thf(fact_310_image__subsetI,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,F3: hF_Mirabelle_hf > hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ! [X3: hF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ X3 @ A4 )
% 0.23/0.57 => ( member1367349282lle_hf @ ( F3 @ X3 ) @ B4 ) )
% 0.23/0.57 => ( ord_le432112161lle_hf @ ( image_1743964010lle_hf @ F3 @ A4 ) @ B4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % image_subsetI
% 0.23/0.57 thf(fact_311_finite__surj,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,F3: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ B4 @ ( image_1743964010lle_hf @ F3 @ A4 ) )
% 0.23/0.57 => ( finite586181922lle_hf @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_surj
% 0.23/0.57 thf(fact_312_finite__surj,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_nat,F3: hF_Mirabelle_hf > nat] :
% 0.23/0.57 ( ( finite586181922lle_hf @ A4 )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ B4 @ ( image_131453538hf_nat @ F3 @ A4 ) )
% 0.23/0.57 => ( finite_finite_nat @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_surj
% 0.23/0.57 thf(fact_313_finite__surj,axiom,
% 0.23/0.57 ! [A4: set_nat,B4: set_HF_Mirabelle_hf,F3: nat > hF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ B4 @ ( image_246164834lle_hf @ F3 @ A4 ) )
% 0.23/0.57 => ( finite586181922lle_hf @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_surj
% 0.23/0.57 thf(fact_314_finite__surj,axiom,
% 0.23/0.57 ! [A4: set_nat,B4: set_nat,F3: nat > nat] :
% 0.23/0.57 ( ( finite_finite_nat @ A4 )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F3 @ A4 ) )
% 0.23/0.57 => ( finite_finite_nat @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_surj
% 0.23/0.57 thf(fact_315_finite__subset__image,axiom,
% 0.23/0.57 ! [B4: set_HF_Mirabelle_hf,F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ B4 @ ( image_1743964010lle_hf @ F3 @ A4 ) )
% 0.23/0.57 => ? [C4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ C4 @ A4 )
% 0.23/0.57 & ( finite586181922lle_hf @ C4 )
% 0.23/0.57 & ( B4
% 0.23/0.57 = ( image_1743964010lle_hf @ F3 @ C4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset_image
% 0.23/0.57 thf(fact_316_finite__subset__image,axiom,
% 0.23/0.57 ! [B4: set_HF_Mirabelle_hf,F3: nat > hF_Mirabelle_hf,A4: set_nat] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ B4 @ ( image_246164834lle_hf @ F3 @ A4 ) )
% 0.23/0.57 => ? [C4: set_nat] :
% 0.23/0.57 ( ( ord_less_eq_set_nat @ C4 @ A4 )
% 0.23/0.57 & ( finite_finite_nat @ C4 )
% 0.23/0.57 & ( B4
% 0.23/0.57 = ( image_246164834lle_hf @ F3 @ C4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset_image
% 0.23/0.57 thf(fact_317_finite__subset__image,axiom,
% 0.23/0.57 ! [B4: set_nat,F3: hF_Mirabelle_hf > nat,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ B4 @ ( image_131453538hf_nat @ F3 @ A4 ) )
% 0.23/0.57 => ? [C4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ C4 @ A4 )
% 0.23/0.57 & ( finite586181922lle_hf @ C4 )
% 0.23/0.57 & ( B4
% 0.23/0.57 = ( image_131453538hf_nat @ F3 @ C4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset_image
% 0.23/0.57 thf(fact_318_finite__subset__image,axiom,
% 0.23/0.57 ! [B4: set_nat,F3: nat > nat,A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B4 )
% 0.23/0.57 => ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F3 @ A4 ) )
% 0.23/0.57 => ? [C4: set_nat] :
% 0.23/0.57 ( ( ord_less_eq_set_nat @ C4 @ A4 )
% 0.23/0.57 & ( finite_finite_nat @ C4 )
% 0.23/0.57 & ( B4
% 0.23/0.57 = ( image_nat_nat @ F3 @ C4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_subset_image
% 0.23/0.57 thf(fact_319_ex__finite__subset__image,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( ? [B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B6 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ B6 @ ( image_1743964010lle_hf @ F3 @ A4 ) )
% 0.23/0.57 & ( P @ B6 ) ) )
% 0.23/0.57 = ( ? [B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B6 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ B6 @ A4 )
% 0.23/0.57 & ( P @ ( image_1743964010lle_hf @ F3 @ B6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % ex_finite_subset_image
% 0.23/0.57 thf(fact_320_ex__finite__subset__image,axiom,
% 0.23/0.57 ! [F3: nat > hF_Mirabelle_hf,A4: set_nat,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( ? [B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B6 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ B6 @ ( image_246164834lle_hf @ F3 @ A4 ) )
% 0.23/0.57 & ( P @ B6 ) ) )
% 0.23/0.57 = ( ? [B6: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B6 )
% 0.23/0.57 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.23/0.57 & ( P @ ( image_246164834lle_hf @ F3 @ B6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % ex_finite_subset_image
% 0.23/0.57 thf(fact_321_ex__finite__subset__image,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > nat,A4: set_HF_Mirabelle_hf,P: set_nat > $o] :
% 0.23/0.57 ( ( ? [B6: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B6 )
% 0.23/0.57 & ( ord_less_eq_set_nat @ B6 @ ( image_131453538hf_nat @ F3 @ A4 ) )
% 0.23/0.57 & ( P @ B6 ) ) )
% 0.23/0.57 = ( ? [B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ B6 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ B6 @ A4 )
% 0.23/0.57 & ( P @ ( image_131453538hf_nat @ F3 @ B6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % ex_finite_subset_image
% 0.23/0.57 thf(fact_322_ex__finite__subset__image,axiom,
% 0.23/0.57 ! [F3: nat > nat,A4: set_nat,P: set_nat > $o] :
% 0.23/0.57 ( ( ? [B6: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B6 )
% 0.23/0.57 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F3 @ A4 ) )
% 0.23/0.57 & ( P @ B6 ) ) )
% 0.23/0.57 = ( ? [B6: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ B6 )
% 0.23/0.57 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.23/0.57 & ( P @ ( image_nat_nat @ F3 @ B6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % ex_finite_subset_image
% 0.23/0.57 thf(fact_323_all__finite__subset__image,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( ! [B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( finite586181922lle_hf @ B6 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ B6 @ ( image_1743964010lle_hf @ F3 @ A4 ) ) )
% 0.23/0.57 => ( P @ B6 ) ) )
% 0.23/0.57 = ( ! [B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( finite586181922lle_hf @ B6 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ B6 @ A4 ) )
% 0.23/0.57 => ( P @ ( image_1743964010lle_hf @ F3 @ B6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % all_finite_subset_image
% 0.23/0.57 thf(fact_324_all__finite__subset__image,axiom,
% 0.23/0.57 ! [F3: nat > hF_Mirabelle_hf,A4: set_nat,P: set_HF_Mirabelle_hf > $o] :
% 0.23/0.57 ( ( ! [B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( finite586181922lle_hf @ B6 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ B6 @ ( image_246164834lle_hf @ F3 @ A4 ) ) )
% 0.23/0.57 => ( P @ B6 ) ) )
% 0.23/0.57 = ( ! [B6: set_nat] :
% 0.23/0.57 ( ( ( finite_finite_nat @ B6 )
% 0.23/0.57 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 0.23/0.57 => ( P @ ( image_246164834lle_hf @ F3 @ B6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % all_finite_subset_image
% 0.23/0.57 thf(fact_325_all__finite__subset__image,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > nat,A4: set_HF_Mirabelle_hf,P: set_nat > $o] :
% 0.23/0.57 ( ( ! [B6: set_nat] :
% 0.23/0.57 ( ( ( finite_finite_nat @ B6 )
% 0.23/0.57 & ( ord_less_eq_set_nat @ B6 @ ( image_131453538hf_nat @ F3 @ A4 ) ) )
% 0.23/0.57 => ( P @ B6 ) ) )
% 0.23/0.57 = ( ! [B6: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ( finite586181922lle_hf @ B6 )
% 0.23/0.57 & ( ord_le432112161lle_hf @ B6 @ A4 ) )
% 0.23/0.57 => ( P @ ( image_131453538hf_nat @ F3 @ B6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % all_finite_subset_image
% 0.23/0.57 thf(fact_326_all__finite__subset__image,axiom,
% 0.23/0.57 ! [F3: nat > nat,A4: set_nat,P: set_nat > $o] :
% 0.23/0.57 ( ( ! [B6: set_nat] :
% 0.23/0.57 ( ( ( finite_finite_nat @ B6 )
% 0.23/0.57 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F3 @ A4 ) ) )
% 0.23/0.57 => ( P @ B6 ) ) )
% 0.23/0.57 = ( ! [B6: set_nat] :
% 0.23/0.57 ( ( ( finite_finite_nat @ B6 )
% 0.23/0.57 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 0.23/0.57 => ( P @ ( image_nat_nat @ F3 @ B6 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % all_finite_subset_image
% 0.23/0.57 thf(fact_327_finite__imageD,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ ( image_899003828lle_hf @ F3 @ A4 ) )
% 0.23/0.57 => ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( finite1450550360lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_imageD
% 0.23/0.57 thf(fact_328_finite__imageD,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite586181922lle_hf @ ( image_1743964010lle_hf @ F3 @ A4 ) )
% 0.23/0.57 => ( ( inj_on755450110lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( finite586181922lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_imageD
% 0.23/0.57 thf(fact_329_finite__imageD,axiom,
% 0.23/0.57 ! [F3: nat > hF_Mirabelle_hf,A4: set_nat] :
% 0.23/0.57 ( ( finite586181922lle_hf @ ( image_246164834lle_hf @ F3 @ A4 ) )
% 0.23/0.57 => ( ( inj_on1988990670lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_imageD
% 0.23/0.57 thf(fact_330_finite__imageD,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > nat,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( finite_finite_nat @ ( image_131453538hf_nat @ F3 @ A4 ) )
% 0.23/0.57 => ( ( inj_on1874279374hf_nat @ F3 @ A4 )
% 0.23/0.57 => ( finite586181922lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_imageD
% 0.23/0.57 thf(fact_331_finite__imageD,axiom,
% 0.23/0.57 ! [F3: nat > nat,A4: set_nat] :
% 0.23/0.57 ( ( finite_finite_nat @ ( image_nat_nat @ F3 @ A4 ) )
% 0.23/0.57 => ( ( inj_on_nat_nat @ F3 @ A4 )
% 0.23/0.57 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_imageD
% 0.23/0.57 thf(fact_332_finite__image__iff,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ( finite586181922lle_hf @ ( image_899003828lle_hf @ F3 @ A4 ) )
% 0.23/0.57 = ( finite1450550360lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_image_iff
% 0.23/0.57 thf(fact_333_finite__image__iff,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on755450110lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ( finite586181922lle_hf @ ( image_1743964010lle_hf @ F3 @ A4 ) )
% 0.23/0.57 = ( finite586181922lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_image_iff
% 0.23/0.57 thf(fact_334_finite__image__iff,axiom,
% 0.23/0.57 ! [F3: nat > hF_Mirabelle_hf,A4: set_nat] :
% 0.23/0.57 ( ( inj_on1988990670lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ( finite586181922lle_hf @ ( image_246164834lle_hf @ F3 @ A4 ) )
% 0.23/0.57 = ( finite_finite_nat @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_image_iff
% 0.23/0.57 thf(fact_335_finite__image__iff,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > nat,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on1874279374hf_nat @ F3 @ A4 )
% 0.23/0.57 => ( ( finite_finite_nat @ ( image_131453538hf_nat @ F3 @ A4 ) )
% 0.23/0.57 = ( finite586181922lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_image_iff
% 0.23/0.57 thf(fact_336_finite__image__iff,axiom,
% 0.23/0.57 ! [F3: nat > nat,A4: set_nat] :
% 0.23/0.57 ( ( inj_on_nat_nat @ F3 @ A4 )
% 0.23/0.57 => ( ( finite_finite_nat @ ( image_nat_nat @ F3 @ A4 ) )
% 0.23/0.57 = ( finite_finite_nat @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % finite_image_iff
% 0.23/0.57 thf(fact_337_inj__on__image__eq__iff,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,C3: set_se933006839lle_hf,A4: set_se933006839lle_hf,B4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ C3 )
% 0.23/0.57 => ( ( ord_le2016357975lle_hf @ A4 @ C3 )
% 0.23/0.57 => ( ( ord_le2016357975lle_hf @ B4 @ C3 )
% 0.23/0.57 => ( ( ( image_899003828lle_hf @ F3 @ A4 )
% 0.23/0.57 = ( image_899003828lle_hf @ F3 @ B4 ) )
% 0.23/0.57 = ( A4 = B4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_image_eq_iff
% 0.23/0.57 thf(fact_338_inj__on__image__mem__iff,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,B4: set_se933006839lle_hf,A2: set_HF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ B4 )
% 0.23/0.57 => ( ( member1490636632lle_hf @ A2 @ B4 )
% 0.23/0.57 => ( ( ord_le2016357975lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ ( F3 @ A2 ) @ ( image_899003828lle_hf @ F3 @ A4 ) )
% 0.23/0.57 = ( member1490636632lle_hf @ A2 @ A4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_image_mem_iff
% 0.23/0.57 thf(fact_339_inj__on__image__mem__iff,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on755450110lle_hf @ F3 @ B4 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ A2 @ B4 )
% 0.23/0.57 => ( ( ord_le432112161lle_hf @ A4 @ B4 )
% 0.23/0.57 => ( ( member1367349282lle_hf @ ( F3 @ A2 ) @ ( image_1743964010lle_hf @ F3 @ A4 ) )
% 0.23/0.57 = ( member1367349282lle_hf @ A2 @ A4 ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_on_image_mem_iff
% 0.23/0.57 thf(fact_340_inj__img__insertE,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_se933006839lle_hf,X2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ X2 @ B4 )
% 0.23/0.57 => ( ( ( insert9649339lle_hf @ X2 @ B4 )
% 0.23/0.57 = ( image_899003828lle_hf @ F3 @ A4 ) )
% 0.23/0.57 => ~ ! [X6: set_HF_Mirabelle_hf,A7: set_se933006839lle_hf] :
% 0.23/0.57 ( ~ ( member1490636632lle_hf @ X6 @ A7 )
% 0.23/0.57 => ( ( A4
% 0.23/0.57 = ( insert1636143089lle_hf @ X6 @ A7 ) )
% 0.23/0.57 => ( ( X2
% 0.23/0.57 = ( F3 @ X6 ) )
% 0.23/0.57 => ( B4
% 0.23/0.57 != ( image_899003828lle_hf @ F3 @ A7 ) ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_img_insertE
% 0.23/0.57 thf(fact_341_inj__img__insertE,axiom,
% 0.23/0.57 ! [F3: hF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,X2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( inj_on755450110lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ~ ( member1367349282lle_hf @ X2 @ B4 )
% 0.23/0.57 => ( ( ( insert9649339lle_hf @ X2 @ B4 )
% 0.23/0.57 = ( image_1743964010lle_hf @ F3 @ A4 ) )
% 0.23/0.57 => ~ ! [X6: hF_Mirabelle_hf,A7: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ~ ( member1367349282lle_hf @ X6 @ A7 )
% 0.23/0.57 => ( ( A4
% 0.23/0.57 = ( insert9649339lle_hf @ X6 @ A7 ) )
% 0.23/0.57 => ( ( X2
% 0.23/0.57 = ( F3 @ X6 ) )
% 0.23/0.57 => ( B4
% 0.23/0.57 != ( image_1743964010lle_hf @ F3 @ A7 ) ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % inj_img_insertE
% 0.23/0.57 thf(fact_342_card__image,axiom,
% 0.23/0.57 ! [F3: set_HF_Mirabelle_hf > hF_Mirabelle_hf,A4: set_se933006839lle_hf] :
% 0.23/0.57 ( ( inj_on811196232lle_hf @ F3 @ A4 )
% 0.23/0.57 => ( ( finite1213132899lle_hf @ ( image_899003828lle_hf @ F3 @ A4 ) )
% 0.23/0.57 = ( finite90088345lle_hf @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % card_image
% 0.23/0.57 thf(fact_343_Diff__insert__absorb,axiom,
% 0.23/0.57 ! [X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ~ ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 => ( ( minus_1450406810lle_hf @ ( insert9649339lle_hf @ X2 @ A4 ) @ ( insert9649339lle_hf @ X2 @ bot_bo53200981lle_hf ) )
% 0.23/0.57 = A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % Diff_insert_absorb
% 0.23/0.57 thf(fact_344_Diff__insert2,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ A2 @ B4 ) )
% 0.23/0.57 = ( minus_1450406810lle_hf @ ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) ) @ B4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % Diff_insert2
% 0.23/0.57 thf(fact_345_insert__Diff,axiom,
% 0.23/0.57 ! [A2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ A2 @ A4 )
% 0.23/0.57 => ( ( insert9649339lle_hf @ A2 @ ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) ) )
% 0.23/0.57 = A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % insert_Diff
% 0.23/0.57 thf(fact_346_Diff__insert,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ A2 @ B4 ) )
% 0.23/0.57 = ( minus_1450406810lle_hf @ ( minus_1450406810lle_hf @ A4 @ B4 ) @ ( insert9649339lle_hf @ A2 @ bot_bo53200981lle_hf ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % Diff_insert
% 0.23/0.57 thf(fact_347_subset__Diff__insert,axiom,
% 0.23/0.57 ! [A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,X2: hF_Mirabelle_hf,C3: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( ord_le432112161lle_hf @ A4 @ ( minus_1450406810lle_hf @ B4 @ ( insert9649339lle_hf @ X2 @ C3 ) ) )
% 0.23/0.57 = ( ( ord_le432112161lle_hf @ A4 @ ( minus_1450406810lle_hf @ B4 @ C3 ) )
% 0.23/0.57 & ~ ( member1367349282lle_hf @ X2 @ A4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % subset_Diff_insert
% 0.23/0.57 thf(fact_348_in__image__insert__iff,axiom,
% 0.23/0.57 ! [B4: set_se933006839lle_hf,X2: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ! [C4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1490636632lle_hf @ C4 @ B4 )
% 0.23/0.57 => ~ ( member1367349282lle_hf @ X2 @ C4 ) )
% 0.23/0.57 => ( ( member1490636632lle_hf @ A4 @ ( image_1514960916lle_hf @ ( insert9649339lle_hf @ X2 ) @ B4 ) )
% 0.23/0.57 = ( ( member1367349282lle_hf @ X2 @ A4 )
% 0.23/0.57 & ( member1490636632lle_hf @ ( minus_1450406810lle_hf @ A4 @ ( insert9649339lle_hf @ X2 @ bot_bo53200981lle_hf ) ) @ B4 ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % in_image_insert_iff
% 0.23/0.57 thf(fact_349_DiffE,axiom,
% 0.23/0.57 ! [C: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ C @ ( minus_1450406810lle_hf @ A4 @ B4 ) )
% 0.23/0.57 => ~ ( ( member1367349282lle_hf @ C @ A4 )
% 0.23/0.57 => ( member1367349282lle_hf @ C @ B4 ) ) ) ).
% 0.23/0.57
% 0.23/0.57 % DiffE
% 0.23/0.57 thf(fact_350_DiffD1,axiom,
% 0.23/0.57 ! [C: hF_Mirabelle_hf,A4: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.23/0.57 ( ( member1367349282lle_hf @ C @ ( minus_1450406810lle_hf @ A4 @ B4 ) )
% 0.23/0.57 => ( member1367349282lle_hf @ C @ A4 ) ) ).
% 0.23/0.57
% 0.23/0.57 % DiffD1
% 0.23/0.57
% 0.23/0.57 % Conjectures (1)
% 0.23/0.57 thf(conj_0,conjecture,
% 0.23/0.57 ( ( z = zero_z189798548lle_hf )
% 0.23/0.57 = ( ! [X: hF_Mirabelle_hf] :
% 0.23/0.57 ~ ( hF_Mirabelle_hmem @ X @ z ) ) ) ).
% 0.23/0.57
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.63 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ZwFo8qLlA0/cvc5---1.0.5_28312.p...
% 0.23/0.63 (declare-sort $$unsorted 0)
% 0.23/0.63 (declare-sort tptp.set_se933006839lle_hf 0)
% 0.23/0.63 (declare-sort tptp.set_HF_Mirabelle_hf 0)
% 0.23/0.63 (declare-sort tptp.hF_Mirabelle_hf 0)
% 0.23/0.63 (declare-sort tptp.set_nat 0)
% 0.23/0.63 (declare-sort tptp.nat 0)
% 0.23/0.63 (declare-fun tptp.finite1213132899lle_hf (tptp.set_HF_Mirabelle_hf) tptp.nat)
% 0.23/0.63 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 0.23/0.63 (declare-fun tptp.finite90088345lle_hf (tptp.set_se933006839lle_hf) tptp.nat)
% 0.23/0.63 (declare-fun tptp.finite586181922lle_hf (tptp.set_HF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 0.23/0.63 (declare-fun tptp.finite1450550360lle_hf (tptp.set_se933006839lle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.inj_on755450110lle_hf ((-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.inj_on1874279374hf_nat ((-> tptp.hF_Mirabelle_hf tptp.nat) tptp.set_HF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.inj_on1988990670lle_hf ((-> tptp.nat tptp.hF_Mirabelle_hf) tptp.set_nat) Bool)
% 0.23/0.63 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 0.23/0.63 (declare-fun tptp.inj_on811196232lle_hf ((-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.set_se933006839lle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.23/0.63 (declare-fun tptp.minus_1450406810lle_hf (tptp.set_HF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 0.23/0.63 (declare-fun tptp.minus_500612048lle_hf (tptp.set_se933006839lle_hf tptp.set_se933006839lle_hf) tptp.set_se933006839lle_hf)
% 0.23/0.63 (declare-fun tptp.zero_z189798548lle_hf () tptp.hF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.23/0.63 (declare-fun tptp.hF_Mirabelle_HF (tptp.set_HF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.hF_Mirabelle_Abs_hf (tptp.nat) tptp.hF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.hF_Mirabelle_hfset (tptp.hF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.hF_Mirabelle_hinsert (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.hF_Mirabelle_hmem (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.lattic710307446hf_nat ((-> tptp.hF_Mirabelle_hf tptp.nat) tptp.set_HF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.lattic1974000059at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 0.23/0.63 (declare-fun tptp.semiring_1_Nats_nat () tptp.set_nat)
% 0.23/0.63 (declare-fun tptp.bot_bo1263054448e_hf_o (tptp.hF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 0.23/0.63 (declare-fun tptp.bot_bo554042810e_hf_o (tptp.set_HF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.bot_bot_o () Bool)
% 0.23/0.63 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 0.23/0.63 (declare-fun tptp.bot_bo53200981lle_hf () tptp.set_HF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 0.23/0.63 (declare-fun tptp.bot_bo2093393035lle_hf () tptp.set_se933006839lle_hf)
% 0.23/0.63 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.23/0.63 (declare-fun tptp.ord_le432112161lle_hf (tptp.set_HF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 0.23/0.63 (declare-fun tptp.ord_le2016357975lle_hf (tptp.set_se933006839lle_hf tptp.set_se933006839lle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.semiri2115134414it_nat (tptp.nat tptp.nat) tptp.nat)
% 0.23/0.63 (declare-fun tptp.semiri2013084963it_nat (tptp.nat tptp.nat) tptp.nat)
% 0.23/0.63 (declare-fun tptp.collec2046588256lle_hf ((-> tptp.hF_Mirabelle_hf Bool)) tptp.set_HF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.23/0.63 (declare-fun tptp.collec1758573718lle_hf ((-> tptp.set_HF_Mirabelle_hf Bool)) tptp.set_se933006839lle_hf)
% 0.23/0.63 (declare-fun tptp.image_1743964010lle_hf ((-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.image_131453538hf_nat ((-> tptp.hF_Mirabelle_hf tptp.nat) tptp.set_HF_Mirabelle_hf) tptp.set_nat)
% 0.23/0.63 (declare-fun tptp.image_246164834lle_hf ((-> tptp.nat tptp.hF_Mirabelle_hf) tptp.set_nat) tptp.set_HF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 0.23/0.63 (declare-fun tptp.image_899003828lle_hf ((-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.set_se933006839lle_hf) tptp.set_HF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.image_1514960916lle_hf ((-> tptp.set_HF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) tptp.set_se933006839lle_hf) tptp.set_se933006839lle_hf)
% 0.23/0.63 (declare-fun tptp.insert9649339lle_hf (tptp.hF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 0.23/0.63 (declare-fun tptp.insert1636143089lle_hf (tptp.set_HF_Mirabelle_hf tptp.set_se933006839lle_hf) tptp.set_se933006839lle_hf)
% 0.23/0.63 (declare-fun tptp.is_emp566801209lle_hf (tptp.set_HF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.is_sin1448700567lle_hf (tptp.set_HF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.the_el1104322134lle_hf (tptp.set_HF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.23/0.63 (declare-fun tptp.member1367349282lle_hf (tptp.hF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.23/0.63 (declare-fun tptp.member1490636632lle_hf (tptp.set_HF_Mirabelle_hf tptp.set_se933006839lle_hf) Bool)
% 0.23/0.63 (declare-fun tptp.z () tptp.hF_Mirabelle_hf)
% 0.23/0.63 (assert (= (lambda ((Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (= Y Z)) (lambda ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (forall ((X tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X))) (= (@ _let_1 A) (@ _let_1 B)))))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A2) tptp.zero_z189798548lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A2) tptp.zero_z189798548lle_hf))))
% 0.23/0.63 (assert (forall ((Y2 tptp.hF_Mirabelle_hf)) (=> (not (= Y2 tptp.zero_z189798548lle_hf)) (not (forall ((A3 tptp.hF_Mirabelle_hf) (B2 tptp.hF_Mirabelle_hf)) (=> (= Y2 (@ (@ tptp.hF_Mirabelle_hinsert A3) B2)) (@ (@ tptp.hF_Mirabelle_hmem A3) B2)))))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem A2))) (= (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert B3) C)) (or (= A2 B3) (@ _let_1 C))))))
% 0.23/0.63 (assert (= tptp.hF_Mirabelle_hmem (lambda ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A) (@ tptp.hF_Mirabelle_hfset B)))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf)) (= (= tptp.zero_z189798548lle_hf X2) (= X2 tptp.zero_z189798548lle_hf))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 0.23/0.63 (assert (= (@ tptp.hF_Mirabelle_Abs_hf tptp.zero_zero_nat) tptp.zero_z189798548lle_hf))
% 0.23/0.63 (assert (= tptp.zero_z189798548lle_hf (@ tptp.hF_Mirabelle_HF tptp.bot_bo53200981lle_hf)))
% 0.23/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.semiri2013084963it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.23/0.63 (assert (forall ((N tptp.nat) (A2 tptp.nat)) (= (= (@ (@ tptp.semiri2013084963it_nat N) A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))))
% 0.23/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.semiri2115134414it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.23/0.63 (assert (@ (@ tptp.member_nat tptp.zero_zero_nat) tptp.semiring_1_Nats_nat))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HF (@ tptp.hF_Mirabelle_hfset A2)) A2)))
% 0.23/0.63 (assert (forall ((C tptp.set_HF_Mirabelle_hf)) (not (@ (@ tptp.member1490636632lle_hf C) tptp.bot_bo2093393035lle_hf))))
% 0.23/0.63 (assert (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))))
% 0.23/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf C) tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_se933006839lle_hf)) (= (forall ((X tptp.set_HF_Mirabelle_hf)) (not (@ (@ tptp.member1490636632lle_hf X) A4))) (= A4 tptp.bot_bo2093393035lle_hf))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat)) (= (forall ((X tptp.nat)) (not (@ (@ tptp.member_nat X) A4))) (= A4 tptp.bot_bot_set_nat))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (forall ((X tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf X) A4))) (= A4 tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X tptp.nat)) (not (@ P X))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (= (@ tptp.collec1758573718lle_hf P) tptp.bot_bo2093393035lle_hf) (forall ((X tptp.set_HF_Mirabelle_hf)) (not (@ P X))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool))) (= (= (@ tptp.collec2046588256lle_hf P) tptp.bot_bo53200981lle_hf) (forall ((X tptp.hF_Mirabelle_hf)) (not (@ P X))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X tptp.nat)) (not (@ P X))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (= tptp.bot_bo2093393035lle_hf (@ tptp.collec1758573718lle_hf P)) (forall ((X tptp.set_HF_Mirabelle_hf)) (not (@ P X))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool))) (= (= tptp.bot_bo53200981lle_hf (@ tptp.collec2046588256lle_hf P)) (forall ((X tptp.hF_Mirabelle_hf)) (not (@ P X))))))
% 0.23/0.63 (assert (= tptp.bot_bo1263054448e_hf_o (lambda ((X tptp.hF_Mirabelle_hf)) tptp.bot_bot_o)))
% 0.23/0.63 (assert (= tptp.bot_bo554042810e_hf_o (lambda ((X tptp.set_HF_Mirabelle_hf)) tptp.bot_bot_o)))
% 0.23/0.63 (assert (= tptp.hF_Mirabelle_hinsert (lambda ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ tptp.hF_Mirabelle_HF (@ (@ tptp.insert9649339lle_hf A) (@ tptp.hF_Mirabelle_hfset B))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (= (@ tptp.hF_Mirabelle_hfset (@ tptp.hF_Mirabelle_HF A4)) A4))))
% 0.23/0.63 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (not (@ (@ tptp.member1490636632lle_hf A2) tptp.bot_bo2093393035lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.member_nat A2) tptp.bot_bot_set_nat))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf A2) tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_se933006839lle_hf) (A2 tptp.set_HF_Mirabelle_hf)) (=> (= A4 tptp.bot_bo2093393035lle_hf) (not (@ (@ tptp.member1490636632lle_hf A2) A4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (A2 tptp.nat)) (=> (= A4 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A2) A4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (=> (= A4 tptp.bot_bo53200981lle_hf) (not (@ (@ tptp.member1367349282lle_hf A2) A4)))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ _let_1 A4))) (= (@ _let_1 _let_2) _let_2)))))
% 0.23/0.63 (assert (forall ((X2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.insert1636143089lle_hf X2))) (let ((_let_2 (@ _let_1 A4))) (= (@ _let_1 _let_2) _let_2)))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X2))) (let ((_let_2 (@ _let_1 A4))) (= (@ _let_1 _let_2) _let_2)))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (= (@ _let_1 (@ (@ tptp.insert_nat B3) A4)) (or (= A2 B3) (@ _let_1 A4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.member1490636632lle_hf A2))) (= (@ _let_1 (@ (@ tptp.insert1636143089lle_hf B3) A4)) (or (= A2 B3) (@ _let_1 A4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf B3) A4)) (or (= A2 B3) (@ _let_1 A4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B3)) (@ _let_1 (@ (@ tptp.insert_nat B3) B4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_se933006839lle_hf) (B3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1490636632lle_hf A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B3)) (@ _let_1 (@ (@ tptp.insert1636143089lle_hf B3) B4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B3)) (@ _let_1 (@ (@ tptp.insert9649339lle_hf B3) B4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.member1490636632lle_hf A2) (@ (@ tptp.insert1636143089lle_hf A2) tptp.bot_bo2093393035lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A2) (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A4) (exists ((B5 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat A2) B5)) (not (@ (@ tptp.member_nat A2) B5)))))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.member1490636632lle_hf A2) A4) (exists ((B5 tptp.set_se933006839lle_hf)) (and (= A4 (@ (@ tptp.insert1636143089lle_hf A2) B5)) (not (@ (@ tptp.member1490636632lle_hf A2) B5)))))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A2) A4) (exists ((B5 tptp.set_HF_Mirabelle_hf)) (and (= A4 (@ (@ tptp.insert9649339lle_hf A2) B5)) (not (@ (@ tptp.member1367349282lle_hf A2) B5)))))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.insert_nat Y2))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))))
% 0.23/0.63 (assert (forall ((X2 tptp.set_HF_Mirabelle_hf) (Y2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.insert1636143089lle_hf X2))) (let ((_let_2 (@ tptp.insert1636143089lle_hf Y2))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X2))) (let ((_let_2 (@ tptp.insert9649339lle_hf Y2))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (A4 tptp.set_nat) (B3 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member_nat A2) A4)) (=> (not (@ (@ tptp.member_nat B3) B4)) (= (= (@ (@ tptp.insert_nat A2) A4) (@ (@ tptp.insert_nat B3) B4)) (and (=> _let_1 (= A4 B4)) (=> (not _let_1) (exists ((C2 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat B3) C2)) (not (@ (@ tptp.member_nat B3) C2)) (= B4 (@ (@ tptp.insert_nat A2) C2)) (not (@ (@ tptp.member_nat A2) C2))))))))))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf) (B3 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member1490636632lle_hf A2) A4)) (=> (not (@ (@ tptp.member1490636632lle_hf B3) B4)) (= (= (@ (@ tptp.insert1636143089lle_hf A2) A4) (@ (@ tptp.insert1636143089lle_hf B3) B4)) (and (=> _let_1 (= A4 B4)) (=> (not _let_1) (exists ((C2 tptp.set_se933006839lle_hf)) (and (= A4 (@ (@ tptp.insert1636143089lle_hf B3) C2)) (not (@ (@ tptp.member1490636632lle_hf B3) C2)) (= B4 (@ (@ tptp.insert1636143089lle_hf A2) C2)) (not (@ (@ tptp.member1490636632lle_hf A2) C2))))))))))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member1367349282lle_hf A2) A4)) (=> (not (@ (@ tptp.member1367349282lle_hf B3) B4)) (= (= (@ (@ tptp.insert9649339lle_hf A2) A4) (@ (@ tptp.insert9649339lle_hf B3) B4)) (and (=> _let_1 (= A4 B4)) (=> (not _let_1) (exists ((C2 tptp.set_HF_Mirabelle_hf)) (and (= A4 (@ (@ tptp.insert9649339lle_hf B3) C2)) (not (@ (@ tptp.member1367349282lle_hf B3) C2)) (= B4 (@ (@ tptp.insert9649339lle_hf A2) C2)) (not (@ (@ tptp.member1367349282lle_hf A2) C2))))))))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A4) (= (@ (@ tptp.insert_nat A2) A4) A4))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.member1490636632lle_hf A2) A4) (= (@ (@ tptp.insert1636143089lle_hf A2) A4) A4))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A2) A4) (= (@ (@ tptp.insert9649339lle_hf A2) A4) A4))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (A4 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.member_nat X2))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A4) (@ _let_1 B4)) (= A4 B4))))))))
% 0.23/0.63 (assert (forall ((X2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.insert1636143089lle_hf X2))) (let ((_let_2 (@ tptp.member1490636632lle_hf X2))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A4) (@ _let_1 B4)) (= A4 B4))))))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X2))) (let ((_let_2 (@ tptp.member1367349282lle_hf X2))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A4) (@ _let_1 B4)) (= A4 B4))))))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) A4) (not (forall ((B5 tptp.set_nat)) (=> (= A4 (@ (@ tptp.insert_nat X2) B5)) (@ (@ tptp.member_nat X2) B5)))))))
% 0.23/0.63 (assert (forall ((X2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.member1490636632lle_hf X2) A4) (not (forall ((B5 tptp.set_se933006839lle_hf)) (=> (= A4 (@ (@ tptp.insert1636143089lle_hf X2) B5)) (@ (@ tptp.member1490636632lle_hf X2) B5)))))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X2) A4) (not (forall ((B5 tptp.set_HF_Mirabelle_hf)) (=> (= A4 (@ (@ tptp.insert9649339lle_hf X2) B5)) (@ (@ tptp.member1367349282lle_hf X2) B5)))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_nat B3) B4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_se933006839lle_hf) (B3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1490636632lle_hf A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert1636143089lle_hf B3) B4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert9649339lle_hf B3) B4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat A2) B4))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_se933006839lle_hf)) (@ (@ tptp.member1490636632lle_hf A2) (@ (@ tptp.insert1636143089lle_hf A2) B4))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A2) (@ (@ tptp.insert9649339lle_hf A2) B4))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert_nat B3) A4)) (=> (not (= A2 B3)) (@ _let_1 A4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.member1490636632lle_hf A2))) (=> (@ _let_1 (@ (@ tptp.insert1636143089lle_hf B3) A4)) (=> (not (= A2 B3)) (@ _let_1 A4))))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ _let_1 (@ (@ tptp.insert9649339lle_hf B3) A4)) (=> (not (= A2 B3)) (@ _let_1 A4))))))
% 0.23/0.63 (assert (forall ((F tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf F) (=> (not (= F tptp.bot_bo2093393035lle_hf)) (not (forall ((A5 tptp.set_se933006839lle_hf) (X3 tptp.set_HF_Mirabelle_hf)) (=> (= F (@ (@ tptp.insert1636143089lle_hf X3) A5)) (=> (not (@ (@ tptp.member1490636632lle_hf X3) A5)) (not (@ tptp.finite1450550360lle_hf A5))))))))))
% 0.23/0.63 (assert (forall ((F tptp.set_nat)) (=> (@ tptp.finite_finite_nat F) (=> (not (= F tptp.bot_bot_set_nat)) (not (forall ((A5 tptp.set_nat) (X3 tptp.nat)) (=> (= F (@ (@ tptp.insert_nat X3) A5)) (=> (not (@ (@ tptp.member_nat X3) A5)) (not (@ tptp.finite_finite_nat A5))))))))))
% 0.23/0.63 (assert (forall ((F tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf F) (=> (not (= F tptp.bot_bo53200981lle_hf)) (not (forall ((A5 tptp.set_HF_Mirabelle_hf) (X3 tptp.hF_Mirabelle_hf)) (=> (= F (@ (@ tptp.insert9649339lle_hf X3) A5)) (=> (not (@ (@ tptp.member1367349282lle_hf X3) A5)) (not (@ tptp.finite586181922lle_hf A5))))))))))
% 0.23/0.63 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))
% 0.23/0.63 (assert (= tptp.bot_bo2093393035lle_hf (@ tptp.collec1758573718lle_hf tptp.bot_bo554042810e_hf_o)))
% 0.23/0.63 (assert (= tptp.bot_bo53200981lle_hf (@ tptp.collec2046588256lle_hf tptp.bot_bo1263054448e_hf_o)))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf)) (=> (= (@ (@ tptp.insert1636143089lle_hf A2) tptp.bot_bo2093393035lle_hf) (@ (@ tptp.insert1636143089lle_hf B3) tptp.bot_bo2093393035lle_hf)) (= A2 B3))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (= (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat B3) tptp.bot_bot_set_nat)) (= A2 B3))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (=> (= (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf) (@ (@ tptp.insert9649339lle_hf B3) tptp.bot_bo53200981lle_hf)) (= A2 B3))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (not (= (@ (@ tptp.insert1636143089lle_hf A2) A4) tptp.bot_bo2093393035lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (A4 tptp.set_nat)) (not (= (@ (@ tptp.insert_nat A2) A4) tptp.bot_bot_set_nat))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (not (= (@ (@ tptp.insert9649339lle_hf A2) A4) tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf) (D tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.insert1636143089lle_hf A2) (@ (@ tptp.insert1636143089lle_hf B3) tptp.bot_bo2093393035lle_hf)) (@ (@ tptp.insert1636143089lle_hf C) (@ (@ tptp.insert1636143089lle_hf D) tptp.bot_bo2093393035lle_hf))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (= (@ (@ tptp.insert_nat A2) (@ (@ tptp.insert_nat B3) tptp.bot_bot_set_nat)) (@ (@ tptp.insert_nat C) (@ (@ tptp.insert_nat D) tptp.bot_bot_set_nat))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.insert9649339lle_hf A2) (@ (@ tptp.insert9649339lle_hf B3) tptp.bot_bo53200981lle_hf)) (@ (@ tptp.insert9649339lle_hf C) (@ (@ tptp.insert9649339lle_hf D) tptp.bot_bo53200981lle_hf))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.member1367349282lle_hf A2) (@ tptp.collec2046588256lle_hf P)) (@ P A2))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (@ (@ tptp.member1490636632lle_hf A2) (@ tptp.collec1758573718lle_hf P)) (@ P A2))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A4))) A4)))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ tptp.collec2046588256lle_hf (lambda ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) A4))) A4)))
% 0.23/0.63 (assert (forall ((A4 tptp.set_se933006839lle_hf)) (= (@ tptp.collec1758573718lle_hf (lambda ((X tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.member1490636632lle_hf X) A4))) A4)))
% 0.23/0.63 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (Q (-> tptp.hF_Mirabelle_hf Bool))) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec2046588256lle_hf P) (@ tptp.collec2046588256lle_hf Q)))))
% 0.23/0.63 (assert (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool)) (Q (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec1758573718lle_hf P) (@ tptp.collec1758573718lle_hf Q)))))
% 0.23/0.63 (assert (forall ((B3 tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.member1490636632lle_hf B3) (@ (@ tptp.insert1636143089lle_hf A2) tptp.bot_bo2093393035lle_hf)) (= B3 A2))))
% 0.23/0.63 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.member_nat B3) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= B3 A2))))
% 0.23/0.63 (assert (forall ((B3 tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.member1367349282lle_hf B3) (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf)) (= B3 A2))))
% 0.23/0.63 (assert (forall ((B3 tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf B3) (@ (@ tptp.insert1636143089lle_hf A2) tptp.bot_bo2093393035lle_hf)) (= B3 A2))))
% 0.23/0.63 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= B3 A2))))
% 0.23/0.63 (assert (forall ((B3 tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf B3) (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf)) (= B3 A2))))
% 0.23/0.63 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (@ tptp.finite586181922lle_hf (@ tptp.hF_Mirabelle_hfset A2))))
% 0.23/0.63 (assert (= tptp.bot_bo1263054448e_hf_o (lambda ((X tptp.hF_Mirabelle_hf)) tptp.bot_bot_o)))
% 0.23/0.63 (assert (= tptp.bot_bo554042810e_hf_o (lambda ((X tptp.set_HF_Mirabelle_hf)) tptp.bot_bot_o)))
% 0.23/0.63 (assert (forall ((A4 tptp.set_se933006839lle_hf)) (= (exists ((X tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.member1490636632lle_hf X) A4)) (not (= A4 tptp.bot_bo2093393035lle_hf)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat)) (= (exists ((X tptp.nat)) (@ (@ tptp.member_nat X) A4)) (not (= A4 tptp.bot_bot_set_nat)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (exists ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) A4)) (not (= A4 tptp.bot_bo53200981lle_hf)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_se933006839lle_hf)) (=> (forall ((Y3 tptp.set_HF_Mirabelle_hf)) (not (@ (@ tptp.member1490636632lle_hf Y3) A4))) (= A4 tptp.bot_bo2093393035lle_hf))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat)) (=> (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member_nat Y3) A4))) (= A4 tptp.bot_bot_set_nat))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((Y3 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf Y3) A4))) (= A4 tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (= (@ tptp.finite1450550360lle_hf (@ (@ tptp.insert1636143089lle_hf A2) A4)) (@ tptp.finite1450550360lle_hf A4))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.insert9649339lle_hf A2) A4)) (@ tptp.finite586181922lle_hf A4))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (A4 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A2) A4)) (@ tptp.finite_finite_nat A4))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf A2) (=> (not (= A2 tptp.bot_bo2093393035lle_hf)) (not (forall ((A5 tptp.set_se933006839lle_hf)) (=> (exists ((A3 tptp.set_HF_Mirabelle_hf)) (= A2 (@ (@ tptp.insert1636143089lle_hf A3) A5))) (not (@ tptp.finite1450550360lle_hf A5)))))))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (not (forall ((A5 tptp.set_nat)) (=> (exists ((A3 tptp.nat)) (= A2 (@ (@ tptp.insert_nat A3) A5))) (not (@ tptp.finite_finite_nat A5)))))))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A2) (=> (not (= A2 tptp.bot_bo53200981lle_hf)) (not (forall ((A5 tptp.set_HF_Mirabelle_hf)) (=> (exists ((A3 tptp.hF_Mirabelle_hf)) (= A2 (@ (@ tptp.insert9649339lle_hf A3) A5))) (not (@ tptp.finite586181922lle_hf A5)))))))))
% 0.23/0.63 (assert (= tptp.finite1450550360lle_hf (lambda ((A tptp.set_se933006839lle_hf)) (or (= A tptp.bot_bo2093393035lle_hf) (exists ((A6 tptp.set_se933006839lle_hf) (B tptp.set_HF_Mirabelle_hf)) (and (= A (@ (@ tptp.insert1636143089lle_hf B) A6)) (@ tptp.finite1450550360lle_hf A6)))))))
% 0.23/0.63 (assert (= tptp.finite_finite_nat (lambda ((A tptp.set_nat)) (or (= A tptp.bot_bot_set_nat) (exists ((A6 tptp.set_nat) (B tptp.nat)) (and (= A (@ (@ tptp.insert_nat B) A6)) (@ tptp.finite_finite_nat A6)))))))
% 0.23/0.63 (assert (= tptp.finite586181922lle_hf (lambda ((A tptp.set_HF_Mirabelle_hf)) (or (= A tptp.bot_bo53200981lle_hf) (exists ((A6 tptp.set_HF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (and (= A (@ (@ tptp.insert9649339lle_hf B) A6)) (@ tptp.finite586181922lle_hf A6)))))))
% 0.23/0.63 (assert (forall ((F tptp.set_se933006839lle_hf) (P (-> tptp.set_se933006839lle_hf Bool))) (=> (@ tptp.finite1450550360lle_hf F) (=> (@ P tptp.bot_bo2093393035lle_hf) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf) (F2 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf F2) (=> (not (@ (@ tptp.member1490636632lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert1636143089lle_hf X3) F2)))))) (@ P F))))))
% 0.23/0.63 (assert (forall ((F tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (F2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F2) (=> (not (@ (@ tptp.member_nat X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat X3) F2)))))) (@ P F))))))
% 0.23/0.63 (assert (forall ((F tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf F) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf F2) (=> (not (@ (@ tptp.member1367349282lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf X3) F2)))))) (@ P F))))))
% 0.23/0.63 (assert (forall ((X2 tptp.set_se933006839lle_hf) (P (-> tptp.set_se933006839lle_hf Bool))) (=> (@ tptp.finite1450550360lle_hf X2) (=> (@ P tptp.bot_bo2093393035lle_hf) (=> (forall ((A5 tptp.set_se933006839lle_hf) (A3 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite1450550360lle_hf A5) (=> (@ P A5) (@ P (@ (@ tptp.insert1636143089lle_hf A3) A5))))) (@ P X2))))))
% 0.23/0.63 (assert (forall ((X2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat X2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A5 tptp.set_nat) (A3 tptp.nat)) (=> (@ tptp.finite_finite_nat A5) (=> (@ P A5) (@ P (@ (@ tptp.insert_nat A3) A5))))) (@ P X2))))))
% 0.23/0.63 (assert (forall ((X2 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf X2) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((A5 tptp.set_HF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A5) (=> (@ P A5) (@ P (@ (@ tptp.insert9649339lle_hf A3) A5))))) (@ P X2))))))
% 0.23/0.63 (assert (forall ((F tptp.set_se933006839lle_hf) (P (-> tptp.set_se933006839lle_hf Bool))) (=> (@ tptp.finite1450550360lle_hf F) (=> (not (= F tptp.bot_bo2093393035lle_hf)) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf)) (@ P (@ (@ tptp.insert1636143089lle_hf X3) tptp.bot_bo2093393035lle_hf))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf) (F2 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf F2) (=> (not (= F2 tptp.bot_bo2093393035lle_hf)) (=> (not (@ (@ tptp.member1490636632lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert1636143089lle_hf X3) F2))))))) (@ P F)))))))
% 0.23/0.63 (assert (forall ((F tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F) (=> (not (= F tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (@ P (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))) (=> (forall ((X3 tptp.nat) (F2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F2) (=> (not (= F2 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat X3) F2))))))) (@ P F)))))))
% 0.23/0.63 (assert (forall ((F tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf F) (=> (not (= F tptp.bot_bo53200981lle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ P (@ (@ tptp.insert9649339lle_hf X3) tptp.bot_bo53200981lle_hf))) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf F2) (=> (not (= F2 tptp.bot_bo53200981lle_hf)) (=> (not (@ (@ tptp.member1367349282lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf X3) F2))))))) (@ P F)))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.set_se933006839lle_hf Bool)) (A4 tptp.set_se933006839lle_hf)) (=> (forall ((A5 tptp.set_se933006839lle_hf)) (=> (not (@ tptp.finite1450550360lle_hf A5)) (@ P A5))) (=> (@ P tptp.bot_bo2093393035lle_hf) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf) (F2 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf F2) (=> (not (@ (@ tptp.member1490636632lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert1636143089lle_hf X3) F2)))))) (@ P A4))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.set_nat Bool)) (A4 tptp.set_nat)) (=> (forall ((A5 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A5)) (@ P A5))) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (F2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F2) (=> (not (@ (@ tptp.member_nat X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat X3) F2)))))) (@ P A4))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((A5 tptp.set_HF_Mirabelle_hf)) (=> (not (@ tptp.finite586181922lle_hf A5)) (@ P A5))) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf F2) (=> (not (@ (@ tptp.member1367349282lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf X3) F2)))))) (@ P A4))))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf)) (= (@ tptp.the_el1104322134lle_hf (@ (@ tptp.insert9649339lle_hf X2) tptp.bot_bo53200981lle_hf)) X2)))
% 0.23/0.63 (assert (@ tptp.finite_finite_nat tptp.bot_bot_set_nat))
% 0.23/0.63 (assert (@ tptp.finite586181922lle_hf tptp.bot_bo53200981lle_hf))
% 0.23/0.63 (assert (forall ((S tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (= S tptp.bot_bot_set_nat)))))
% 0.23/0.63 (assert (forall ((S tptp.set_HF_Mirabelle_hf)) (=> (not (@ tptp.finite586181922lle_hf S)) (not (= S tptp.bot_bo53200981lle_hf)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (@ tptp.finite586181922lle_hf (@ (@ tptp.insert9649339lle_hf A2) A4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A2) A4)))))
% 0.23/0.63 (assert (= tptp.bot_bo1263054448e_hf_o (lambda ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (= (@ tptp.collec1758573718lle_hf P) tptp.bot_bo2093393035lle_hf) (= P tptp.bot_bo554042810e_hf_o))))
% 0.23/0.63 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool))) (= (= (@ tptp.collec2046588256lle_hf P) tptp.bot_bo53200981lle_hf) (= P tptp.bot_bo1263054448e_hf_o))))
% 0.23/0.63 (assert (= tptp.is_sin1448700567lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf)) (= A6 (@ (@ tptp.insert9649339lle_hf (@ tptp.the_el1104322134lle_hf A6)) tptp.bot_bo53200981lle_hf)))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf)) (@ tptp.is_sin1448700567lle_hf (@ (@ tptp.insert9649339lle_hf X2) tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (= tptp.is_emp566801209lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf)) (= A6 tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (= tptp.is_sin1448700567lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf)) (exists ((X tptp.hF_Mirabelle_hf)) (= A6 (@ (@ tptp.insert9649339lle_hf X) tptp.bot_bo53200981lle_hf))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.is_sin1448700567lle_hf A4) (not (forall ((X3 tptp.hF_Mirabelle_hf)) (not (= A4 (@ (@ tptp.insert9649339lle_hf X3) tptp.bot_bo53200981lle_hf))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (not (= A4 tptp.bot_bo53200981lle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X3) A4) (=> (@ (@ tptp.member1367349282lle_hf Y3) A4) (= X3 Y3)))) (@ tptp.is_sin1448700567lle_hf A4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_nat)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (= (= (@ tptp.finite1213132899lle_hf A4) tptp.zero_zero_nat) (= A4 tptp.bot_bo53200981lle_hf)))))
% 0.23/0.63 (assert (forall ((F tptp.set_nat) (A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F) (=> (@ (@ tptp.ord_less_eq_set_nat F) A4) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F2) (=> (@ _let_1 A4) (=> (not (@ _let_1 F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat A3) F2)))))))) (@ P F)))))))
% 0.23/0.63 (assert (forall ((F tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf F) (=> (@ (@ tptp.ord_le432112161lle_hf F) A4) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((A3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A3))) (=> (@ tptp.finite586181922lle_hf F2) (=> (@ _let_1 A4) (=> (not (@ _let_1 F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf A3) F2)))))))) (@ P F)))))))
% 0.23/0.63 (assert (forall ((F tptp.set_nat) (A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F) (=> (@ (@ tptp.ord_less_eq_set_nat F) A4) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F2) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_less_eq_set_nat F2) A4) (=> (not (@ _let_1 F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat A3) F2))))))))) (@ P F)))))))
% 0.23/0.63 (assert (forall ((F tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf F) (=> (@ (@ tptp.ord_le432112161lle_hf F) A4) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((A3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A3))) (=> (@ tptp.finite586181922lle_hf F2) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le432112161lle_hf F2) A4) (=> (not (@ _let_1 F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf A3) F2))))))))) (@ P F)))))))
% 0.23/0.63 (assert (@ (@ tptp.inj_on811196232lle_hf tptp.hF_Mirabelle_HF) (@ tptp.collec1758573718lle_hf tptp.finite586181922lle_hf)))
% 0.23/0.63 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf X3))) (=> (@ _let_1 A4) (@ _let_1 B4)))) (@ (@ tptp.ord_le432112161lle_hf A4) B4))))
% 0.23/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.ord_le432112161lle_hf A4) tptp.bot_bo53200981lle_hf) (= A4 tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.ord_le432112161lle_hf tptp.bot_bo53200981lle_hf) A4)))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.insert9649339lle_hf X2) A4)) B4) (and (@ (@ tptp.member1367349282lle_hf X2) B4) (@ (@ tptp.ord_le432112161lle_hf A4) B4)))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.insert9649339lle_hf B3) tptp.bot_bo53200981lle_hf))) (= (= (@ (@ tptp.insert9649339lle_hf A2) A4) _let_1) (and (= A2 B3) (@ (@ tptp.ord_le432112161lle_hf A4) _let_1))))))
% 0.23/0.63 (assert (forall ((B3 tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.insert9649339lle_hf B3) tptp.bot_bo53200981lle_hf))) (= (= _let_1 (@ (@ tptp.insert9649339lle_hf A2) A4)) (and (= A2 B3) (@ (@ tptp.ord_le432112161lle_hf A4) _let_1))))))
% 0.23/0.63 (assert (= (@ tptp.finite1213132899lle_hf tptp.bot_bo53200981lle_hf) tptp.zero_zero_nat))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (not (@ tptp.finite586181922lle_hf A4)) (= (@ tptp.finite1213132899lle_hf A4) tptp.zero_zero_nat))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat))))
% 0.23/0.63 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= A2 B3)))))
% 0.23/0.63 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A tptp.nat) (B tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 0.23/0.63 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B3 tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A2) B3)))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= A2 B3)))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (@ (@ tptp.ord_less_eq_nat A2) C)))))
% 0.23/0.63 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A tptp.nat) (B tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat B) A)))))
% 0.23/0.63 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y2) (= X2 Y2)))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y2))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (@ _let_1 C))))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat Y2) X2))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= X2 Y2)))))
% 0.23/0.63 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((X tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_nat Y4) X)))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F3 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (= (@ F3 B3) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F3 X3)) (@ F3 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F3 A2)) C))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (F3 (-> tptp.nat tptp.nat)) (B3 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F3 B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F3 X3)) (@ F3 Y3)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F3 C)))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F3 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ F3 B3)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F3 X3)) (@ F3 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F3 A2)) C))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat) (F3 (-> tptp.nat tptp.nat)) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F3 B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F3 X3)) (@ F3 Y3)))) (@ _let_1 (@ F3 C))))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool)) (Q (-> tptp.set_HF_Mirabelle_hf Bool))) (= (@ (@ tptp.ord_le2016357975lle_hf (@ tptp.collec1758573718lle_hf P)) (@ tptp.collec1758573718lle_hf Q)) (forall ((X tptp.set_HF_Mirabelle_hf)) (=> (@ P X) (@ Q X))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool)) (Q (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le2016357975lle_hf (@ tptp.collec1758573718lle_hf P)) (@ tptp.collec1758573718lle_hf Q)))))
% 0.23/0.63 (assert (= tptp.ord_le432112161lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf) (B6 tptp.set_HF_Mirabelle_hf)) (forall ((T tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 0.23/0.63 (assert (= tptp.ord_le432112161lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf) (B6 tptp.set_HF_Mirabelle_hf)) (forall ((X tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf X2))) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (= (@ tptp.finite1213132899lle_hf A4) (@ tptp.finite1213132899lle_hf B4)) (= A4 B4))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (=> (= (@ tptp.finite_card_nat A4) (@ tptp.finite_card_nat B4)) (= A4 B4))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (N tptp.nat)) (=> (not (@ tptp.finite586181922lle_hf A4)) (exists ((B5 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B5) (= (@ tptp.finite1213132899lle_hf B5) N) (@ (@ tptp.ord_le432112161lle_hf B5) A4))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat A4)) (exists ((B5 tptp.set_nat)) (and (@ tptp.finite_finite_nat B5) (= (@ tptp.finite_card_nat B5) N) (@ (@ tptp.ord_less_eq_set_nat B5) A4))))))
% 0.23/0.63 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)))
% 0.23/0.63 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.ord_le432112161lle_hf tptp.bot_bo53200981lle_hf) A2)))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A2)))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.ord_le432112161lle_hf A2) tptp.bot_bo53200981lle_hf) (= A2 tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 0.23/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf A2) tptp.bot_bo53200981lle_hf) (= A2 tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A2) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat A2) X3) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A2) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat X3) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (@ tptp.finite586181922lle_hf B4) (@ tptp.finite586181922lle_hf A4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (=> (@ tptp.finite_finite_nat B4) (@ tptp.finite_finite_nat A4)))))
% 0.23/0.63 (assert (forall ((S tptp.set_HF_Mirabelle_hf) (T2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf S) T2) (=> (not (@ tptp.finite586181922lle_hf S)) (not (@ tptp.finite586181922lle_hf T2))))))
% 0.23/0.63 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T2))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (@ tptp.finite586181922lle_hf A4)))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (@ tptp.finite_finite_nat A4)))))
% 0.23/0.63 (assert (forall ((C3 tptp.set_HF_Mirabelle_hf) (D2 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (=> (@ (@ tptp.ord_le432112161lle_hf C3) D2) (@ (@ tptp.ord_le432112161lle_hf (@ _let_1 C3)) (@ _let_1 D2))))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le432112161lle_hf A4))) (=> (not (@ (@ tptp.member1367349282lle_hf X2) A4)) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf X2) B4)) (@ _let_1 B4))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.insert9649339lle_hf A2) B4))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le432112161lle_hf A4))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert9649339lle_hf B3) B4))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 0.23/0.63 (assert (forall ((X4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf))) (= (@ (@ tptp.ord_le432112161lle_hf X4) _let_1) (or (= X4 tptp.bot_bo53200981lle_hf) (= X4 _let_1))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.insert9649339lle_hf X2) tptp.bot_bo53200981lle_hf))) (=> (@ (@ tptp.ord_le432112161lle_hf A4) _let_1) (or (= A4 tptp.bot_bo53200981lle_hf) (= A4 _let_1))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_nat) (not (@ tptp.finite_finite_nat A4))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (= (@ tptp.finite1213132899lle_hf A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bo53200981lle_hf) (not (@ tptp.finite586181922lle_hf A4))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (@ (@ tptp.inj_on811196232lle_hf F3) tptp.bot_bo2093393035lle_hf)))
% 0.23/0.63 (assert (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F3 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S2) (@ (@ tptp.ord_less_eq_nat (@ F3 Y5)) (@ F3 X3)))) (=> (@ P S2) (@ P (@ (@ tptp.insert_nat X3) S2)))))) (@ P S))))))
% 0.23/0.63 (assert (forall ((S tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool)) (F3 (-> tptp.hF_Mirabelle_hf tptp.nat))) (=> (@ tptp.finite586181922lle_hf S) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (S2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf S2) (=> (forall ((Y5 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf Y5) S2) (@ (@ tptp.ord_less_eq_nat (@ F3 Y5)) (@ F3 X3)))) (=> (@ P S2) (@ P (@ (@ tptp.insert9649339lle_hf X3) S2)))))) (@ P S))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.inj_on811196232lle_hf F3))) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le2016357975lle_hf B4) A4) (@ _let_1 B4))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (B4 tptp.set_se933006839lle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.inj_on811196232lle_hf F3))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_le2016357975lle_hf A4) B4) (@ _let_1 A4))))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (X4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X2) A4) (=> (@ (@ tptp.ord_le432112161lle_hf X4) A4) (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.insert9649339lle_hf X2) X4)) A4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf X3) A4))) (@ (@ tptp.ord_le432112161lle_hf A4) tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2)))
% 0.23/0.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))))
% 0.23/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.23/0.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.23/0.63 (assert (forall ((F tptp.set_HF_Mirabelle_hf) (C3 tptp.nat)) (=> (forall ((G tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf G) F) (=> (@ tptp.finite586181922lle_hf G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf G)) C3)))) (and (@ tptp.finite586181922lle_hf F) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf F)) C3)))))
% 0.23/0.63 (assert (forall ((F tptp.set_nat) (C3 tptp.nat)) (=> (forall ((G tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat G) F) (=> (@ tptp.finite_finite_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat G)) C3)))) (and (@ tptp.finite_finite_nat F) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat F)) C3)))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf B4)) (@ tptp.finite1213132899lle_hf A4)) (= A4 B4))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B4)) (@ tptp.finite_card_nat A4)) (= A4 B4))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite1213132899lle_hf B4))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B4))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite1213132899lle_hf (@ (@ tptp.insert9649339lle_hf X2) A4))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (X2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X2) A4))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_se933006839lle_hf) (G2 (-> tptp.hF_Mirabelle_hf tptp.set_HF_Mirabelle_hf)) (F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf X3) A4) (= (@ G2 (@ F3 X3)) X3))) (@ (@ tptp.inj_on811196232lle_hf F3) A4))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (X2 tptp.set_HF_Mirabelle_hf) (Y2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (not (= X2 Y2)) (=> (@ (@ tptp.member1490636632lle_hf X2) A4) (=> (@ (@ tptp.member1490636632lle_hf Y2) A4) (not (= (@ F3 X2) (@ F3 Y2)))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (X2 tptp.set_HF_Mirabelle_hf) (Y2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (@ (@ tptp.member1490636632lle_hf X2) A4) (=> (@ (@ tptp.member1490636632lle_hf Y2) A4) (= (= (@ F3 X2) (@ F3 Y2)) (= X2 Y2)))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_se933006839lle_hf) (F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (G2 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (forall ((A3 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf A3) A4) (= (@ F3 A3) (@ G2 A3)))) (= (@ (@ tptp.inj_on811196232lle_hf F3) A4) (@ (@ tptp.inj_on811196232lle_hf G2) A4)))))
% 0.23/0.63 (assert (= tptp.inj_on811196232lle_hf (lambda ((F4 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A6 tptp.set_se933006839lle_hf)) (forall ((X tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf X) A6) (forall ((Y4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf Y4) A6) (=> (= (@ F4 X) (@ F4 Y4)) (= X Y4)))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_se933006839lle_hf) (F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf X3) A4) (=> (@ (@ tptp.member1490636632lle_hf Y3) A4) (=> (= (@ F3 X3) (@ F3 Y3)) (= X3 Y3))))) (@ (@ tptp.inj_on811196232lle_hf F3) A4))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (X2 tptp.set_HF_Mirabelle_hf) (Y2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (= (@ F3 X2) (@ F3 Y2)) (=> (@ (@ tptp.member1490636632lle_hf X2) A4) (=> (@ (@ tptp.member1490636632lle_hf Y2) A4) (= X2 Y2)))))))
% 0.23/0.63 (assert (forall ((N tptp.nat) (S tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite1213132899lle_hf S)) (not (forall ((T3 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf T3) S) (=> (= (@ tptp.finite1213132899lle_hf T3) N) (not (@ tptp.finite586181922lle_hf T3)))))))))
% 0.23/0.63 (assert (forall ((N tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_nat S)) (not (forall ((T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat T3) S) (=> (= (@ tptp.finite_card_nat T3) N) (not (@ tptp.finite_finite_nat T3)))))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf B4) (=> (forall ((A3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A3) A4) (exists ((B7 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.member1367349282lle_hf B7) B4) (@ (@ R A3) B7))))) (=> (forall ((A1 tptp.hF_Mirabelle_hf) (A22 tptp.hF_Mirabelle_hf) (B2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A1) A4) (=> (@ (@ tptp.member1367349282lle_hf A22) A4) (=> (@ (@ tptp.member1367349282lle_hf B2) B4) (=> (@ (@ R A1) B2) (=> (@ (@ R A22) B2) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite1213132899lle_hf B4)))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_HF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B4) (=> (forall ((A3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A3) A4) (exists ((B7 tptp.nat)) (and (@ (@ tptp.member_nat B7) B4) (@ (@ R A3) B7))))) (=> (forall ((A1 tptp.hF_Mirabelle_hf) (A22 tptp.hF_Mirabelle_hf) (B2 tptp.nat)) (=> (@ (@ tptp.member1367349282lle_hf A1) A4) (=> (@ (@ tptp.member1367349282lle_hf A22) A4) (=> (@ (@ tptp.member_nat B2) B4) (=> (@ (@ R A1) B2) (=> (@ (@ R A22) B2) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite_card_nat B4)))))))
% 0.23/0.63 (assert (forall ((S tptp.set_nat) (Y2 tptp.nat) (F3 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y2) S) (@ (@ tptp.ord_less_eq_nat (@ F3 (@ (@ tptp.lattic1974000059at_nat F3) S))) (@ F3 Y2)))))))
% 0.23/0.63 (assert (forall ((S tptp.set_HF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.nat))) (=> (@ tptp.finite586181922lle_hf S) (=> (not (= S tptp.bot_bo53200981lle_hf)) (=> (@ (@ tptp.member1367349282lle_hf Y2) S) (@ (@ tptp.ord_less_eq_nat (@ F3 (@ (@ tptp.lattic710307446hf_nat F3) S))) (@ F3 Y2)))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (M tptp.nat)) (=> (@ P X2) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M))) (not (forall ((M2 tptp.nat)) (=> (@ P M2) (not (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M2)))))))))))
% 0.23/0.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B3 tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B3))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X3)))))))))
% 0.23/0.63 (assert (forall ((M3 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_nat N) M3))))
% 0.23/0.63 (assert (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (=> (@ (@ tptp.ord_less_eq_nat N) M3) (= M3 N)))))
% 0.23/0.63 (assert (forall ((M3 tptp.nat) (N tptp.nat)) (=> (= M3 N) (@ (@ tptp.ord_less_eq_nat M3) N))))
% 0.23/0.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.23/0.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.23/0.63 (assert (= tptp.finite_finite_nat (lambda ((N2 tptp.set_nat)) (exists ((M4 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N2) (@ (@ tptp.ord_less_eq_nat X) M4)))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (X2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf (@ (@ tptp.minus_1450406810lle_hf A4) (@ (@ tptp.insert9649339lle_hf X2) tptp.bot_bo53200981lle_hf)))) (@ tptp.finite1213132899lle_hf A4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_se933006839lle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite1450550360lle_hf A4) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite90088345lle_hf A4)) (@ tptp.finite1213132899lle_hf B4)) (exists ((F5 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (and (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_899003828lle_hf F5) A4)) B4) (@ (@ tptp.inj_on811196232lle_hf F5) A4))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite1213132899lle_hf B4)) (exists ((F5 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (and (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_1743964010lle_hf F5) A4)) B4) (@ (@ tptp.inj_on755450110lle_hf F5) A4))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_nat)) (=> (@ tptp.finite586181922lle_hf A4) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite_card_nat B4)) (exists ((F5 (-> tptp.hF_Mirabelle_hf tptp.nat))) (and (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_131453538hf_nat F5) A4)) B4) (@ (@ tptp.inj_on1874279374hf_nat F5) A4))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite1213132899lle_hf B4)) (exists ((F5 (-> tptp.nat tptp.hF_Mirabelle_hf))) (and (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_246164834lle_hf F5) A4)) B4) (@ (@ tptp.inj_on1988990670lle_hf F5) A4))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B4)) (exists ((F5 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F5) A4)) B4) (@ (@ tptp.inj_on_nat_nat F5) A4))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_899003828lle_hf F3) A4)) B4) (=> (@ tptp.finite586181922lle_hf B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite90088345lle_hf A4)) (@ tptp.finite1213132899lle_hf B4)))))))
% 0.23/0.63 (assert (forall ((B3 tptp.hF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (= B3 (@ F3 X2)) (=> (@ (@ tptp.member1367349282lle_hf X2) A4) (@ (@ tptp.member1367349282lle_hf B3) (@ (@ tptp.image_1743964010lle_hf F3) A4))))))
% 0.23/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) B4)))))))
% 0.23/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (= (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) B4)) (and (@ _let_1 A4) (not (@ _let_1 B4)))))))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) A2) tptp.zero_zero_nat)))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) tptp.zero_zero_nat) A2)))
% 0.23/0.63 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.image_1743964010lle_hf F3) tptp.bot_bo53200981lle_hf) tptp.bot_bo53200981lle_hf)))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (= (= tptp.bot_bo53200981lle_hf (@ (@ tptp.image_1743964010lle_hf F3) A4)) (= A4 tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.image_1743964010lle_hf F3) A4) tptp.bot_bo53200981lle_hf) (= A4 tptp.bot_bo53200981lle_hf))))
% 0.23/0.63 (assert (forall ((F tptp.set_HF_Mirabelle_hf) (H (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (@ tptp.finite586181922lle_hf F) (@ tptp.finite586181922lle_hf (@ (@ tptp.image_1743964010lle_hf H) F)))))
% 0.23/0.63 (assert (forall ((F tptp.set_HF_Mirabelle_hf) (H (-> tptp.hF_Mirabelle_hf tptp.nat))) (=> (@ tptp.finite586181922lle_hf F) (@ tptp.finite_finite_nat (@ (@ tptp.image_131453538hf_nat H) F)))))
% 0.23/0.63 (assert (forall ((F tptp.set_nat) (H (-> tptp.nat tptp.hF_Mirabelle_hf))) (=> (@ tptp.finite_finite_nat F) (@ tptp.finite586181922lle_hf (@ (@ tptp.image_246164834lle_hf H) F)))))
% 0.23/0.63 (assert (forall ((F tptp.set_nat) (H (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat F) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat H) F)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.image_1743964010lle_hf F3))) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf A2) B4)) (@ (@ tptp.insert9649339lle_hf (@ F3 A2)) (@ _let_1 B4))))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (let ((_let_1 (@ (@ tptp.image_1743964010lle_hf F3) A4))) (=> (@ (@ tptp.member1367349282lle_hf X2) A4) (= (@ (@ tptp.insert9649339lle_hf (@ F3 X2)) _let_1) _let_1)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.minus_1450406810lle_hf A4) tptp.bot_bo53200981lle_hf) A4)))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.minus_1450406810lle_hf tptp.bot_bo53200981lle_hf) A4) tptp.bot_bo53200981lle_hf)))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.minus_1450406810lle_hf A4) A4) tptp.bot_bo53200981lle_hf)))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (@ tptp.finite586181922lle_hf (@ (@ tptp.minus_1450406810lle_hf A4) B4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A4) B4)))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.minus_1450406810lle_hf A4) B4)) (@ tptp.finite586181922lle_hf A4)))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A4) B4)) (@ tptp.finite_finite_nat A4)))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.minus_1450406810lle_hf A4))) (=> (not (@ (@ tptp.member1367349282lle_hf X2) A4)) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf X2) B4)) (@ _let_1 B4))))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X2) B4) (= (@ (@ tptp.minus_1450406810lle_hf (@ (@ tptp.insert9649339lle_hf X2) A4)) B4) (@ (@ tptp.minus_1450406810lle_hf A4) B4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.minus_1450406810lle_hf A4) B4) tptp.bot_bo53200981lle_hf) (@ (@ tptp.ord_le432112161lle_hf A4) B4))))
% 0.23/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (= (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) (@ _let_1 tptp.bot_bo53200981lle_hf))) (@ _let_1 A4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.minus_1450406810lle_hf A4))) (= (@ tptp.finite586181922lle_hf (@ _let_1 (@ (@ tptp.insert9649339lle_hf A2) B4))) (@ tptp.finite586181922lle_hf (@ _let_1 B4))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A4))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A2) B4))) (@ tptp.finite_finite_nat (@ _let_1 B4))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.insert1636143089lle_hf A2))) (let ((_let_2 (@ tptp.inj_on811196232lle_hf F3))) (= (@ _let_2 (@ _let_1 A4)) (and (@ _let_2 A4) (not (@ (@ tptp.member1367349282lle_hf (@ F3 A2)) (@ (@ tptp.image_899003828lle_hf F3) (@ (@ tptp.minus_500612048lle_hf A4) (@ _let_1 tptp.bot_bo2093393035lle_hf)))))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (let ((_let_2 (@ tptp.inj_on755450110lle_hf F3))) (= (@ _let_2 (@ _let_1 A4)) (and (@ _let_2 A4) (not (@ (@ tptp.member1367349282lle_hf (@ F3 A2)) (@ (@ tptp.image_1743964010lle_hf F3) (@ (@ tptp.minus_1450406810lle_hf A4) (@ _let_1 tptp.bot_bo53200981lle_hf)))))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (C3 tptp.set_se933006839lle_hf) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.image_899003828lle_hf F3))) (let ((_let_2 (@ (@ tptp.minus_500612048lle_hf A4) B4))) (=> (@ (@ tptp.inj_on811196232lle_hf F3) C3) (=> (@ (@ tptp.ord_le2016357975lle_hf _let_2) C3) (=> (@ (@ tptp.ord_le2016357975lle_hf B4) C3) (= (@ _let_1 _let_2) (@ (@ tptp.minus_1450406810lle_hf (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (B4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X3) A4) (@ (@ tptp.member1367349282lle_hf (@ F3 X3)) B4))) (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_1743964010lle_hf F3) A4)) B4))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (@ tptp.finite586181922lle_hf A4) (=> (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (@ tptp.finite586181922lle_hf B4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_nat) (F3 (-> tptp.hF_Mirabelle_hf tptp.nat))) (=> (@ tptp.finite586181922lle_hf A4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_131453538hf_nat F3) A4)) (@ tptp.finite_finite_nat B4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.nat tptp.hF_Mirabelle_hf))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.image_246164834lle_hf F3) A4)) (@ tptp.finite586181922lle_hf B4)))))
% 0.23/0.63 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (F3 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_nat_nat F3) A4)) (@ tptp.finite_finite_nat B4)))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (exists ((C4 tptp.set_HF_Mirabelle_hf)) (and (@ (@ tptp.ord_le432112161lle_hf C4) A4) (@ tptp.finite586181922lle_hf C4) (= B4 (@ (@ tptp.image_1743964010lle_hf F3) C4))))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.image_246164834lle_hf F3) A4)) (exists ((C4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat C4) A4) (@ tptp.finite_finite_nat C4) (= B4 (@ (@ tptp.image_246164834lle_hf F3) C4))))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_nat) (F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_131453538hf_nat F3) A4)) (exists ((C4 tptp.set_HF_Mirabelle_hf)) (and (@ (@ tptp.ord_le432112161lle_hf C4) A4) (@ tptp.finite586181922lle_hf C4) (= B4 (@ (@ tptp.image_131453538hf_nat F3) C4))))))))
% 0.23/0.63 (assert (forall ((B4 tptp.set_nat) (F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_nat_nat F3) A4)) (exists ((C4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat C4) A4) (@ tptp.finite_finite_nat C4) (= B4 (@ (@ tptp.image_nat_nat F3) C4))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (@ P B6))) (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) A4) (@ P (@ (@ tptp.image_1743964010lle_hf F3) B6)))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) (@ (@ tptp.image_246164834lle_hf F3) A4)) (@ P B6))) (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A4) (@ P (@ (@ tptp.image_246164834lle_hf F3) B6)))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_nat Bool))) (= (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_131453538hf_nat F3) A4)) (@ P B6))) (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) A4) (@ P (@ (@ tptp.image_131453538hf_nat F3) B6)))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_nat_nat F3) A4)) (@ P B6))) (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A4) (@ P (@ (@ tptp.image_nat_nat F3) B6)))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) (@ (@ tptp.image_1743964010lle_hf F3) A4))) (@ P B6))) (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) A4)) (@ P (@ (@ tptp.image_1743964010lle_hf F3) B6)))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) (@ (@ tptp.image_246164834lle_hf F3) A4))) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A4)) (@ P (@ (@ tptp.image_246164834lle_hf F3) B6)))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_nat Bool))) (= (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_131453538hf_nat F3) A4))) (@ P B6))) (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) A4)) (@ P (@ (@ tptp.image_131453538hf_nat F3) B6)))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_nat_nat F3) A4))) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A4)) (@ P (@ (@ tptp.image_nat_nat F3) B6)))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite586181922lle_hf (@ (@ tptp.image_899003828lle_hf F3) A4)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (@ tptp.finite1450550360lle_hf A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf (@ (@ tptp.image_1743964010lle_hf F3) A4)) (=> (@ (@ tptp.inj_on755450110lle_hf F3) A4) (@ tptp.finite586181922lle_hf A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat)) (=> (@ tptp.finite586181922lle_hf (@ (@ tptp.image_246164834lle_hf F3) A4)) (=> (@ (@ tptp.inj_on1988990670lle_hf F3) A4) (@ tptp.finite_finite_nat A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_131453538hf_nat F3) A4)) (=> (@ (@ tptp.inj_on1874279374hf_nat F3) A4) (@ tptp.finite586181922lle_hf A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat F3) A4)) (=> (@ (@ tptp.inj_on_nat_nat F3) A4) (@ tptp.finite_finite_nat A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.image_899003828lle_hf F3) A4)) (@ tptp.finite1450550360lle_hf A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on755450110lle_hf F3) A4) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.image_1743964010lle_hf F3) A4)) (@ tptp.finite586181922lle_hf A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat)) (=> (@ (@ tptp.inj_on1988990670lle_hf F3) A4) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.image_246164834lle_hf F3) A4)) (@ tptp.finite_finite_nat A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on1874279374hf_nat F3) A4) (= (@ tptp.finite_finite_nat (@ (@ tptp.image_131453538hf_nat F3) A4)) (@ tptp.finite586181922lle_hf A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (@ (@ tptp.inj_on_nat_nat F3) A4) (= (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat F3) A4)) (@ tptp.finite_finite_nat A4)))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (C3 tptp.set_se933006839lle_hf) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.image_899003828lle_hf F3))) (=> (@ (@ tptp.inj_on811196232lle_hf F3) C3) (=> (@ (@ tptp.ord_le2016357975lle_hf A4) C3) (=> (@ (@ tptp.ord_le2016357975lle_hf B4) C3) (= (= (@ _let_1 A4) (@ _let_1 B4)) (= A4 B4))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (B4 tptp.set_se933006839lle_hf) (A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.member1490636632lle_hf A2))) (=> (@ (@ tptp.inj_on811196232lle_hf F3) B4) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_le2016357975lle_hf A4) B4) (= (@ (@ tptp.member1367349282lle_hf (@ F3 A2)) (@ (@ tptp.image_899003828lle_hf F3) A4)) (@ _let_1 A4))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (B4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ (@ tptp.inj_on755450110lle_hf F3) B4) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (= (@ (@ tptp.member1367349282lle_hf (@ F3 A2)) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (@ _let_1 A4))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (X2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (not (@ (@ tptp.member1367349282lle_hf X2) B4)) (=> (= (@ (@ tptp.insert9649339lle_hf X2) B4) (@ (@ tptp.image_899003828lle_hf F3) A4)) (not (forall ((X6 tptp.set_HF_Mirabelle_hf) (A7 tptp.set_se933006839lle_hf)) (=> (not (@ (@ tptp.member1490636632lle_hf X6) A7)) (=> (= A4 (@ (@ tptp.insert1636143089lle_hf X6) A7)) (=> (= X2 (@ F3 X6)) (not (= B4 (@ (@ tptp.image_899003828lle_hf F3) A7)))))))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on755450110lle_hf F3) A4) (=> (not (@ (@ tptp.member1367349282lle_hf X2) B4)) (=> (= (@ (@ tptp.insert9649339lle_hf X2) B4) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (not (forall ((X6 tptp.hF_Mirabelle_hf) (A7 tptp.set_HF_Mirabelle_hf)) (=> (not (@ (@ tptp.member1367349282lle_hf X6) A7)) (=> (= A4 (@ (@ tptp.insert9649339lle_hf X6) A7)) (=> (= X2 (@ F3 X6)) (not (= B4 (@ (@ tptp.image_1743964010lle_hf F3) A7)))))))))))))
% 0.23/0.63 (assert (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (= (@ tptp.finite1213132899lle_hf (@ (@ tptp.image_899003828lle_hf F3) A4)) (@ tptp.finite90088345lle_hf A4)))))
% 0.23/0.63 (assert (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X2))) (=> (not (@ (@ tptp.member1367349282lle_hf X2) A4)) (= (@ (@ tptp.minus_1450406810lle_hf (@ _let_1 A4)) (@ _let_1 tptp.bot_bo53200981lle_hf)) A4)))))
% 0.95/1.20 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (let ((_let_2 (@ tptp.minus_1450406810lle_hf A4))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_1450406810lle_hf (@ _let_2 (@ _let_1 tptp.bot_bo53200981lle_hf))) B4))))))
% 0.95/1.20 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (=> (@ (@ tptp.member1367349282lle_hf A2) A4) (= (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) (@ _let_1 tptp.bot_bo53200981lle_hf))) A4)))))
% 0.95/1.20 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (let ((_let_2 (@ tptp.minus_1450406810lle_hf A4))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_1450406810lle_hf (@ _let_2 B4)) (@ _let_1 tptp.bot_bo53200981lle_hf)))))))
% 0.95/1.20 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf) (C3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.minus_1450406810lle_hf B4))) (let ((_let_2 (@ tptp.ord_le432112161lle_hf A4))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert9649339lle_hf X2) C3))) (and (@ _let_2 (@ _let_1 C3)) (not (@ (@ tptp.member1367349282lle_hf X2) A4))))))))
% 0.95/1.20 (assert (forall ((B4 tptp.set_se933006839lle_hf) (X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X2))) (=> (forall ((C4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf C4) B4) (not (@ (@ tptp.member1367349282lle_hf X2) C4)))) (= (@ (@ tptp.member1490636632lle_hf A4) (@ (@ tptp.image_1514960916lle_hf _let_1) B4)) (and (@ (@ tptp.member1367349282lle_hf X2) A4) (@ (@ tptp.member1490636632lle_hf (@ (@ tptp.minus_1450406810lle_hf A4) (@ _let_1 tptp.bot_bo53200981lle_hf))) B4)))))))
% 0.95/1.20 (assert (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) B4)) (not (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.95/1.20 (assert (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) B4)) (@ _let_1 A4)))))
% 0.95/1.20 (assert (not (= (= tptp.z tptp.zero_z189798548lle_hf) (forall ((X tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem X) tptp.z))))))
% 0.95/1.20 (set-info :filename cvc5---1.0.5_28312)
% 0.95/1.20 (check-sat-assuming ( true ))
% 0.95/1.20 ------- get file name : TPTP file name is ITP072^1
% 0.95/1.20 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_28312.smt2...
% 0.95/1.20 --- Run --ho-elim --full-saturate-quant at 10...
% 0.95/1.20 % SZS status Theorem for ITP072^1
% 0.95/1.20 % SZS output start Proof for ITP072^1
% 0.95/1.20 (
% 0.95/1.20 (let ((_let_1 (forall ((X tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem X) tptp.z))))) (let ((_let_2 (not (= (= tptp.z tptp.zero_z189798548lle_hf) _let_1)))) (let ((_let_3 (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X2))) (=> (not (@ (@ tptp.member1367349282lle_hf X2) A4)) (= (@ (@ tptp.minus_1450406810lle_hf (@ _let_1 A4)) (@ _let_1 tptp.bot_bo53200981lle_hf)) A4)))))) (let ((_let_4 (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.minus_1450406810lle_hf A4) B4) tptp.bot_bo53200981lle_hf) (@ (@ tptp.ord_le432112161lle_hf A4) B4))))) (let ((_let_5 (forall ((X2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X2) B4) (= (@ (@ tptp.minus_1450406810lle_hf (@ (@ tptp.insert9649339lle_hf X2) A4)) B4) (@ (@ tptp.minus_1450406810lle_hf A4) B4)))))) (let ((_let_6 (= tptp.finite_finite_nat (lambda ((N2 tptp.set_nat)) (exists ((M4 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N2) (@ (@ tptp.ord_less_eq_nat X) M4)))))))) (let ((_let_7 (= tptp.inj_on811196232lle_hf (lambda ((F4 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A6 tptp.set_se933006839lle_hf)) (forall ((X tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf X) A6) (forall ((Y4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf Y4) A6) (=> (= (@ F4 X) (@ F4 Y4)) (= X Y4)))))))))) (let ((_let_8 (= tptp.ord_le432112161lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf) (B6 tptp.set_HF_Mirabelle_hf)) (forall ((T tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_9 (@ tptp.finite1213132899lle_hf tptp.bot_bo53200981lle_hf))) (let ((_let_10 (= _let_9 tptp.zero_zero_nat))) (let ((_let_11 (= tptp.is_emp566801209lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf)) (= A6 tptp.bot_bo53200981lle_hf))))) (let ((_let_12 (= tptp.is_sin1448700567lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf)) (= A6 (@ (@ tptp.insert9649339lle_hf (@ tptp.the_el1104322134lle_hf A6)) tptp.bot_bo53200981lle_hf)))))) (let ((_let_13 (@ tptp.finite586181922lle_hf tptp.bot_bo53200981lle_hf))) (let ((_let_14 (= tptp.bot_bot_nat tptp.zero_zero_nat))) (let ((_let_15 (= tptp.bot_bo53200981lle_hf (@ tptp.collec2046588256lle_hf tptp.bot_bo1263054448e_hf_o)))) (let ((_let_16 (= tptp.bot_bo2093393035lle_hf (@ tptp.collec1758573718lle_hf tptp.bot_bo554042810e_hf_o)))) (let ((_let_17 (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))) (let ((_let_18 (forall ((A2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A2) (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf))))) (let ((_let_19 (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (= (@ tptp.hF_Mirabelle_hfset (@ tptp.hF_Mirabelle_HF A4)) A4))))) (let ((_let_20 (= tptp.hF_Mirabelle_hinsert (lambda ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ tptp.hF_Mirabelle_HF (@ (@ tptp.insert9649339lle_hf A) (@ tptp.hF_Mirabelle_hfset B))))))) (let ((_let_21 (= tptp.bot_bo554042810e_hf_o (lambda ((X tptp.set_HF_Mirabelle_hf)) tptp.bot_bot_o)))) (let ((_let_22 (lambda ((X tptp.hF_Mirabelle_hf)) tptp.bot_bot_o))) (let ((_let_23 (= tptp.bot_bo1263054448e_hf_o _let_22))) (let ((_let_24 (forall ((C tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf C) tptp.bot_bo53200981lle_hf))))) (let ((_let_25 (forall ((A2 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HF (@ tptp.hF_Mirabelle_hfset A2)) A2)))) (let ((_let_26 (= tptp.zero_z189798548lle_hf (@ tptp.hF_Mirabelle_HF tptp.bot_bo53200981lle_hf)))) (let ((_let_27 (= (@ tptp.hF_Mirabelle_Abs_hf tptp.zero_zero_nat) tptp.zero_z189798548lle_hf))) (let ((_let_28 (= tptp.hF_Mirabelle_hmem (lambda ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A) (@ tptp.hF_Mirabelle_hfset B)))))) (let ((_let_29 (forall ((X tptp.hF_Mirabelle_hf)) (not (ho_28 (ho_30 k_29 X) (ho_89 k_88 tptp.z)))))) (let ((_let_30 (ho_89 k_88 tptp.z))) (let ((_let_31 (ho_30 k_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169))) (let ((_let_32 (ho_28 _let_31 _let_30))) (let ((_let_33 (ho_44 k_43 k_41))) (let ((_let_34 (ho_93 k_92 (ho_91 k_90 _let_33)))) (let ((_let_35 (= tptp.z _let_34))) (let ((_let_36 (ho_30 k_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_145))) (let ((_let_37 (ho_28 _let_36 _let_30))) (let ((_let_38 (ho_46 k_94 _let_33))) (let ((_let_39 (= _let_34 _let_38))) (let ((_let_40 (= _let_33 (ho_89 k_88 _let_38)))) (let ((_let_41 (ho_28 _let_36 _let_33))) (let ((_let_42 (not _let_35))) (let ((_let_43 (@ tptp.collec2046588256lle_hf ll_4))) (let ((_let_44 (@ tptp.hF_Mirabelle_Abs_hf (@ tptp.finite1213132899lle_hf _let_43)))) (let ((_let_45 (forall ((X tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf X) (@ tptp.hF_Mirabelle_hfset tptp.z)))))) (let ((_let_46 (not (= _let_45 (= tptp.z _let_44))))) (let ((_let_47 (@ tptp.collec2046588256lle_hf _let_22))) (let ((_let_48 (@ tptp.hF_Mirabelle_Abs_hf (@ tptp.finite1213132899lle_hf _let_47)))) (let ((_let_49 (ASSUME :args (_let_28)))) (let ((_let_50 (SYMM (ASSUME :args (_let_27))))) (let ((_let_51 (ASSUME :args (_let_23)))) (let ((_let_52 (ASSUME :args (_let_21)))) (let ((_let_53 (ASSUME :args (_let_20)))) (let ((_let_54 (ASSUME :args (_let_17)))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (SYMM (ASSUME :args (_let_14))))) (let ((_let_58 (AND_INTRO _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO _let_58 :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_59 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49) :args ((= tptp.is_emp566801209lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf)) (= tptp.bot_bo53200981lle_hf A6))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (SYMM (ASSUME :args (_let_10))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_60 _let_59 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49) :args ((= tptp.zero_zero_nat _let_9) SB_DEFAULT SBA_FIXPOINT))) _let_60 _let_59 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_61 :args ((not (= _let_1 (= tptp.zero_z189798548lle_hf tptp.z))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (= (= tptp.z _let_48) _let_45)) _let_46))) (PREPROCESS :args ((= _let_46 (not (= _let_35 _let_29))))))))) (let ((_let_63 (or))) (let ((_let_64 (not _let_29))) (let ((_let_65 (not _let_37))) (let ((_let_66 (_let_64))) (let ((_let_67 (= _let_44 (@ tptp.hF_Mirabelle_HF _let_43)))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_26)) (TRANS (MACRO_SR_EQ_INTRO _let_61 :args (_let_26 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_48 (@ tptp.hF_Mirabelle_HF _let_47)) _let_67))) (PREPROCESS :args ((= _let_67 _let_39))))))) (let ((_let_69 (ho_28 k_53 _let_33))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_70 _let_40))) (let ((_let_72 (forall ((A4 tptp.set_HF_Mirabelle_hf)) (or (not (ho_28 k_53 A4)) (= A4 (ho_89 k_88 (ho_46 k_94 A4))))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_19)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A4 tptp.set_HF_Mirabelle_hf)) (or (not (@ tptp.finite586181922lle_hf A4)) (= A4 (@ tptp.hF_Mirabelle_hfset (@ tptp.hF_Mirabelle_HF A4))))) _let_72))))))) (let ((_let_74 (@ tptp.finite586181922lle_hf _let_43))) (let ((_let_75 (forall ((C tptp.hF_Mirabelle_hf)) (not (ho_28 (ho_30 k_29 C) (ho_44 k_43 k_41)))))) (let ((_let_76 (not _let_41))) (let ((_let_77 (forall ((C tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf C) (@ tptp.collec2046588256lle_hf ll_4)))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_24)) (TRANS (MACRO_SR_EQ_INTRO _let_61 :args (_let_24 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((C tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf C) (@ tptp.collec2046588256lle_hf (lambda ((X tptp.hF_Mirabelle_hf)) tptp.bot_bot_o))))) _let_77))) (PREPROCESS :args ((= _let_77 _let_75))))))) (let ((_let_79 (not _let_40))) (let ((_let_80 (not _let_39))) (let ((_let_81 (and _let_39 _let_35 _let_40 _let_76))) (let ((_let_82 (ASSUME :args (_let_76)))) (let ((_let_83 (ASSUME :args (_let_40)))) (let ((_let_84 (SYMM _let_68))) (let ((_let_85 (ASSUME :args (_let_35)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_81)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_82 _let_83 _let_68 _let_85) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (_let_36)) (TRANS (CONG (REFL :args (k_88)) (TRANS (SYMM (SYMM _let_85)) (SYMM _let_84)) :args (APPLY_UF ho_89)) (SYMM _let_83)) :args (APPLY_UF ho_28)) (FALSE_INTRO _let_82))) :args (_let_76 _let_40 _let_39 _let_35))) :args (_let_39 _let_35 _let_40 _let_76))) :args (true _let_81)) (CONG (REFL :args (_let_80)) (REFL :args (_let_42)) (REFL :args (_let_79)) (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_41))) (REFL :args (_let_65)) :args _let_63)) :args ((or _let_80 _let_42 _let_65 _let_79 _let_41))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_145 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_75))) _let_78 :args (_let_76 false _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_70 _let_40 (not _let_71)))) (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO _let_58 :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ tptp.finite586181922lle_hf _let_47) _let_74))) (PREPROCESS :args ((= _let_74 _let_69))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_33 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_72))) _let_73 :args (_let_71 false _let_72)) :args (_let_40 false _let_69 false _let_71)) _let_68 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66) (REWRITE :args ((=> _let_64 (not _let_65)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_29))) (REFL :args (_let_37)) :args _let_63)) (NOT_EQUIV_ELIM2 _let_62) :args (_let_42 true _let_41 false _let_40 false _let_39 false _let_37 true _let_29)))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (NOT_EQUIV_ELIM1 _let_62) _let_86 :args (_let_29 true _let_35)))) (let ((_let_88 (ho_48 k_47 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_145))) (let ((_let_89 (ho_49 _let_88 _let_33))) (let ((_let_90 (not _let_32))) (let ((_let_91 (or _let_90 (ho_28 _let_31 _let_89)))) (let ((_let_92 (forall ((T tptp.hF_Mirabelle_hf)) (let ((_let_1 (ho_30 k_29 T))) (or (not (ho_28 _let_1 (ho_89 k_88 tptp.z))) (ho_28 _let_1 (ho_49 (ho_48 k_47 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_145) (ho_44 k_43 k_41)))))))) (let ((_let_93 (not _let_91))) (let ((_let_94 (ho_49 (ho_114 k_113 _let_30) _let_89))) (let ((_let_95 (= _let_33 _let_94))) (let ((_let_96 (= _let_92 _let_95))) (let ((_let_97 (not _let_92))) (let ((_let_98 (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (= (forall ((T 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(lambda ((X tptp.hF_Mirabelle_hf)) tptp.bot_bot_o))) (forall ((T tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf T))) (or (not (@ _let_1 A4)) (@ _let_1 B4)))))) _let_99))) (PREPROCESS :args ((= _let_99 _let_98))))))) (let ((_let_101 (ho_49 (ho_114 k_113 (ho_49 _let_88 _let_30)) _let_89))) (let ((_let_102 (= _let_101 _let_94))) (let ((_let_103 (= _let_30 _let_101))) (let ((_let_104 (= _let_33 _let_30))) (let ((_let_105 (not _let_95))) (let ((_let_106 (ho_28 _let_36 _let_89))) (let ((_let_107 (not _let_106))) (let ((_let_108 (or _let_107 _let_102))) (let ((_let_109 (forall ((X2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (or (not (ho_28 (ho_30 k_29 X2) B4)) (= (ho_49 (ho_114 k_113 A4) B4) (ho_49 (ho_114 k_113 (ho_49 (ho_48 k_47 X2) A4)) B4)))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X2 tptp.hF_Mirabelle_hf) (B4 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((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))) _let_27 _let_26 (forall ((N tptp.nat)) (= (@ (@ tptp.semiri2013084963it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N tptp.nat) (A2 tptp.nat)) (= (= (@ (@ tptp.semiri2013084963it_nat N) A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.semiri2115134414it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (@ (@ tptp.member_nat tptp.zero_zero_nat) tptp.semiring_1_Nats_nat) _let_25 (forall ((C tptp.set_HF_Mirabelle_hf)) (not (@ (@ tptp.member1490636632lle_hf C) tptp.bot_bo2093393035lle_hf))) (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))) _let_24 (forall ((A4 tptp.set_se933006839lle_hf)) (= (forall ((X tptp.set_HF_Mirabelle_hf)) (not (@ (@ tptp.member1490636632lle_hf X) A4))) (= A4 tptp.bot_bo2093393035lle_hf))) (forall ((A4 tptp.set_nat)) (= (forall ((X tptp.nat)) (not (@ (@ tptp.member_nat X) A4))) (= A4 tptp.bot_bot_set_nat))) (forall 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tptp.member_nat A2) A4) (exists ((B5 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat A2) B5)) (not (@ (@ tptp.member_nat A2) B5)))))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.member1490636632lle_hf A2) A4) (exists ((B5 tptp.set_se933006839lle_hf)) (and (= A4 (@ (@ tptp.insert1636143089lle_hf A2) B5)) (not (@ (@ tptp.member1490636632lle_hf A2) B5)))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A2) A4) (exists ((B5 tptp.set_HF_Mirabelle_hf)) (and (= A4 (@ (@ tptp.insert9649339lle_hf A2) B5)) (not (@ (@ tptp.member1367349282lle_hf A2) B5)))))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.insert_nat Y2))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))) (forall ((X2 tptp.set_HF_Mirabelle_hf) (Y2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.insert1636143089lle_hf X2))) (let ((_let_2 (@ tptp.insert1636143089lle_hf Y2))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))) (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X2))) (let ((_let_2 (@ tptp.insert9649339lle_hf Y2))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))) (forall ((A2 tptp.nat) (A4 tptp.set_nat) (B3 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member_nat A2) A4)) (=> (not (@ (@ tptp.member_nat B3) B4)) (= (= (@ (@ tptp.insert_nat A2) A4) (@ (@ tptp.insert_nat B3) B4)) (and (=> _let_1 (= A4 B4)) (=> (not _let_1) (exists ((C2 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat B3) C2)) (not (@ (@ tptp.member_nat B3) C2)) (= B4 (@ (@ tptp.insert_nat A2) C2)) (not (@ (@ tptp.member_nat A2) C2))))))))))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf) (B3 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member1490636632lle_hf A2) A4)) (=> (not (@ (@ tptp.member1490636632lle_hf B3) B4)) (= (= (@ (@ tptp.insert1636143089lle_hf A2) A4) (@ (@ tptp.insert1636143089lle_hf B3) B4)) (and (=> _let_1 (= A4 B4)) (=> (not _let_1) (exists ((C2 tptp.set_se933006839lle_hf)) (and (= A4 (@ (@ tptp.insert1636143089lle_hf B3) C2)) (not (@ (@ tptp.member1490636632lle_hf B3) C2)) (= B4 (@ (@ tptp.insert1636143089lle_hf A2) C2)) (not (@ (@ tptp.member1490636632lle_hf A2) C2))))))))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member1367349282lle_hf A2) A4)) (=> (not (@ (@ tptp.member1367349282lle_hf B3) B4)) (= (= (@ (@ tptp.insert9649339lle_hf A2) A4) (@ (@ tptp.insert9649339lle_hf B3) B4)) (and (=> _let_1 (= A4 B4)) (=> (not _let_1) (exists ((C2 tptp.set_HF_Mirabelle_hf)) (and (= A4 (@ (@ tptp.insert9649339lle_hf B3) C2)) (not (@ (@ tptp.member1367349282lle_hf B3) C2)) (= B4 (@ (@ tptp.insert9649339lle_hf A2) C2)) (not (@ (@ tptp.member1367349282lle_hf A2) C2))))))))))) (forall ((A2 tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A4) (= (@ (@ tptp.insert_nat A2) A4) A4))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.member1490636632lle_hf A2) A4) (= (@ (@ tptp.insert1636143089lle_hf A2) A4) A4))) (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A2) A4) (= (@ (@ tptp.insert9649339lle_hf A2) A4) A4))) (forall ((X2 tptp.nat) (A4 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.member_nat X2))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A4) (@ _let_1 B4)) (= A4 B4))))))) (forall ((X2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.insert1636143089lle_hf X2))) (let ((_let_2 (@ tptp.member1490636632lle_hf X2))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A4) (@ _let_1 B4)) (= A4 B4))))))) (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X2))) (let ((_let_2 (@ tptp.member1367349282lle_hf X2))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A4) (@ _let_1 B4)) (= A4 B4))))))) (forall ((X2 tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) A4) (not (forall ((B5 tptp.set_nat)) (=> (= A4 (@ (@ tptp.insert_nat X2) B5)) (@ (@ tptp.member_nat X2) B5)))))) (forall ((X2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.member1490636632lle_hf X2) A4) (not (forall ((B5 tptp.set_se933006839lle_hf)) (=> (= A4 (@ (@ tptp.insert1636143089lle_hf X2) B5)) (@ (@ tptp.member1490636632lle_hf X2) B5)))))) (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X2) A4) (not (forall ((B5 tptp.set_HF_Mirabelle_hf)) (=> (= A4 (@ (@ tptp.insert9649339lle_hf X2) B5)) (@ (@ tptp.member1367349282lle_hf X2) B5)))))) (forall ((A2 tptp.nat) (B4 tptp.set_nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_nat B3) B4))))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_se933006839lle_hf) (B3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1490636632lle_hf A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert1636143089lle_hf B3) B4))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert9649339lle_hf B3) B4))))) (forall ((A2 tptp.nat) (B4 tptp.set_nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat A2) B4))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_se933006839lle_hf)) (@ (@ tptp.member1490636632lle_hf A2) (@ (@ tptp.insert1636143089lle_hf A2) B4))) (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A2) (@ (@ tptp.insert9649339lle_hf A2) B4))) (forall ((A2 tptp.nat) (B3 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert_nat B3) A4)) (=> (not (= A2 B3)) (@ _let_1 A4))))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.member1490636632lle_hf A2))) (=> (@ _let_1 (@ (@ tptp.insert1636143089lle_hf B3) A4)) (=> (not (= A2 B3)) (@ _let_1 A4))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ _let_1 (@ (@ tptp.insert9649339lle_hf B3) A4)) (=> (not (= A2 B3)) (@ _let_1 A4))))) (forall ((F tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf F) (=> (not (= F tptp.bot_bo2093393035lle_hf)) (not (forall ((A5 tptp.set_se933006839lle_hf) (X3 tptp.set_HF_Mirabelle_hf)) (=> (= F (@ (@ tptp.insert1636143089lle_hf X3) A5)) (=> (not (@ (@ tptp.member1490636632lle_hf X3) A5)) (not (@ tptp.finite1450550360lle_hf A5))))))))) (forall ((F tptp.set_nat)) (=> (@ tptp.finite_finite_nat F) (=> (not (= F tptp.bot_bot_set_nat)) (not (forall ((A5 tptp.set_nat) (X3 tptp.nat)) (=> (= F (@ (@ tptp.insert_nat X3) A5)) (=> (not (@ (@ tptp.member_nat X3) A5)) (not (@ tptp.finite_finite_nat A5))))))))) (forall ((F tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf F) (=> (not (= F tptp.bot_bo53200981lle_hf)) (not (forall ((A5 tptp.set_HF_Mirabelle_hf) (X3 tptp.hF_Mirabelle_hf)) (=> (= F (@ (@ tptp.insert9649339lle_hf X3) A5)) (=> (not (@ (@ tptp.member1367349282lle_hf X3) A5)) (not (@ tptp.finite586181922lle_hf A5))))))))) _let_17 _let_16 _let_15 (forall ((A2 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf)) (=> (= (@ (@ tptp.insert1636143089lle_hf A2) tptp.bot_bo2093393035lle_hf) (@ (@ tptp.insert1636143089lle_hf B3) tptp.bot_bo2093393035lle_hf)) (= A2 B3))) (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (= (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat B3) tptp.bot_bot_set_nat)) (= A2 B3))) (forall ((A2 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (=> (= (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf) (@ (@ tptp.insert9649339lle_hf B3) tptp.bot_bo53200981lle_hf)) (= A2 B3))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (not (= (@ (@ tptp.insert1636143089lle_hf A2) A4) tptp.bot_bo2093393035lle_hf))) (forall ((A2 tptp.nat) (A4 tptp.set_nat)) (not (= (@ (@ tptp.insert_nat A2) A4) tptp.bot_bot_set_nat))) (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (not (= (@ (@ tptp.insert9649339lle_hf A2) A4) tptp.bot_bo53200981lle_hf))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf) (D tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.insert1636143089lle_hf A2) (@ (@ tptp.insert1636143089lle_hf B3) tptp.bot_bo2093393035lle_hf)) (@ (@ tptp.insert1636143089lle_hf C) (@ (@ tptp.insert1636143089lle_hf D) tptp.bot_bo2093393035lle_hf))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))) (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (= (@ (@ tptp.insert_nat A2) (@ (@ tptp.insert_nat B3) tptp.bot_bot_set_nat)) (@ (@ tptp.insert_nat C) (@ (@ tptp.insert_nat D) tptp.bot_bot_set_nat))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.insert9649339lle_hf A2) (@ (@ tptp.insert9649339lle_hf B3) tptp.bot_bo53200981lle_hf)) (@ (@ tptp.insert9649339lle_hf C) (@ (@ tptp.insert9649339lle_hf D) tptp.bot_bo53200981lle_hf))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))) (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))) (forall ((A2 tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.member1367349282lle_hf A2) (@ tptp.collec2046588256lle_hf P)) (@ P A2))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (@ (@ tptp.member1490636632lle_hf A2) (@ tptp.collec1758573718lle_hf P)) (@ P A2))) (forall ((A4 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A4))) A4)) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ tptp.collec2046588256lle_hf (lambda ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) A4))) A4)) (forall ((A4 tptp.set_se933006839lle_hf)) (= (@ tptp.collec1758573718lle_hf (lambda ((X tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.member1490636632lle_hf X) A4))) A4)) (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (Q (-> tptp.hF_Mirabelle_hf Bool))) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec2046588256lle_hf P) (@ tptp.collec2046588256lle_hf Q)))) (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool)) (Q (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec1758573718lle_hf P) (@ tptp.collec1758573718lle_hf Q)))) (forall ((B3 tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.member1490636632lle_hf B3) (@ (@ tptp.insert1636143089lle_hf A2) tptp.bot_bo2093393035lle_hf)) (= B3 A2))) (forall ((B3 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.member_nat B3) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= B3 A2))) (forall ((B3 tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.member1367349282lle_hf B3) (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf)) (= B3 A2))) (forall ((B3 tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf B3) (@ (@ tptp.insert1636143089lle_hf A2) tptp.bot_bo2093393035lle_hf)) (= B3 A2))) (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= B3 A2))) (forall ((B3 tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf B3) (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf)) (= B3 A2))) _let_14 (forall ((A2 tptp.hF_Mirabelle_hf)) (@ tptp.finite586181922lle_hf (@ tptp.hF_Mirabelle_hfset A2))) (= tptp.bot_bo1263054448e_hf_o (lambda ((X tptp.hF_Mirabelle_hf)) tptp.bot_bot_o)) (= tptp.bot_bo554042810e_hf_o (lambda ((X tptp.set_HF_Mirabelle_hf)) tptp.bot_bot_o)) (forall ((A4 tptp.set_se933006839lle_hf)) (= (exists ((X tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.member1490636632lle_hf X) A4)) (not (= A4 tptp.bot_bo2093393035lle_hf)))) (forall ((A4 tptp.set_nat)) (= (exists ((X tptp.nat)) (@ (@ tptp.member_nat X) A4)) (not (= A4 tptp.bot_bot_set_nat)))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (exists ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) A4)) (not (= A4 tptp.bot_bo53200981lle_hf)))) (forall ((A4 tptp.set_se933006839lle_hf)) (=> (forall ((Y3 tptp.set_HF_Mirabelle_hf)) (not (@ (@ tptp.member1490636632lle_hf Y3) A4))) (= A4 tptp.bot_bo2093393035lle_hf))) (forall ((A4 tptp.set_nat)) (=> (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member_nat Y3) A4))) (= A4 tptp.bot_bot_set_nat))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((Y3 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf Y3) A4))) (= A4 tptp.bot_bo53200981lle_hf))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (= (@ tptp.finite1450550360lle_hf (@ (@ tptp.insert1636143089lle_hf A2) A4)) (@ tptp.finite1450550360lle_hf A4))) (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.insert9649339lle_hf A2) A4)) (@ tptp.finite586181922lle_hf A4))) (forall ((A2 tptp.nat) (A4 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A2) A4)) (@ tptp.finite_finite_nat A4))) (forall ((A2 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf A2) (=> (not (= A2 tptp.bot_bo2093393035lle_hf)) (not (forall ((A5 tptp.set_se933006839lle_hf)) (=> (exists ((A3 tptp.set_HF_Mirabelle_hf)) (= A2 (@ (@ tptp.insert1636143089lle_hf A3) A5))) (not (@ tptp.finite1450550360lle_hf A5)))))))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (not (forall ((A5 tptp.set_nat)) (=> (exists ((A3 tptp.nat)) (= A2 (@ (@ tptp.insert_nat A3) A5))) (not (@ tptp.finite_finite_nat A5)))))))) (forall ((A2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A2) (=> (not (= A2 tptp.bot_bo53200981lle_hf)) (not (forall ((A5 tptp.set_HF_Mirabelle_hf)) (=> (exists ((A3 tptp.hF_Mirabelle_hf)) (= A2 (@ (@ tptp.insert9649339lle_hf A3) A5))) (not (@ tptp.finite586181922lle_hf A5)))))))) (= tptp.finite1450550360lle_hf (lambda ((A tptp.set_se933006839lle_hf)) (or (= A tptp.bot_bo2093393035lle_hf) (exists ((A6 tptp.set_se933006839lle_hf) (B tptp.set_HF_Mirabelle_hf)) (and (= A (@ (@ tptp.insert1636143089lle_hf B) A6)) (@ tptp.finite1450550360lle_hf A6)))))) (= tptp.finite_finite_nat (lambda ((A tptp.set_nat)) (or (= A tptp.bot_bot_set_nat) (exists ((A6 tptp.set_nat) (B tptp.nat)) (and (= A (@ (@ tptp.insert_nat B) A6)) (@ tptp.finite_finite_nat A6)))))) (= tptp.finite586181922lle_hf (lambda ((A tptp.set_HF_Mirabelle_hf)) (or (= A tptp.bot_bo53200981lle_hf) (exists ((A6 tptp.set_HF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (and (= A (@ (@ tptp.insert9649339lle_hf B) A6)) (@ tptp.finite586181922lle_hf A6)))))) (forall ((F tptp.set_se933006839lle_hf) (P (-> tptp.set_se933006839lle_hf Bool))) (=> (@ tptp.finite1450550360lle_hf F) (=> (@ P tptp.bot_bo2093393035lle_hf) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf) (F2 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf F2) (=> (not (@ (@ tptp.member1490636632lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert1636143089lle_hf X3) F2)))))) (@ P F))))) (forall ((F tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (F2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F2) (=> (not (@ (@ tptp.member_nat X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat X3) F2)))))) (@ P F))))) (forall ((F tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf F) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf F2) (=> (not (@ (@ tptp.member1367349282lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf X3) F2)))))) (@ P F))))) (forall ((X2 tptp.set_se933006839lle_hf) (P (-> tptp.set_se933006839lle_hf Bool))) (=> (@ tptp.finite1450550360lle_hf X2) (=> (@ P tptp.bot_bo2093393035lle_hf) (=> (forall ((A5 tptp.set_se933006839lle_hf) (A3 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite1450550360lle_hf A5) (=> (@ P A5) (@ P (@ (@ tptp.insert1636143089lle_hf A3) A5))))) (@ P X2))))) (forall ((X2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat X2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A5 tptp.set_nat) (A3 tptp.nat)) (=> (@ tptp.finite_finite_nat A5) (=> (@ P A5) (@ P (@ (@ tptp.insert_nat A3) A5))))) (@ P X2))))) (forall ((X2 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf X2) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((A5 tptp.set_HF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A5) (=> (@ P A5) (@ P (@ (@ tptp.insert9649339lle_hf A3) A5))))) (@ P X2))))) (forall ((F tptp.set_se933006839lle_hf) (P (-> tptp.set_se933006839lle_hf Bool))) (=> (@ tptp.finite1450550360lle_hf F) (=> (not (= F tptp.bot_bo2093393035lle_hf)) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf)) (@ P (@ (@ tptp.insert1636143089lle_hf X3) tptp.bot_bo2093393035lle_hf))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf) (F2 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf F2) (=> (not (= F2 tptp.bot_bo2093393035lle_hf)) (=> (not (@ (@ tptp.member1490636632lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert1636143089lle_hf X3) F2))))))) (@ P F)))))) (forall ((F tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F) (=> (not (= F tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (@ P (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))) (=> (forall ((X3 tptp.nat) (F2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F2) (=> (not (= F2 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat X3) F2))))))) (@ P F)))))) (forall ((F tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf F) (=> (not (= F tptp.bot_bo53200981lle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ P (@ (@ tptp.insert9649339lle_hf X3) tptp.bot_bo53200981lle_hf))) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf F2) (=> (not (= F2 tptp.bot_bo53200981lle_hf)) (=> (not (@ (@ tptp.member1367349282lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf X3) F2))))))) (@ P F)))))) (forall ((P (-> tptp.set_se933006839lle_hf Bool)) (A4 tptp.set_se933006839lle_hf)) (=> (forall ((A5 tptp.set_se933006839lle_hf)) (=> (not (@ tptp.finite1450550360lle_hf A5)) (@ P A5))) (=> (@ P tptp.bot_bo2093393035lle_hf) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf) (F2 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite1450550360lle_hf F2) (=> (not (@ (@ tptp.member1490636632lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert1636143089lle_hf X3) F2)))))) (@ P A4))))) (forall ((P (-> tptp.set_nat Bool)) (A4 tptp.set_nat)) (=> (forall ((A5 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A5)) (@ P A5))) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (F2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F2) (=> (not (@ (@ tptp.member_nat X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat X3) F2)))))) (@ P A4))))) (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((A5 tptp.set_HF_Mirabelle_hf)) (=> (not (@ tptp.finite586181922lle_hf A5)) (@ P A5))) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf F2) (=> (not (@ (@ tptp.member1367349282lle_hf X3) F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf X3) F2)))))) (@ P A4))))) (forall ((X2 tptp.hF_Mirabelle_hf)) (= (@ tptp.the_el1104322134lle_hf (@ (@ tptp.insert9649339lle_hf X2) tptp.bot_bo53200981lle_hf)) X2)) (@ tptp.finite_finite_nat tptp.bot_bot_set_nat) _let_13 (forall ((S tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (= S tptp.bot_bot_set_nat)))) (forall ((S tptp.set_HF_Mirabelle_hf)) (=> (not (@ tptp.finite586181922lle_hf S)) (not (= S tptp.bot_bo53200981lle_hf)))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (@ tptp.finite586181922lle_hf (@ (@ tptp.insert9649339lle_hf A2) A4)))) (forall ((A4 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A2) A4)))) (= tptp.bot_bo1263054448e_hf_o (lambda ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) tptp.bot_bo53200981lle_hf))) (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (= (@ tptp.collec1758573718lle_hf P) tptp.bot_bo2093393035lle_hf) (= P tptp.bot_bo554042810e_hf_o))) (forall ((P (-> tptp.hF_Mirabelle_hf Bool))) (= (= (@ tptp.collec2046588256lle_hf P) tptp.bot_bo53200981lle_hf) (= P tptp.bot_bo1263054448e_hf_o))) _let_12 (forall ((X2 tptp.hF_Mirabelle_hf)) (@ tptp.is_sin1448700567lle_hf (@ (@ tptp.insert9649339lle_hf X2) tptp.bot_bo53200981lle_hf))) _let_11 (= tptp.is_sin1448700567lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf)) (exists ((X tptp.hF_Mirabelle_hf)) (= A6 (@ (@ tptp.insert9649339lle_hf X) tptp.bot_bo53200981lle_hf))))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.is_sin1448700567lle_hf A4) (not (forall ((X3 tptp.hF_Mirabelle_hf)) (not (= A4 (@ (@ tptp.insert9649339lle_hf X3) tptp.bot_bo53200981lle_hf))))))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (not (= A4 tptp.bot_bo53200981lle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X3) A4) (=> (@ (@ tptp.member1367349282lle_hf Y3) A4) (= X3 Y3)))) (@ tptp.is_sin1448700567lle_hf A4)))) (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_nat)))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (= (= (@ tptp.finite1213132899lle_hf A4) tptp.zero_zero_nat) (= A4 tptp.bot_bo53200981lle_hf)))) (forall ((F tptp.set_nat) (A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F) (=> (@ (@ tptp.ord_less_eq_set_nat F) A4) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F2) (=> (@ _let_1 A4) (=> (not (@ _let_1 F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat A3) F2)))))))) (@ P F)))))) (forall ((F tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf F) (=> (@ (@ tptp.ord_le432112161lle_hf F) A4) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((A3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A3))) (=> (@ tptp.finite586181922lle_hf F2) (=> (@ _let_1 A4) (=> (not (@ _let_1 F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf A3) F2)))))))) (@ P F)))))) (forall ((F tptp.set_nat) (A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F) (=> (@ (@ tptp.ord_less_eq_set_nat F) A4) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F2) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_less_eq_set_nat F2) A4) (=> (not (@ _let_1 F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert_nat A3) F2))))))))) (@ P F)))))) (forall ((F tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf F) (=> (@ (@ tptp.ord_le432112161lle_hf F) A4) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((A3 tptp.hF_Mirabelle_hf) (F2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A3))) (=> (@ tptp.finite586181922lle_hf F2) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le432112161lle_hf F2) A4) (=> (not (@ _let_1 F2)) (=> (@ P F2) (@ P (@ (@ tptp.insert9649339lle_hf A3) F2))))))))) (@ P F)))))) (@ (@ tptp.inj_on811196232lle_hf tptp.hF_Mirabelle_HF) (@ tptp.collec1758573718lle_hf tptp.finite586181922lle_hf)) (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf X3))) (=> (@ _let_1 A4) (@ _let_1 B4)))) (@ (@ tptp.ord_le432112161lle_hf A4) B4))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.ord_le432112161lle_hf A4) tptp.bot_bo53200981lle_hf) (= A4 tptp.bot_bo53200981lle_hf))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.ord_le432112161lle_hf tptp.bot_bo53200981lle_hf) A4)) (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.insert9649339lle_hf X2) A4)) B4) (and (@ (@ tptp.member1367349282lle_hf X2) B4) (@ (@ tptp.ord_le432112161lle_hf A4) B4)))) (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.insert9649339lle_hf B3) tptp.bot_bo53200981lle_hf))) (= (= (@ (@ tptp.insert9649339lle_hf A2) A4) _let_1) (and (= A2 B3) (@ (@ tptp.ord_le432112161lle_hf A4) _let_1))))) (forall ((B3 tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.insert9649339lle_hf B3) tptp.bot_bo53200981lle_hf))) (= (= _let_1 (@ (@ tptp.insert9649339lle_hf A2) A4)) (and (= A2 B3) (@ (@ tptp.ord_le432112161lle_hf A4) _let_1))))) _let_10 (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (not (@ tptp.finite586181922lle_hf A4)) (= (@ tptp.finite1213132899lle_hf A4) tptp.zero_zero_nat))) (forall ((A4 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat))) (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= A2 B3)))) (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A tptp.nat) (B tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B3 tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A2) B3)))) (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2))))) (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= A2 B3)))) (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (@ (@ tptp.ord_less_eq_nat A2) C)))) (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A tptp.nat) (B tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat B) A)))) (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y2) (= X2 Y2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y2))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (@ _let_1 C))))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= X2 Y2)))) (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((X tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_nat Y4) X)))) (forall ((A2 tptp.nat) (B3 tptp.nat) (F3 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (= (@ F3 B3) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F3 X3)) (@ F3 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F3 A2)) C))))) (forall ((A2 tptp.nat) (F3 (-> tptp.nat tptp.nat)) (B3 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F3 B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F3 X3)) (@ F3 Y3)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F3 C)))))) (forall ((A2 tptp.nat) (B3 tptp.nat) (F3 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ F3 B3)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F3 X3)) (@ F3 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F3 A2)) C))))) (forall ((A2 tptp.nat) (F3 (-> tptp.nat tptp.nat)) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F3 B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F3 X3)) (@ F3 Y3)))) (@ _let_1 (@ F3 C))))))) (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool)) (Q (-> tptp.set_HF_Mirabelle_hf Bool))) (= (@ (@ tptp.ord_le2016357975lle_hf (@ tptp.collec1758573718lle_hf P)) (@ tptp.collec1758573718lle_hf Q)) (forall ((X tptp.set_HF_Mirabelle_hf)) (=> (@ P X) (@ Q X))))) (forall ((P (-> tptp.set_HF_Mirabelle_hf Bool)) (Q (-> tptp.set_HF_Mirabelle_hf Bool))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le2016357975lle_hf (@ tptp.collec1758573718lle_hf P)) (@ tptp.collec1758573718lle_hf Q)))) _let_8 (= tptp.ord_le432112161lle_hf (lambda ((A6 tptp.set_HF_Mirabelle_hf) (B6 tptp.set_HF_Mirabelle_hf)) (forall ((X tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf X2))) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (= (@ tptp.finite1213132899lle_hf A4) (@ tptp.finite1213132899lle_hf B4)) (= A4 B4))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (=> (= (@ tptp.finite_card_nat A4) (@ tptp.finite_card_nat B4)) (= A4 B4))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (N tptp.nat)) (=> (not (@ tptp.finite586181922lle_hf A4)) (exists ((B5 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B5) (= (@ tptp.finite1213132899lle_hf B5) N) (@ (@ tptp.ord_le432112161lle_hf B5) A4))))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat A4)) (exists ((B5 tptp.set_nat)) (and (@ tptp.finite_finite_nat B5) (= (@ tptp.finite_card_nat B5) N) (@ (@ tptp.ord_less_eq_set_nat B5) A4))))) (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((A2 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.ord_le432112161lle_hf tptp.bot_bo53200981lle_hf) A2)) (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A2)) (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.ord_le432112161lle_hf A2) tptp.bot_bo53200981lle_hf) (= A2 tptp.bot_bo53200981lle_hf))) (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))) (forall ((A2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf A2) tptp.bot_bo53200981lle_hf) (= A2 tptp.bot_bo53200981lle_hf))) (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))) (forall ((A4 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A2) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat A2) X3) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A2) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat X3) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (@ tptp.finite586181922lle_hf B4) (@ tptp.finite586181922lle_hf A4)))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (=> (@ tptp.finite_finite_nat B4) (@ tptp.finite_finite_nat A4)))) (forall ((S tptp.set_HF_Mirabelle_hf) (T2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf S) T2) (=> (not (@ tptp.finite586181922lle_hf S)) (not (@ tptp.finite586181922lle_hf T2))))) (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T2))))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (@ tptp.finite586181922lle_hf A4)))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (@ tptp.finite_finite_nat A4)))) (forall ((C3 tptp.set_HF_Mirabelle_hf) (D2 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (=> (@ (@ tptp.ord_le432112161lle_hf C3) D2) (@ (@ tptp.ord_le432112161lle_hf (@ _let_1 C3)) (@ _let_1 D2))))) (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le432112161lle_hf A4))) (=> (not (@ (@ tptp.member1367349282lle_hf X2) A4)) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf X2) B4)) (@ _let_1 B4))))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.insert9649339lle_hf A2) B4))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le432112161lle_hf A4))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert9649339lle_hf B3) B4))))) (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))) (forall ((X4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.insert9649339lle_hf A2) tptp.bot_bo53200981lle_hf))) (= (@ (@ tptp.ord_le432112161lle_hf X4) _let_1) (or (= X4 tptp.bot_bo53200981lle_hf) (= X4 _let_1))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.insert9649339lle_hf X2) tptp.bot_bo53200981lle_hf))) (=> (@ (@ tptp.ord_le432112161lle_hf A4) _let_1) (or (= A4 tptp.bot_bo53200981lle_hf) (= A4 _let_1))))) (forall ((A4 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_nat) (not (@ tptp.finite_finite_nat A4))))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (= (@ tptp.finite1213132899lle_hf A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bo53200981lle_hf) (not (@ tptp.finite586181922lle_hf A4))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (@ (@ tptp.inj_on811196232lle_hf F3) tptp.bot_bo2093393035lle_hf)) (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F3 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S2) (@ (@ tptp.ord_less_eq_nat (@ F3 Y5)) (@ F3 X3)))) (=> (@ P S2) (@ P (@ (@ tptp.insert_nat X3) S2)))))) (@ P S))))) (forall ((S tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool)) (F3 (-> tptp.hF_Mirabelle_hf tptp.nat))) (=> (@ tptp.finite586181922lle_hf S) (=> (@ P tptp.bot_bo53200981lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (S2 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf S2) (=> (forall ((Y5 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf Y5) S2) (@ (@ tptp.ord_less_eq_nat (@ F3 Y5)) (@ F3 X3)))) (=> (@ P S2) (@ P (@ (@ tptp.insert9649339lle_hf X3) S2)))))) (@ P S))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.inj_on811196232lle_hf F3))) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le2016357975lle_hf B4) A4) (@ _let_1 B4))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (B4 tptp.set_se933006839lle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.inj_on811196232lle_hf F3))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_le2016357975lle_hf A4) B4) (@ _let_1 A4))))) (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (X4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X2) A4) (=> (@ (@ tptp.ord_le432112161lle_hf X4) A4) (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.insert9649339lle_hf X2) X4)) A4)))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.member1367349282lle_hf X3) A4))) (@ (@ tptp.ord_le432112161lle_hf A4) tptp.bot_bo53200981lle_hf))) (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))) (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((F tptp.set_HF_Mirabelle_hf) (C3 tptp.nat)) (=> (forall ((G tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf G) F) (=> (@ tptp.finite586181922lle_hf G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf G)) C3)))) (and (@ tptp.finite586181922lle_hf F) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf F)) C3)))) (forall ((F tptp.set_nat) (C3 tptp.nat)) (=> (forall ((G tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat G) F) (=> (@ tptp.finite_finite_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat G)) C3)))) (and (@ tptp.finite_finite_nat F) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat F)) C3)))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf B4)) (@ tptp.finite1213132899lle_hf A4)) (= A4 B4))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B4)) (@ tptp.finite_card_nat A4)) (= A4 B4))))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite1213132899lle_hf B4))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B4))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite1213132899lle_hf (@ (@ tptp.insert9649339lle_hf X2) A4))))) (forall ((A4 tptp.set_nat) (X2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X2) A4))))) (forall ((A4 tptp.set_se933006839lle_hf) (G2 (-> tptp.hF_Mirabelle_hf tptp.set_HF_Mirabelle_hf)) (F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf X3) A4) (= (@ G2 (@ F3 X3)) X3))) (@ (@ tptp.inj_on811196232lle_hf F3) A4))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (X2 tptp.set_HF_Mirabelle_hf) (Y2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (not (= X2 Y2)) (=> (@ (@ tptp.member1490636632lle_hf X2) A4) (=> (@ (@ tptp.member1490636632lle_hf Y2) A4) (not (= (@ F3 X2) (@ F3 Y2)))))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (X2 tptp.set_HF_Mirabelle_hf) (Y2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (@ (@ tptp.member1490636632lle_hf X2) A4) (=> (@ (@ tptp.member1490636632lle_hf Y2) A4) (= (= (@ F3 X2) (@ F3 Y2)) (= X2 Y2)))))) (forall ((A4 tptp.set_se933006839lle_hf) (F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (G2 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (forall ((A3 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf A3) A4) (= (@ F3 A3) (@ G2 A3)))) (= (@ (@ tptp.inj_on811196232lle_hf F3) A4) (@ (@ tptp.inj_on811196232lle_hf G2) A4)))) _let_7 (forall ((A4 tptp.set_se933006839lle_hf) (F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (forall ((X3 tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf X3) A4) (=> (@ (@ tptp.member1490636632lle_hf Y3) A4) (=> (= (@ F3 X3) (@ F3 Y3)) (= X3 Y3))))) (@ (@ tptp.inj_on811196232lle_hf F3) A4))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (X2 tptp.set_HF_Mirabelle_hf) (Y2 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (= (@ F3 X2) (@ F3 Y2)) (=> (@ (@ tptp.member1490636632lle_hf X2) A4) (=> (@ (@ tptp.member1490636632lle_hf Y2) A4) (= X2 Y2)))))) (forall ((N tptp.nat) (S tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite1213132899lle_hf S)) (not (forall ((T3 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le432112161lle_hf T3) S) (=> (= (@ tptp.finite1213132899lle_hf T3) N) (not (@ tptp.finite586181922lle_hf T3)))))))) (forall ((N tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_nat S)) (not (forall ((T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat T3) S) (=> (= (@ tptp.finite_card_nat T3) N) (not (@ tptp.finite_finite_nat T3)))))))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (=> (@ tptp.finite586181922lle_hf B4) (=> (forall ((A3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A3) A4) (exists ((B7 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.member1367349282lle_hf B7) B4) (@ (@ R A3) B7))))) (=> (forall ((A1 tptp.hF_Mirabelle_hf) (A22 tptp.hF_Mirabelle_hf) (B2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A1) A4) (=> (@ (@ tptp.member1367349282lle_hf A22) A4) (=> (@ (@ tptp.member1367349282lle_hf B2) B4) (=> (@ (@ R A1) B2) (=> (@ (@ R A22) B2) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite1213132899lle_hf B4)))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_HF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B4) (=> (forall ((A3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A3) A4) (exists ((B7 tptp.nat)) (and (@ (@ tptp.member_nat B7) B4) (@ (@ R A3) B7))))) (=> (forall ((A1 tptp.hF_Mirabelle_hf) (A22 tptp.hF_Mirabelle_hf) (B2 tptp.nat)) (=> (@ (@ tptp.member1367349282lle_hf A1) A4) (=> (@ (@ tptp.member1367349282lle_hf A22) A4) (=> (@ (@ tptp.member_nat B2) B4) (=> (@ (@ R A1) B2) (=> (@ (@ R A22) B2) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite_card_nat B4)))))) (forall ((S tptp.set_nat) (Y2 tptp.nat) (F3 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y2) S) (@ (@ tptp.ord_less_eq_nat (@ F3 (@ (@ tptp.lattic1974000059at_nat F3) S))) (@ F3 Y2)))))) (forall ((S tptp.set_HF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.nat))) (=> (@ tptp.finite586181922lle_hf S) (=> (not (= S tptp.bot_bo53200981lle_hf)) (=> (@ (@ tptp.member1367349282lle_hf Y2) S) (@ (@ tptp.ord_less_eq_nat (@ F3 (@ (@ tptp.lattic710307446hf_nat F3) S))) (@ F3 Y2)))))) (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (M tptp.nat)) (=> (@ P X2) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M))) (not (forall ((M2 tptp.nat)) (=> (@ P M2) (not (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M2)))))))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B3 tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B3))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X3)))))))) (forall ((M3 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_nat N) M3))) (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (=> (@ (@ tptp.ord_less_eq_nat N) M3) (= M3 N)))) (forall ((M3 tptp.nat) (N tptp.nat)) (=> (= M3 N) (@ (@ tptp.ord_less_eq_nat M3) N))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) _let_6 (forall ((A4 tptp.set_nat) (X2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A4)))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf (@ (@ tptp.minus_1450406810lle_hf A4) (@ (@ tptp.insert9649339lle_hf X2) tptp.bot_bo53200981lle_hf)))) (@ tptp.finite1213132899lle_hf A4)))) (forall ((A4 tptp.set_se933006839lle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite1450550360lle_hf A4) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite90088345lle_hf A4)) (@ tptp.finite1213132899lle_hf B4)) (exists ((F5 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (and (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_899003828lle_hf F5) A4)) B4) (@ (@ tptp.inj_on811196232lle_hf F5) A4))))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite1213132899lle_hf B4)) (exists ((F5 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (and (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_1743964010lle_hf F5) A4)) B4) (@ (@ tptp.inj_on755450110lle_hf F5) A4))))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_nat)) (=> (@ tptp.finite586181922lle_hf A4) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1213132899lle_hf A4)) (@ tptp.finite_card_nat B4)) (exists ((F5 (-> tptp.hF_Mirabelle_hf tptp.nat))) (and (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_131453538hf_nat F5) A4)) B4) (@ (@ tptp.inj_on1874279374hf_nat F5) A4))))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite1213132899lle_hf B4)) (exists ((F5 (-> tptp.nat tptp.hF_Mirabelle_hf))) (and (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_246164834lle_hf F5) A4)) B4) (@ (@ tptp.inj_on1988990670lle_hf F5) A4))))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B4)) (exists ((F5 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F5) A4)) B4) (@ (@ tptp.inj_on_nat_nat F5) A4))))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_899003828lle_hf F3) A4)) B4) (=> (@ tptp.finite586181922lle_hf B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite90088345lle_hf A4)) (@ tptp.finite1213132899lle_hf B4)))))) (forall ((B3 tptp.hF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (= B3 (@ F3 X2)) (=> (@ (@ tptp.member1367349282lle_hf X2) A4) (@ (@ tptp.member1367349282lle_hf B3) (@ (@ tptp.image_1743964010lle_hf F3) A4))))) (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) B4)))))) (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (= (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) B4)) (and (@ _let_1 A4) (not (@ _let_1 B4)))))) (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) A2) tptp.zero_zero_nat)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) tptp.zero_zero_nat) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.image_1743964010lle_hf F3) tptp.bot_bo53200981lle_hf) tptp.bot_bo53200981lle_hf)) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (= (= tptp.bot_bo53200981lle_hf (@ (@ tptp.image_1743964010lle_hf F3) A4)) (= A4 tptp.bot_bo53200981lle_hf))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.image_1743964010lle_hf F3) A4) tptp.bot_bo53200981lle_hf) (= A4 tptp.bot_bo53200981lle_hf))) (forall ((F tptp.set_HF_Mirabelle_hf) (H (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (@ tptp.finite586181922lle_hf F) (@ tptp.finite586181922lle_hf (@ (@ tptp.image_1743964010lle_hf H) F)))) (forall ((F tptp.set_HF_Mirabelle_hf) (H (-> tptp.hF_Mirabelle_hf tptp.nat))) (=> (@ tptp.finite586181922lle_hf F) (@ tptp.finite_finite_nat (@ (@ tptp.image_131453538hf_nat H) F)))) (forall ((F tptp.set_nat) (H (-> tptp.nat tptp.hF_Mirabelle_hf))) (=> (@ tptp.finite_finite_nat F) (@ tptp.finite586181922lle_hf (@ (@ tptp.image_246164834lle_hf H) F)))) (forall ((F tptp.set_nat) (H (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat F) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat H) F)))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.image_1743964010lle_hf F3))) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf A2) B4)) (@ (@ tptp.insert9649339lle_hf (@ F3 A2)) (@ _let_1 B4))))) (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (let ((_let_1 (@ (@ tptp.image_1743964010lle_hf F3) A4))) (=> (@ (@ tptp.member1367349282lle_hf X2) A4) (= (@ (@ tptp.insert9649339lle_hf (@ F3 X2)) _let_1) _let_1)))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.minus_1450406810lle_hf A4) tptp.bot_bo53200981lle_hf) A4)) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.minus_1450406810lle_hf tptp.bot_bo53200981lle_hf) A4) tptp.bot_bo53200981lle_hf)) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.minus_1450406810lle_hf A4) A4) tptp.bot_bo53200981lle_hf)) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf A4) (@ tptp.finite586181922lle_hf (@ (@ tptp.minus_1450406810lle_hf A4) B4)))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A4) B4)))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.minus_1450406810lle_hf A4) B4)) (@ tptp.finite586181922lle_hf A4)))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A4) B4)) (@ tptp.finite_finite_nat A4)))) (forall ((X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.minus_1450406810lle_hf A4))) (=> (not (@ (@ tptp.member1367349282lle_hf X2) A4)) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf X2) B4)) (@ _let_1 B4))))) _let_5 _let_4 (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (= (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) (@ _let_1 tptp.bot_bo53200981lle_hf))) (@ _let_1 A4)))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.minus_1450406810lle_hf A4))) (= (@ tptp.finite586181922lle_hf (@ _let_1 (@ (@ tptp.insert9649339lle_hf A2) B4))) (@ tptp.finite586181922lle_hf (@ _let_1 B4))))) (forall ((A4 tptp.set_nat) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A4))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A2) B4))) (@ tptp.finite_finite_nat (@ _let_1 B4))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.insert1636143089lle_hf A2))) (let ((_let_2 (@ tptp.inj_on811196232lle_hf F3))) (= (@ _let_2 (@ _let_1 A4)) (and (@ _let_2 A4) (not (@ (@ tptp.member1367349282lle_hf (@ F3 A2)) (@ (@ tptp.image_899003828lle_hf F3) (@ (@ tptp.minus_500612048lle_hf A4) (@ _let_1 tptp.bot_bo2093393035lle_hf)))))))))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (let ((_let_2 (@ tptp.inj_on755450110lle_hf F3))) (= (@ _let_2 (@ _let_1 A4)) (and (@ _let_2 A4) (not (@ (@ tptp.member1367349282lle_hf (@ F3 A2)) (@ (@ tptp.image_1743964010lle_hf F3) (@ (@ tptp.minus_1450406810lle_hf A4) (@ _let_1 tptp.bot_bo53200981lle_hf)))))))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (C3 tptp.set_se933006839lle_hf) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.image_899003828lle_hf F3))) (let ((_let_2 (@ (@ tptp.minus_500612048lle_hf A4) B4))) (=> (@ (@ tptp.inj_on811196232lle_hf F3) C3) (=> (@ (@ tptp.ord_le2016357975lle_hf _let_2) C3) (=> (@ (@ tptp.ord_le2016357975lle_hf B4) C3) (= (@ _let_1 _let_2) (@ (@ tptp.minus_1450406810lle_hf (@ _let_1 A4)) (@ _let_1 B4))))))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (B4 tptp.set_HF_Mirabelle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X3) A4) (@ (@ tptp.member1367349282lle_hf (@ F3 X3)) B4))) (@ (@ tptp.ord_le432112161lle_hf (@ (@ tptp.image_1743964010lle_hf F3) A4)) B4))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (@ tptp.finite586181922lle_hf A4) (=> (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (@ tptp.finite586181922lle_hf B4)))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_nat) (F3 (-> tptp.hF_Mirabelle_hf tptp.nat))) (=> (@ tptp.finite586181922lle_hf A4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_131453538hf_nat F3) A4)) (@ tptp.finite_finite_nat B4)))) (forall ((A4 tptp.set_nat) (B4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.nat tptp.hF_Mirabelle_hf))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.image_246164834lle_hf F3) A4)) (@ tptp.finite586181922lle_hf B4)))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (F3 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_nat_nat F3) A4)) (@ tptp.finite_finite_nat B4)))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (exists ((C4 tptp.set_HF_Mirabelle_hf)) (and (@ (@ tptp.ord_le432112161lle_hf C4) A4) (@ tptp.finite586181922lle_hf C4) (= B4 (@ (@ tptp.image_1743964010lle_hf F3) C4))))))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat)) (=> (@ tptp.finite586181922lle_hf B4) (=> (@ (@ tptp.ord_le432112161lle_hf B4) (@ (@ tptp.image_246164834lle_hf F3) A4)) (exists ((C4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat C4) A4) (@ tptp.finite_finite_nat C4) (= B4 (@ (@ tptp.image_246164834lle_hf F3) C4))))))) (forall ((B4 tptp.set_nat) (F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_131453538hf_nat F3) A4)) (exists ((C4 tptp.set_HF_Mirabelle_hf)) (and (@ (@ tptp.ord_le432112161lle_hf C4) A4) (@ tptp.finite586181922lle_hf C4) (= B4 (@ (@ tptp.image_131453538hf_nat F3) C4))))))) (forall ((B4 tptp.set_nat) (F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_nat_nat F3) A4)) (exists ((C4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat C4) A4) (@ tptp.finite_finite_nat C4) (= B4 (@ (@ tptp.image_nat_nat F3) C4))))))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (@ P B6))) (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) A4) (@ P (@ (@ tptp.image_1743964010lle_hf F3) B6)))))) (forall ((F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) (@ (@ tptp.image_246164834lle_hf F3) A4)) (@ P B6))) (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A4) (@ P (@ (@ tptp.image_246164834lle_hf F3) B6)))))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_nat Bool))) (= (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_131453538hf_nat F3) A4)) (@ P B6))) (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) A4) (@ P (@ (@ tptp.image_131453538hf_nat F3) B6)))))) (forall ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_nat_nat F3) A4)) (@ P B6))) (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A4) (@ P (@ (@ tptp.image_nat_nat F3) B6)))))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) (@ (@ tptp.image_1743964010lle_hf F3) A4))) (@ P B6))) (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) A4)) (@ P (@ (@ tptp.image_1743964010lle_hf F3) B6)))))) (forall ((F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat) (P (-> tptp.set_HF_Mirabelle_hf Bool))) (= (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) (@ (@ tptp.image_246164834lle_hf F3) A4))) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A4)) (@ P (@ (@ tptp.image_246164834lle_hf F3) B6)))))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf) (P (-> tptp.set_nat Bool))) (= (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_131453538hf_nat F3) A4))) (@ P B6))) (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (and (@ tptp.finite586181922lle_hf B6) (@ (@ tptp.ord_le432112161lle_hf B6) A4)) (@ P (@ (@ tptp.image_131453538hf_nat F3) B6)))))) (forall ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_nat_nat F3) A4))) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A4)) (@ P (@ (@ tptp.image_nat_nat F3) B6)))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf)) (=> (@ tptp.finite586181922lle_hf (@ (@ tptp.image_899003828lle_hf F3) A4)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (@ tptp.finite1450550360lle_hf A4)))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite586181922lle_hf (@ (@ tptp.image_1743964010lle_hf F3) A4)) (=> (@ (@ tptp.inj_on755450110lle_hf F3) A4) (@ tptp.finite586181922lle_hf A4)))) (forall ((F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat)) (=> (@ tptp.finite586181922lle_hf (@ (@ tptp.image_246164834lle_hf F3) A4)) (=> (@ (@ tptp.inj_on1988990670lle_hf F3) A4) (@ tptp.finite_finite_nat A4)))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_131453538hf_nat F3) A4)) (=> (@ (@ tptp.inj_on1874279374hf_nat F3) A4) (@ tptp.finite586181922lle_hf A4)))) (forall ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat F3) A4)) (=> (@ (@ tptp.inj_on_nat_nat F3) A4) (@ tptp.finite_finite_nat A4)))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.image_899003828lle_hf F3) A4)) (@ tptp.finite1450550360lle_hf A4)))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on755450110lle_hf F3) A4) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.image_1743964010lle_hf F3) A4)) (@ tptp.finite586181922lle_hf A4)))) (forall ((F3 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A4 tptp.set_nat)) (=> (@ (@ tptp.inj_on1988990670lle_hf F3) A4) (= (@ tptp.finite586181922lle_hf (@ (@ tptp.image_246164834lle_hf F3) A4)) (@ tptp.finite_finite_nat A4)))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.nat)) (A4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on1874279374hf_nat F3) A4) (= (@ tptp.finite_finite_nat (@ (@ tptp.image_131453538hf_nat F3) A4)) (@ tptp.finite586181922lle_hf A4)))) (forall ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (@ (@ tptp.inj_on_nat_nat F3) A4) (= (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat F3) A4)) (@ tptp.finite_finite_nat A4)))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (C3 tptp.set_se933006839lle_hf) (A4 tptp.set_se933006839lle_hf) (B4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.image_899003828lle_hf F3))) (=> (@ (@ tptp.inj_on811196232lle_hf F3) C3) (=> (@ (@ tptp.ord_le2016357975lle_hf A4) C3) (=> (@ (@ tptp.ord_le2016357975lle_hf B4) C3) (= (= (@ _let_1 A4) (@ _let_1 B4)) (= A4 B4))))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (B4 tptp.set_se933006839lle_hf) (A2 tptp.set_HF_Mirabelle_hf) (A4 tptp.set_se933006839lle_hf)) (let ((_let_1 (@ tptp.member1490636632lle_hf A2))) (=> (@ (@ tptp.inj_on811196232lle_hf F3) B4) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_le2016357975lle_hf A4) B4) (= (@ (@ tptp.member1367349282lle_hf (@ F3 A2)) (@ (@ tptp.image_899003828lle_hf F3) A4)) (@ _let_1 A4))))))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (B4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ (@ tptp.inj_on755450110lle_hf F3) B4) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_le432112161lle_hf A4) B4) (= (@ (@ tptp.member1367349282lle_hf (@ F3 A2)) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (@ _let_1 A4))))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf) (X2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (=> (not (@ (@ tptp.member1367349282lle_hf X2) B4)) (=> (= (@ (@ tptp.insert9649339lle_hf X2) B4) (@ (@ tptp.image_899003828lle_hf F3) A4)) (not (forall ((X6 tptp.set_HF_Mirabelle_hf) (A7 tptp.set_se933006839lle_hf)) (=> (not (@ (@ tptp.member1490636632lle_hf X6) A7)) (=> (= A4 (@ (@ tptp.insert1636143089lle_hf X6) A7)) (=> (= X2 (@ F3 X6)) (not (= B4 (@ (@ tptp.image_899003828lle_hf F3) A7)))))))))))) (forall ((F3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.inj_on755450110lle_hf F3) A4) (=> (not (@ (@ tptp.member1367349282lle_hf X2) B4)) (=> (= (@ (@ tptp.insert9649339lle_hf X2) B4) (@ (@ tptp.image_1743964010lle_hf F3) A4)) (not (forall ((X6 tptp.hF_Mirabelle_hf) (A7 tptp.set_HF_Mirabelle_hf)) (=> (not (@ (@ tptp.member1367349282lle_hf X6) A7)) (=> (= A4 (@ (@ tptp.insert9649339lle_hf X6) A7)) (=> (= X2 (@ F3 X6)) (not (= B4 (@ (@ tptp.image_1743964010lle_hf F3) A7)))))))))))) (forall ((F3 (-> tptp.set_HF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (A4 tptp.set_se933006839lle_hf)) (=> (@ (@ tptp.inj_on811196232lle_hf F3) A4) (= (@ tptp.finite1213132899lle_hf (@ (@ tptp.image_899003828lle_hf F3) A4)) (@ tptp.finite90088345lle_hf A4)))) _let_3 (forall ((A4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (let ((_let_2 (@ tptp.minus_1450406810lle_hf A4))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_1450406810lle_hf (@ _let_2 (@ _let_1 tptp.bot_bo53200981lle_hf))) B4))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (=> (@ (@ tptp.member1367349282lle_hf A2) A4) (= (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) (@ _let_1 tptp.bot_bo53200981lle_hf))) A4)))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (let ((_let_2 (@ tptp.minus_1450406810lle_hf A4))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_1450406810lle_hf (@ _let_2 B4)) (@ _let_1 tptp.bot_bo53200981lle_hf)))))) (forall ((A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (X2 tptp.hF_Mirabelle_hf) (C3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.minus_1450406810lle_hf B4))) (let ((_let_2 (@ tptp.ord_le432112161lle_hf A4))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert9649339lle_hf X2) C3))) (and (@ _let_2 (@ _let_1 C3)) (not (@ (@ tptp.member1367349282lle_hf X2) A4))))))) (forall ((B4 tptp.set_se933006839lle_hf) (X2 tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X2))) (=> (forall ((C4 tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1490636632lle_hf C4) B4) (not (@ (@ tptp.member1367349282lle_hf X2) C4)))) (= (@ (@ tptp.member1490636632lle_hf A4) (@ (@ tptp.image_1514960916lle_hf _let_1) B4)) (and (@ (@ tptp.member1367349282lle_hf X2) A4) (@ (@ tptp.member1490636632lle_hf (@ (@ tptp.minus_1450406810lle_hf A4) (@ _let_1 tptp.bot_bo53200981lle_hf))) B4)))))) (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) B4)) (not (=> (@ _let_1 A4) (@ _let_1 B4)))))) (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.minus_1450406810lle_hf A4) B4)) (@ _let_1 A4)))) _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.95/1.21 )
% 0.95/1.21 % SZS output end Proof for ITP072^1
% 0.95/1.21 % cvc5---1.0.5 exiting
% 0.95/1.21 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------