TSTP Solution File: ITP076^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP076^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 03:18:01 EDT 2023
% Result : Theorem 0.69s 0.93s
% Output : Proof 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : ITP076^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.17 % Command : do_cvc5 %s %d
% 0.17/0.38 % Computer : n027.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun Aug 27 12:22:21 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.24/0.55 %----Proving TH0
% 0.24/0.55 %------------------------------------------------------------------------------
% 0.24/0.55 % File : ITP076^1 : TPTP v8.1.2. Released v7.5.0.
% 0.24/0.55 % Domain : Interactive Theorem Proving
% 0.24/0.55 % Problem : Sledgehammer HF problem prob_850__5339526_1
% 0.24/0.55 % Version : Especial.
% 0.24/0.55 % English :
% 0.24/0.55
% 0.24/0.55 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.24/0.55 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.24/0.55 % Source : [Des21]
% 0.24/0.55 % Names : HF/prob_850__5339526_1 [Des21]
% 0.24/0.55
% 0.24/0.55 % Status : Theorem
% 0.24/0.55 % Rating : 0.54 v8.1.0, 0.45 v7.5.0
% 0.24/0.55 % Syntax : Number of formulae : 408 ( 258 unt; 52 typ; 0 def)
% 0.24/0.55 % Number of atoms : 781 ( 477 equ; 0 cnn)
% 0.24/0.55 % Maximal formula atoms : 5 ( 2 avg)
% 0.24/0.55 % Number of connectives : 2218 ( 71 ~; 9 |; 60 &;1909 @)
% 0.24/0.55 % ( 0 <=>; 169 =>; 0 <=; 0 <~>)
% 0.24/0.55 % Maximal formula depth : 13 ( 4 avg)
% 0.24/0.55 % Number of types : 5 ( 4 usr)
% 0.24/0.55 % Number of type conns : 179 ( 179 >; 0 *; 0 +; 0 <<)
% 0.24/0.55 % Number of symbols : 49 ( 48 usr; 7 con; 0-3 aty)
% 0.24/0.55 % Number of variables : 871 ( 62 ^; 784 !; 25 ?; 871 :)
% 0.24/0.55 % SPC : TH0_THM_EQU_NAR
% 0.24/0.55
% 0.24/0.55 % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:21.238
% 0.24/0.55 %------------------------------------------------------------------------------
% 0.24/0.55 % Could-be-implicit typings (4)
% 0.24/0.55 thf(ty_n_t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.24/0.55 set_HF_Mirabelle_hf: $tType ).
% 0.24/0.55
% 0.24/0.55 thf(ty_n_t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.55 hF_Mirabelle_hf: $tType ).
% 0.24/0.55
% 0.24/0.55 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.24/0.55 set_nat: $tType ).
% 0.24/0.55
% 0.24/0.55 thf(ty_n_t__Nat__Onat,type,
% 0.24/0.55 nat: $tType ).
% 0.24/0.55
% 0.24/0.55 % Explicit typings (48)
% 0.24/0.55 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.24/0.55 plus_plus_nat: nat > nat > nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Groups_Ozero__class_Ozero_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.55 zero_z189798548lle_hf: hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.24/0.55 zero_zero_nat: nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_OHCollect,type,
% 0.24/0.55 hF_Mir818139703ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_OHF,type,
% 0.24/0.55 hF_Mirabelle_HF: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_OHInter,type,
% 0.24/0.55 hF_Mirabelle_HInter: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_OHUnion,type,
% 0.24/0.55 hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_OPrimReplace,type,
% 0.24/0.55 hF_Mir1248913145eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_ORepFun,type,
% 0.24/0.55 hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_OReplace,type,
% 0.24/0.55 hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohcard,type,
% 0.24/0.55 hF_Mirabelle_hcard: hF_Mirabelle_hf > nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohf_OAbs__hf,type,
% 0.24/0.55 hF_Mirabelle_Abs_hf: nat > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohf_ORep__hf,type,
% 0.24/0.55 hF_Mirabelle_Rep_hf: hF_Mirabelle_hf > nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohfset,type,
% 0.24/0.55 hF_Mirabelle_hfset: hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohfst,type,
% 0.24/0.55 hF_Mirabelle_hfst: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohfunction,type,
% 0.24/0.55 hF_Mir199975595nction: hF_Mirabelle_hf > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohinsert,type,
% 0.24/0.55 hF_Mirabelle_hinsert: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohmem,type,
% 0.24/0.55 hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohpair,type,
% 0.24/0.55 hF_Mirabelle_hpair: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohrelation,type,
% 0.24/0.55 hF_Mir434065167lation: hF_Mirabelle_hf > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohrestrict,type,
% 0.24/0.55 hF_Mir1653039215strict: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ohsnd,type,
% 0.24/0.55 hF_Mirabelle_hsnd: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_HF__Mirabelle__glliljednj_Ois__hpair,type,
% 0.24/0.55 hF_Mir137170979_hpair: hF_Mirabelle_hf > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__HF____Mirabelle____glliljednj__Ohf_M_Eo_J,type,
% 0.24/0.55 inf_in307783154e_hf_o: ( hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.24/0.55 inf_inf_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Oinf__class_Oinf_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.55 inf_in956532509lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.24/0.55 inf_in923488851lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.24/0.55 inf_inf_set_nat: set_nat > set_nat > set_nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__HF____Mirabelle____glliljednj__Ohf_M_Eo_J,type,
% 0.24/0.55 sup_su1199008216e_hf_o: ( hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.24/0.55 sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Osup__class_Osup_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.55 sup_su638957495lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.24/0.55 sup_su1790843629lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.24/0.55 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Nat_OSuc,type,
% 0.24/0.55 suc: nat > nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__HF____Mirabelle____glliljednj__Ohf_M_Eo_J,type,
% 0.24/0.55 top_to22270292e_hf_o: hF_Mirabelle_hf > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.24/0.55 top_top_nat_o: nat > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
% 0.24/0.55 top_top_o: $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.24/0.55 top_to489427057lle_hf: set_HF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.24/0.55 top_top_set_nat: set_nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Set_OCollect_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.55 collec2046588256lle_hf: ( hF_Mirabelle_hf > $o ) > set_HF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.24/0.55 collect_nat: ( nat > $o ) > set_nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Set_Oinsert_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.55 insert9649339lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 0.24/0.55 insert_nat: nat > set_nat > set_nat ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_Typedef_Otype__definition_001t__HF____Mirabelle____glliljednj__Ohf_001t__Nat__Onat,type,
% 0.24/0.55 type_d1794767497hf_nat: ( hF_Mirabelle_hf > nat ) > ( nat > hF_Mirabelle_hf ) > set_nat > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_member_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.55 member1367349282lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_c_member_001t__Nat__Onat,type,
% 0.24/0.55 member_nat: nat > set_nat > $o ).
% 0.24/0.55
% 0.24/0.55 thf(sy_v_r,type,
% 0.24/0.55 r: hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 thf(sy_v_x,type,
% 0.24/0.55 x: hF_Mirabelle_hf ).
% 0.24/0.55
% 0.24/0.55 % Relevant facts (354)
% 0.24/0.55 thf(fact_0_hrelation__restr,axiom,
% 0.24/0.55 ! [R: hF_Mirabelle_hf,X: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ R @ X ) ) ).
% 0.24/0.55
% 0.24/0.55 % hrelation_restr
% 0.24/0.55 thf(fact_1_hfunction__def,axiom,
% 0.24/0.55 ( hF_Mir199975595nction
% 0.24/0.55 = ( ^ [R2: hF_Mirabelle_hf] :
% 0.24/0.55 ! [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X2 @ Y ) @ R2 )
% 0.24/0.55 => ! [Y2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X2 @ Y2 ) @ R2 )
% 0.24/0.55 => ( Y = Y2 ) ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hfunction_def
% 0.24/0.55 thf(fact_2_hrestrict__iff,axiom,
% 0.24/0.55 ! [Z: hF_Mirabelle_hf,R: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ Z @ ( hF_Mir1653039215strict @ R @ A ) )
% 0.24/0.55 = ( ( hF_Mirabelle_hmem @ Z @ R )
% 0.24/0.55 & ? [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( Z
% 0.24/0.55 = ( hF_Mirabelle_hpair @ X2 @ Y ) )
% 0.24/0.55 & ( hF_Mirabelle_hmem @ X2 @ A ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hrestrict_iff
% 0.24/0.55 thf(fact_3_hpair__iff,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A3: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( ( hF_Mirabelle_hpair @ A2 @ B )
% 0.24/0.55 = ( hF_Mirabelle_hpair @ A3 @ B2 ) )
% 0.24/0.55 = ( ( A2 = A3 )
% 0.24/0.55 & ( B = B2 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hpair_iff
% 0.24/0.55 thf(fact_4_Rep__hf__inject,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( ( hF_Mirabelle_Rep_hf @ X )
% 0.24/0.55 = ( hF_Mirabelle_Rep_hf @ Y3 ) )
% 0.24/0.55 = ( X = Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % Rep_hf_inject
% 0.24/0.55 thf(fact_5_hf__equalityI,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ! [X3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ X3 @ A2 )
% 0.24/0.55 = ( hF_Mirabelle_hmem @ X3 @ B ) )
% 0.24/0.55 => ( A2 = B ) ) ).
% 0.24/0.55
% 0.24/0.55 % hf_equalityI
% 0.24/0.55 thf(fact_6_hf__ext,axiom,
% 0.24/0.55 ( ( ^ [Y4: hF_Mirabelle_hf,Z2: hF_Mirabelle_hf] : ( Y4 = Z2 ) )
% 0.24/0.55 = ( ^ [A4: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.24/0.55 ! [X2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ X2 @ A4 )
% 0.24/0.55 = ( hF_Mirabelle_hmem @ X2 @ B3 ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hf_ext
% 0.24/0.55 thf(fact_7_hmem__ne,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ X @ Y3 )
% 0.24/0.55 => ( X != Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % hmem_ne
% 0.24/0.55 thf(fact_8_replacement,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,R3: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ! [U: hF_Mirabelle_hf,V: hF_Mirabelle_hf,V2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U @ X )
% 0.24/0.55 => ( ( R3 @ U @ V )
% 0.24/0.55 => ( ( R3 @ U @ V2 )
% 0.24/0.55 => ( V2 = V ) ) ) )
% 0.24/0.55 => ? [Z3: hF_Mirabelle_hf] :
% 0.24/0.55 ! [V3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ V3 @ Z3 )
% 0.24/0.55 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U2 @ X )
% 0.24/0.55 & ( R3 @ U2 @ V3 ) ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % replacement
% 0.24/0.55 thf(fact_9_binary__union,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ? [Z3: hF_Mirabelle_hf] :
% 0.24/0.55 ! [U3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U3 @ Z3 )
% 0.24/0.55 = ( ( hF_Mirabelle_hmem @ U3 @ X )
% 0.24/0.55 | ( hF_Mirabelle_hmem @ U3 @ Y3 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % binary_union
% 0.24/0.55 thf(fact_10_hmem__not__sym,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ~ ( ( hF_Mirabelle_hmem @ X @ Y3 )
% 0.24/0.55 & ( hF_Mirabelle_hmem @ Y3 @ X ) ) ).
% 0.24/0.55
% 0.24/0.55 % hmem_not_sym
% 0.24/0.55 thf(fact_11_hpair__inject,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A3: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( ( hF_Mirabelle_hpair @ A2 @ B )
% 0.24/0.55 = ( hF_Mirabelle_hpair @ A3 @ B2 ) )
% 0.24/0.55 => ~ ( ( A2 = A3 )
% 0.24/0.55 => ( B != B2 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hpair_inject
% 0.24/0.55 thf(fact_12_union__of__set,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf] :
% 0.24/0.55 ? [Z3: hF_Mirabelle_hf] :
% 0.24/0.55 ! [U3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U3 @ Z3 )
% 0.24/0.55 = ( ? [Y: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ Y @ X )
% 0.24/0.55 & ( hF_Mirabelle_hmem @ U3 @ Y ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % union_of_set
% 0.24/0.55 thf(fact_13_comprehension,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ? [Z3: hF_Mirabelle_hf] :
% 0.24/0.55 ! [U3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U3 @ Z3 )
% 0.24/0.55 = ( ( hF_Mirabelle_hmem @ U3 @ X )
% 0.24/0.55 & ( P @ U3 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % comprehension
% 0.24/0.55 thf(fact_14_hmem__not__refl,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf] :
% 0.24/0.55 ~ ( hF_Mirabelle_hmem @ X @ X ) ).
% 0.24/0.55
% 0.24/0.55 % hmem_not_refl
% 0.24/0.55 thf(fact_15_hpair__neq__fst,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hpair @ A2 @ B )
% 0.24/0.55 != A2 ) ).
% 0.24/0.55
% 0.24/0.55 % hpair_neq_fst
% 0.24/0.55 thf(fact_16_hpair__neq__snd,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hpair @ A2 @ B )
% 0.24/0.55 != B ) ).
% 0.24/0.55
% 0.24/0.55 % hpair_neq_snd
% 0.24/0.55 thf(fact_17_replacement__fun,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.55 ? [Z3: hF_Mirabelle_hf] :
% 0.24/0.55 ! [V3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ V3 @ Z3 )
% 0.24/0.55 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U2 @ X )
% 0.24/0.55 & ( V3
% 0.24/0.55 = ( F @ U2 ) ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % replacement_fun
% 0.24/0.55 thf(fact_18_hfst__conv,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A2 @ B ) )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % hfst_conv
% 0.24/0.55 thf(fact_19_hsnd__conv,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A2 @ B ) )
% 0.24/0.55 = B ) ).
% 0.24/0.55
% 0.24/0.55 % hsnd_conv
% 0.24/0.55 thf(fact_20_hrelation__def,axiom,
% 0.24/0.55 ( hF_Mir434065167lation
% 0.24/0.55 = ( ^ [R2: hF_Mirabelle_hf] :
% 0.24/0.55 ! [Z4: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ Z4 @ R2 )
% 0.24/0.55 => ( hF_Mir137170979_hpair @ Z4 ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hrelation_def
% 0.24/0.55 thf(fact_21_is__hpair__def,axiom,
% 0.24/0.55 ( hF_Mir137170979_hpair
% 0.24/0.55 = ( ^ [Z4: hF_Mirabelle_hf] :
% 0.24/0.55 ? [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.55 ( Z4
% 0.24/0.55 = ( hF_Mirabelle_hpair @ X2 @ Y ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % is_hpair_def
% 0.24/0.55 thf(fact_22_PrimReplace__iff,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf,R3: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,V4: hF_Mirabelle_hf] :
% 0.24/0.55 ( ! [U: hF_Mirabelle_hf,V: hF_Mirabelle_hf,V2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U @ A )
% 0.24/0.55 => ( ( R3 @ U @ V )
% 0.24/0.55 => ( ( R3 @ U @ V2 )
% 0.24/0.55 => ( V2 = V ) ) ) )
% 0.24/0.55 => ( ( hF_Mirabelle_hmem @ V4 @ ( hF_Mir1248913145eplace @ A @ R3 ) )
% 0.24/0.55 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U2 @ A )
% 0.24/0.55 & ( R3 @ U2 @ V4 ) ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % PrimReplace_iff
% 0.24/0.55 thf(fact_23_HUnion__iff,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ X @ ( hF_Mirabelle_HUnion @ A ) )
% 0.24/0.55 = ( ? [Y: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ Y @ A )
% 0.24/0.55 & ( hF_Mirabelle_hmem @ X @ Y ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % HUnion_iff
% 0.24/0.55 thf(fact_24_Replace__iff,axiom,
% 0.24/0.55 ! [V4: hF_Mirabelle_hf,A: hF_Mirabelle_hf,R3: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ V4 @ ( hF_Mirabelle_Replace @ A @ R3 ) )
% 0.24/0.55 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U2 @ A )
% 0.24/0.55 & ( R3 @ U2 @ V4 )
% 0.24/0.55 & ! [Y: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( R3 @ U2 @ Y )
% 0.24/0.55 => ( Y = V4 ) ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % Replace_iff
% 0.24/0.55 thf(fact_25_HCollect__iff,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ X @ ( hF_Mir818139703ollect @ P @ A ) )
% 0.24/0.55 = ( ( P @ X )
% 0.24/0.55 & ( hF_Mirabelle_hmem @ X @ A ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % HCollect_iff
% 0.24/0.55 thf(fact_26_RepFun__iff,axiom,
% 0.24/0.55 ! [V4: hF_Mirabelle_hf,A: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ V4 @ ( hF_Mirabelle_RepFun @ A @ F ) )
% 0.24/0.55 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U2 @ A )
% 0.24/0.55 & ( V4
% 0.24/0.55 = ( F @ U2 ) ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % RepFun_iff
% 0.24/0.55 thf(fact_27_Rep__hf__inverse,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_Abs_hf @ ( hF_Mirabelle_Rep_hf @ X ) )
% 0.24/0.55 = X ) ).
% 0.24/0.55
% 0.24/0.55 % Rep_hf_inverse
% 0.24/0.55 thf(fact_28_RepFun__cong,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf,G: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.55 ( ( A = B4 )
% 0.24/0.55 => ( ! [X3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ X3 @ B4 )
% 0.24/0.55 => ( ( F @ X3 )
% 0.24/0.55 = ( G @ X3 ) ) )
% 0.24/0.55 => ( ( hF_Mirabelle_RepFun @ A @ F )
% 0.24/0.55 = ( hF_Mirabelle_RepFun @ B4 @ G ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % RepFun_cong
% 0.24/0.55 thf(fact_29_Replace__cong,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,P: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,Q: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( A = B4 )
% 0.24/0.55 => ( ! [X3: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ X3 @ B4 )
% 0.24/0.55 => ( ( P @ X3 @ Y5 )
% 0.24/0.55 = ( Q @ X3 @ Y5 ) ) )
% 0.24/0.55 => ( ( hF_Mirabelle_Replace @ A @ P )
% 0.24/0.55 = ( hF_Mirabelle_Replace @ B4 @ Q ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % Replace_cong
% 0.24/0.55 thf(fact_30_hmem__Sup__ne,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ X @ Y3 )
% 0.24/0.55 => ( ( hF_Mirabelle_HUnion @ X )
% 0.24/0.55 != Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % hmem_Sup_ne
% 0.24/0.55 thf(fact_31_Abs__hf__inverse,axiom,
% 0.24/0.55 ! [Y3: nat] :
% 0.24/0.55 ( ( member_nat @ Y3 @ top_top_set_nat )
% 0.24/0.55 => ( ( hF_Mirabelle_Rep_hf @ ( hF_Mirabelle_Abs_hf @ Y3 ) )
% 0.24/0.55 = Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % Abs_hf_inverse
% 0.24/0.55 thf(fact_32_zero__notin__hpair,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ~ ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mirabelle_hpair @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % zero_notin_hpair
% 0.24/0.55 thf(fact_33_hmem__def,axiom,
% 0.24/0.55 ( hF_Mirabelle_hmem
% 0.24/0.55 = ( ^ [A4: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A4 @ ( hF_Mirabelle_hfset @ B3 ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hmem_def
% 0.24/0.55 thf(fact_34_HCollect__hempty,axiom,
% 0.24/0.55 ! [P: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( hF_Mir818139703ollect @ P @ zero_z189798548lle_hf )
% 0.24/0.55 = zero_z189798548lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % HCollect_hempty
% 0.24/0.55 thf(fact_35_HUnion__hempty,axiom,
% 0.24/0.55 ( ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf )
% 0.24/0.55 = zero_z189798548lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % HUnion_hempty
% 0.24/0.55 thf(fact_36_Replace__0,axiom,
% 0.24/0.55 ! [R3: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ R3 )
% 0.24/0.55 = zero_z189798548lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % Replace_0
% 0.24/0.55 thf(fact_37_RepFun__0,axiom,
% 0.24/0.55 ! [F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_RepFun @ zero_z189798548lle_hf @ F )
% 0.24/0.55 = zero_z189798548lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % RepFun_0
% 0.24/0.55 thf(fact_38_RepFun__hinsert,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_RepFun @ ( hF_Mirabelle_hinsert @ A2 @ B ) @ F )
% 0.24/0.55 = ( hF_Mirabelle_hinsert @ ( F @ A2 ) @ ( hF_Mirabelle_RepFun @ B @ F ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % RepFun_hinsert
% 0.24/0.55 thf(fact_39_hrelation__hunion,axiom,
% 0.24/0.55 ! [F: hF_Mirabelle_hf,G: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mir434065167lation @ ( sup_su638957495lle_hf @ F @ G ) )
% 0.24/0.55 = ( ( hF_Mir434065167lation @ F )
% 0.24/0.55 & ( hF_Mir434065167lation @ G ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hrelation_hunion
% 0.24/0.55 thf(fact_40_hmem__hinsert,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ A2 @ ( hF_Mirabelle_hinsert @ B @ C ) )
% 0.24/0.55 = ( ( A2 = B )
% 0.24/0.55 | ( hF_Mirabelle_hmem @ A2 @ C ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hmem_hinsert
% 0.24/0.55 thf(fact_41_singleton__eq__iff,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( ( hF_Mirabelle_hinsert @ A2 @ zero_z189798548lle_hf )
% 0.24/0.55 = ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) )
% 0.24/0.55 = ( A2 = B ) ) ).
% 0.24/0.55
% 0.24/0.55 % singleton_eq_iff
% 0.24/0.55 thf(fact_42_hunion__iff,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ X @ ( sup_su638957495lle_hf @ A2 @ B ) )
% 0.24/0.55 = ( ( hF_Mirabelle_hmem @ X @ A2 )
% 0.24/0.55 | ( hF_Mirabelle_hmem @ X @ B ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hunion_iff
% 0.24/0.55 thf(fact_43_hunion__hempty__left,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ zero_z189798548lle_hf @ A )
% 0.24/0.55 = A ) ).
% 0.24/0.55
% 0.24/0.55 % hunion_hempty_left
% 0.24/0.55 thf(fact_44_mem__Collect__eq,axiom,
% 0.24/0.55 ! [A2: nat,P: nat > $o] :
% 0.24/0.55 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 0.24/0.55 = ( P @ A2 ) ) ).
% 0.24/0.55
% 0.24/0.55 % mem_Collect_eq
% 0.24/0.55 thf(fact_45_mem__Collect__eq,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( member1367349282lle_hf @ A2 @ ( collec2046588256lle_hf @ P ) )
% 0.24/0.55 = ( P @ A2 ) ) ).
% 0.24/0.55
% 0.24/0.55 % mem_Collect_eq
% 0.24/0.55 thf(fact_46_Collect__mem__eq,axiom,
% 0.24/0.55 ! [A: set_nat] :
% 0.24/0.55 ( ( collect_nat
% 0.24/0.55 @ ^ [X2: nat] : ( member_nat @ X2 @ A ) )
% 0.24/0.55 = A ) ).
% 0.24/0.55
% 0.24/0.55 % Collect_mem_eq
% 0.24/0.55 thf(fact_47_Collect__mem__eq,axiom,
% 0.24/0.55 ! [A: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( collec2046588256lle_hf
% 0.24/0.55 @ ^ [X2: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X2 @ A ) )
% 0.24/0.55 = A ) ).
% 0.24/0.55
% 0.24/0.55 % Collect_mem_eq
% 0.24/0.55 thf(fact_48_Collect__cong,axiom,
% 0.24/0.55 ! [P: hF_Mirabelle_hf > $o,Q: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ! [X3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( P @ X3 )
% 0.24/0.55 = ( Q @ X3 ) )
% 0.24/0.55 => ( ( collec2046588256lle_hf @ P )
% 0.24/0.55 = ( collec2046588256lle_hf @ Q ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % Collect_cong
% 0.24/0.55 thf(fact_49_Collect__cong,axiom,
% 0.24/0.55 ! [P: nat > $o,Q: nat > $o] :
% 0.24/0.55 ( ! [X3: nat] :
% 0.24/0.55 ( ( P @ X3 )
% 0.24/0.55 = ( Q @ X3 ) )
% 0.24/0.55 => ( ( collect_nat @ P )
% 0.24/0.55 = ( collect_nat @ Q ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % Collect_cong
% 0.24/0.55 thf(fact_50_hunion__hempty__right,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
% 0.24/0.55 = A ) ).
% 0.24/0.55
% 0.24/0.55 % hunion_hempty_right
% 0.24/0.55 thf(fact_51_RepFun__hunion,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_RepFun @ ( sup_su638957495lle_hf @ A @ B4 ) @ F )
% 0.24/0.55 = ( sup_su638957495lle_hf @ ( hF_Mirabelle_RepFun @ A @ F ) @ ( hF_Mirabelle_RepFun @ B4 @ F ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % RepFun_hunion
% 0.24/0.55 thf(fact_52_HUnion__hunion,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B4 ) )
% 0.24/0.55 = ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B4 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % HUnion_hunion
% 0.24/0.55 thf(fact_53_Replace__hunion,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,R3: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( hF_Mirabelle_Replace @ ( sup_su638957495lle_hf @ A @ B4 ) @ R3 )
% 0.24/0.55 = ( sup_su638957495lle_hf @ ( hF_Mirabelle_Replace @ A @ R3 ) @ ( hF_Mirabelle_Replace @ B4 @ R3 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % Replace_hunion
% 0.24/0.55 thf(fact_54_HUnion__hinsert,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hinsert @ A2 @ A ) )
% 0.24/0.55 = ( sup_su638957495lle_hf @ A2 @ ( hF_Mirabelle_HUnion @ A ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % HUnion_hinsert
% 0.24/0.55 thf(fact_55_hf__induct__ax,axiom,
% 0.24/0.55 ! [P: hF_Mirabelle_hf > $o,X: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( P @ zero_z189798548lle_hf )
% 0.24/0.55 => ( ! [X3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( P @ X3 )
% 0.24/0.55 => ! [Y5: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( P @ Y5 )
% 0.24/0.55 => ( P @ ( hF_Mirabelle_hinsert @ Y5 @ X3 ) ) ) )
% 0.24/0.55 => ( P @ X ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hf_induct_ax
% 0.24/0.55 thf(fact_56_hinsert__eq__sup,axiom,
% 0.24/0.55 ( hF_Mirabelle_hinsert
% 0.24/0.55 = ( ^ [A4: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B3 @ ( hF_Mirabelle_hinsert @ A4 @ zero_z189798548lle_hf ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hinsert_eq_sup
% 0.24/0.55 thf(fact_57_hinsert__commute,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hinsert @ X @ ( hF_Mirabelle_hinsert @ Y3 @ Z ) )
% 0.24/0.55 = ( hF_Mirabelle_hinsert @ Y3 @ ( hF_Mirabelle_hinsert @ X @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hinsert_commute
% 0.24/0.55 thf(fact_58_HF__Mirabelle__glliljednj_Odoubleton__eq__iff,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( ( hF_Mirabelle_hinsert @ A2 @ ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) )
% 0.24/0.55 = ( hF_Mirabelle_hinsert @ C @ ( hF_Mirabelle_hinsert @ D @ zero_z189798548lle_hf ) ) )
% 0.24/0.55 = ( ( ( A2 = C )
% 0.24/0.55 & ( B = D ) )
% 0.24/0.55 | ( ( A2 = D )
% 0.24/0.55 & ( B = C ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % HF_Mirabelle_glliljednj.doubleton_eq_iff
% 0.24/0.55 thf(fact_59_hinsert__nonempty,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hinsert @ A2 @ A )
% 0.24/0.55 != zero_z189798548lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % hinsert_nonempty
% 0.24/0.55 thf(fact_60_hunion__hinsert__left,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,A: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_hinsert @ X @ A ) @ B4 )
% 0.24/0.55 = ( hF_Mirabelle_hinsert @ X @ ( sup_su638957495lle_hf @ A @ B4 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hunion_hinsert_left
% 0.24/0.55 thf(fact_61_hunion__hinsert__right,axiom,
% 0.24/0.55 ! [B4: hF_Mirabelle_hf,X: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ B4 @ ( hF_Mirabelle_hinsert @ X @ A ) )
% 0.24/0.55 = ( hF_Mirabelle_hinsert @ X @ ( sup_su638957495lle_hf @ B4 @ A ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hunion_hinsert_right
% 0.24/0.55 thf(fact_62_hf__cases,axiom,
% 0.24/0.55 ! [Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( Y3 != zero_z189798548lle_hf )
% 0.24/0.55 => ~ ! [A5: hF_Mirabelle_hf,B5: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( Y3
% 0.24/0.55 = ( hF_Mirabelle_hinsert @ A5 @ B5 ) )
% 0.24/0.55 => ( hF_Mirabelle_hmem @ A5 @ B5 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hf_cases
% 0.24/0.55 thf(fact_63_hf__induct,axiom,
% 0.24/0.55 ! [P: hF_Mirabelle_hf > $o,Z: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( P @ zero_z189798548lle_hf )
% 0.24/0.55 => ( ! [X3: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( P @ X3 )
% 0.24/0.55 => ( ( P @ Y5 )
% 0.24/0.55 => ( ~ ( hF_Mirabelle_hmem @ X3 @ Y5 )
% 0.24/0.55 => ( P @ ( hF_Mirabelle_hinsert @ X3 @ Y5 ) ) ) ) )
% 0.24/0.55 => ( P @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hf_induct
% 0.24/0.55 thf(fact_64_hpair__def,axiom,
% 0.24/0.55 ( hF_Mirabelle_hpair
% 0.24/0.55 = ( ^ [A4: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A4 @ zero_z189798548lle_hf ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A4 @ ( hF_Mirabelle_hinsert @ B3 @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hpair_def
% 0.24/0.55 thf(fact_65_hpair__def_H,axiom,
% 0.24/0.55 ( hF_Mirabelle_hpair
% 0.24/0.55 = ( ^ [A4: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A4 @ ( hF_Mirabelle_hinsert @ A4 @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A4 @ ( hF_Mirabelle_hinsert @ B3 @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hpair_def'
% 0.24/0.55 thf(fact_66_hinsert__iff,axiom,
% 0.24/0.55 ! [Z: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( Z
% 0.24/0.55 = ( hF_Mirabelle_hinsert @ Y3 @ X ) )
% 0.24/0.55 = ( ! [U2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ U2 @ Z )
% 0.24/0.55 = ( ( hF_Mirabelle_hmem @ U2 @ X )
% 0.24/0.55 | ( U2 = Y3 ) ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hinsert_iff
% 0.24/0.55 thf(fact_67_hemptyE,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf] :
% 0.24/0.55 ~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % hemptyE
% 0.24/0.55 thf(fact_68_hempty__iff,axiom,
% 0.24/0.55 ! [Z: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( Z = zero_z189798548lle_hf )
% 0.24/0.55 = ( ! [X2: hF_Mirabelle_hf] :
% 0.24/0.55 ~ ( hF_Mirabelle_hmem @ X2 @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % hempty_iff
% 0.24/0.55 thf(fact_69_hmem__hempty,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf] :
% 0.24/0.55 ~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % hmem_hempty
% 0.24/0.55 thf(fact_70_hpair__nonzero,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hpair @ X @ Y3 )
% 0.24/0.55 != zero_z189798548lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % hpair_nonzero
% 0.24/0.55 thf(fact_71_Rep__hf,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf] : ( member_nat @ ( hF_Mirabelle_Rep_hf @ X ) @ top_top_set_nat ) ).
% 0.24/0.55
% 0.24/0.55 % Rep_hf
% 0.24/0.55 thf(fact_72_Rep__hf__cases,axiom,
% 0.24/0.55 ! [Y3: nat] :
% 0.24/0.55 ( ( member_nat @ Y3 @ top_top_set_nat )
% 0.24/0.55 => ~ ! [X3: hF_Mirabelle_hf] :
% 0.24/0.55 ( Y3
% 0.24/0.55 != ( hF_Mirabelle_Rep_hf @ X3 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % Rep_hf_cases
% 0.24/0.55 thf(fact_73_Rep__hf__induct,axiom,
% 0.24/0.55 ! [Y3: nat,P: nat > $o] :
% 0.24/0.55 ( ( member_nat @ Y3 @ top_top_set_nat )
% 0.24/0.55 => ( ! [X3: hF_Mirabelle_hf] : ( P @ ( hF_Mirabelle_Rep_hf @ X3 ) )
% 0.24/0.55 => ( P @ Y3 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % Rep_hf_induct
% 0.24/0.55 thf(fact_74_Abs__hf__cases,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf] :
% 0.24/0.55 ~ ! [Y5: nat] :
% 0.24/0.55 ( ( X
% 0.24/0.55 = ( hF_Mirabelle_Abs_hf @ Y5 ) )
% 0.24/0.55 => ~ ( member_nat @ Y5 @ top_top_set_nat ) ) ).
% 0.24/0.55
% 0.24/0.55 % Abs_hf_cases
% 0.24/0.55 thf(fact_75_Abs__hf__induct,axiom,
% 0.24/0.55 ! [P: hF_Mirabelle_hf > $o,X: hF_Mirabelle_hf] :
% 0.24/0.55 ( ! [Y5: nat] :
% 0.24/0.55 ( ( member_nat @ Y5 @ top_top_set_nat )
% 0.24/0.55 => ( P @ ( hF_Mirabelle_Abs_hf @ Y5 ) ) )
% 0.24/0.55 => ( P @ X ) ) ).
% 0.24/0.55
% 0.24/0.55 % Abs_hf_induct
% 0.24/0.55 thf(fact_76_Abs__hf__inject,axiom,
% 0.24/0.55 ! [X: nat,Y3: nat] :
% 0.24/0.55 ( ( member_nat @ X @ top_top_set_nat )
% 0.24/0.55 => ( ( member_nat @ Y3 @ top_top_set_nat )
% 0.24/0.55 => ( ( ( hF_Mirabelle_Abs_hf @ X )
% 0.24/0.55 = ( hF_Mirabelle_Abs_hf @ Y3 ) )
% 0.24/0.55 = ( X = Y3 ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % Abs_hf_inject
% 0.24/0.55 thf(fact_77_hrelation__0,axiom,
% 0.24/0.55 hF_Mir434065167lation @ zero_z189798548lle_hf ).
% 0.24/0.55
% 0.24/0.55 % hrelation_0
% 0.24/0.55 thf(fact_78_sup__top__left,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ top_to489427057lle_hf @ X )
% 0.24/0.55 = top_to489427057lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % sup_top_left
% 0.24/0.55 thf(fact_79_sup__top__left,axiom,
% 0.24/0.55 ! [X: nat > $o] :
% 0.24/0.55 ( ( sup_sup_nat_o @ top_top_nat_o @ X )
% 0.24/0.55 = top_top_nat_o ) ).
% 0.24/0.55
% 0.24/0.55 % sup_top_left
% 0.24/0.55 thf(fact_80_sup__top__left,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( sup_su1199008216e_hf_o @ top_to22270292e_hf_o @ X )
% 0.24/0.55 = top_to22270292e_hf_o ) ).
% 0.24/0.55
% 0.24/0.55 % sup_top_left
% 0.24/0.55 thf(fact_81_sup__top__left,axiom,
% 0.24/0.55 ! [X: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ top_top_set_nat @ X )
% 0.24/0.55 = top_top_set_nat ) ).
% 0.24/0.55
% 0.24/0.55 % sup_top_left
% 0.24/0.55 thf(fact_82_sup__top__right,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ X @ top_to489427057lle_hf )
% 0.24/0.55 = top_to489427057lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % sup_top_right
% 0.24/0.55 thf(fact_83_sup__top__right,axiom,
% 0.24/0.55 ! [X: nat > $o] :
% 0.24/0.55 ( ( sup_sup_nat_o @ X @ top_top_nat_o )
% 0.24/0.55 = top_top_nat_o ) ).
% 0.24/0.55
% 0.24/0.55 % sup_top_right
% 0.24/0.55 thf(fact_84_sup__top__right,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( sup_su1199008216e_hf_o @ X @ top_to22270292e_hf_o )
% 0.24/0.55 = top_to22270292e_hf_o ) ).
% 0.24/0.55
% 0.24/0.55 % sup_top_right
% 0.24/0.55 thf(fact_85_sup__top__right,axiom,
% 0.24/0.55 ! [X: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ X @ top_top_set_nat )
% 0.24/0.55 = top_top_set_nat ) ).
% 0.24/0.55
% 0.24/0.55 % sup_top_right
% 0.24/0.55 thf(fact_86_HInter__iff,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( A != zero_z189798548lle_hf )
% 0.24/0.55 => ( ( hF_Mirabelle_hmem @ X @ ( hF_Mirabelle_HInter @ A ) )
% 0.24/0.55 = ( ! [Y: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( hF_Mirabelle_hmem @ Y @ A )
% 0.24/0.55 => ( hF_Mirabelle_hmem @ X @ Y ) ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % HInter_iff
% 0.24/0.55 thf(fact_87_sup_Oidem,axiom,
% 0.24/0.55 ! [A2: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ A2 @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % sup.idem
% 0.24/0.55 thf(fact_88_sup_Oidem,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ A2 @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % sup.idem
% 0.24/0.55 thf(fact_89_sup_Oidem,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ A2 @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % sup.idem
% 0.24/0.55 thf(fact_90_sup__idem,axiom,
% 0.24/0.55 ! [X: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ X @ X )
% 0.24/0.55 = X ) ).
% 0.24/0.55
% 0.24/0.55 % sup_idem
% 0.24/0.55 thf(fact_91_sup__idem,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ X @ X )
% 0.24/0.55 = X ) ).
% 0.24/0.55
% 0.24/0.55 % sup_idem
% 0.24/0.55 thf(fact_92_sup__idem,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ X @ X )
% 0.24/0.55 = X ) ).
% 0.24/0.55
% 0.24/0.55 % sup_idem
% 0.24/0.55 thf(fact_93_sup_Oleft__idem,axiom,
% 0.24/0.55 ! [A2: set_nat,B: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.24/0.55 = ( sup_sup_set_nat @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.left_idem
% 0.24/0.55 thf(fact_94_sup_Oleft__idem,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ A2 @ ( sup_su1790843629lle_hf @ A2 @ B ) )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.left_idem
% 0.24/0.55 thf(fact_95_sup_Oleft__idem,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ A2 @ ( sup_su638957495lle_hf @ A2 @ B ) )
% 0.24/0.55 = ( sup_su638957495lle_hf @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.left_idem
% 0.24/0.55 thf(fact_96_sup__left__idem,axiom,
% 0.24/0.55 ! [X: set_nat,Y3: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y3 ) )
% 0.24/0.55 = ( sup_sup_set_nat @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_left_idem
% 0.24/0.55 thf(fact_97_sup__left__idem,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ X @ ( sup_su1790843629lle_hf @ X @ Y3 ) )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_left_idem
% 0.24/0.55 thf(fact_98_sup__left__idem,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ X @ Y3 ) )
% 0.24/0.55 = ( sup_su638957495lle_hf @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_left_idem
% 0.24/0.55 thf(fact_99_sup_Oright__idem,axiom,
% 0.24/0.55 ! [A2: set_nat,B: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B ) @ B )
% 0.24/0.55 = ( sup_sup_set_nat @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.right_idem
% 0.24/0.55 thf(fact_100_sup_Oright__idem,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ ( sup_su1790843629lle_hf @ A2 @ B ) @ B )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.right_idem
% 0.24/0.55 thf(fact_101_sup_Oright__idem,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A2 @ B ) @ B )
% 0.24/0.55 = ( sup_su638957495lle_hf @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.right_idem
% 0.24/0.55 thf(fact_102_HInter__hempty,axiom,
% 0.24/0.55 ( ( hF_Mirabelle_HInter @ zero_z189798548lle_hf )
% 0.24/0.55 = zero_z189798548lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % HInter_hempty
% 0.24/0.55 thf(fact_103_sup__left__commute,axiom,
% 0.24/0.55 ! [X: set_nat,Y3: set_nat,Z: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y3 @ Z ) )
% 0.24/0.55 = ( sup_sup_set_nat @ Y3 @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_left_commute
% 0.24/0.55 thf(fact_104_sup__left__commute,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf,Z: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ X @ ( sup_su1790843629lle_hf @ Y3 @ Z ) )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ Y3 @ ( sup_su1790843629lle_hf @ X @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_left_commute
% 0.24/0.55 thf(fact_105_sup__left__commute,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ Y3 @ Z ) )
% 0.24/0.55 = ( sup_su638957495lle_hf @ Y3 @ ( sup_su638957495lle_hf @ X @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_left_commute
% 0.24/0.55 thf(fact_106_sup_Oleft__commute,axiom,
% 0.24/0.55 ! [B: set_nat,A2: set_nat,C: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A2 @ C ) )
% 0.24/0.55 = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.left_commute
% 0.24/0.55 thf(fact_107_sup_Oleft__commute,axiom,
% 0.24/0.55 ! [B: set_HF_Mirabelle_hf,A2: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ B @ ( sup_su1790843629lle_hf @ A2 @ C ) )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ A2 @ ( sup_su1790843629lle_hf @ B @ C ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.left_commute
% 0.24/0.55 thf(fact_108_sup_Oleft__commute,axiom,
% 0.24/0.55 ! [B: hF_Mirabelle_hf,A2: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A2 @ C ) )
% 0.24/0.55 = ( sup_su638957495lle_hf @ A2 @ ( sup_su638957495lle_hf @ B @ C ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.left_commute
% 0.24/0.55 thf(fact_109_sup__commute,axiom,
% 0.24/0.55 ( sup_sup_set_nat
% 0.24/0.55 = ( ^ [X2: set_nat,Y: set_nat] : ( sup_sup_set_nat @ Y @ X2 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_commute
% 0.24/0.55 thf(fact_110_sup__commute,axiom,
% 0.24/0.55 ( sup_su1790843629lle_hf
% 0.24/0.55 = ( ^ [X2: set_HF_Mirabelle_hf,Y: set_HF_Mirabelle_hf] : ( sup_su1790843629lle_hf @ Y @ X2 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_commute
% 0.24/0.55 thf(fact_111_sup__commute,axiom,
% 0.24/0.55 ( sup_su638957495lle_hf
% 0.24/0.55 = ( ^ [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ Y @ X2 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_commute
% 0.24/0.55 thf(fact_112_sup_Ocommute,axiom,
% 0.24/0.55 ( sup_sup_set_nat
% 0.24/0.55 = ( ^ [A4: set_nat,B3: set_nat] : ( sup_sup_set_nat @ B3 @ A4 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.commute
% 0.24/0.55 thf(fact_113_sup_Ocommute,axiom,
% 0.24/0.55 ( sup_su1790843629lle_hf
% 0.24/0.55 = ( ^ [A4: set_HF_Mirabelle_hf,B3: set_HF_Mirabelle_hf] : ( sup_su1790843629lle_hf @ B3 @ A4 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.commute
% 0.24/0.55 thf(fact_114_sup_Ocommute,axiom,
% 0.24/0.55 ( sup_su638957495lle_hf
% 0.24/0.55 = ( ^ [A4: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B3 @ A4 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.commute
% 0.24/0.55 thf(fact_115_sup__assoc,axiom,
% 0.24/0.55 ! [X: set_nat,Y3: set_nat,Z: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y3 ) @ Z )
% 0.24/0.55 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y3 @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_assoc
% 0.24/0.55 thf(fact_116_sup__assoc,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf,Z: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ ( sup_su1790843629lle_hf @ X @ Y3 ) @ Z )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ X @ ( sup_su1790843629lle_hf @ Y3 @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_assoc
% 0.24/0.55 thf(fact_117_sup__assoc,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ X @ Y3 ) @ Z )
% 0.24/0.55 = ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ Y3 @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup_assoc
% 0.24/0.55 thf(fact_118_sup_Oassoc,axiom,
% 0.24/0.55 ! [A2: set_nat,B: set_nat,C: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B ) @ C )
% 0.24/0.55 = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.assoc
% 0.24/0.55 thf(fact_119_sup_Oassoc,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ ( sup_su1790843629lle_hf @ A2 @ B ) @ C )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ A2 @ ( sup_su1790843629lle_hf @ B @ C ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.assoc
% 0.24/0.55 thf(fact_120_sup_Oassoc,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A2 @ B ) @ C )
% 0.24/0.55 = ( sup_su638957495lle_hf @ A2 @ ( sup_su638957495lle_hf @ B @ C ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % sup.assoc
% 0.24/0.55 thf(fact_121_boolean__algebra__cancel_Osup2,axiom,
% 0.24/0.55 ! [B4: set_nat,K: set_nat,B: set_nat,A2: set_nat] :
% 0.24/0.55 ( ( B4
% 0.24/0.55 = ( sup_sup_set_nat @ K @ B ) )
% 0.24/0.55 => ( ( sup_sup_set_nat @ A2 @ B4 )
% 0.24/0.55 = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A2 @ B ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % boolean_algebra_cancel.sup2
% 0.24/0.55 thf(fact_122_boolean__algebra__cancel_Osup2,axiom,
% 0.24/0.55 ! [B4: set_HF_Mirabelle_hf,K: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf,A2: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( B4
% 0.24/0.55 = ( sup_su1790843629lle_hf @ K @ B ) )
% 0.24/0.55 => ( ( sup_su1790843629lle_hf @ A2 @ B4 )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ K @ ( sup_su1790843629lle_hf @ A2 @ B ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % boolean_algebra_cancel.sup2
% 0.24/0.55 thf(fact_123_boolean__algebra__cancel_Osup2,axiom,
% 0.24/0.55 ! [B4: hF_Mirabelle_hf,K: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( B4
% 0.24/0.55 = ( sup_su638957495lle_hf @ K @ B ) )
% 0.24/0.55 => ( ( sup_su638957495lle_hf @ A2 @ B4 )
% 0.24/0.55 = ( sup_su638957495lle_hf @ K @ ( sup_su638957495lle_hf @ A2 @ B ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % boolean_algebra_cancel.sup2
% 0.24/0.55 thf(fact_124_boolean__algebra__cancel_Osup1,axiom,
% 0.24/0.55 ! [A: set_nat,K: set_nat,A2: set_nat,B: set_nat] :
% 0.24/0.55 ( ( A
% 0.24/0.55 = ( sup_sup_set_nat @ K @ A2 ) )
% 0.24/0.55 => ( ( sup_sup_set_nat @ A @ B )
% 0.24/0.55 = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A2 @ B ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % boolean_algebra_cancel.sup1
% 0.24/0.55 thf(fact_125_boolean__algebra__cancel_Osup1,axiom,
% 0.24/0.55 ! [A: set_HF_Mirabelle_hf,K: set_HF_Mirabelle_hf,A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( A
% 0.24/0.55 = ( sup_su1790843629lle_hf @ K @ A2 ) )
% 0.24/0.55 => ( ( sup_su1790843629lle_hf @ A @ B )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ K @ ( sup_su1790843629lle_hf @ A2 @ B ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % boolean_algebra_cancel.sup1
% 0.24/0.55 thf(fact_126_boolean__algebra__cancel_Osup1,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf,K: hF_Mirabelle_hf,A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( A
% 0.24/0.55 = ( sup_su638957495lle_hf @ K @ A2 ) )
% 0.24/0.55 => ( ( sup_su638957495lle_hf @ A @ B )
% 0.24/0.55 = ( sup_su638957495lle_hf @ K @ ( sup_su638957495lle_hf @ A2 @ B ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % boolean_algebra_cancel.sup1
% 0.24/0.55 thf(fact_127_inf__sup__aci_I5_J,axiom,
% 0.24/0.55 ( sup_sup_set_nat
% 0.24/0.55 = ( ^ [X2: set_nat,Y: set_nat] : ( sup_sup_set_nat @ Y @ X2 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(5)
% 0.24/0.55 thf(fact_128_inf__sup__aci_I5_J,axiom,
% 0.24/0.55 ( sup_su1790843629lle_hf
% 0.24/0.55 = ( ^ [X2: set_HF_Mirabelle_hf,Y: set_HF_Mirabelle_hf] : ( sup_su1790843629lle_hf @ Y @ X2 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(5)
% 0.24/0.55 thf(fact_129_inf__sup__aci_I5_J,axiom,
% 0.24/0.55 ( sup_su638957495lle_hf
% 0.24/0.55 = ( ^ [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ Y @ X2 ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(5)
% 0.24/0.55 thf(fact_130_inf__sup__aci_I6_J,axiom,
% 0.24/0.55 ! [X: set_nat,Y3: set_nat,Z: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y3 ) @ Z )
% 0.24/0.55 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y3 @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(6)
% 0.24/0.55 thf(fact_131_inf__sup__aci_I6_J,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf,Z: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ ( sup_su1790843629lle_hf @ X @ Y3 ) @ Z )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ X @ ( sup_su1790843629lle_hf @ Y3 @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(6)
% 0.24/0.55 thf(fact_132_inf__sup__aci_I6_J,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ X @ Y3 ) @ Z )
% 0.24/0.55 = ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ Y3 @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(6)
% 0.24/0.55 thf(fact_133_inf__sup__aci_I7_J,axiom,
% 0.24/0.55 ! [X: set_nat,Y3: set_nat,Z: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y3 @ Z ) )
% 0.24/0.55 = ( sup_sup_set_nat @ Y3 @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(7)
% 0.24/0.55 thf(fact_134_inf__sup__aci_I7_J,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf,Z: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ X @ ( sup_su1790843629lle_hf @ Y3 @ Z ) )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ Y3 @ ( sup_su1790843629lle_hf @ X @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(7)
% 0.24/0.55 thf(fact_135_inf__sup__aci_I7_J,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ Y3 @ Z ) )
% 0.24/0.55 = ( sup_su638957495lle_hf @ Y3 @ ( sup_su638957495lle_hf @ X @ Z ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(7)
% 0.24/0.55 thf(fact_136_inf__sup__aci_I8_J,axiom,
% 0.24/0.55 ! [X: set_nat,Y3: set_nat] :
% 0.24/0.55 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y3 ) )
% 0.24/0.55 = ( sup_sup_set_nat @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(8)
% 0.24/0.55 thf(fact_137_inf__sup__aci_I8_J,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su1790843629lle_hf @ X @ ( sup_su1790843629lle_hf @ X @ Y3 ) )
% 0.24/0.55 = ( sup_su1790843629lle_hf @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(8)
% 0.24/0.55 thf(fact_138_inf__sup__aci_I8_J,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ X @ Y3 ) )
% 0.24/0.55 = ( sup_su638957495lle_hf @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_sup_aci(8)
% 0.24/0.55 thf(fact_139_iso__tuple__UNIV__I,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X @ top_to489427057lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % iso_tuple_UNIV_I
% 0.24/0.55 thf(fact_140_iso__tuple__UNIV__I,axiom,
% 0.24/0.55 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.24/0.55
% 0.24/0.55 % iso_tuple_UNIV_I
% 0.24/0.55 thf(fact_141_UNIV__I,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X @ top_to489427057lle_hf ) ).
% 0.24/0.55
% 0.24/0.55 % UNIV_I
% 0.24/0.55 thf(fact_142_UNIV__I,axiom,
% 0.24/0.55 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.24/0.55
% 0.24/0.55 % UNIV_I
% 0.24/0.55 thf(fact_143_top__apply,axiom,
% 0.24/0.55 ( top_top_nat_o
% 0.24/0.55 = ( ^ [X2: nat] : top_top_o ) ) ).
% 0.24/0.55
% 0.24/0.55 % top_apply
% 0.24/0.55 thf(fact_144_top__apply,axiom,
% 0.24/0.55 ( top_to22270292e_hf_o
% 0.24/0.55 = ( ^ [X2: hF_Mirabelle_hf] : top_top_o ) ) ).
% 0.24/0.55
% 0.24/0.55 % top_apply
% 0.24/0.55 thf(fact_145_HInter__hinsert,axiom,
% 0.24/0.55 ! [A: hF_Mirabelle_hf,A2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( A != zero_z189798548lle_hf )
% 0.24/0.55 => ( ( hF_Mirabelle_HInter @ ( hF_Mirabelle_hinsert @ A2 @ A ) )
% 0.24/0.55 = ( inf_in956532509lle_hf @ A2 @ ( hF_Mirabelle_HInter @ A ) ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % HInter_hinsert
% 0.24/0.55 thf(fact_146_type__definition__hf,axiom,
% 0.24/0.55 type_d1794767497hf_nat @ hF_Mirabelle_Rep_hf @ hF_Mirabelle_Abs_hf @ top_top_set_nat ).
% 0.24/0.55
% 0.24/0.55 % type_definition_hf
% 0.24/0.55 thf(fact_147_inf__right__idem,axiom,
% 0.24/0.55 ! [X: set_nat,Y3: set_nat] :
% 0.24/0.55 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y3 ) @ Y3 )
% 0.24/0.55 = ( inf_inf_set_nat @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_right_idem
% 0.24/0.55 thf(fact_148_inf__right__idem,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in923488851lle_hf @ ( inf_in923488851lle_hf @ X @ Y3 ) @ Y3 )
% 0.24/0.55 = ( inf_in923488851lle_hf @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_right_idem
% 0.24/0.55 thf(fact_149_inf__right__idem,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ X @ Y3 ) @ Y3 )
% 0.24/0.55 = ( inf_in956532509lle_hf @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_right_idem
% 0.24/0.55 thf(fact_150_inf_Oright__idem,axiom,
% 0.24/0.55 ! [A2: set_nat,B: set_nat] :
% 0.24/0.55 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A2 @ B ) @ B )
% 0.24/0.55 = ( inf_inf_set_nat @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf.right_idem
% 0.24/0.55 thf(fact_151_inf_Oright__idem,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in923488851lle_hf @ ( inf_in923488851lle_hf @ A2 @ B ) @ B )
% 0.24/0.55 = ( inf_in923488851lle_hf @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf.right_idem
% 0.24/0.55 thf(fact_152_inf_Oright__idem,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A2 @ B ) @ B )
% 0.24/0.55 = ( inf_in956532509lle_hf @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf.right_idem
% 0.24/0.55 thf(fact_153_inf__left__idem,axiom,
% 0.24/0.55 ! [X: set_nat,Y3: set_nat] :
% 0.24/0.55 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y3 ) )
% 0.24/0.55 = ( inf_inf_set_nat @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_left_idem
% 0.24/0.55 thf(fact_154_inf__left__idem,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in923488851lle_hf @ X @ ( inf_in923488851lle_hf @ X @ Y3 ) )
% 0.24/0.55 = ( inf_in923488851lle_hf @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_left_idem
% 0.24/0.55 thf(fact_155_inf__left__idem,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ X @ Y3 ) )
% 0.24/0.55 = ( inf_in956532509lle_hf @ X @ Y3 ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_left_idem
% 0.24/0.55 thf(fact_156_inf_Oleft__idem,axiom,
% 0.24/0.55 ! [A2: set_nat,B: set_nat] :
% 0.24/0.55 ( ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ A2 @ B ) )
% 0.24/0.55 = ( inf_inf_set_nat @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf.left_idem
% 0.24/0.55 thf(fact_157_inf_Oleft__idem,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in923488851lle_hf @ A2 @ ( inf_in923488851lle_hf @ A2 @ B ) )
% 0.24/0.55 = ( inf_in923488851lle_hf @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf.left_idem
% 0.24/0.55 thf(fact_158_inf_Oleft__idem,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in956532509lle_hf @ A2 @ ( inf_in956532509lle_hf @ A2 @ B ) )
% 0.24/0.55 = ( inf_in956532509lle_hf @ A2 @ B ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf.left_idem
% 0.24/0.55 thf(fact_159_inf__idem,axiom,
% 0.24/0.55 ! [X: set_nat] :
% 0.24/0.55 ( ( inf_inf_set_nat @ X @ X )
% 0.24/0.55 = X ) ).
% 0.24/0.55
% 0.24/0.55 % inf_idem
% 0.24/0.55 thf(fact_160_inf__idem,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in923488851lle_hf @ X @ X )
% 0.24/0.55 = X ) ).
% 0.24/0.55
% 0.24/0.55 % inf_idem
% 0.24/0.55 thf(fact_161_inf__idem,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in956532509lle_hf @ X @ X )
% 0.24/0.55 = X ) ).
% 0.24/0.55
% 0.24/0.55 % inf_idem
% 0.24/0.55 thf(fact_162_inf_Oidem,axiom,
% 0.24/0.55 ! [A2: set_nat] :
% 0.24/0.55 ( ( inf_inf_set_nat @ A2 @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf.idem
% 0.24/0.55 thf(fact_163_inf_Oidem,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in923488851lle_hf @ A2 @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf.idem
% 0.24/0.55 thf(fact_164_inf_Oidem,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in956532509lle_hf @ A2 @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf.idem
% 0.24/0.55 thf(fact_165_inf__top_Oright__neutral,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in923488851lle_hf @ A2 @ top_to489427057lle_hf )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.right_neutral
% 0.24/0.55 thf(fact_166_inf__top_Oright__neutral,axiom,
% 0.24/0.55 ! [A2: nat > $o] :
% 0.24/0.55 ( ( inf_inf_nat_o @ A2 @ top_top_nat_o )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.right_neutral
% 0.24/0.55 thf(fact_167_inf__top_Oright__neutral,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( inf_in307783154e_hf_o @ A2 @ top_to22270292e_hf_o )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.right_neutral
% 0.24/0.55 thf(fact_168_inf__top_Oright__neutral,axiom,
% 0.24/0.55 ! [A2: set_nat] :
% 0.24/0.55 ( ( inf_inf_set_nat @ A2 @ top_top_set_nat )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.right_neutral
% 0.24/0.55 thf(fact_169_inf__top_Oneutr__eq__iff,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( top_to489427057lle_hf
% 0.24/0.55 = ( inf_in923488851lle_hf @ A2 @ B ) )
% 0.24/0.55 = ( ( A2 = top_to489427057lle_hf )
% 0.24/0.55 & ( B = top_to489427057lle_hf ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.neutr_eq_iff
% 0.24/0.55 thf(fact_170_inf__top_Oneutr__eq__iff,axiom,
% 0.24/0.55 ! [A2: nat > $o,B: nat > $o] :
% 0.24/0.55 ( ( top_top_nat_o
% 0.24/0.55 = ( inf_inf_nat_o @ A2 @ B ) )
% 0.24/0.55 = ( ( A2 = top_top_nat_o )
% 0.24/0.55 & ( B = top_top_nat_o ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.neutr_eq_iff
% 0.24/0.55 thf(fact_171_inf__top_Oneutr__eq__iff,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( top_to22270292e_hf_o
% 0.24/0.55 = ( inf_in307783154e_hf_o @ A2 @ B ) )
% 0.24/0.55 = ( ( A2 = top_to22270292e_hf_o )
% 0.24/0.55 & ( B = top_to22270292e_hf_o ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.neutr_eq_iff
% 0.24/0.55 thf(fact_172_inf__top_Oneutr__eq__iff,axiom,
% 0.24/0.55 ! [A2: set_nat,B: set_nat] :
% 0.24/0.55 ( ( top_top_set_nat
% 0.24/0.55 = ( inf_inf_set_nat @ A2 @ B ) )
% 0.24/0.55 = ( ( A2 = top_top_set_nat )
% 0.24/0.55 & ( B = top_top_set_nat ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.neutr_eq_iff
% 0.24/0.55 thf(fact_173_inf__top_Oleft__neutral,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( inf_in923488851lle_hf @ top_to489427057lle_hf @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.left_neutral
% 0.24/0.55 thf(fact_174_inf__top_Oleft__neutral,axiom,
% 0.24/0.55 ! [A2: nat > $o] :
% 0.24/0.55 ( ( inf_inf_nat_o @ top_top_nat_o @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.left_neutral
% 0.24/0.55 thf(fact_175_inf__top_Oleft__neutral,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( inf_in307783154e_hf_o @ top_to22270292e_hf_o @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.left_neutral
% 0.24/0.55 thf(fact_176_inf__top_Oleft__neutral,axiom,
% 0.24/0.55 ! [A2: set_nat] :
% 0.24/0.55 ( ( inf_inf_set_nat @ top_top_set_nat @ A2 )
% 0.24/0.55 = A2 ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.left_neutral
% 0.24/0.55 thf(fact_177_inf__top_Oeq__neutr__iff,axiom,
% 0.24/0.55 ! [A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( ( inf_in923488851lle_hf @ A2 @ B )
% 0.24/0.55 = top_to489427057lle_hf )
% 0.24/0.55 = ( ( A2 = top_to489427057lle_hf )
% 0.24/0.55 & ( B = top_to489427057lle_hf ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.eq_neutr_iff
% 0.24/0.55 thf(fact_178_inf__top_Oeq__neutr__iff,axiom,
% 0.24/0.55 ! [A2: nat > $o,B: nat > $o] :
% 0.24/0.55 ( ( ( inf_inf_nat_o @ A2 @ B )
% 0.24/0.55 = top_top_nat_o )
% 0.24/0.55 = ( ( A2 = top_top_nat_o )
% 0.24/0.55 & ( B = top_top_nat_o ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.eq_neutr_iff
% 0.24/0.55 thf(fact_179_inf__top_Oeq__neutr__iff,axiom,
% 0.24/0.55 ! [A2: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( ( inf_in307783154e_hf_o @ A2 @ B )
% 0.24/0.55 = top_to22270292e_hf_o )
% 0.24/0.55 = ( ( A2 = top_to22270292e_hf_o )
% 0.24/0.55 & ( B = top_to22270292e_hf_o ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.eq_neutr_iff
% 0.24/0.55 thf(fact_180_inf__top_Oeq__neutr__iff,axiom,
% 0.24/0.55 ! [A2: set_nat,B: set_nat] :
% 0.24/0.55 ( ( ( inf_inf_set_nat @ A2 @ B )
% 0.24/0.55 = top_top_set_nat )
% 0.24/0.55 = ( ( A2 = top_top_set_nat )
% 0.24/0.55 & ( B = top_top_set_nat ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % inf_top.eq_neutr_iff
% 0.24/0.55 thf(fact_181_top__eq__inf__iff,axiom,
% 0.24/0.55 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf] :
% 0.24/0.55 ( ( top_to489427057lle_hf
% 0.24/0.55 = ( inf_in923488851lle_hf @ X @ Y3 ) )
% 0.24/0.55 = ( ( X = top_to489427057lle_hf )
% 0.24/0.55 & ( Y3 = top_to489427057lle_hf ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % top_eq_inf_iff
% 0.24/0.55 thf(fact_182_top__eq__inf__iff,axiom,
% 0.24/0.55 ! [X: nat > $o,Y3: nat > $o] :
% 0.24/0.55 ( ( top_top_nat_o
% 0.24/0.55 = ( inf_inf_nat_o @ X @ Y3 ) )
% 0.24/0.55 = ( ( X = top_top_nat_o )
% 0.24/0.55 & ( Y3 = top_top_nat_o ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % top_eq_inf_iff
% 0.24/0.55 thf(fact_183_top__eq__inf__iff,axiom,
% 0.24/0.55 ! [X: hF_Mirabelle_hf > $o,Y3: hF_Mirabelle_hf > $o] :
% 0.24/0.55 ( ( top_to22270292e_hf_o
% 0.24/0.55 = ( inf_in307783154e_hf_o @ X @ Y3 ) )
% 0.24/0.55 = ( ( X = top_to22270292e_hf_o )
% 0.24/0.55 & ( Y3 = top_to22270292e_hf_o ) ) ) ).
% 0.24/0.55
% 0.24/0.55 % top_eq_inf_iff
% 0.24/0.56 thf(fact_184_top__eq__inf__iff,axiom,
% 0.24/0.56 ! [X: set_nat,Y3: set_nat] :
% 0.24/0.56 ( ( top_top_set_nat
% 0.24/0.56 = ( inf_inf_set_nat @ X @ Y3 ) )
% 0.24/0.56 = ( ( X = top_top_set_nat )
% 0.24/0.56 & ( Y3 = top_top_set_nat ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % top_eq_inf_iff
% 0.24/0.56 thf(fact_185_inf__eq__top__iff,axiom,
% 0.24/0.56 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( ( inf_in923488851lle_hf @ X @ Y3 )
% 0.24/0.56 = top_to489427057lle_hf )
% 0.24/0.56 = ( ( X = top_to489427057lle_hf )
% 0.24/0.56 & ( Y3 = top_to489427057lle_hf ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_eq_top_iff
% 0.24/0.56 thf(fact_186_inf__eq__top__iff,axiom,
% 0.24/0.56 ! [X: nat > $o,Y3: nat > $o] :
% 0.24/0.56 ( ( ( inf_inf_nat_o @ X @ Y3 )
% 0.24/0.56 = top_top_nat_o )
% 0.24/0.56 = ( ( X = top_top_nat_o )
% 0.24/0.56 & ( Y3 = top_top_nat_o ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_eq_top_iff
% 0.24/0.56 thf(fact_187_inf__eq__top__iff,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf > $o,Y3: hF_Mirabelle_hf > $o] :
% 0.24/0.56 ( ( ( inf_in307783154e_hf_o @ X @ Y3 )
% 0.24/0.56 = top_to22270292e_hf_o )
% 0.24/0.56 = ( ( X = top_to22270292e_hf_o )
% 0.24/0.56 & ( Y3 = top_to22270292e_hf_o ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_eq_top_iff
% 0.24/0.56 thf(fact_188_inf__eq__top__iff,axiom,
% 0.24/0.56 ! [X: set_nat,Y3: set_nat] :
% 0.24/0.56 ( ( ( inf_inf_set_nat @ X @ Y3 )
% 0.24/0.56 = top_top_set_nat )
% 0.24/0.56 = ( ( X = top_top_set_nat )
% 0.24/0.56 & ( Y3 = top_top_set_nat ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_eq_top_iff
% 0.24/0.56 thf(fact_189_inf__top__right,axiom,
% 0.24/0.56 ! [X: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in923488851lle_hf @ X @ top_to489427057lle_hf )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_top_right
% 0.24/0.56 thf(fact_190_inf__top__right,axiom,
% 0.24/0.56 ! [X: nat > $o] :
% 0.24/0.56 ( ( inf_inf_nat_o @ X @ top_top_nat_o )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_top_right
% 0.24/0.56 thf(fact_191_inf__top__right,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf > $o] :
% 0.24/0.56 ( ( inf_in307783154e_hf_o @ X @ top_to22270292e_hf_o )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_top_right
% 0.24/0.56 thf(fact_192_inf__top__right,axiom,
% 0.24/0.56 ! [X: set_nat] :
% 0.24/0.56 ( ( inf_inf_set_nat @ X @ top_top_set_nat )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_top_right
% 0.24/0.56 thf(fact_193_inf__top__left,axiom,
% 0.24/0.56 ! [X: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in923488851lle_hf @ top_to489427057lle_hf @ X )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_top_left
% 0.24/0.56 thf(fact_194_inf__top__left,axiom,
% 0.24/0.56 ! [X: nat > $o] :
% 0.24/0.56 ( ( inf_inf_nat_o @ top_top_nat_o @ X )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_top_left
% 0.24/0.56 thf(fact_195_inf__top__left,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf > $o] :
% 0.24/0.56 ( ( inf_in307783154e_hf_o @ top_to22270292e_hf_o @ X )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_top_left
% 0.24/0.56 thf(fact_196_inf__top__left,axiom,
% 0.24/0.56 ! [X: set_nat] :
% 0.24/0.56 ( ( inf_inf_set_nat @ top_top_set_nat @ X )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_top_left
% 0.24/0.56 thf(fact_197_inf__sup__absorb,axiom,
% 0.24/0.56 ! [X: set_nat,Y3: set_nat] :
% 0.24/0.56 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ X @ Y3 ) )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_absorb
% 0.24/0.56 thf(fact_198_inf__sup__absorb,axiom,
% 0.24/0.56 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in923488851lle_hf @ X @ ( sup_su1790843629lle_hf @ X @ Y3 ) )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_absorb
% 0.24/0.56 thf(fact_199_inf__sup__absorb,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ X @ ( sup_su638957495lle_hf @ X @ Y3 ) )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_absorb
% 0.24/0.56 thf(fact_200_sup__inf__absorb,axiom,
% 0.24/0.56 ! [X: set_nat,Y3: set_nat] :
% 0.24/0.56 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ X @ Y3 ) )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % sup_inf_absorb
% 0.24/0.56 thf(fact_201_sup__inf__absorb,axiom,
% 0.24/0.56 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( sup_su1790843629lle_hf @ X @ ( inf_in923488851lle_hf @ X @ Y3 ) )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % sup_inf_absorb
% 0.24/0.56 thf(fact_202_sup__inf__absorb,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( sup_su638957495lle_hf @ X @ ( inf_in956532509lle_hf @ X @ Y3 ) )
% 0.24/0.56 = X ) ).
% 0.24/0.56
% 0.24/0.56 % sup_inf_absorb
% 0.24/0.56 thf(fact_203_hinter__iff,axiom,
% 0.24/0.56 ! [U4: hF_Mirabelle_hf,X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( hF_Mirabelle_hmem @ U4 @ ( inf_in956532509lle_hf @ X @ Y3 ) )
% 0.24/0.56 = ( ( hF_Mirabelle_hmem @ U4 @ X )
% 0.24/0.56 & ( hF_Mirabelle_hmem @ U4 @ Y3 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % hinter_iff
% 0.24/0.56 thf(fact_204_hinter__hempty__left,axiom,
% 0.24/0.56 ! [A: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ zero_z189798548lle_hf @ A )
% 0.24/0.56 = zero_z189798548lle_hf ) ).
% 0.24/0.56
% 0.24/0.56 % hinter_hempty_left
% 0.24/0.56 thf(fact_205_hinter__hempty__right,axiom,
% 0.24/0.56 ! [A: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ A @ zero_z189798548lle_hf )
% 0.24/0.56 = zero_z189798548lle_hf ) ).
% 0.24/0.56
% 0.24/0.56 % hinter_hempty_right
% 0.24/0.56 thf(fact_206_Abs__hf__0,axiom,
% 0.24/0.56 ( ( hF_Mirabelle_Abs_hf @ zero_zero_nat )
% 0.24/0.56 = zero_z189798548lle_hf ) ).
% 0.24/0.56
% 0.24/0.56 % Abs_hf_0
% 0.24/0.56 thf(fact_207_inf__left__commute,axiom,
% 0.24/0.56 ! [X: set_nat,Y3: set_nat,Z: set_nat] :
% 0.24/0.56 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y3 @ Z ) )
% 0.24/0.56 = ( inf_inf_set_nat @ Y3 @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_left_commute
% 0.24/0.56 thf(fact_208_inf__left__commute,axiom,
% 0.24/0.56 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf,Z: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in923488851lle_hf @ X @ ( inf_in923488851lle_hf @ Y3 @ Z ) )
% 0.24/0.56 = ( inf_in923488851lle_hf @ Y3 @ ( inf_in923488851lle_hf @ X @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_left_commute
% 0.24/0.56 thf(fact_209_inf__left__commute,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ Y3 @ Z ) )
% 0.24/0.56 = ( inf_in956532509lle_hf @ Y3 @ ( inf_in956532509lle_hf @ X @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_left_commute
% 0.24/0.56 thf(fact_210_inf_Oleft__commute,axiom,
% 0.24/0.56 ! [B: set_nat,A2: set_nat,C: set_nat] :
% 0.24/0.56 ( ( inf_inf_set_nat @ B @ ( inf_inf_set_nat @ A2 @ C ) )
% 0.24/0.56 = ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf.left_commute
% 0.24/0.56 thf(fact_211_inf_Oleft__commute,axiom,
% 0.24/0.56 ! [B: set_HF_Mirabelle_hf,A2: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in923488851lle_hf @ B @ ( inf_in923488851lle_hf @ A2 @ C ) )
% 0.24/0.56 = ( inf_in923488851lle_hf @ A2 @ ( inf_in923488851lle_hf @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf.left_commute
% 0.24/0.56 thf(fact_212_inf_Oleft__commute,axiom,
% 0.24/0.56 ! [B: hF_Mirabelle_hf,A2: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ A2 @ C ) )
% 0.24/0.56 = ( inf_in956532509lle_hf @ A2 @ ( inf_in956532509lle_hf @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf.left_commute
% 0.24/0.56 thf(fact_213_inf__commute,axiom,
% 0.24/0.56 ( inf_inf_set_nat
% 0.24/0.56 = ( ^ [X2: set_nat,Y: set_nat] : ( inf_inf_set_nat @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_commute
% 0.24/0.56 thf(fact_214_inf__commute,axiom,
% 0.24/0.56 ( inf_in923488851lle_hf
% 0.24/0.56 = ( ^ [X2: set_HF_Mirabelle_hf,Y: set_HF_Mirabelle_hf] : ( inf_in923488851lle_hf @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_commute
% 0.24/0.56 thf(fact_215_inf__commute,axiom,
% 0.24/0.56 ( inf_in956532509lle_hf
% 0.24/0.56 = ( ^ [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_commute
% 0.24/0.56 thf(fact_216_inf_Ocommute,axiom,
% 0.24/0.56 ( inf_inf_set_nat
% 0.24/0.56 = ( ^ [A4: set_nat,B3: set_nat] : ( inf_inf_set_nat @ B3 @ A4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf.commute
% 0.24/0.56 thf(fact_217_inf_Ocommute,axiom,
% 0.24/0.56 ( inf_in923488851lle_hf
% 0.24/0.56 = ( ^ [A4: set_HF_Mirabelle_hf,B3: set_HF_Mirabelle_hf] : ( inf_in923488851lle_hf @ B3 @ A4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf.commute
% 0.24/0.56 thf(fact_218_inf_Ocommute,axiom,
% 0.24/0.56 ( inf_in956532509lle_hf
% 0.24/0.56 = ( ^ [A4: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ B3 @ A4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf.commute
% 0.24/0.56 thf(fact_219_inf__assoc,axiom,
% 0.24/0.56 ! [X: set_nat,Y3: set_nat,Z: set_nat] :
% 0.24/0.56 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y3 ) @ Z )
% 0.24/0.56 = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y3 @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_assoc
% 0.24/0.56 thf(fact_220_inf__assoc,axiom,
% 0.24/0.56 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf,Z: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in923488851lle_hf @ ( inf_in923488851lle_hf @ X @ Y3 ) @ Z )
% 0.24/0.56 = ( inf_in923488851lle_hf @ X @ ( inf_in923488851lle_hf @ Y3 @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_assoc
% 0.24/0.56 thf(fact_221_inf__assoc,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ X @ Y3 ) @ Z )
% 0.24/0.56 = ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ Y3 @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_assoc
% 0.24/0.56 thf(fact_222_inf_Oassoc,axiom,
% 0.24/0.56 ! [A2: set_nat,B: set_nat,C: set_nat] :
% 0.24/0.56 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A2 @ B ) @ C )
% 0.24/0.56 = ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf.assoc
% 0.24/0.56 thf(fact_223_inf_Oassoc,axiom,
% 0.24/0.56 ! [A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in923488851lle_hf @ ( inf_in923488851lle_hf @ A2 @ B ) @ C )
% 0.24/0.56 = ( inf_in923488851lle_hf @ A2 @ ( inf_in923488851lle_hf @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf.assoc
% 0.24/0.56 thf(fact_224_inf_Oassoc,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A2 @ B ) @ C )
% 0.24/0.56 = ( inf_in956532509lle_hf @ A2 @ ( inf_in956532509lle_hf @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf.assoc
% 0.24/0.56 thf(fact_225_boolean__algebra__cancel_Oinf2,axiom,
% 0.24/0.56 ! [B4: set_nat,K: set_nat,B: set_nat,A2: set_nat] :
% 0.24/0.56 ( ( B4
% 0.24/0.56 = ( inf_inf_set_nat @ K @ B ) )
% 0.24/0.56 => ( ( inf_inf_set_nat @ A2 @ B4 )
% 0.24/0.56 = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A2 @ B ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % boolean_algebra_cancel.inf2
% 0.24/0.56 thf(fact_226_boolean__algebra__cancel_Oinf2,axiom,
% 0.24/0.56 ! [B4: set_HF_Mirabelle_hf,K: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf,A2: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( B4
% 0.24/0.56 = ( inf_in923488851lle_hf @ K @ B ) )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ A2 @ B4 )
% 0.24/0.56 = ( inf_in923488851lle_hf @ K @ ( inf_in923488851lle_hf @ A2 @ B ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % boolean_algebra_cancel.inf2
% 0.24/0.56 thf(fact_227_boolean__algebra__cancel_Oinf2,axiom,
% 0.24/0.56 ! [B4: hF_Mirabelle_hf,K: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A2: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( B4
% 0.24/0.56 = ( inf_in956532509lle_hf @ K @ B ) )
% 0.24/0.56 => ( ( inf_in956532509lle_hf @ A2 @ B4 )
% 0.24/0.56 = ( inf_in956532509lle_hf @ K @ ( inf_in956532509lle_hf @ A2 @ B ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % boolean_algebra_cancel.inf2
% 0.24/0.56 thf(fact_228_boolean__algebra__cancel_Oinf1,axiom,
% 0.24/0.56 ! [A: set_nat,K: set_nat,A2: set_nat,B: set_nat] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( inf_inf_set_nat @ K @ A2 ) )
% 0.24/0.56 => ( ( inf_inf_set_nat @ A @ B )
% 0.24/0.56 = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A2 @ B ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % boolean_algebra_cancel.inf1
% 0.24/0.56 thf(fact_229_boolean__algebra__cancel_Oinf1,axiom,
% 0.24/0.56 ! [A: set_HF_Mirabelle_hf,K: set_HF_Mirabelle_hf,A2: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( inf_in923488851lle_hf @ K @ A2 ) )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ A @ B )
% 0.24/0.56 = ( inf_in923488851lle_hf @ K @ ( inf_in923488851lle_hf @ A2 @ B ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % boolean_algebra_cancel.inf1
% 0.24/0.56 thf(fact_230_boolean__algebra__cancel_Oinf1,axiom,
% 0.24/0.56 ! [A: hF_Mirabelle_hf,K: hF_Mirabelle_hf,A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( inf_in956532509lle_hf @ K @ A2 ) )
% 0.24/0.56 => ( ( inf_in956532509lle_hf @ A @ B )
% 0.24/0.56 = ( inf_in956532509lle_hf @ K @ ( inf_in956532509lle_hf @ A2 @ B ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % boolean_algebra_cancel.inf1
% 0.24/0.56 thf(fact_231_inf__sup__aci_I1_J,axiom,
% 0.24/0.56 ( inf_inf_set_nat
% 0.24/0.56 = ( ^ [X2: set_nat,Y: set_nat] : ( inf_inf_set_nat @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_aci(1)
% 0.24/0.56 thf(fact_232_inf__sup__aci_I1_J,axiom,
% 0.24/0.56 ( inf_in923488851lle_hf
% 0.24/0.56 = ( ^ [X2: set_HF_Mirabelle_hf,Y: set_HF_Mirabelle_hf] : ( inf_in923488851lle_hf @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_aci(1)
% 0.24/0.56 thf(fact_233_inf__sup__aci_I1_J,axiom,
% 0.24/0.56 ( inf_in956532509lle_hf
% 0.24/0.56 = ( ^ [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_aci(1)
% 0.24/0.56 thf(fact_234_inf__sup__aci_I2_J,axiom,
% 0.24/0.56 ! [X: set_HF_Mirabelle_hf,Y3: set_HF_Mirabelle_hf,Z: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in923488851lle_hf @ ( inf_in923488851lle_hf @ X @ Y3 ) @ Z )
% 0.24/0.56 = ( inf_in923488851lle_hf @ X @ ( inf_in923488851lle_hf @ Y3 @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_aci(2)
% 0.24/0.56 thf(fact_235_inf__sup__aci_I2_J,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ X @ Y3 ) @ Z )
% 0.24/0.56 = ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ Y3 @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_aci(2)
% 0.24/0.56 thf(fact_236_inf__sup__aci_I3_J,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ Y3 @ Z ) )
% 0.24/0.56 = ( inf_in956532509lle_hf @ Y3 @ ( inf_in956532509lle_hf @ X @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_aci(3)
% 0.24/0.56 thf(fact_237_inf__sup__aci_I4_J,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ X @ Y3 ) )
% 0.24/0.56 = ( inf_in956532509lle_hf @ X @ Y3 ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_aci(4)
% 0.24/0.56 thf(fact_238_sup__inf__distrib2,axiom,
% 0.24/0.56 ! [Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ Y3 @ Z ) @ X )
% 0.24/0.56 = ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ Y3 @ X ) @ ( sup_su638957495lle_hf @ Z @ X ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % sup_inf_distrib2
% 0.24/0.56 thf(fact_239_sup__inf__distrib1,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( sup_su638957495lle_hf @ X @ ( inf_in956532509lle_hf @ Y3 @ Z ) )
% 0.24/0.56 = ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ X @ Y3 ) @ ( sup_su638957495lle_hf @ X @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % sup_inf_distrib1
% 0.24/0.56 thf(fact_240_inf__sup__distrib2,axiom,
% 0.24/0.56 ! [Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ Y3 @ Z ) @ X )
% 0.24/0.56 = ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ Y3 @ X ) @ ( inf_in956532509lle_hf @ Z @ X ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_distrib2
% 0.24/0.56 thf(fact_241_inf__sup__distrib1,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ X @ ( sup_su638957495lle_hf @ Y3 @ Z ) )
% 0.24/0.56 = ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ X @ Y3 ) @ ( inf_in956532509lle_hf @ X @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % inf_sup_distrib1
% 0.24/0.56 thf(fact_242_distrib__imp2,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.56 ( ! [X3: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf,Z3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( sup_su638957495lle_hf @ X3 @ ( inf_in956532509lle_hf @ Y5 @ Z3 ) )
% 0.24/0.56 = ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ X3 @ Y5 ) @ ( sup_su638957495lle_hf @ X3 @ Z3 ) ) )
% 0.24/0.56 => ( ( inf_in956532509lle_hf @ X @ ( sup_su638957495lle_hf @ Y3 @ Z ) )
% 0.24/0.56 = ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ X @ Y3 ) @ ( inf_in956532509lle_hf @ X @ Z ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % distrib_imp2
% 0.24/0.56 thf(fact_243_distrib__imp1,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.56 ( ! [X3: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf,Z3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in956532509lle_hf @ X3 @ ( sup_su638957495lle_hf @ Y5 @ Z3 ) )
% 0.24/0.56 = ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ X3 @ Y5 ) @ ( inf_in956532509lle_hf @ X3 @ Z3 ) ) )
% 0.24/0.56 => ( ( sup_su638957495lle_hf @ X @ ( inf_in956532509lle_hf @ Y3 @ Z ) )
% 0.24/0.56 = ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ X @ Y3 ) @ ( sup_su638957495lle_hf @ X @ Z ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % distrib_imp1
% 0.24/0.56 thf(fact_244_foundation,axiom,
% 0.24/0.56 ! [Z: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( Z != zero_z189798548lle_hf )
% 0.24/0.56 => ? [W: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( hF_Mirabelle_hmem @ W @ Z )
% 0.24/0.56 & ( ( inf_in956532509lle_hf @ W @ Z )
% 0.24/0.56 = zero_z189798548lle_hf ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % foundation
% 0.24/0.56 thf(fact_245_hinter__hinsert__right,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.56 => ( ( inf_in956532509lle_hf @ B4 @ ( hF_Mirabelle_hinsert @ X @ A ) )
% 0.24/0.56 = ( hF_Mirabelle_hinsert @ X @ ( inf_in956532509lle_hf @ B4 @ A ) ) ) )
% 0.24/0.56 & ( ~ ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.56 => ( ( inf_in956532509lle_hf @ B4 @ ( hF_Mirabelle_hinsert @ X @ A ) )
% 0.24/0.56 = ( inf_in956532509lle_hf @ B4 @ A ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % hinter_hinsert_right
% 0.24/0.56 thf(fact_246_hinter__hinsert__left,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.56 => ( ( inf_in956532509lle_hf @ ( hF_Mirabelle_hinsert @ X @ A ) @ B4 )
% 0.24/0.56 = ( hF_Mirabelle_hinsert @ X @ ( inf_in956532509lle_hf @ A @ B4 ) ) ) )
% 0.24/0.56 & ( ~ ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.56 => ( ( inf_in956532509lle_hf @ ( hF_Mirabelle_hinsert @ X @ A ) @ B4 )
% 0.24/0.56 = ( inf_in956532509lle_hf @ A @ B4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % hinter_hinsert_left
% 0.24/0.56 thf(fact_247_zero__reorient,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( zero_z189798548lle_hf = X )
% 0.24/0.56 = ( X = zero_z189798548lle_hf ) ) ).
% 0.24/0.56
% 0.24/0.56 % zero_reorient
% 0.24/0.56 thf(fact_248_zero__reorient,axiom,
% 0.24/0.56 ! [X: nat] :
% 0.24/0.56 ( ( zero_zero_nat = X )
% 0.24/0.56 = ( X = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % zero_reorient
% 0.24/0.56 thf(fact_249_UNIV__eq__I,axiom,
% 0.24/0.56 ! [A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ! [X3: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X3 @ A )
% 0.24/0.56 => ( top_to489427057lle_hf = A ) ) ).
% 0.24/0.56
% 0.24/0.56 % UNIV_eq_I
% 0.24/0.56 thf(fact_250_UNIV__eq__I,axiom,
% 0.24/0.56 ! [A: set_nat] :
% 0.24/0.56 ( ! [X3: nat] : ( member_nat @ X3 @ A )
% 0.24/0.56 => ( top_top_set_nat = A ) ) ).
% 0.24/0.56
% 0.24/0.56 % UNIV_eq_I
% 0.24/0.56 thf(fact_251_UNIV__witness,axiom,
% 0.24/0.56 ? [X3: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X3 @ top_to489427057lle_hf ) ).
% 0.24/0.56
% 0.24/0.56 % UNIV_witness
% 0.24/0.56 thf(fact_252_UNIV__witness,axiom,
% 0.24/0.56 ? [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ).
% 0.24/0.56
% 0.24/0.56 % UNIV_witness
% 0.24/0.56 thf(fact_253_Un__UNIV__right,axiom,
% 0.24/0.56 ! [A: set_nat] :
% 0.24/0.56 ( ( sup_sup_set_nat @ A @ top_top_set_nat )
% 0.24/0.56 = top_top_set_nat ) ).
% 0.24/0.56
% 0.24/0.56 % Un_UNIV_right
% 0.24/0.56 thf(fact_254_Un__UNIV__left,axiom,
% 0.24/0.56 ! [B4: set_nat] :
% 0.24/0.56 ( ( sup_sup_set_nat @ top_top_set_nat @ B4 )
% 0.24/0.56 = top_top_set_nat ) ).
% 0.24/0.56
% 0.24/0.56 % Un_UNIV_left
% 0.24/0.56 thf(fact_255_top__set__def,axiom,
% 0.24/0.56 ( top_top_set_nat
% 0.24/0.56 = ( collect_nat @ top_top_nat_o ) ) ).
% 0.24/0.56
% 0.24/0.56 % top_set_def
% 0.24/0.56 thf(fact_256_type__copy__ex__RepI,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,F2: nat > $o] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ top_top_set_nat )
% 0.24/0.56 => ( ( ? [X4: nat] : ( F2 @ X4 ) )
% 0.24/0.56 = ( ? [B3: hF_Mirabelle_hf] : ( F2 @ ( Rep @ B3 ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_copy_ex_RepI
% 0.24/0.56 thf(fact_257_type__copy__obj__one__point__absE,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,S: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ top_top_set_nat )
% 0.24/0.56 => ~ ! [X3: nat] :
% 0.24/0.56 ( S
% 0.24/0.56 != ( Abs @ X3 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_copy_obj_one_point_absE
% 0.24/0.56 thf(fact_258_HF__hfset,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A2 ) )
% 0.24/0.56 = A2 ) ).
% 0.24/0.56
% 0.24/0.56 % HF_hfset
% 0.24/0.56 thf(fact_259_type__definition_ORep,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,A: set_nat,X: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ A )
% 0.24/0.56 => ( member_nat @ ( Rep @ X ) @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.Rep
% 0.24/0.56 thf(fact_260_type__definition__def,axiom,
% 0.24/0.56 ( type_d1794767497hf_nat
% 0.24/0.56 = ( ^ [Rep2: hF_Mirabelle_hf > nat,Abs2: nat > hF_Mirabelle_hf,A6: set_nat] :
% 0.24/0.56 ( ! [X2: hF_Mirabelle_hf] : ( member_nat @ ( Rep2 @ X2 ) @ A6 )
% 0.24/0.56 & ! [X2: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( Abs2 @ ( Rep2 @ X2 ) )
% 0.24/0.56 = X2 )
% 0.24/0.56 & ! [Y: nat] :
% 0.24/0.56 ( ( member_nat @ Y @ A6 )
% 0.24/0.56 => ( ( Rep2 @ ( Abs2 @ Y ) )
% 0.24/0.56 = Y ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition_def
% 0.24/0.56 thf(fact_261_Int__UNIV,axiom,
% 0.24/0.56 ! [A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( ( inf_inf_set_nat @ A @ B4 )
% 0.24/0.56 = top_top_set_nat )
% 0.24/0.56 = ( ( A = top_top_set_nat )
% 0.24/0.56 & ( B4 = top_top_set_nat ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_UNIV
% 0.24/0.56 thf(fact_262_UnCI,axiom,
% 0.24/0.56 ! [C: nat,B4: set_nat,A: set_nat] :
% 0.24/0.56 ( ( ~ ( member_nat @ C @ B4 )
% 0.24/0.56 => ( member_nat @ C @ A ) )
% 0.24/0.56 => ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % UnCI
% 0.24/0.56 thf(fact_263_UnCI,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( ~ ( member1367349282lle_hf @ C @ B4 )
% 0.24/0.56 => ( member1367349282lle_hf @ C @ A ) )
% 0.24/0.56 => ( member1367349282lle_hf @ C @ ( sup_su1790843629lle_hf @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % UnCI
% 0.24/0.56 thf(fact_264_Un__iff,axiom,
% 0.24/0.56 ! [C: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) )
% 0.24/0.56 = ( ( member_nat @ C @ A )
% 0.24/0.56 | ( member_nat @ C @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Un_iff
% 0.24/0.56 thf(fact_265_Un__iff,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ C @ ( sup_su1790843629lle_hf @ A @ B4 ) )
% 0.24/0.56 = ( ( member1367349282lle_hf @ C @ A )
% 0.24/0.56 | ( member1367349282lle_hf @ C @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Un_iff
% 0.24/0.56 thf(fact_266_UnE,axiom,
% 0.24/0.56 ! [C: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) )
% 0.24/0.56 => ( ~ ( member_nat @ C @ A )
% 0.24/0.56 => ( member_nat @ C @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % UnE
% 0.24/0.56 thf(fact_267_UnE,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ C @ ( sup_su1790843629lle_hf @ A @ B4 ) )
% 0.24/0.56 => ( ~ ( member1367349282lle_hf @ C @ A )
% 0.24/0.56 => ( member1367349282lle_hf @ C @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % UnE
% 0.24/0.56 thf(fact_268_UnI1,axiom,
% 0.24/0.56 ! [C: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ C @ A )
% 0.24/0.56 => ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % UnI1
% 0.24/0.56 thf(fact_269_UnI1,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ C @ A )
% 0.24/0.56 => ( member1367349282lle_hf @ C @ ( sup_su1790843629lle_hf @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % UnI1
% 0.24/0.56 thf(fact_270_UnI2,axiom,
% 0.24/0.56 ! [C: nat,B4: set_nat,A: set_nat] :
% 0.24/0.56 ( ( member_nat @ C @ B4 )
% 0.24/0.56 => ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % UnI2
% 0.24/0.56 thf(fact_271_UnI2,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ C @ B4 )
% 0.24/0.56 => ( member1367349282lle_hf @ C @ ( sup_su1790843629lle_hf @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % UnI2
% 0.24/0.56 thf(fact_272_Int__UNIV__left,axiom,
% 0.24/0.56 ! [B4: set_nat] :
% 0.24/0.56 ( ( inf_inf_set_nat @ top_top_set_nat @ B4 )
% 0.24/0.56 = B4 ) ).
% 0.24/0.56
% 0.24/0.56 % Int_UNIV_left
% 0.24/0.56 thf(fact_273_Int__UNIV__right,axiom,
% 0.24/0.56 ! [A: set_nat] :
% 0.24/0.56 ( ( inf_inf_set_nat @ A @ top_top_set_nat )
% 0.24/0.56 = A ) ).
% 0.24/0.56
% 0.24/0.56 % Int_UNIV_right
% 0.24/0.56 thf(fact_274_type__definition_ORep__inverse,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,A: set_nat,X: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ A )
% 0.24/0.56 => ( ( Abs @ ( Rep @ X ) )
% 0.24/0.56 = X ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.Rep_inverse
% 0.24/0.56 thf(fact_275_type__definition_OAbs__inverse,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,A: set_nat,Y3: nat] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ A )
% 0.24/0.56 => ( ( member_nat @ Y3 @ A )
% 0.24/0.56 => ( ( Rep @ ( Abs @ Y3 ) )
% 0.24/0.56 = Y3 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.Abs_inverse
% 0.24/0.56 thf(fact_276_type__definition_ORep__inject,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,A: set_nat,X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ A )
% 0.24/0.56 => ( ( ( Rep @ X )
% 0.24/0.56 = ( Rep @ Y3 ) )
% 0.24/0.56 = ( X = Y3 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.Rep_inject
% 0.24/0.56 thf(fact_277_type__definition_ORep__induct,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,A: set_nat,Y3: nat,P: nat > $o] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ A )
% 0.24/0.56 => ( ( member_nat @ Y3 @ A )
% 0.24/0.56 => ( ! [X3: hF_Mirabelle_hf] : ( P @ ( Rep @ X3 ) )
% 0.24/0.56 => ( P @ Y3 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.Rep_induct
% 0.24/0.56 thf(fact_278_type__definition_OAbs__inject,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,A: set_nat,X: nat,Y3: nat] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ A )
% 0.24/0.56 => ( ( member_nat @ X @ A )
% 0.24/0.56 => ( ( member_nat @ Y3 @ A )
% 0.24/0.56 => ( ( ( Abs @ X )
% 0.24/0.56 = ( Abs @ Y3 ) )
% 0.24/0.56 = ( X = Y3 ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.Abs_inject
% 0.24/0.56 thf(fact_279_type__definition_OAbs__induct,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,A: set_nat,P: hF_Mirabelle_hf > $o,X: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ A )
% 0.24/0.56 => ( ! [Y5: nat] :
% 0.24/0.56 ( ( member_nat @ Y5 @ A )
% 0.24/0.56 => ( P @ ( Abs @ Y5 ) ) )
% 0.24/0.56 => ( P @ X ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.Abs_induct
% 0.24/0.56 thf(fact_280_type__definition_ORep__cases,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,A: set_nat,Y3: nat] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ A )
% 0.24/0.56 => ( ( member_nat @ Y3 @ A )
% 0.24/0.56 => ~ ! [X3: hF_Mirabelle_hf] :
% 0.24/0.56 ( Y3
% 0.24/0.56 != ( Rep @ X3 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.Rep_cases
% 0.24/0.56 thf(fact_281_type__definition_OAbs__cases,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,Abs: nat > hF_Mirabelle_hf,A: set_nat,X: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( type_d1794767497hf_nat @ Rep @ Abs @ A )
% 0.24/0.56 => ~ ! [Y5: nat] :
% 0.24/0.56 ( ( X
% 0.24/0.56 = ( Abs @ Y5 ) )
% 0.24/0.56 => ~ ( member_nat @ Y5 @ A ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.Abs_cases
% 0.24/0.56 thf(fact_282_type__definition_Ointro,axiom,
% 0.24/0.56 ! [Rep: hF_Mirabelle_hf > nat,A: set_nat,Abs: nat > hF_Mirabelle_hf] :
% 0.24/0.56 ( ! [X3: hF_Mirabelle_hf] : ( member_nat @ ( Rep @ X3 ) @ A )
% 0.24/0.56 => ( ! [X3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( Abs @ ( Rep @ X3 ) )
% 0.24/0.56 = X3 )
% 0.24/0.56 => ( ! [Y5: nat] :
% 0.24/0.56 ( ( member_nat @ Y5 @ A )
% 0.24/0.56 => ( ( Rep @ ( Abs @ Y5 ) )
% 0.24/0.56 = Y5 ) )
% 0.24/0.56 => ( type_d1794767497hf_nat @ Rep @ Abs @ A ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % type_definition.intro
% 0.24/0.56 thf(fact_283_top__empty__eq,axiom,
% 0.24/0.56 ( top_to22270292e_hf_o
% 0.24/0.56 = ( ^ [X2: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X2 @ top_to489427057lle_hf ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % top_empty_eq
% 0.24/0.56 thf(fact_284_top__empty__eq,axiom,
% 0.24/0.56 ( top_top_nat_o
% 0.24/0.56 = ( ^ [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % top_empty_eq
% 0.24/0.56 thf(fact_285_hcard__0,axiom,
% 0.24/0.56 ( ( hF_Mirabelle_hcard @ zero_z189798548lle_hf )
% 0.24/0.56 = zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % hcard_0
% 0.24/0.56 thf(fact_286_hinsert__def,axiom,
% 0.24/0.56 ( hF_Mirabelle_hinsert
% 0.24/0.56 = ( ^ [A4: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ A4 @ ( hF_Mirabelle_hfset @ B3 ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % hinsert_def
% 0.24/0.56 thf(fact_287_insert__absorb2,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( insert9649339lle_hf @ X @ ( insert9649339lle_hf @ X @ A ) )
% 0.24/0.56 = ( insert9649339lle_hf @ X @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_absorb2
% 0.24/0.56 thf(fact_288_insert__iff,axiom,
% 0.24/0.56 ! [A2: nat,B: nat,A: set_nat] :
% 0.24/0.56 ( ( member_nat @ A2 @ ( insert_nat @ B @ A ) )
% 0.24/0.56 = ( ( A2 = B )
% 0.24/0.56 | ( member_nat @ A2 @ A ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_iff
% 0.24/0.56 thf(fact_289_insert__iff,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ B @ A ) )
% 0.24/0.56 = ( ( A2 = B )
% 0.24/0.56 | ( member1367349282lle_hf @ A2 @ A ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_iff
% 0.24/0.56 thf(fact_290_insertCI,axiom,
% 0.24/0.56 ! [A2: nat,B4: set_nat,B: nat] :
% 0.24/0.56 ( ( ~ ( member_nat @ A2 @ B4 )
% 0.24/0.56 => ( A2 = B ) )
% 0.24/0.56 => ( member_nat @ A2 @ ( insert_nat @ B @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insertCI
% 0.24/0.56 thf(fact_291_insertCI,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( ~ ( member1367349282lle_hf @ A2 @ B4 )
% 0.24/0.56 => ( A2 = B ) )
% 0.24/0.56 => ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ B @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insertCI
% 0.24/0.56 thf(fact_292_IntI,axiom,
% 0.24/0.56 ! [C: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ C @ A )
% 0.24/0.56 => ( ( member_nat @ C @ B4 )
% 0.24/0.56 => ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % IntI
% 0.24/0.56 thf(fact_293_IntI,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ C @ A )
% 0.24/0.56 => ( ( member1367349282lle_hf @ C @ B4 )
% 0.24/0.56 => ( member1367349282lle_hf @ C @ ( inf_in923488851lle_hf @ A @ B4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % IntI
% 0.24/0.56 thf(fact_294_Int__iff,axiom,
% 0.24/0.56 ! [C: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) )
% 0.24/0.56 = ( ( member_nat @ C @ A )
% 0.24/0.56 & ( member_nat @ C @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_iff
% 0.24/0.56 thf(fact_295_Int__iff,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ C @ ( inf_in923488851lle_hf @ A @ B4 ) )
% 0.24/0.56 = ( ( member1367349282lle_hf @ C @ A )
% 0.24/0.56 & ( member1367349282lle_hf @ C @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_iff
% 0.24/0.56 thf(fact_296_Int__insert__left__if0,axiom,
% 0.24/0.56 ! [A2: nat,C2: set_nat,B4: set_nat] :
% 0.24/0.56 ( ~ ( member_nat @ A2 @ C2 )
% 0.24/0.56 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B4 ) @ C2 )
% 0.24/0.56 = ( inf_inf_set_nat @ B4 @ C2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_left_if0
% 0.24/0.56 thf(fact_297_Int__insert__left__if0,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,C2: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ~ ( member1367349282lle_hf @ A2 @ C2 )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ ( insert9649339lle_hf @ A2 @ B4 ) @ C2 )
% 0.24/0.56 = ( inf_in923488851lle_hf @ B4 @ C2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_left_if0
% 0.24/0.56 thf(fact_298_Int__insert__left__if1,axiom,
% 0.24/0.56 ! [A2: nat,C2: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ A2 @ C2 )
% 0.24/0.56 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B4 ) @ C2 )
% 0.24/0.56 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ B4 @ C2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_left_if1
% 0.24/0.56 thf(fact_299_Int__insert__left__if1,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,C2: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ A2 @ C2 )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ ( insert9649339lle_hf @ A2 @ B4 ) @ C2 )
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ ( inf_in923488851lle_hf @ B4 @ C2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_left_if1
% 0.24/0.56 thf(fact_300_insert__inter__insert,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( inf_in923488851lle_hf @ ( insert9649339lle_hf @ A2 @ A ) @ ( insert9649339lle_hf @ A2 @ B4 ) )
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ ( inf_in923488851lle_hf @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_inter_insert
% 0.24/0.56 thf(fact_301_Int__insert__right__if0,axiom,
% 0.24/0.56 ! [A2: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ~ ( member_nat @ A2 @ A )
% 0.24/0.56 => ( ( inf_inf_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 0.24/0.56 = ( inf_inf_set_nat @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_right_if0
% 0.24/0.56 thf(fact_302_Int__insert__right__if0,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ~ ( member1367349282lle_hf @ A2 @ A )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ A @ ( insert9649339lle_hf @ A2 @ B4 ) )
% 0.24/0.56 = ( inf_in923488851lle_hf @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_right_if0
% 0.24/0.56 thf(fact_303_Int__insert__right__if1,axiom,
% 0.24/0.56 ! [A2: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ A2 @ A )
% 0.24/0.56 => ( ( inf_inf_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 0.24/0.56 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_right_if1
% 0.24/0.56 thf(fact_304_Int__insert__right__if1,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ A2 @ A )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ A @ ( insert9649339lle_hf @ A2 @ B4 ) )
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ ( inf_in923488851lle_hf @ A @ B4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_right_if1
% 0.24/0.56 thf(fact_305_Un__insert__left,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,C2: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( sup_su1790843629lle_hf @ ( insert9649339lle_hf @ A2 @ B4 ) @ C2 )
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ ( sup_su1790843629lle_hf @ B4 @ C2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Un_insert_left
% 0.24/0.56 thf(fact_306_Un__insert__right,axiom,
% 0.24/0.56 ! [A: set_HF_Mirabelle_hf,A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( sup_su1790843629lle_hf @ A @ ( insert9649339lle_hf @ A2 @ B4 ) )
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ ( sup_su1790843629lle_hf @ A @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Un_insert_right
% 0.24/0.56 thf(fact_307_insert__UNIV,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( insert9649339lle_hf @ X @ top_to489427057lle_hf )
% 0.24/0.56 = top_to489427057lle_hf ) ).
% 0.24/0.56
% 0.24/0.56 % insert_UNIV
% 0.24/0.56 thf(fact_308_insert__UNIV,axiom,
% 0.24/0.56 ! [X: nat] :
% 0.24/0.56 ( ( insert_nat @ X @ top_top_set_nat )
% 0.24/0.56 = top_top_set_nat ) ).
% 0.24/0.56
% 0.24/0.56 % insert_UNIV
% 0.24/0.56 thf(fact_309_IntE,axiom,
% 0.24/0.56 ! [C: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) )
% 0.24/0.56 => ~ ( ( member_nat @ C @ A )
% 0.24/0.56 => ~ ( member_nat @ C @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % IntE
% 0.24/0.56 thf(fact_310_IntE,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ C @ ( inf_in923488851lle_hf @ A @ B4 ) )
% 0.24/0.56 => ~ ( ( member1367349282lle_hf @ C @ A )
% 0.24/0.56 => ~ ( member1367349282lle_hf @ C @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % IntE
% 0.24/0.56 thf(fact_311_IntD1,axiom,
% 0.24/0.56 ! [C: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) )
% 0.24/0.56 => ( member_nat @ C @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % IntD1
% 0.24/0.56 thf(fact_312_IntD1,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ C @ ( inf_in923488851lle_hf @ A @ B4 ) )
% 0.24/0.56 => ( member1367349282lle_hf @ C @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % IntD1
% 0.24/0.56 thf(fact_313_IntD2,axiom,
% 0.24/0.56 ! [C: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) )
% 0.24/0.56 => ( member_nat @ C @ B4 ) ) ).
% 0.24/0.56
% 0.24/0.56 % IntD2
% 0.24/0.56 thf(fact_314_IntD2,axiom,
% 0.24/0.56 ! [C: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ C @ ( inf_in923488851lle_hf @ A @ B4 ) )
% 0.24/0.56 => ( member1367349282lle_hf @ C @ B4 ) ) ).
% 0.24/0.56
% 0.24/0.56 % IntD2
% 0.24/0.56 thf(fact_315_Int__insert__left,axiom,
% 0.24/0.56 ! [A2: nat,C2: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( ( member_nat @ A2 @ C2 )
% 0.24/0.56 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B4 ) @ C2 )
% 0.24/0.56 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ B4 @ C2 ) ) ) )
% 0.24/0.56 & ( ~ ( member_nat @ A2 @ C2 )
% 0.24/0.56 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B4 ) @ C2 )
% 0.24/0.56 = ( inf_inf_set_nat @ B4 @ C2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_left
% 0.24/0.56 thf(fact_316_Int__insert__left,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,C2: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( ( member1367349282lle_hf @ A2 @ C2 )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ ( insert9649339lle_hf @ A2 @ B4 ) @ C2 )
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ ( inf_in923488851lle_hf @ B4 @ C2 ) ) ) )
% 0.24/0.56 & ( ~ ( member1367349282lle_hf @ A2 @ C2 )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ ( insert9649339lle_hf @ A2 @ B4 ) @ C2 )
% 0.24/0.56 = ( inf_in923488851lle_hf @ B4 @ C2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_left
% 0.24/0.56 thf(fact_317_Int__insert__right,axiom,
% 0.24/0.56 ! [A2: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ( ( member_nat @ A2 @ A )
% 0.24/0.56 => ( ( inf_inf_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 0.24/0.56 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ A @ B4 ) ) ) )
% 0.24/0.56 & ( ~ ( member_nat @ A2 @ A )
% 0.24/0.56 => ( ( inf_inf_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 0.24/0.56 = ( inf_inf_set_nat @ A @ B4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_right
% 0.24/0.56 thf(fact_318_Int__insert__right,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( ( member1367349282lle_hf @ A2 @ A )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ A @ ( insert9649339lle_hf @ A2 @ B4 ) )
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ ( inf_in923488851lle_hf @ A @ B4 ) ) ) )
% 0.24/0.56 & ( ~ ( member1367349282lle_hf @ A2 @ A )
% 0.24/0.56 => ( ( inf_in923488851lle_hf @ A @ ( insert9649339lle_hf @ A2 @ B4 ) )
% 0.24/0.56 = ( inf_in923488851lle_hf @ A @ B4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Int_insert_right
% 0.24/0.56 thf(fact_319_mk__disjoint__insert,axiom,
% 0.24/0.56 ! [A2: nat,A: set_nat] :
% 0.24/0.56 ( ( member_nat @ A2 @ A )
% 0.24/0.56 => ? [B6: set_nat] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( insert_nat @ A2 @ B6 ) )
% 0.24/0.56 & ~ ( member_nat @ A2 @ B6 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % mk_disjoint_insert
% 0.24/0.56 thf(fact_320_mk__disjoint__insert,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ A2 @ A )
% 0.24/0.56 => ? [B6: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ B6 ) )
% 0.24/0.56 & ~ ( member1367349282lle_hf @ A2 @ B6 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % mk_disjoint_insert
% 0.24/0.56 thf(fact_321_insert__commute,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( insert9649339lle_hf @ X @ ( insert9649339lle_hf @ Y3 @ A ) )
% 0.24/0.56 = ( insert9649339lle_hf @ Y3 @ ( insert9649339lle_hf @ X @ A ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_commute
% 0.24/0.56 thf(fact_322_insert__eq__iff,axiom,
% 0.24/0.56 ! [A2: nat,A: set_nat,B: nat,B4: set_nat] :
% 0.24/0.56 ( ~ ( member_nat @ A2 @ A )
% 0.24/0.56 => ( ~ ( member_nat @ B @ B4 )
% 0.24/0.56 => ( ( ( insert_nat @ A2 @ A )
% 0.24/0.56 = ( insert_nat @ B @ B4 ) )
% 0.24/0.56 = ( ( ( A2 = B )
% 0.24/0.56 => ( A = B4 ) )
% 0.24/0.56 & ( ( A2 != B )
% 0.24/0.56 => ? [C3: set_nat] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( insert_nat @ B @ C3 ) )
% 0.24/0.56 & ~ ( member_nat @ B @ C3 )
% 0.24/0.56 & ( B4
% 0.24/0.56 = ( insert_nat @ A2 @ C3 ) )
% 0.24/0.56 & ~ ( member_nat @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_eq_iff
% 0.24/0.56 thf(fact_323_insert__eq__iff,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ~ ( member1367349282lle_hf @ A2 @ A )
% 0.24/0.56 => ( ~ ( member1367349282lle_hf @ B @ B4 )
% 0.24/0.56 => ( ( ( insert9649339lle_hf @ A2 @ A )
% 0.24/0.56 = ( insert9649339lle_hf @ B @ B4 ) )
% 0.24/0.56 = ( ( ( A2 = B )
% 0.24/0.56 => ( A = B4 ) )
% 0.24/0.56 & ( ( A2 != B )
% 0.24/0.56 => ? [C3: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( insert9649339lle_hf @ B @ C3 ) )
% 0.24/0.56 & ~ ( member1367349282lle_hf @ B @ C3 )
% 0.24/0.56 & ( B4
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ C3 ) )
% 0.24/0.56 & ~ ( member1367349282lle_hf @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_eq_iff
% 0.24/0.56 thf(fact_324_insert__absorb,axiom,
% 0.24/0.56 ! [A2: nat,A: set_nat] :
% 0.24/0.56 ( ( member_nat @ A2 @ A )
% 0.24/0.56 => ( ( insert_nat @ A2 @ A )
% 0.24/0.56 = A ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_absorb
% 0.24/0.56 thf(fact_325_insert__absorb,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ A2 @ A )
% 0.24/0.56 => ( ( insert9649339lle_hf @ A2 @ A )
% 0.24/0.56 = A ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_absorb
% 0.24/0.56 thf(fact_326_insert__ident,axiom,
% 0.24/0.56 ! [X: nat,A: set_nat,B4: set_nat] :
% 0.24/0.56 ( ~ ( member_nat @ X @ A )
% 0.24/0.56 => ( ~ ( member_nat @ X @ B4 )
% 0.24/0.56 => ( ( ( insert_nat @ X @ A )
% 0.24/0.56 = ( insert_nat @ X @ B4 ) )
% 0.24/0.56 = ( A = B4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_ident
% 0.24/0.56 thf(fact_327_insert__ident,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ~ ( member1367349282lle_hf @ X @ A )
% 0.24/0.56 => ( ~ ( member1367349282lle_hf @ X @ B4 )
% 0.24/0.56 => ( ( ( insert9649339lle_hf @ X @ A )
% 0.24/0.56 = ( insert9649339lle_hf @ X @ B4 ) )
% 0.24/0.56 = ( A = B4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insert_ident
% 0.24/0.56 thf(fact_328_Set_Oset__insert,axiom,
% 0.24/0.56 ! [X: nat,A: set_nat] :
% 0.24/0.56 ( ( member_nat @ X @ A )
% 0.24/0.56 => ~ ! [B6: set_nat] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( insert_nat @ X @ B6 ) )
% 0.24/0.56 => ( member_nat @ X @ B6 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Set.set_insert
% 0.24/0.56 thf(fact_329_Set_Oset__insert,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ X @ A )
% 0.24/0.56 => ~ ! [B6: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( insert9649339lle_hf @ X @ B6 ) )
% 0.24/0.56 => ( member1367349282lle_hf @ X @ B6 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Set.set_insert
% 0.24/0.56 thf(fact_330_insertI2,axiom,
% 0.24/0.56 ! [A2: nat,B4: set_nat,B: nat] :
% 0.24/0.56 ( ( member_nat @ A2 @ B4 )
% 0.24/0.56 => ( member_nat @ A2 @ ( insert_nat @ B @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insertI2
% 0.24/0.56 thf(fact_331_insertI2,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ A2 @ B4 )
% 0.24/0.56 => ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ B @ B4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insertI2
% 0.24/0.56 thf(fact_332_insertI1,axiom,
% 0.24/0.56 ! [A2: nat,B4: set_nat] : ( member_nat @ A2 @ ( insert_nat @ A2 @ B4 ) ) ).
% 0.24/0.56
% 0.24/0.56 % insertI1
% 0.24/0.56 thf(fact_333_insertI1,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,B4: set_HF_Mirabelle_hf] : ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ A2 @ B4 ) ) ).
% 0.24/0.56
% 0.24/0.56 % insertI1
% 0.24/0.56 thf(fact_334_insertE,axiom,
% 0.24/0.56 ! [A2: nat,B: nat,A: set_nat] :
% 0.24/0.56 ( ( member_nat @ A2 @ ( insert_nat @ B @ A ) )
% 0.24/0.56 => ( ( A2 != B )
% 0.24/0.56 => ( member_nat @ A2 @ A ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insertE
% 0.24/0.56 thf(fact_335_insertE,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
% 0.24/0.56 ( ( member1367349282lle_hf @ A2 @ ( insert9649339lle_hf @ B @ A ) )
% 0.24/0.56 => ( ( A2 != B )
% 0.24/0.56 => ( member1367349282lle_hf @ A2 @ A ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % insertE
% 0.24/0.56 thf(fact_336_hfset__hinsert,axiom,
% 0.24/0.56 ! [A2: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( hF_Mirabelle_hfset @ ( hF_Mirabelle_hinsert @ A2 @ B ) )
% 0.24/0.56 = ( insert9649339lle_hf @ A2 @ ( hF_Mirabelle_hfset @ B ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % hfset_hinsert
% 0.24/0.56 thf(fact_337_hcard__union__inter,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( plus_plus_nat @ ( hF_Mirabelle_hcard @ ( sup_su638957495lle_hf @ X @ Y3 ) ) @ ( hF_Mirabelle_hcard @ ( inf_in956532509lle_hf @ X @ Y3 ) ) )
% 0.24/0.56 = ( plus_plus_nat @ ( hF_Mirabelle_hcard @ X ) @ ( hF_Mirabelle_hcard @ Y3 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % hcard_union_inter
% 0.24/0.56 thf(fact_338_hcard__hinsert__if,axiom,
% 0.24/0.56 ! [X: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.56 ( ( ( hF_Mirabelle_hmem @ X @ Y3 )
% 0.24/0.56 => ( ( hF_Mirabelle_hcard @ ( hF_Mirabelle_hinsert @ X @ Y3 ) )
% 0.24/0.63 = ( hF_Mirabelle_hcard @ Y3 ) ) )
% 0.24/0.63 & ( ~ ( hF_Mirabelle_hmem @ X @ Y3 )
% 0.24/0.63 => ( ( hF_Mirabelle_hcard @ ( hF_Mirabelle_hinsert @ X @ Y3 ) )
% 0.24/0.63 = ( suc @ ( hF_Mirabelle_hcard @ Y3 ) ) ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % hcard_hinsert_if
% 0.24/0.63 thf(fact_339_add__left__cancel,axiom,
% 0.24/0.63 ! [A2: nat,B: nat,C: nat] :
% 0.24/0.63 ( ( ( plus_plus_nat @ A2 @ B )
% 0.24/0.63 = ( plus_plus_nat @ A2 @ C ) )
% 0.24/0.63 = ( B = C ) ) ).
% 0.24/0.63
% 0.24/0.63 % add_left_cancel
% 0.24/0.63 thf(fact_340_add__right__cancel,axiom,
% 0.24/0.63 ! [B: nat,A2: nat,C: nat] :
% 0.24/0.63 ( ( ( plus_plus_nat @ B @ A2 )
% 0.24/0.63 = ( plus_plus_nat @ C @ A2 ) )
% 0.24/0.63 = ( B = C ) ) ).
% 0.24/0.63
% 0.24/0.63 % add_right_cancel
% 0.24/0.63 thf(fact_341_zero__eq__add__iff__both__eq__0,axiom,
% 0.24/0.63 ! [X: nat,Y3: nat] :
% 0.24/0.63 ( ( zero_zero_nat
% 0.24/0.63 = ( plus_plus_nat @ X @ Y3 ) )
% 0.24/0.63 = ( ( X = zero_zero_nat )
% 0.24/0.63 & ( Y3 = zero_zero_nat ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % zero_eq_add_iff_both_eq_0
% 0.24/0.63 thf(fact_342_add__eq__0__iff__both__eq__0,axiom,
% 0.24/0.63 ! [X: nat,Y3: nat] :
% 0.24/0.63 ( ( ( plus_plus_nat @ X @ Y3 )
% 0.24/0.63 = zero_zero_nat )
% 0.24/0.63 = ( ( X = zero_zero_nat )
% 0.24/0.63 & ( Y3 = zero_zero_nat ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % add_eq_0_iff_both_eq_0
% 0.24/0.63 thf(fact_343_add__cancel__right__right,axiom,
% 0.24/0.63 ! [A2: nat,B: nat] :
% 0.24/0.63 ( ( A2
% 0.24/0.63 = ( plus_plus_nat @ A2 @ B ) )
% 0.24/0.63 = ( B = zero_zero_nat ) ) ).
% 0.24/0.63
% 0.24/0.63 % add_cancel_right_right
% 0.24/0.63 thf(fact_344_add__cancel__right__left,axiom,
% 0.24/0.63 ! [A2: nat,B: nat] :
% 0.24/0.63 ( ( A2
% 0.24/0.63 = ( plus_plus_nat @ B @ A2 ) )
% 0.24/0.63 = ( B = zero_zero_nat ) ) ).
% 0.24/0.63
% 0.24/0.63 % add_cancel_right_left
% 0.24/0.63 thf(fact_345_add__cancel__left__right,axiom,
% 0.24/0.63 ! [A2: nat,B: nat] :
% 0.24/0.63 ( ( ( plus_plus_nat @ A2 @ B )
% 0.24/0.63 = A2 )
% 0.24/0.63 = ( B = zero_zero_nat ) ) ).
% 0.24/0.63
% 0.24/0.63 % add_cancel_left_right
% 0.24/0.63 thf(fact_346_add__cancel__left__left,axiom,
% 0.24/0.63 ! [B: nat,A2: nat] :
% 0.24/0.63 ( ( ( plus_plus_nat @ B @ A2 )
% 0.24/0.63 = A2 )
% 0.24/0.63 = ( B = zero_zero_nat ) ) ).
% 0.24/0.63
% 0.24/0.63 % add_cancel_left_left
% 0.24/0.63 thf(fact_347_add_Oright__neutral,axiom,
% 0.24/0.63 ! [A2: nat] :
% 0.24/0.63 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 0.24/0.63 = A2 ) ).
% 0.24/0.63
% 0.24/0.63 % add.right_neutral
% 0.24/0.63 thf(fact_348_add_Oleft__neutral,axiom,
% 0.24/0.63 ! [A2: nat] :
% 0.24/0.63 ( ( plus_plus_nat @ zero_zero_nat @ A2 )
% 0.24/0.63 = A2 ) ).
% 0.24/0.63
% 0.24/0.63 % add.left_neutral
% 0.24/0.63 thf(fact_349_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.24/0.63 ! [A2: nat,B: nat,C: nat] :
% 0.24/0.63 ( ( plus_plus_nat @ ( plus_plus_nat @ A2 @ B ) @ C )
% 0.24/0.63 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % ab_semigroup_add_class.add_ac(1)
% 0.24/0.63 thf(fact_350_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.24/0.63 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.24/0.63 ( ( ( I = J )
% 0.24/0.63 & ( K = L ) )
% 0.24/0.63 => ( ( plus_plus_nat @ I @ K )
% 0.24/0.63 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % add_mono_thms_linordered_semiring(4)
% 0.24/0.63 thf(fact_351_group__cancel_Oadd1,axiom,
% 0.24/0.63 ! [A: nat,K: nat,A2: nat,B: nat] :
% 0.24/0.63 ( ( A
% 0.24/0.63 = ( plus_plus_nat @ K @ A2 ) )
% 0.24/0.63 => ( ( plus_plus_nat @ A @ B )
% 0.24/0.63 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A2 @ B ) ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % group_cancel.add1
% 0.24/0.63 thf(fact_352_group__cancel_Oadd2,axiom,
% 0.24/0.63 ! [B4: nat,K: nat,B: nat,A2: nat] :
% 0.24/0.63 ( ( B4
% 0.24/0.63 = ( plus_plus_nat @ K @ B ) )
% 0.24/0.63 => ( ( plus_plus_nat @ A2 @ B4 )
% 0.24/0.63 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A2 @ B ) ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % group_cancel.add2
% 0.24/0.63 thf(fact_353_add_Oassoc,axiom,
% 0.24/0.63 ! [A2: nat,B: nat,C: nat] :
% 0.24/0.63 ( ( plus_plus_nat @ ( plus_plus_nat @ A2 @ B ) @ C )
% 0.24/0.63 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % add.assoc
% 0.24/0.63
% 0.24/0.63 % Conjectures (2)
% 0.24/0.63 thf(conj_0,hypothesis,
% 0.24/0.63 hF_Mir199975595nction @ r ).
% 0.24/0.63
% 0.24/0.63 thf(conj_1,conjecture,
% 0.24/0.63 hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) ).
% 0.24/0.63
% 0.24/0.63 %------------------------------------------------------------------------------
% 0.24/0.63 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.piUKFVrNVx/cvc5---1.0.5_23655.p...
% 0.24/0.63 (declare-sort $$unsorted 0)
% 0.24/0.63 (declare-sort tptp.set_HF_Mirabelle_hf 0)
% 0.24/0.63 (declare-sort tptp.hF_Mirabelle_hf 0)
% 0.24/0.63 (declare-sort tptp.set_nat 0)
% 0.24/0.63 (declare-sort tptp.nat 0)
% 0.24/0.63 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.24/0.63 (declare-fun tptp.zero_z189798548lle_hf () tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.24/0.63 (declare-fun tptp.hF_Mir818139703ollect ((-> tptp.hF_Mirabelle_hf Bool) tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_HF (tptp.set_HF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_HInter (tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_HUnion (tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mir1248913145eplace (tptp.hF_Mirabelle_hf (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool)) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_RepFun (tptp.hF_Mirabelle_hf (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_Replace (tptp.hF_Mirabelle_hf (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool)) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_hcard (tptp.hF_Mirabelle_hf) tptp.nat)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_Abs_hf (tptp.nat) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_Rep_hf (tptp.hF_Mirabelle_hf) tptp.nat)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_hfset (tptp.hF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_hfst (tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mir199975595nction (tptp.hF_Mirabelle_hf) Bool)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_hinsert (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_hmem (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) Bool)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_hpair (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mir434065167lation (tptp.hF_Mirabelle_hf) Bool)
% 0.24/0.63 (declare-fun tptp.hF_Mir1653039215strict (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mirabelle_hsnd (tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.hF_Mir137170979_hpair (tptp.hF_Mirabelle_hf) Bool)
% 0.24/0.63 (declare-fun tptp.inf_in307783154e_hf_o ((-> tptp.hF_Mirabelle_hf Bool) (-> tptp.hF_Mirabelle_hf Bool) tptp.hF_Mirabelle_hf) Bool)
% 0.24/0.63 (declare-fun tptp.inf_inf_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.24/0.63 (declare-fun tptp.inf_in956532509lle_hf (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.inf_in923488851lle_hf (tptp.set_HF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.inf_inf_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 0.24/0.63 (declare-fun tptp.sup_su1199008216e_hf_o ((-> tptp.hF_Mirabelle_hf Bool) (-> tptp.hF_Mirabelle_hf Bool) tptp.hF_Mirabelle_hf) Bool)
% 0.24/0.63 (declare-fun tptp.sup_sup_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.24/0.63 (declare-fun tptp.sup_su638957495lle_hf (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.sup_su1790843629lle_hf (tptp.set_HF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 0.24/0.63 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.24/0.63 (declare-fun tptp.top_to22270292e_hf_o (tptp.hF_Mirabelle_hf) Bool)
% 0.24/0.63 (declare-fun tptp.top_top_nat_o (tptp.nat) Bool)
% 0.24/0.63 (declare-fun tptp.top_top_o () Bool)
% 0.24/0.63 (declare-fun tptp.top_to489427057lle_hf () tptp.set_HF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 0.24/0.63 (declare-fun tptp.collec2046588256lle_hf ((-> tptp.hF_Mirabelle_hf Bool)) tptp.set_HF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.24/0.63 (declare-fun tptp.insert9649339lle_hf (tptp.hF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 0.24/0.63 (declare-fun tptp.type_d1794767497hf_nat ((-> tptp.hF_Mirabelle_hf tptp.nat) (-> tptp.nat tptp.hF_Mirabelle_hf) tptp.set_nat) Bool)
% 0.24/0.63 (declare-fun tptp.member1367349282lle_hf (tptp.hF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) Bool)
% 0.24/0.63 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.24/0.63 (declare-fun tptp.r () tptp.hF_Mirabelle_hf)
% 0.24/0.63 (declare-fun tptp.x () tptp.hF_Mirabelle_hf)
% 0.24/0.63 (assert (forall ((R tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (@ tptp.hF_Mir434065167lation (@ (@ tptp.hF_Mir1653039215strict R) X))))
% 0.24/0.63 (assert (= tptp.hF_Mir199975595nction (lambda ((R2 tptp.hF_Mirabelle_hf)) (forall ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem (@ (@ tptp.hF_Mirabelle_hpair X2) Y)) R2) (forall ((Y2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem (@ (@ tptp.hF_Mirabelle_hpair X2) Y2)) R2) (= Y Y2))))))))
% 0.24/0.63 (assert (forall ((Z tptp.hF_Mirabelle_hf) (R tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem Z))) (= (@ _let_1 (@ (@ tptp.hF_Mir1653039215strict R) A)) (and (@ _let_1 R) (exists ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (and (= Z (@ (@ tptp.hF_Mirabelle_hpair X2) Y)) (@ (@ tptp.hF_Mirabelle_hmem X2) A))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf) (B2 tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hpair A2) B) (@ (@ tptp.hF_Mirabelle_hpair A3) B2)) (and (= A2 A3) (= B B2)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (= (@ tptp.hF_Mirabelle_Rep_hf X) (@ tptp.hF_Mirabelle_Rep_hf Y3)) (= X Y3))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X3))) (= (@ _let_1 A2) (@ _let_1 B)))) (= A2 B))))
% 0.24/0.63 (assert (= (lambda ((Y4 tptp.hF_Mirabelle_hf) (Z2 tptp.hF_Mirabelle_hf)) (= Y4 Z2)) (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (forall ((X2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X2))) (= (@ _let_1 A4) (@ _let_1 B3)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X) Y3) (not (= X Y3)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (R3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (=> (forall ((U tptp.hF_Mirabelle_hf) (V tptp.hF_Mirabelle_hf) (V2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ R3 U))) (=> (@ (@ tptp.hF_Mirabelle_hmem U) X) (=> (@ _let_1 V) (=> (@ _let_1 V2) (= V2 V)))))) (exists ((Z3 tptp.hF_Mirabelle_hf)) (forall ((V3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem V3) Z3) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) X) (@ (@ R3 U2) V3)))))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (exists ((Z3 tptp.hF_Mirabelle_hf)) (forall ((U3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U3))) (= (@ _let_1 Z3) (or (@ _let_1 X) (@ _let_1 Y3))))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (not (and (@ (@ tptp.hF_Mirabelle_hmem X) Y3) (@ (@ tptp.hF_Mirabelle_hmem Y3) X)))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf) (B2 tptp.hF_Mirabelle_hf)) (=> (= (@ (@ tptp.hF_Mirabelle_hpair A2) B) (@ (@ tptp.hF_Mirabelle_hpair A3) B2)) (not (=> (= A2 A3) (not (= B B2)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (exists ((Z3 tptp.hF_Mirabelle_hf)) (forall ((U3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem U3) Z3) (exists ((Y tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem Y) X) (@ (@ tptp.hF_Mirabelle_hmem U3) Y))))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool))) (exists ((Z3 tptp.hF_Mirabelle_hf)) (forall ((U3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U3))) (= (@ _let_1 Z3) (and (@ _let_1 X) (@ P U3))))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem X) X))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hpair A2) B) A2))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hpair A2) B) B))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (exists ((Z3 tptp.hF_Mirabelle_hf)) (forall ((V3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem V3) Z3) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) X) (= V3 (@ F U2)))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_hfst (@ (@ tptp.hF_Mirabelle_hpair A2) B)) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_hsnd (@ (@ tptp.hF_Mirabelle_hpair A2) B)) B)))
% 0.24/0.63 (assert (= tptp.hF_Mir434065167lation (lambda ((R2 tptp.hF_Mirabelle_hf)) (forall ((Z4 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem Z4) R2) (@ tptp.hF_Mir137170979_hpair Z4))))))
% 0.24/0.63 (assert (= tptp.hF_Mir137170979_hpair (lambda ((Z4 tptp.hF_Mirabelle_hf)) (exists ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (= Z4 (@ (@ tptp.hF_Mirabelle_hpair X2) Y))))))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (R3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool)) (V4 tptp.hF_Mirabelle_hf)) (=> (forall ((U tptp.hF_Mirabelle_hf) (V tptp.hF_Mirabelle_hf) (V2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ R3 U))) (=> (@ (@ tptp.hF_Mirabelle_hmem U) A) (=> (@ _let_1 V) (=> (@ _let_1 V2) (= V2 V)))))) (= (@ (@ tptp.hF_Mirabelle_hmem V4) (@ (@ tptp.hF_Mir1248913145eplace A) R3)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A) (@ (@ R3 U2) V4)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem X) (@ tptp.hF_Mirabelle_HUnion A)) (exists ((Y tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem Y) A) (@ (@ tptp.hF_Mirabelle_hmem X) Y))))))
% 0.24/0.63 (assert (forall ((V4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (R3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_hmem V4) (@ (@ tptp.hF_Mirabelle_Replace A) R3)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A) (@ (@ R3 U2) V4) (forall ((Y tptp.hF_Mirabelle_hf)) (=> (@ (@ R3 U2) Y) (= Y V4))))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool)) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X))) (= (@ _let_1 (@ (@ tptp.hF_Mir818139703ollect P) A)) (and (@ P X) (@ _let_1 A))))))
% 0.24/0.63 (assert (forall ((V4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_hmem V4) (@ (@ tptp.hF_Mirabelle_RepFun A) F)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A) (= V4 (@ F U2)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_Abs_hf (@ tptp.hF_Mirabelle_Rep_hf X)) X)))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (G (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (= A B4) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X3) B4) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.hF_Mirabelle_RepFun A) F) (@ (@ tptp.hF_Mirabelle_RepFun B4) G))))))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool)) (Q (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (=> (= A B4) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y5 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X3) B4) (= (@ (@ P X3) Y5) (@ (@ Q X3) Y5)))) (= (@ (@ tptp.hF_Mirabelle_Replace A) P) (@ (@ tptp.hF_Mirabelle_Replace B4) Q))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X) Y3) (not (= (@ tptp.hF_Mirabelle_HUnion X) Y3)))))
% 0.24/0.63 (assert (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) tptp.top_top_set_nat) (= (@ tptp.hF_Mirabelle_Rep_hf (@ tptp.hF_Mirabelle_Abs_hf Y3)) Y3))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem tptp.zero_z189798548lle_hf) (@ (@ tptp.hF_Mirabelle_hpair X) Y3)))))
% 0.24/0.63 (assert (= tptp.hF_Mirabelle_hmem (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A4) (@ tptp.hF_Mirabelle_hfset B3)))))
% 0.24/0.63 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mir818139703ollect P) tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf)))
% 0.24/0.63 (assert (= (@ tptp.hF_Mirabelle_HUnion tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf))
% 0.24/0.63 (assert (forall ((R3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_Replace tptp.zero_z189798548lle_hf) R3) tptp.zero_z189798548lle_hf)))
% 0.24/0.63 (assert (forall ((F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_RepFun tptp.zero_z189798548lle_hf) F) tptp.zero_z189798548lle_hf)))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_RepFun (@ (@ tptp.hF_Mirabelle_hinsert A2) B)) F) (@ (@ tptp.hF_Mirabelle_hinsert (@ F A2)) (@ (@ tptp.hF_Mirabelle_RepFun B) F)))))
% 0.24/0.63 (assert (forall ((F tptp.hF_Mirabelle_hf) (G tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mir434065167lation (@ (@ tptp.sup_su638957495lle_hf F) G)) (and (@ tptp.hF_Mir434065167lation F) (@ tptp.hF_Mir434065167lation G)))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem A2))) (= (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert B) C)) (or (= A2 B) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hinsert A2) tptp.zero_z189798548lle_hf) (@ (@ tptp.hF_Mirabelle_hinsert B) tptp.zero_z189798548lle_hf)) (= A2 B))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A2) B)) (or (@ _let_1 A2) (@ _let_1 B))))))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf tptp.zero_z189798548lle_hf) A) A)))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.member1367349282lle_hf A2) (@ tptp.collec2046588256lle_hf P)) (@ P A2))))
% 0.24/0.63 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A))) A)))
% 0.24/0.63 (assert (forall ((A tptp.set_HF_Mirabelle_hf)) (= (@ tptp.collec2046588256lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X2) A))) A)))
% 0.24/0.63 (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)))))
% 0.24/0.63 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A) tptp.zero_z189798548lle_hf) A)))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_RepFun (@ (@ tptp.sup_su638957495lle_hf A) B4)) F) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.hF_Mirabelle_RepFun A) F)) (@ (@ tptp.hF_Mirabelle_RepFun B4) F)))))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HUnion (@ (@ tptp.sup_su638957495lle_hf A) B4)) (@ (@ tptp.sup_su638957495lle_hf (@ tptp.hF_Mirabelle_HUnion A)) (@ tptp.hF_Mirabelle_HUnion B4)))))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (R3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_Replace (@ (@ tptp.sup_su638957495lle_hf A) B4)) R3) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.hF_Mirabelle_Replace A) R3)) (@ (@ tptp.hF_Mirabelle_Replace B4) R3)))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HUnion (@ (@ tptp.hF_Mirabelle_hinsert A2) A)) (@ (@ tptp.sup_su638957495lle_hf A2) (@ tptp.hF_Mirabelle_HUnion A)))))
% 0.24/0.63 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (X tptp.hF_Mirabelle_hf)) (=> (@ P tptp.zero_z189798548lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (=> (@ P X3) (forall ((Y5 tptp.hF_Mirabelle_hf)) (=> (@ P Y5) (@ P (@ (@ tptp.hF_Mirabelle_hinsert Y5) X3)))))) (@ P X)))))
% 0.24/0.63 (assert (= tptp.hF_Mirabelle_hinsert (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf B3) (@ (@ tptp.hF_Mirabelle_hinsert A4) tptp.zero_z189798548lle_hf)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hinsert A2) (@ (@ tptp.hF_Mirabelle_hinsert B) tptp.zero_z189798548lle_hf)) (@ (@ tptp.hF_Mirabelle_hinsert C) (@ (@ tptp.hF_Mirabelle_hinsert D) tptp.zero_z189798548lle_hf))) (or (and (= A2 C) (= B D)) (and (= A2 D) (= B C))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hinsert A2) A) tptp.zero_z189798548lle_hf))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 A)) B4) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B4))))))
% 0.24/0.63 (assert (forall ((B4 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 0.24/0.63 (assert (forall ((Y3 tptp.hF_Mirabelle_hf)) (=> (not (= Y3 tptp.zero_z189798548lle_hf)) (not (forall ((A5 tptp.hF_Mirabelle_hf) (B5 tptp.hF_Mirabelle_hf)) (=> (= Y3 (@ (@ tptp.hF_Mirabelle_hinsert A5) B5)) (@ (@ tptp.hF_Mirabelle_hmem A5) B5)))))))
% 0.24/0.63 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (Z tptp.hF_Mirabelle_hf)) (=> (@ P tptp.zero_z189798548lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y5 tptp.hF_Mirabelle_hf)) (=> (@ P X3) (=> (@ P Y5) (=> (not (@ (@ tptp.hF_Mirabelle_hmem X3) Y5)) (@ P (@ (@ tptp.hF_Mirabelle_hinsert X3) Y5)))))) (@ P Z)))))
% 0.24/0.63 (assert (= tptp.hF_Mirabelle_hpair (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A4))) (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_1 tptp.zero_z189798548lle_hf)) (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert B3) tptp.zero_z189798548lle_hf))) tptp.zero_z189798548lle_hf))))))
% 0.24/0.63 (assert (= tptp.hF_Mirabelle_hpair (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A4))) (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_1 (@ _let_1 tptp.zero_z189798548lle_hf))) (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert B3) tptp.zero_z189798548lle_hf))) tptp.zero_z189798548lle_hf))))))
% 0.24/0.63 (assert (forall ((Z tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (= Z (@ (@ tptp.hF_Mirabelle_hinsert Y3) X)) (forall ((U2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U2))) (= (@ _let_1 Z) (or (@ _let_1 X) (= U2 Y3))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A2) tptp.zero_z189798548lle_hf))))
% 0.24/0.63 (assert (forall ((Z tptp.hF_Mirabelle_hf)) (= (= Z tptp.zero_z189798548lle_hf) (forall ((X2 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem X2) Z))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A2) tptp.zero_z189798548lle_hf))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hpair X) Y3) tptp.zero_z189798548lle_hf))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member_nat (@ tptp.hF_Mirabelle_Rep_hf X)) tptp.top_top_set_nat)))
% 0.24/0.63 (assert (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) tptp.top_top_set_nat) (not (forall ((X3 tptp.hF_Mirabelle_hf)) (not (= Y3 (@ tptp.hF_Mirabelle_Rep_hf X3))))))))
% 0.24/0.63 (assert (forall ((Y3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat Y3) tptp.top_top_set_nat) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ P (@ tptp.hF_Mirabelle_Rep_hf X3))) (@ P Y3)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (not (forall ((Y5 tptp.nat)) (=> (= X (@ tptp.hF_Mirabelle_Abs_hf Y5)) (not (@ (@ tptp.member_nat Y5) tptp.top_top_set_nat)))))))
% 0.24/0.63 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (X tptp.hF_Mirabelle_hf)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) tptp.top_top_set_nat) (@ P (@ tptp.hF_Mirabelle_Abs_hf Y5)))) (@ P X))))
% 0.24/0.63 (assert (forall ((X tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.member_nat X) tptp.top_top_set_nat) (=> (@ (@ tptp.member_nat Y3) tptp.top_top_set_nat) (= (= (@ tptp.hF_Mirabelle_Abs_hf X) (@ tptp.hF_Mirabelle_Abs_hf Y3)) (= X Y3))))))
% 0.24/0.63 (assert (@ tptp.hF_Mir434065167lation tptp.zero_z189798548lle_hf))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf tptp.top_to489427057lle_hf) X) tptp.top_to489427057lle_hf)))
% 0.24/0.63 (assert (forall ((X (-> tptp.nat Bool))) (= (@ (@ tptp.sup_sup_nat_o tptp.top_top_nat_o) X) tptp.top_top_nat_o)))
% 0.24/0.63 (assert (forall ((X (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.sup_su1199008216e_hf_o tptp.top_to22270292e_hf_o) X) tptp.top_to22270292e_hf_o)))
% 0.24/0.63 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.top_top_set_nat) X) tptp.top_top_set_nat)))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf X) tptp.top_to489427057lle_hf) tptp.top_to489427057lle_hf)))
% 0.24/0.63 (assert (forall ((X (-> tptp.nat Bool))) (= (@ (@ tptp.sup_sup_nat_o X) tptp.top_top_nat_o) tptp.top_top_nat_o)))
% 0.24/0.63 (assert (forall ((X (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.sup_su1199008216e_hf_o X) tptp.top_to22270292e_hf_o) tptp.top_to22270292e_hf_o)))
% 0.24/0.63 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.top_top_set_nat) tptp.top_top_set_nat)))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (not (= A tptp.zero_z189798548lle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem X) (@ tptp.hF_Mirabelle_HInter A)) (forall ((Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem Y) A) (@ (@ tptp.hF_Mirabelle_hmem X) Y)))))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) A2) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf A2) A2) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A2) A2) A2)))
% 0.24/0.63 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) X) X)))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf X) X) X)))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X) X) X)))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.sup_sup_set_nat A2) B))) (= (@ (@ tptp.sup_sup_set_nat _let_1) B) _let_1))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.sup_su1790843629lle_hf A2) B))) (= (@ (@ tptp.sup_su1790843629lle_hf _let_1) B) _let_1))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.sup_su638957495lle_hf A2) B))) (= (@ (@ tptp.sup_su638957495lle_hf _let_1) B) _let_1))))
% 0.24/0.63 (assert (= (@ tptp.hF_Mirabelle_HInter tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (let ((_let_2 (@ tptp.sup_su1790843629lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat B))) (let ((_let_2 (@ tptp.sup_sup_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.63 (assert (forall ((B tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf B))) (let ((_let_2 (@ tptp.sup_su1790843629lle_hf A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.63 (assert (forall ((B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf B))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.63 (assert (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y) X2))))
% 0.24/0.63 (assert (= tptp.sup_su1790843629lle_hf (lambda ((X2 tptp.set_HF_Mirabelle_hf) (Y tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.sup_su1790843629lle_hf Y) X2))))
% 0.24/0.63 (assert (= tptp.sup_su638957495lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf Y) X2))))
% 0.24/0.63 (assert (= tptp.sup_sup_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B3) A4))))
% 0.24/0.63 (assert (= tptp.sup_su1790843629lle_hf (lambda ((A4 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.sup_su1790843629lle_hf B3) A4))))
% 0.24/0.63 (assert (= tptp.sup_su638957495lle_hf (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf B3) A4))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y3) Z))))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (= (@ (@ tptp.sup_su1790843629lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf Y3) Z))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y3) Z))))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C))))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf A2))) (= (@ (@ tptp.sup_su1790843629lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf B) C))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A2))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf B) C))))))
% 0.24/0.63 (assert (forall ((B4 tptp.set_nat) (K tptp.set_nat) (B tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (let ((_let_2 (@ tptp.sup_sup_set_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (K tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf A2))) (let ((_let_2 (@ tptp.sup_su1790843629lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.63 (assert (forall ((B4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A2))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.63 (assert (forall ((A tptp.set_nat) (K tptp.set_nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.sup_sup_set_nat A) B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B)))))))
% 0.24/0.63 (assert (forall ((A tptp.set_HF_Mirabelle_hf) (K tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.sup_su1790843629lle_hf A) B) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A2) B)))))))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.sup_su638957495lle_hf A) B) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A2) B)))))))
% 0.24/0.63 (assert (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y) X2))))
% 0.24/0.63 (assert (= tptp.sup_su1790843629lle_hf (lambda ((X2 tptp.set_HF_Mirabelle_hf) (Y tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.sup_su1790843629lle_hf Y) X2))))
% 0.24/0.63 (assert (= tptp.sup_su638957495lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf Y) X2))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y3) Z))))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (= (@ (@ tptp.sup_su1790843629lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf Y3) Z))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y3) Z))))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (let ((_let_2 (@ tptp.sup_su1790843629lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) tptp.top_to489427057lle_hf)))
% 0.24/0.63 (assert (forall ((X tptp.nat)) (@ (@ tptp.member_nat X) tptp.top_top_set_nat)))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) tptp.top_to489427057lle_hf)))
% 0.24/0.63 (assert (forall ((X tptp.nat)) (@ (@ tptp.member_nat X) tptp.top_top_set_nat)))
% 0.24/0.63 (assert (= tptp.top_top_nat_o (lambda ((X2 tptp.nat)) tptp.top_top_o)))
% 0.24/0.63 (assert (= tptp.top_to22270292e_hf_o (lambda ((X2 tptp.hF_Mirabelle_hf)) tptp.top_top_o)))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (=> (not (= A tptp.zero_z189798548lle_hf)) (= (@ tptp.hF_Mirabelle_HInter (@ (@ tptp.hF_Mirabelle_hinsert A2) A)) (@ (@ tptp.inf_in956532509lle_hf A2) (@ tptp.hF_Mirabelle_HInter A))))))
% 0.24/0.63 (assert (@ (@ (@ tptp.type_d1794767497hf_nat tptp.hF_Mirabelle_Rep_hf) tptp.hF_Mirabelle_Abs_hf) tptp.top_top_set_nat))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat X) Y3))) (= (@ (@ tptp.inf_inf_set_nat _let_1) Y3) _let_1))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in923488851lle_hf X) Y3))) (= (@ (@ tptp.inf_in923488851lle_hf _let_1) Y3) _let_1))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf X) Y3))) (= (@ (@ tptp.inf_in956532509lle_hf _let_1) Y3) _let_1))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat A2) B))) (= (@ (@ tptp.inf_inf_set_nat _let_1) B) _let_1))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in923488851lle_hf A2) B))) (= (@ (@ tptp.inf_in923488851lle_hf _let_1) B) _let_1))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf A2) B))) (= (@ (@ tptp.inf_in956532509lle_hf _let_1) B) _let_1))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) X) X)))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf X) X) X)))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X) X) X)))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A2) A2) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf A2) A2) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A2) A2) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf A2) tptp.top_to489427057lle_hf) A2)))
% 0.24/0.63 (assert (forall ((A2 (-> tptp.nat Bool))) (= (@ (@ tptp.inf_inf_nat_o A2) tptp.top_top_nat_o) A2)))
% 0.24/0.63 (assert (forall ((A2 (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.inf_in307783154e_hf_o A2) tptp.top_to22270292e_hf_o) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A2) tptp.top_top_set_nat) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (= (= tptp.top_to489427057lle_hf (@ (@ tptp.inf_in923488851lle_hf A2) B)) (and (= A2 tptp.top_to489427057lle_hf) (= B tptp.top_to489427057lle_hf)))))
% 0.24/0.63 (assert (forall ((A2 (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (= (= tptp.top_top_nat_o (@ (@ tptp.inf_inf_nat_o A2) B)) (and (= A2 tptp.top_top_nat_o) (= B tptp.top_top_nat_o)))))
% 0.24/0.63 (assert (forall ((A2 (-> tptp.hF_Mirabelle_hf Bool)) (B (-> tptp.hF_Mirabelle_hf Bool))) (= (= tptp.top_to22270292e_hf_o (@ (@ tptp.inf_in307783154e_hf_o A2) B)) (and (= A2 tptp.top_to22270292e_hf_o) (= B tptp.top_to22270292e_hf_o)))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (= tptp.top_top_set_nat (@ (@ tptp.inf_inf_set_nat A2) B)) (and (= A2 tptp.top_top_set_nat) (= B tptp.top_top_set_nat)))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf tptp.top_to489427057lle_hf) A2) A2)))
% 0.24/0.63 (assert (forall ((A2 (-> tptp.nat Bool))) (= (@ (@ tptp.inf_inf_nat_o tptp.top_top_nat_o) A2) A2)))
% 0.24/0.63 (assert (forall ((A2 (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.inf_in307783154e_hf_o tptp.top_to22270292e_hf_o) A2) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) A2) A2)))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.inf_in923488851lle_hf A2) B) tptp.top_to489427057lle_hf) (and (= A2 tptp.top_to489427057lle_hf) (= B tptp.top_to489427057lle_hf)))))
% 0.24/0.63 (assert (forall ((A2 (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (= (= (@ (@ tptp.inf_inf_nat_o A2) B) tptp.top_top_nat_o) (and (= A2 tptp.top_top_nat_o) (= B tptp.top_top_nat_o)))))
% 0.24/0.63 (assert (forall ((A2 (-> tptp.hF_Mirabelle_hf Bool)) (B (-> tptp.hF_Mirabelle_hf Bool))) (= (= (@ (@ tptp.inf_in307783154e_hf_o A2) B) tptp.top_to22270292e_hf_o) (and (= A2 tptp.top_to22270292e_hf_o) (= B tptp.top_to22270292e_hf_o)))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A2) B) tptp.top_top_set_nat) (and (= A2 tptp.top_top_set_nat) (= B tptp.top_top_set_nat)))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (= (= tptp.top_to489427057lle_hf (@ (@ tptp.inf_in923488851lle_hf X) Y3)) (and (= X tptp.top_to489427057lle_hf) (= Y3 tptp.top_to489427057lle_hf)))))
% 0.24/0.63 (assert (forall ((X (-> tptp.nat Bool)) (Y3 (-> tptp.nat Bool))) (= (= tptp.top_top_nat_o (@ (@ tptp.inf_inf_nat_o X) Y3)) (and (= X tptp.top_top_nat_o) (= Y3 tptp.top_top_nat_o)))))
% 0.24/0.63 (assert (forall ((X (-> tptp.hF_Mirabelle_hf Bool)) (Y3 (-> tptp.hF_Mirabelle_hf Bool))) (= (= tptp.top_to22270292e_hf_o (@ (@ tptp.inf_in307783154e_hf_o X) Y3)) (and (= X tptp.top_to22270292e_hf_o) (= Y3 tptp.top_to22270292e_hf_o)))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (= (= tptp.top_top_set_nat (@ (@ tptp.inf_inf_set_nat X) Y3)) (and (= X tptp.top_top_set_nat) (= Y3 tptp.top_top_set_nat)))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.inf_in923488851lle_hf X) Y3) tptp.top_to489427057lle_hf) (and (= X tptp.top_to489427057lle_hf) (= Y3 tptp.top_to489427057lle_hf)))))
% 0.24/0.63 (assert (forall ((X (-> tptp.nat Bool)) (Y3 (-> tptp.nat Bool))) (= (= (@ (@ tptp.inf_inf_nat_o X) Y3) tptp.top_top_nat_o) (and (= X tptp.top_top_nat_o) (= Y3 tptp.top_top_nat_o)))))
% 0.24/0.63 (assert (forall ((X (-> tptp.hF_Mirabelle_hf Bool)) (Y3 (-> tptp.hF_Mirabelle_hf Bool))) (= (= (@ (@ tptp.inf_in307783154e_hf_o X) Y3) tptp.top_to22270292e_hf_o) (and (= X tptp.top_to22270292e_hf_o) (= Y3 tptp.top_to22270292e_hf_o)))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat X) Y3) tptp.top_top_set_nat) (and (= X tptp.top_top_set_nat) (= Y3 tptp.top_top_set_nat)))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf X) tptp.top_to489427057lle_hf) X)))
% 0.24/0.63 (assert (forall ((X (-> tptp.nat Bool))) (= (@ (@ tptp.inf_inf_nat_o X) tptp.top_top_nat_o) X)))
% 0.24/0.63 (assert (forall ((X (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.inf_in307783154e_hf_o X) tptp.top_to22270292e_hf_o) X)))
% 0.24/0.63 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.top_top_set_nat) X)))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf tptp.top_to489427057lle_hf) X) X)))
% 0.24/0.63 (assert (forall ((X (-> tptp.nat Bool))) (= (@ (@ tptp.inf_inf_nat_o tptp.top_top_nat_o) X) X)))
% 0.24/0.63 (assert (forall ((X (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.inf_in307783154e_hf_o tptp.top_to22270292e_hf_o) X) X)))
% 0.24/0.63 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) X) X)))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y3)) X)))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf X) (@ (@ tptp.sup_su1790843629lle_hf X) Y3)) X)))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X) (@ (@ tptp.sup_su638957495lle_hf X) Y3)) X)))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) (@ (@ tptp.inf_inf_set_nat X) Y3)) X)))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf X) (@ (@ tptp.inf_in923488851lle_hf X) Y3)) X)))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X) (@ (@ tptp.inf_in956532509lle_hf X) Y3)) X)))
% 0.24/0.63 (assert (forall ((U4 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U4))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf X) Y3)) (and (@ _let_1 X) (@ _let_1 Y3))))))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf tptp.zero_z189798548lle_hf) A) tptp.zero_z189798548lle_hf)))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A) tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf)))
% 0.24/0.63 (assert (= (@ tptp.hF_Mirabelle_Abs_hf tptp.zero_zero_nat) tptp.zero_z189798548lle_hf))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf X))) (let ((_let_2 (@ tptp.inf_in923488851lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B))) (let ((_let_2 (@ tptp.inf_inf_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.63 (assert (forall ((B tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf B))) (let ((_let_2 (@ tptp.inf_in923488851lle_hf A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.63 (assert (forall ((B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf B))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.63 (assert (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y) X2))))
% 0.24/0.63 (assert (= tptp.inf_in923488851lle_hf (lambda ((X2 tptp.set_HF_Mirabelle_hf) (Y tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.inf_in923488851lle_hf Y) X2))))
% 0.24/0.63 (assert (= tptp.inf_in956532509lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf Y) X2))))
% 0.24/0.63 (assert (= tptp.inf_inf_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B3) A4))))
% 0.24/0.63 (assert (= tptp.inf_in923488851lle_hf (lambda ((A4 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.inf_in923488851lle_hf B3) A4))))
% 0.24/0.63 (assert (= tptp.inf_in956532509lle_hf (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf B3) A4))))
% 0.24/0.63 (assert (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y3) Z))))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf X))) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf Y3) Z))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y3) Z))))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C))))))
% 0.24/0.63 (assert (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A2))) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf B) C))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A2))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C))))))
% 0.24/0.63 (assert (forall ((B4 tptp.set_nat) (K tptp.set_nat) (B tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (let ((_let_2 (@ tptp.inf_inf_set_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.63 (assert (forall ((B4 tptp.set_HF_Mirabelle_hf) (K tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A2))) (let ((_let_2 (@ tptp.inf_in923488851lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.63 (assert (forall ((B4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A2))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.63 (assert (forall ((A tptp.set_nat) (K tptp.set_nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.inf_inf_set_nat A) B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A2) B)))))))
% 0.24/0.63 (assert (forall ((A tptp.set_HF_Mirabelle_hf) (K tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.inf_in923488851lle_hf A) B) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A2) B)))))))
% 0.24/0.63 (assert (forall ((A tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.inf_in956532509lle_hf A) B) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf A2) B)))))))
% 0.24/0.63 (assert (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y) X2))))
% 0.24/0.63 (assert (= tptp.inf_in923488851lle_hf (lambda ((X2 tptp.set_HF_Mirabelle_hf) (Y tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.inf_in923488851lle_hf Y) X2))))
% 0.24/0.63 (assert (= tptp.inf_in956532509lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf Y) X2))))
% 0.24/0.63 (assert (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf X))) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf Y3) Z))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y3) Z))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.inf_in956532509lle_hf Y3) Z)) X) (@ (@ tptp.inf_in956532509lle_hf (@ (@ tptp.sup_su638957495lle_hf Y3) X)) (@ (@ tptp.sup_su638957495lle_hf Z) X)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y3) Z)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y3)) (@ _let_1 Z))))))
% 0.24/0.63 (assert (forall ((Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf (@ (@ tptp.sup_su638957495lle_hf Y3) Z)) X) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.inf_in956532509lle_hf Y3) X)) (@ (@ tptp.inf_in956532509lle_hf Z) X)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y3) Z)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y3)) (@ _let_1 Z))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y5 tptp.hF_Mirabelle_hf) (Z3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X3))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y5) Z3)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y5)) (@ _let_1 Z3))))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y3) Z)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y3)) (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y5 tptp.hF_Mirabelle_hf) (Z3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X3))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y5) Z3)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y5)) (@ _let_1 Z3))))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y3) Z)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y3)) (@ _let_1 Z)))))))
% 0.24/0.63 (assert (forall ((Z tptp.hF_Mirabelle_hf)) (=> (not (= Z tptp.zero_z189798548lle_hf)) (exists ((W tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem W) Z) (= (@ (@ tptp.inf_in956532509lle_hf W) Z) tptp.zero_z189798548lle_hf))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf B4))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.hF_Mirabelle_hmem X) B4))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf A) B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_3 (@ (@ tptp.inf_in956532509lle_hf (@ _let_2 A)) B4))) (let ((_let_4 (@ (@ tptp.hF_Mirabelle_hmem X) B4))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (= tptp.zero_z189798548lle_hf X) (= X tptp.zero_z189798548lle_hf))))
% 0.24/0.63 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((A tptp.set_HF_Mirabelle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X3) A)) (= tptp.top_to489427057lle_hf A))))
% 0.24/0.63 (assert (forall ((A tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A)) (= tptp.top_top_set_nat A))))
% 0.24/0.63 (assert (exists ((X3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X3) tptp.top_to489427057lle_hf)))
% 0.24/0.63 (assert (exists ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) tptp.top_top_set_nat)))
% 0.24/0.63 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) tptp.top_top_set_nat) tptp.top_top_set_nat)))
% 0.24/0.63 (assert (forall ((B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.top_top_set_nat) B4) tptp.top_top_set_nat)))
% 0.24/0.63 (assert (= tptp.top_top_set_nat (@ tptp.collect_nat tptp.top_top_nat_o)))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (F2 (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) tptp.top_top_set_nat) (= (exists ((X4 tptp.nat)) (@ F2 X4)) (exists ((B3 tptp.hF_Mirabelle_hf)) (@ F2 (@ Rep B3)))))))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (S tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) tptp.top_top_set_nat) (not (forall ((X3 tptp.nat)) (not (= S (@ Abs X3))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HF (@ tptp.hF_Mirabelle_hfset A2)) A2)))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (@ (@ tptp.member_nat (@ Rep X)) A))))
% 0.24/0.63 (assert (= tptp.type_d1794767497hf_nat (lambda ((Rep2 (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs2 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A6 tptp.set_nat)) (and (forall ((X2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member_nat (@ Rep2 X2)) A6)) (forall ((X2 tptp.hF_Mirabelle_hf)) (= (@ Abs2 (@ Rep2 X2)) X2)) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A6) (= (@ Rep2 (@ Abs2 Y)) Y)))))))
% 0.24/0.63 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.top_top_set_nat) (and (= A tptp.top_top_set_nat) (= B4 tptp.top_top_set_nat)))))
% 0.24/0.63 (assert (forall ((C tptp.nat) (B4 tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (=> (not (@ _let_1 B4)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (=> (not (@ _let_1 B4)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4))))))
% 0.24/0.63 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (or (@ _let_1 A) (@ _let_1 B4))))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (= (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4)) (or (@ _let_1 A) (@ _let_1 B4))))))
% 0.24/0.63 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (=> (not (@ _let_1 A)) (@ _let_1 B4))))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4)) (=> (not (@ _let_1 A)) (@ _let_1 B4))))))
% 0.24/0.63 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4))))))
% 0.24/0.63 (assert (forall ((C tptp.nat) (B4 tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4))))))
% 0.24/0.63 (assert (forall ((B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) B4) B4)))
% 0.24/0.63 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) tptp.top_top_set_nat) A)))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (= (@ Abs (@ Rep X)) X))))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (Y3 tptp.nat)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (@ (@ tptp.member_nat Y3) A) (= (@ Rep (@ Abs Y3)) Y3)))))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (= (= (@ Rep X) (@ Rep Y3)) (= X Y3)))))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (Y3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (@ (@ tptp.member_nat Y3) A) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ P (@ Rep X3))) (@ P Y3))))))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.nat) (Y3 tptp.nat)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (@ (@ tptp.member_nat X) A) (=> (@ (@ tptp.member_nat Y3) A) (= (= (@ Abs X) (@ Abs Y3)) (= X Y3)))))))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (P (-> tptp.hF_Mirabelle_hf Bool)) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A) (@ P (@ Abs Y5)))) (@ P X)))))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (Y3 tptp.nat)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (@ (@ tptp.member_nat Y3) A) (not (forall ((X3 tptp.hF_Mirabelle_hf)) (not (= Y3 (@ Rep X3)))))))))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (not (forall ((Y5 tptp.nat)) (=> (= X (@ Abs Y5)) (not (@ (@ tptp.member_nat Y5) A))))))))
% 0.24/0.63 (assert (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (A tptp.set_nat) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf))) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member_nat (@ Rep X3)) A)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (= (@ Abs (@ Rep X3)) X3)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A) (= (@ Rep (@ Abs Y5)) Y5))) (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A))))))
% 0.24/0.63 (assert (= tptp.top_to22270292e_hf_o (lambda ((X2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X2) tptp.top_to489427057lle_hf))))
% 0.24/0.63 (assert (= tptp.top_top_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) tptp.top_top_set_nat))))
% 0.24/0.63 (assert (= (@ tptp.hF_Mirabelle_hcard tptp.zero_z189798548lle_hf) tptp.zero_zero_nat))
% 0.24/0.63 (assert (= tptp.hF_Mirabelle_hinsert (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ tptp.hF_Mirabelle_HF (@ (@ tptp.insert9649339lle_hf A4) (@ tptp.hF_Mirabelle_hfset B3))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (= (@ _let_1 (@ (@ tptp.insert_nat B) A)) (or (= A2 B) (@ _let_1 A))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf B) A)) (or (= A2 B) (@ _let_1 A))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B)) (@ _let_1 (@ (@ tptp.insert_nat B) B4))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B)) (@ _let_1 (@ (@ tptp.insert9649339lle_hf B) B4))))))
% 0.24/0.63 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)))))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)))))))
% 0.24/0.63 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (= (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B4 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat A2) C2)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A2) B4)) C2) (@ (@ tptp.inf_inf_set_nat B4) C2)))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (C2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (not (@ (@ tptp.member1367349282lle_hf A2) C2)) (= (@ (@ tptp.inf_in923488851lle_hf (@ (@ tptp.insert9649339lle_hf A2) B4)) C2) (@ (@ tptp.inf_in923488851lle_hf B4) C2)))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) C2) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B4)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B4) C2)))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (C2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (=> (@ (@ tptp.member1367349282lle_hf A2) C2) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 B4)) C2) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf B4) C2)))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 A)) (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (=> (not (@ (@ tptp.member_nat A2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat A2) B4)) (@ _let_1 B4))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A))) (=> (not (@ (@ tptp.member1367349282lle_hf A2) A)) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf A2) B4)) (@ _let_1 B4))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) A) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A))) (let ((_let_2 (@ tptp.insert9649339lle_hf A2))) (=> (@ (@ tptp.member1367349282lle_hf A2) A) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (C2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (= (@ (@ tptp.sup_su1790843629lle_hf (@ _let_1 B4)) C2) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf B4) C2))))))
% 0.24/0.63 (assert (forall ((A tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf A))) (let ((_let_2 (@ tptp.insert9649339lle_hf A2))) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.insert9649339lle_hf X) tptp.top_to489427057lle_hf) tptp.top_to489427057lle_hf)))
% 0.24/0.63 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.insert_nat X) tptp.top_top_set_nat) tptp.top_top_set_nat)))
% 0.24/0.63 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (not (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)) (not (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 0.24/0.63 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (@ _let_1 A)))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)) (@ _let_1 A)))))
% 0.24/0.63 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (@ _let_1 B4)))))
% 0.24/0.63 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)) (@ _let_1 B4)))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat B4) C2))) (let ((_let_2 (@ tptp.insert_nat A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_nat (@ _let_2 B4)) C2))) (let ((_let_4 (@ (@ tptp.member_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (C2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in923488851lle_hf B4) C2))) (let ((_let_2 (@ tptp.insert9649339lle_hf A2))) (let ((_let_3 (@ (@ tptp.inf_in923488851lle_hf (@ _let_2 B4)) C2))) (let ((_let_4 (@ (@ tptp.member1367349282lle_hf A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ tptp.insert_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B4)))) (let ((_let_5 (@ (@ tptp.member_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ tptp.insert9649339lle_hf A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B4)))) (let ((_let_5 (@ (@ tptp.member1367349282lle_hf A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A) (exists ((B6 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat A2) B6)) (not (@ (@ tptp.member_nat A2) B6)))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A2) A) (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (= A (@ (@ tptp.insert9649339lle_hf A2) B6)) (not (@ (@ tptp.member1367349282lle_hf A2) B6)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X))) (let ((_let_2 (@ tptp.insert9649339lle_hf Y3))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (= A2 B))) (=> (not (@ (@ tptp.member_nat A2) A)) (=> (not (@ (@ tptp.member_nat B) B4)) (= (= (@ (@ tptp.insert_nat A2) A) (@ (@ tptp.insert_nat B) B4)) (and (=> _let_1 (= A B4)) (=> (not _let_1) (exists ((C3 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat B) C3)) (not (@ (@ tptp.member_nat B) C3)) (= B4 (@ (@ tptp.insert_nat A2) C3)) (not (@ (@ tptp.member_nat A2) C3))))))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (= A2 B))) (=> (not (@ (@ tptp.member1367349282lle_hf A2) A)) (=> (not (@ (@ tptp.member1367349282lle_hf B) B4)) (= (= (@ (@ tptp.insert9649339lle_hf A2) A) (@ (@ tptp.insert9649339lle_hf B) B4)) (and (=> _let_1 (= A B4)) (=> (not _let_1) (exists ((C3 tptp.set_HF_Mirabelle_hf)) (and (= A (@ (@ tptp.insert9649339lle_hf B) C3)) (not (@ (@ tptp.member1367349282lle_hf B) C3)) (= B4 (@ (@ tptp.insert9649339lle_hf A2) C3)) (not (@ (@ tptp.member1367349282lle_hf A2) C3))))))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A) (= (@ (@ tptp.insert_nat A2) A) A))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A2) A) (= (@ (@ tptp.insert9649339lle_hf A2) A) A))))
% 0.24/0.63 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.member_nat X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A) (@ _let_1 B4)) (= A B4))))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X))) (let ((_let_2 (@ tptp.member1367349282lle_hf X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A) (@ _let_1 B4)) (= A B4))))))))
% 0.24/0.63 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A) (not (forall ((B6 tptp.set_nat)) (=> (= A (@ (@ tptp.insert_nat X) B6)) (@ (@ tptp.member_nat X) B6)))))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X) A) (not (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (= A (@ (@ tptp.insert9649339lle_hf X) B6)) (@ (@ tptp.member1367349282lle_hf X) B6)))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_nat B) B4))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert9649339lle_hf B) B4))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat A2) B4))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A2) (@ (@ tptp.insert9649339lle_hf A2) B4))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert_nat B) A)) (=> (not (= A2 B)) (@ _let_1 A))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ _let_1 (@ (@ tptp.insert9649339lle_hf B) A)) (=> (not (= A2 B)) (@ _let_1 A))))))
% 0.24/0.63 (assert (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_hfset (@ (@ tptp.hF_Mirabelle_hinsert A2) B)) (@ (@ tptp.insert9649339lle_hf A2) (@ tptp.hF_Mirabelle_hfset B)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.plus_plus_nat (@ tptp.hF_Mirabelle_hcard (@ (@ tptp.sup_su638957495lle_hf X) Y3))) (@ tptp.hF_Mirabelle_hcard (@ (@ tptp.inf_in956532509lle_hf X) Y3))) (@ (@ tptp.plus_plus_nat (@ tptp.hF_Mirabelle_hcard X)) (@ tptp.hF_Mirabelle_hcard Y3)))))
% 0.24/0.63 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hcard Y3))) (let ((_let_2 (@ tptp.hF_Mirabelle_hcard (@ (@ tptp.hF_Mirabelle_hinsert X) Y3)))) (let ((_let_3 (@ (@ tptp.hF_Mirabelle_hmem X) Y3))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1)))))))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B C))))
% 0.24/0.63 (assert (forall ((X tptp.nat) (Y3 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y3)) (and (= X tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y3) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat A2) B)) (= B tptp.zero_zero_nat))))
% 0.69/0.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat B) A2)) (= B tptp.zero_zero_nat))))
% 0.69/0.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A2) B) A2) (= B tptp.zero_zero_nat))))
% 0.69/0.93 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A2) A2) (= B tptp.zero_zero_nat))))
% 0.69/0.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 0.69/0.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)))
% 0.69/0.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 0.69/0.93 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.69/0.93 (assert (forall ((A tptp.nat) (K tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_nat A) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B)))))))
% 0.69/0.93 (assert (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.69/0.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 0.69/0.93 (assert (@ tptp.hF_Mir199975595nction tptp.r))
% 0.69/0.93 (assert (not (@ tptp.hF_Mir199975595nction (@ (@ tptp.hF_Mir1653039215strict tptp.r) tptp.x))))
% 0.69/0.93 (set-info :filename cvc5---1.0.5_23655)
% 0.69/0.93 (check-sat-assuming ( true ))
% 0.69/0.93 ------- get file name : TPTP file name is ITP076^1
% 0.69/0.93 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23655.smt2...
% 0.69/0.93 --- Run --ho-elim --full-saturate-quant at 10...
% 0.69/0.93 % SZS status Theorem for ITP076^1
% 0.69/0.93 % SZS output start Proof for ITP076^1
% 0.69/0.93 (
% 0.69/0.93 (let ((_let_1 (not (@ tptp.hF_Mir199975595nction (@ (@ tptp.hF_Mir1653039215strict tptp.r) tptp.x))))) (let ((_let_2 (@ tptp.hF_Mir199975595nction tptp.r))) (let ((_let_3 (= tptp.hF_Mirabelle_hinsert (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ tptp.hF_Mirabelle_HF (@ (@ tptp.insert9649339lle_hf A4) (@ tptp.hF_Mirabelle_hfset B3))))))) (let ((_let_4 (= tptp.type_d1794767497hf_nat (lambda ((Rep2 (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs2 (-> tptp.nat tptp.hF_Mirabelle_hf)) (A6 tptp.set_nat)) (and (forall ((X2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member_nat (@ Rep2 X2)) A6)) (forall ((X2 tptp.hF_Mirabelle_hf)) (= (@ Abs2 (@ Rep2 X2)) X2)) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A6) (= (@ Rep2 (@ Abs2 Y)) Y)))))))) (let ((_let_5 (= tptp.top_top_set_nat (@ tptp.collect_nat tptp.top_top_nat_o)))) (let ((_let_6 (= (@ tptp.hF_Mirabelle_Abs_hf tptp.zero_zero_nat) tptp.zero_z189798548lle_hf))) (let ((_let_7 (= tptp.top_to22270292e_hf_o (lambda ((X2 tptp.hF_Mirabelle_hf)) tptp.top_top_o)))) (let ((_let_8 (= tptp.top_top_nat_o (lambda ((X2 tptp.nat)) tptp.top_top_o)))) (let ((_let_9 (= tptp.hF_Mirabelle_hpair (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A4))) (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_1 tptp.zero_z189798548lle_hf)) (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert B3) tptp.zero_z189798548lle_hf))) tptp.zero_z189798548lle_hf))))))) (let ((_let_10 (= tptp.hF_Mirabelle_hmem (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A4) (@ tptp.hF_Mirabelle_hfset B3)))))) (let ((_let_11 (= tptp.hF_Mir137170979_hpair (lambda ((Z4 tptp.hF_Mirabelle_hf)) (exists ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (= Z4 (@ (@ tptp.hF_Mirabelle_hpair X2) Y))))))) (let ((_let_12 (= tptp.hF_Mir434065167lation (lambda ((R2 tptp.hF_Mirabelle_hf)) (forall ((Z4 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem Z4) R2) (@ tptp.hF_Mir137170979_hpair Z4))))))) (let ((_let_13 (forall ((Z tptp.hF_Mirabelle_hf) (R tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem Z))) (= (@ _let_1 (@ (@ tptp.hF_Mir1653039215strict R) A)) (and (@ _let_1 R) (exists ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (and (= Z (@ (@ tptp.hF_Mirabelle_hpair X2) Y)) (@ (@ tptp.hF_Mirabelle_hmem X2) A))))))))) (let ((_let_14 (= tptp.hF_Mir199975595nction (lambda ((R2 tptp.hF_Mirabelle_hf)) (forall ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem (@ (@ tptp.hF_Mirabelle_hpair X2) Y)) R2) (forall ((Y2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem (@ (@ tptp.hF_Mirabelle_hpair X2) Y2)) R2) (= Y Y2))))))))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_131 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_132))) (let ((_let_16 (ho_80 k_79 tptp.r))) (let ((_let_17 (ho_80 k_79 (ho_78 k_77 tptp.zero_zero_nat)))) (let ((_let_18 (ho_82 k_81 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130))) (let ((_let_19 (ho_82 k_81 (ho_84 k_83 (ho_51 _let_18 _let_17))))) (let ((_let_20 (ho_84 k_83 (ho_51 _let_19 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 (ho_84 k_83 (ho_51 _let_18 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_132) _let_17)))))) _let_17))))))) (let ((_let_21 (ho_43 k_42 _let_20))) (let ((_let_22 (ho_44 _let_21 _let_16))) (let ((_let_23 (not _let_22))) (let ((_let_24 (ho_84 k_83 (ho_51 _let_19 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 (ho_84 k_83 (ho_51 _let_18 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_131) _let_17)))))) _let_17))))))) (let ((_let_25 (ho_43 k_42 _let_24))) (let ((_let_26 (ho_44 _let_25 _let_16))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_23 _let_15))) (let ((_let_29 (ho_80 k_79 (ho_47 (ho_46 k_95 tptp.r) tptp.x)))) (let ((_let_30 (ho_44 _let_21 _let_29))) (let ((_let_31 (not _let_30))) (let ((_let_32 (ho_44 _let_25 _let_29))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31 _let_15))) (let ((_let_35 (forall ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (BOUND_VARIABLE_4736 tptp.hF_Mirabelle_hf)) (let ((_let_1 (ho_80 k_79 (ho_47 (ho_46 k_95 tptp.r) tptp.x)))) (let ((_let_2 (ho_80 k_79 (ho_78 k_77 tptp.zero_zero_nat)))) (let ((_let_3 (ho_82 k_81 X2))) (let ((_let_4 (ho_82 k_81 (ho_84 k_83 (ho_51 _let_3 _let_2))))) (or (not (ho_44 (ho_43 k_42 (ho_84 k_83 (ho_51 _let_4 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 (ho_84 k_83 (ho_51 _let_3 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 Y) _let_2)))))) _let_2)))))) _let_1)) (not (ho_44 (ho_43 k_42 (ho_84 k_83 (ho_51 _let_4 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 (ho_84 k_83 (ho_51 _let_3 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 BOUND_VARIABLE_4736) _let_2)))))) _let_2)))))) _let_1)) (= Y BOUND_VARIABLE_4736))))))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (not _let_35))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (ASSUME :args (_let_10)))) (let ((_let_42 (ASSUME :args (_let_9)))) (let ((_let_43 (ASSUME :args (_let_8)))) (let ((_let_44 (ASSUME :args (_let_7)))) (let ((_let_45 (SYMM (ASSUME :args (_let_6))))) (let ((_let_46 (AND_INTRO (ASSUME :args (_let_3)) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38) :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_46 :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (BOUND_VARIABLE_4736 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hfset (@ (@ tptp.hF_Mir1653039215strict tptp.r) tptp.x)))) (let ((_let_2 (@ tptp.hF_Mirabelle_hfset (@ tptp.hF_Mirabelle_Abs_hf tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.insert9649339lle_hf X2))) (let ((_let_4 (@ tptp.insert9649339lle_hf (@ tptp.hF_Mirabelle_HF (@ _let_3 _let_2))))) (or (not (@ (@ tptp.member1367349282lle_hf (@ tptp.hF_Mirabelle_HF (@ _let_4 (@ tptp.hF_Mirabelle_hfset (@ tptp.hF_Mirabelle_HF (@ (@ tptp.insert9649339lle_hf (@ tptp.hF_Mirabelle_HF (@ _let_3 (@ tptp.hF_Mirabelle_hfset (@ tptp.hF_Mirabelle_HF (@ (@ tptp.insert9649339lle_hf Y) _let_2)))))) _let_2)))))) _let_1)) (not (@ (@ tptp.member1367349282lle_hf (@ tptp.hF_Mirabelle_HF (@ _let_4 (@ tptp.hF_Mirabelle_hfset (@ tptp.hF_Mirabelle_HF (@ (@ tptp.insert9649339lle_hf (@ tptp.hF_Mirabelle_HF (@ _let_3 (@ tptp.hF_Mirabelle_hfset (@ tptp.hF_Mirabelle_HF (@ (@ tptp.insert9649339lle_hf BOUND_VARIABLE_4736) _let_2)))))) _let_2)))))) _let_1)) (= Y BOUND_VARIABLE_4736)))))))) _let_37))))))) (let ((_let_48 (or))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_47) :args (_let_37))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_35))) (REFL :args (_let_36)) :args _let_48)) _let_47 :args (_let_36 true _let_35)))) (let ((_let_50 (forall ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (BOUND_VARIABLE_4736 tptp.hF_Mirabelle_hf)) (let ((_let_1 (ho_80 k_79 tptp.r))) (let ((_let_2 (ho_80 k_79 (ho_78 k_77 tptp.zero_zero_nat)))) (let ((_let_3 (ho_82 k_81 X2))) (let ((_let_4 (ho_82 k_81 (ho_84 k_83 (ho_51 _let_3 _let_2))))) (or (not (ho_44 (ho_43 k_42 (ho_84 k_83 (ho_51 _let_4 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 (ho_84 k_83 (ho_51 _let_3 (ho_80 k_79 (ho_84 k_83 (ho_51 (ho_82 k_81 Y) _let_2)))))) _let_2)))))) _let_1)) (not (ho_44 (ho_43 k_42 (ho_84 k_83 (ho_51 _let_4 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(@ tptp.hF_Mirabelle_hmem X) Y))))) (forall ((V4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (R3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_hmem V4) (@ (@ tptp.hF_Mirabelle_Replace A) R3)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A) (@ (@ R3 U2) V4) (forall ((Y tptp.hF_Mirabelle_hf)) (=> (@ (@ R3 U2) Y) (= Y V4))))))) (forall ((X tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool)) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X))) (= (@ _let_1 (@ (@ tptp.hF_Mir818139703ollect P) A)) (and (@ P X) (@ _let_1 A))))) (forall ((V4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_hmem V4) (@ (@ tptp.hF_Mirabelle_RepFun A) F)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A) (= V4 (@ F U2)))))) (forall ((X tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_Abs_hf (@ tptp.hF_Mirabelle_Rep_hf X)) X)) (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (G (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (=> (= A B4) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X3) B4) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.hF_Mirabelle_RepFun A) F) (@ (@ tptp.hF_Mirabelle_RepFun B4) G))))) (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool)) (Q (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (=> (= A B4) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y5 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X3) B4) (= (@ (@ P X3) Y5) (@ (@ Q X3) Y5)))) (= (@ (@ tptp.hF_Mirabelle_Replace A) P) (@ (@ tptp.hF_Mirabelle_Replace B4) Q))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X) Y3) (not (= (@ tptp.hF_Mirabelle_HUnion X) Y3)))) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) tptp.top_top_set_nat) (= (@ tptp.hF_Mirabelle_Rep_hf (@ tptp.hF_Mirabelle_Abs_hf Y3)) Y3))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem tptp.zero_z189798548lle_hf) (@ (@ tptp.hF_Mirabelle_hpair X) Y3)))) _let_10 (forall ((P (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mir818139703ollect P) tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf)) (= (@ tptp.hF_Mirabelle_HUnion tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf) (forall ((R3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_Replace tptp.zero_z189798548lle_hf) R3) tptp.zero_z189798548lle_hf)) (forall ((F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_RepFun tptp.zero_z189798548lle_hf) F) tptp.zero_z189798548lle_hf)) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_RepFun (@ (@ tptp.hF_Mirabelle_hinsert A2) B)) F) (@ (@ tptp.hF_Mirabelle_hinsert (@ F A2)) (@ (@ tptp.hF_Mirabelle_RepFun B) F)))) (forall ((F tptp.hF_Mirabelle_hf) (G tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mir434065167lation (@ (@ tptp.sup_su638957495lle_hf F) G)) (and (@ tptp.hF_Mir434065167lation F) (@ tptp.hF_Mir434065167lation G)))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem A2))) (= (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert B) C)) (or (= A2 B) (@ _let_1 C))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hinsert A2) tptp.zero_z189798548lle_hf) (@ (@ tptp.hF_Mirabelle_hinsert B) tptp.zero_z189798548lle_hf)) (= A2 B))) (forall ((X tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A2) B)) (or (@ _let_1 A2) (@ _let_1 B))))) (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf tptp.zero_z189798548lle_hf) A) A)) (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 ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A))) A)) (forall ((A tptp.set_HF_Mirabelle_hf)) (= (@ tptp.collec2046588256lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X2) A))) A)) (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.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))) (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A) tptp.zero_z189798548lle_hf) A)) (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_RepFun (@ (@ tptp.sup_su638957495lle_hf A) B4)) F) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.hF_Mirabelle_RepFun A) F)) (@ (@ tptp.hF_Mirabelle_RepFun B4) F)))) (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HUnion (@ (@ tptp.sup_su638957495lle_hf A) B4)) (@ (@ tptp.sup_su638957495lle_hf (@ tptp.hF_Mirabelle_HUnion A)) (@ tptp.hF_Mirabelle_HUnion B4)))) (forall ((A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (R3 (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_Replace (@ (@ tptp.sup_su638957495lle_hf A) B4)) R3) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.hF_Mirabelle_Replace A) R3)) (@ (@ tptp.hF_Mirabelle_Replace B4) R3)))) (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HUnion (@ (@ tptp.hF_Mirabelle_hinsert A2) A)) (@ (@ tptp.sup_su638957495lle_hf A2) (@ tptp.hF_Mirabelle_HUnion A)))) (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (X tptp.hF_Mirabelle_hf)) (=> (@ P tptp.zero_z189798548lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (=> (@ P X3) (forall ((Y5 tptp.hF_Mirabelle_hf)) (=> (@ P Y5) (@ P (@ (@ tptp.hF_Mirabelle_hinsert Y5) X3)))))) (@ P X)))) (= tptp.hF_Mirabelle_hinsert (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf B3) (@ (@ tptp.hF_Mirabelle_hinsert A4) tptp.zero_z189798548lle_hf)))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hinsert A2) (@ (@ tptp.hF_Mirabelle_hinsert B) tptp.zero_z189798548lle_hf)) (@ (@ tptp.hF_Mirabelle_hinsert C) (@ (@ tptp.hF_Mirabelle_hinsert D) tptp.zero_z189798548lle_hf))) (or (and (= A2 C) (= B D)) (and (= A2 D) (= B C))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hinsert A2) A) tptp.zero_z189798548lle_hf))) (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 A)) B4) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B4))))) (forall ((B4 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))) (forall ((Y3 tptp.hF_Mirabelle_hf)) (=> (not (= Y3 tptp.zero_z189798548lle_hf)) (not (forall ((A5 tptp.hF_Mirabelle_hf) (B5 tptp.hF_Mirabelle_hf)) (=> (= Y3 (@ (@ tptp.hF_Mirabelle_hinsert A5) B5)) (@ (@ tptp.hF_Mirabelle_hmem A5) B5)))))) (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (Z tptp.hF_Mirabelle_hf)) (=> (@ P tptp.zero_z189798548lle_hf) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y5 tptp.hF_Mirabelle_hf)) (=> (@ P X3) (=> (@ P Y5) (=> (not (@ (@ tptp.hF_Mirabelle_hmem X3) Y5)) (@ P (@ (@ tptp.hF_Mirabelle_hinsert X3) Y5)))))) (@ P Z)))) _let_9 (= tptp.hF_Mirabelle_hpair (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A4))) (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_1 (@ _let_1 tptp.zero_z189798548lle_hf))) (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert B3) tptp.zero_z189798548lle_hf))) tptp.zero_z189798548lle_hf))))) (forall ((Z tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (= Z (@ (@ tptp.hF_Mirabelle_hinsert Y3) X)) (forall ((U2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U2))) (= (@ _let_1 Z) (or (@ _let_1 X) (= U2 Y3))))))) (forall ((A2 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A2) tptp.zero_z189798548lle_hf))) (forall ((Z tptp.hF_Mirabelle_hf)) (= (= Z tptp.zero_z189798548lle_hf) (forall ((X2 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem X2) Z))))) (forall ((A2 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A2) tptp.zero_z189798548lle_hf))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hpair X) Y3) tptp.zero_z189798548lle_hf))) (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member_nat (@ tptp.hF_Mirabelle_Rep_hf X)) tptp.top_top_set_nat)) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) tptp.top_top_set_nat) (not (forall ((X3 tptp.hF_Mirabelle_hf)) (not (= Y3 (@ tptp.hF_Mirabelle_Rep_hf X3))))))) (forall ((Y3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat Y3) tptp.top_top_set_nat) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ P (@ tptp.hF_Mirabelle_Rep_hf X3))) (@ P Y3)))) (forall ((X tptp.hF_Mirabelle_hf)) (not (forall ((Y5 tptp.nat)) (=> (= X (@ tptp.hF_Mirabelle_Abs_hf Y5)) (not (@ (@ tptp.member_nat Y5) tptp.top_top_set_nat)))))) (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (X tptp.hF_Mirabelle_hf)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) tptp.top_top_set_nat) (@ P (@ tptp.hF_Mirabelle_Abs_hf Y5)))) (@ P X))) (forall ((X tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.member_nat X) tptp.top_top_set_nat) (=> (@ (@ tptp.member_nat Y3) tptp.top_top_set_nat) (= (= (@ tptp.hF_Mirabelle_Abs_hf X) (@ tptp.hF_Mirabelle_Abs_hf Y3)) (= X Y3))))) (@ tptp.hF_Mir434065167lation tptp.zero_z189798548lle_hf) (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf tptp.top_to489427057lle_hf) X) tptp.top_to489427057lle_hf)) (forall ((X (-> tptp.nat Bool))) (= (@ (@ tptp.sup_sup_nat_o tptp.top_top_nat_o) X) tptp.top_top_nat_o)) (forall ((X (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.sup_su1199008216e_hf_o tptp.top_to22270292e_hf_o) X) tptp.top_to22270292e_hf_o)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.top_top_set_nat) X) tptp.top_top_set_nat)) (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf X) tptp.top_to489427057lle_hf) tptp.top_to489427057lle_hf)) (forall ((X (-> tptp.nat Bool))) (= (@ (@ tptp.sup_sup_nat_o X) tptp.top_top_nat_o) tptp.top_top_nat_o)) (forall ((X (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.sup_su1199008216e_hf_o X) tptp.top_to22270292e_hf_o) tptp.top_to22270292e_hf_o)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.top_top_set_nat) tptp.top_top_set_nat)) (forall ((A tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (not (= A tptp.zero_z189798548lle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem X) (@ tptp.hF_Mirabelle_HInter A)) (forall ((Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem Y) A) (@ (@ tptp.hF_Mirabelle_hmem X) Y)))))) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) A2) A2)) (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf A2) A2) A2)) (forall ((A2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A2) A2) A2)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) X) X)) (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf X) X) X)) (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X) X) X)) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.sup_sup_set_nat A2) B))) (= (@ (@ tptp.sup_sup_set_nat _let_1) B) _let_1))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.sup_su1790843629lle_hf A2) B))) (= (@ (@ tptp.sup_su1790843629lle_hf _let_1) B) _let_1))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.sup_su638957495lle_hf A2) B))) (= (@ (@ tptp.sup_su638957495lle_hf _let_1) B) _let_1))) (= (@ tptp.hF_Mirabelle_HInter tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf) (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (let ((_let_2 (@ tptp.sup_su1790843629lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat B))) (let ((_let_2 (@ tptp.sup_sup_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf B))) (let ((_let_2 (@ tptp.sup_su1790843629lle_hf A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf B))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y) X2))) (= tptp.sup_su1790843629lle_hf (lambda ((X2 tptp.set_HF_Mirabelle_hf) (Y tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.sup_su1790843629lle_hf Y) X2))) (= tptp.sup_su638957495lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf Y) X2))) (= tptp.sup_sup_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B3) A4))) (= tptp.sup_su1790843629lle_hf (lambda ((A4 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.sup_su1790843629lle_hf B3) A4))) (= tptp.sup_su638957495lle_hf (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf B3) A4))) (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y3) Z))))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (= (@ (@ tptp.sup_su1790843629lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf Y3) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y3) Z))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C))))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf A2))) (= (@ (@ tptp.sup_su1790843629lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf B) C))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A2))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf B) C))))) (forall ((B4 tptp.set_nat) (K tptp.set_nat) (B tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (let ((_let_2 (@ tptp.sup_sup_set_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (K tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf A2))) (let ((_let_2 (@ tptp.sup_su1790843629lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((B4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A2))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((A tptp.set_nat) (K tptp.set_nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.sup_sup_set_nat A) B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B)))))) (forall ((A tptp.set_HF_Mirabelle_hf) (K tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.sup_su1790843629lle_hf A) B) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A2) B)))))) (forall ((A tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.sup_su638957495lle_hf A) B) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A2) B)))))) (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y) X2))) (= tptp.sup_su1790843629lle_hf (lambda ((X2 tptp.set_HF_Mirabelle_hf) (Y tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.sup_su1790843629lle_hf Y) X2))) (= tptp.sup_su638957495lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf Y) X2))) (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y3) Z))))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (= (@ (@ tptp.sup_su1790843629lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf Y3) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y3) Z))))) (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (let ((_let_2 (@ tptp.sup_su1790843629lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) tptp.top_to489427057lle_hf)) (forall ((X tptp.nat)) (@ (@ tptp.member_nat X) tptp.top_top_set_nat)) (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X) tptp.top_to489427057lle_hf)) (forall ((X tptp.nat)) (@ (@ tptp.member_nat X) tptp.top_top_set_nat)) _let_8 _let_7 (forall ((A tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (=> (not (= A tptp.zero_z189798548lle_hf)) (= (@ tptp.hF_Mirabelle_HInter (@ (@ tptp.hF_Mirabelle_hinsert A2) A)) (@ (@ tptp.inf_in956532509lle_hf A2) (@ tptp.hF_Mirabelle_HInter A))))) (@ (@ (@ tptp.type_d1794767497hf_nat tptp.hF_Mirabelle_Rep_hf) tptp.hF_Mirabelle_Abs_hf) tptp.top_top_set_nat) (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat X) Y3))) (= (@ (@ tptp.inf_inf_set_nat _let_1) Y3) _let_1))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in923488851lle_hf X) Y3))) (= (@ (@ tptp.inf_in923488851lle_hf _let_1) Y3) _let_1))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf X) Y3))) (= (@ (@ tptp.inf_in956532509lle_hf _let_1) Y3) _let_1))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat A2) B))) (= (@ (@ tptp.inf_inf_set_nat _let_1) B) _let_1))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in923488851lle_hf A2) B))) (= (@ (@ tptp.inf_in923488851lle_hf _let_1) B) _let_1))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf A2) B))) (= (@ (@ tptp.inf_in956532509lle_hf _let_1) B) _let_1))) (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A2))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) X) X)) (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf X) X) X)) (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X) X) X)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A2) A2) A2)) (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf A2) A2) A2)) (forall ((A2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A2) A2) A2)) (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf A2) tptp.top_to489427057lle_hf) A2)) (forall ((A2 (-> tptp.nat Bool))) (= (@ (@ tptp.inf_inf_nat_o A2) tptp.top_top_nat_o) A2)) (forall ((A2 (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.inf_in307783154e_hf_o A2) tptp.top_to22270292e_hf_o) A2)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A2) tptp.top_top_set_nat) A2)) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (= (= tptp.top_to489427057lle_hf (@ (@ tptp.inf_in923488851lle_hf A2) B)) (and (= A2 tptp.top_to489427057lle_hf) (= B tptp.top_to489427057lle_hf)))) (forall ((A2 (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (= (= tptp.top_top_nat_o (@ (@ tptp.inf_inf_nat_o A2) B)) (and (= A2 tptp.top_top_nat_o) (= B tptp.top_top_nat_o)))) (forall ((A2 (-> tptp.hF_Mirabelle_hf Bool)) (B (-> tptp.hF_Mirabelle_hf Bool))) (= (= tptp.top_to22270292e_hf_o (@ (@ tptp.inf_in307783154e_hf_o A2) B)) (and (= A2 tptp.top_to22270292e_hf_o) (= B tptp.top_to22270292e_hf_o)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (= tptp.top_top_set_nat (@ (@ tptp.inf_inf_set_nat A2) B)) (and (= A2 tptp.top_top_set_nat) (= B tptp.top_top_set_nat)))) (forall ((A2 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf tptp.top_to489427057lle_hf) A2) A2)) (forall ((A2 (-> tptp.nat Bool))) (= (@ (@ tptp.inf_inf_nat_o tptp.top_top_nat_o) A2) A2)) (forall ((A2 (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.inf_in307783154e_hf_o tptp.top_to22270292e_hf_o) A2) A2)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) A2) A2)) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.inf_in923488851lle_hf A2) B) tptp.top_to489427057lle_hf) (and (= A2 tptp.top_to489427057lle_hf) (= B tptp.top_to489427057lle_hf)))) (forall ((A2 (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (= (= (@ (@ tptp.inf_inf_nat_o A2) B) tptp.top_top_nat_o) (and (= A2 tptp.top_top_nat_o) (= B tptp.top_top_nat_o)))) (forall ((A2 (-> tptp.hF_Mirabelle_hf Bool)) (B (-> tptp.hF_Mirabelle_hf Bool))) (= (= (@ (@ tptp.inf_in307783154e_hf_o A2) B) tptp.top_to22270292e_hf_o) (and (= A2 tptp.top_to22270292e_hf_o) (= B tptp.top_to22270292e_hf_o)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A2) B) tptp.top_top_set_nat) (and (= A2 tptp.top_top_set_nat) (= B tptp.top_top_set_nat)))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (= (= tptp.top_to489427057lle_hf (@ (@ tptp.inf_in923488851lle_hf X) Y3)) (and (= X tptp.top_to489427057lle_hf) (= Y3 tptp.top_to489427057lle_hf)))) (forall ((X (-> tptp.nat Bool)) (Y3 (-> tptp.nat Bool))) (= (= tptp.top_top_nat_o (@ (@ tptp.inf_inf_nat_o X) Y3)) (and (= X tptp.top_top_nat_o) (= Y3 tptp.top_top_nat_o)))) (forall ((X (-> tptp.hF_Mirabelle_hf Bool)) (Y3 (-> tptp.hF_Mirabelle_hf Bool))) (= (= tptp.top_to22270292e_hf_o (@ (@ tptp.inf_in307783154e_hf_o X) Y3)) (and (= X tptp.top_to22270292e_hf_o) (= Y3 tptp.top_to22270292e_hf_o)))) (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (= (= tptp.top_top_set_nat (@ (@ tptp.inf_inf_set_nat X) Y3)) (and (= X tptp.top_top_set_nat) (= Y3 tptp.top_top_set_nat)))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (= (= (@ (@ tptp.inf_in923488851lle_hf X) Y3) tptp.top_to489427057lle_hf) (and (= X tptp.top_to489427057lle_hf) (= Y3 tptp.top_to489427057lle_hf)))) (forall ((X (-> tptp.nat Bool)) (Y3 (-> tptp.nat Bool))) (= (= (@ (@ tptp.inf_inf_nat_o X) Y3) tptp.top_top_nat_o) (and (= X tptp.top_top_nat_o) (= Y3 tptp.top_top_nat_o)))) (forall ((X (-> tptp.hF_Mirabelle_hf Bool)) (Y3 (-> tptp.hF_Mirabelle_hf Bool))) (= (= (@ (@ tptp.inf_in307783154e_hf_o X) Y3) tptp.top_to22270292e_hf_o) (and (= X tptp.top_to22270292e_hf_o) (= Y3 tptp.top_to22270292e_hf_o)))) (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat X) Y3) tptp.top_top_set_nat) (and (= X tptp.top_top_set_nat) (= Y3 tptp.top_top_set_nat)))) (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf X) tptp.top_to489427057lle_hf) X)) (forall ((X (-> tptp.nat Bool))) (= (@ (@ tptp.inf_inf_nat_o X) tptp.top_top_nat_o) X)) (forall ((X (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.inf_in307783154e_hf_o X) tptp.top_to22270292e_hf_o) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.top_top_set_nat) X)) (forall ((X tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf tptp.top_to489427057lle_hf) X) X)) (forall ((X (-> tptp.nat Bool))) (= (@ (@ tptp.inf_inf_nat_o tptp.top_top_nat_o) X) X)) (forall ((X (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.inf_in307783154e_hf_o tptp.top_to22270292e_hf_o) X) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) X) X)) (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y3)) X)) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.inf_in923488851lle_hf X) (@ (@ tptp.sup_su1790843629lle_hf X) Y3)) X)) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X) (@ (@ tptp.sup_su638957495lle_hf X) Y3)) X)) (forall ((X tptp.set_nat) (Y3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) (@ (@ tptp.inf_inf_set_nat X) Y3)) X)) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf)) (= (@ (@ tptp.sup_su1790843629lle_hf X) (@ (@ tptp.inf_in923488851lle_hf X) Y3)) X)) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X) (@ (@ tptp.inf_in956532509lle_hf X) Y3)) X)) (forall ((U4 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U4))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf X) Y3)) (and (@ _let_1 X) (@ _let_1 Y3))))) (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf tptp.zero_z189798548lle_hf) A) tptp.zero_z189798548lle_hf)) (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A) tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf)) _let_6 (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf X))) (let ((_let_2 (@ tptp.inf_in923488851lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B))) (let ((_let_2 (@ tptp.inf_inf_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf B))) (let ((_let_2 (@ tptp.inf_in923488851lle_hf A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf B))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y) X2))) (= tptp.inf_in923488851lle_hf (lambda ((X2 tptp.set_HF_Mirabelle_hf) (Y tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.inf_in923488851lle_hf Y) X2))) (= tptp.inf_in956532509lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf Y) X2))) (= tptp.inf_inf_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B3) A4))) (= tptp.inf_in923488851lle_hf (lambda ((A4 tptp.set_HF_Mirabelle_hf) (B3 tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.inf_in923488851lle_hf B3) A4))) (= tptp.inf_in956532509lle_hf (lambda ((A4 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf B3) A4))) (forall ((X tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y3) Z))))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf X))) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf Y3) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y3) Z))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C))))) (forall ((A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf) (C tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A2))) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf B) C))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A2))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C))))) (forall ((B4 tptp.set_nat) (K tptp.set_nat) (B tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (let ((_let_2 (@ tptp.inf_inf_set_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((B4 tptp.set_HF_Mirabelle_hf) (K tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A2))) (let ((_let_2 (@ tptp.inf_in923488851lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((B4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A2))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((A tptp.set_nat) (K tptp.set_nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.inf_inf_set_nat A) B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A2) B)))))) (forall ((A tptp.set_HF_Mirabelle_hf) (K tptp.set_HF_Mirabelle_hf) (A2 tptp.set_HF_Mirabelle_hf) (B tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.inf_in923488851lle_hf A) B) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A2) B)))))) (forall ((A tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.inf_in956532509lle_hf A) B) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf A2) B)))))) (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y) X2))) (= tptp.inf_in923488851lle_hf (lambda ((X2 tptp.set_HF_Mirabelle_hf) (Y tptp.set_HF_Mirabelle_hf)) (@ (@ tptp.inf_in923488851lle_hf Y) X2))) (= tptp.inf_in956532509lle_hf (lambda ((X2 tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf Y) X2))) (forall ((X tptp.set_HF_Mirabelle_hf) (Y3 tptp.set_HF_Mirabelle_hf) (Z tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf X))) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf Y3) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y3) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.inf_in956532509lle_hf Y3) Z)) X) (@ (@ tptp.inf_in956532509lle_hf (@ (@ tptp.sup_su638957495lle_hf Y3) X)) (@ (@ tptp.sup_su638957495lle_hf Z) X)))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y3) Z)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y3)) (@ _let_1 Z))))) (forall ((Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf (@ (@ tptp.sup_su638957495lle_hf Y3) Z)) X) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.inf_in956532509lle_hf Y3) X)) (@ (@ tptp.inf_in956532509lle_hf Z) X)))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y3) Z)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y3)) (@ _let_1 Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y5 tptp.hF_Mirabelle_hf) (Z3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X3))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y5) Z3)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y5)) (@ _let_1 Z3))))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y3) Z)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y3)) (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (=> (forall ((X3 tptp.hF_Mirabelle_hf) (Y5 tptp.hF_Mirabelle_hf) (Z3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X3))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y5) Z3)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y5)) (@ _let_1 Z3))))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y3) Z)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y3)) (@ _let_1 Z)))))) (forall ((Z tptp.hF_Mirabelle_hf)) (=> (not (= Z tptp.zero_z189798548lle_hf)) (exists ((W tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem W) Z) (= (@ (@ tptp.inf_in956532509lle_hf W) Z) tptp.zero_z189798548lle_hf))))) (forall ((X tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf B4))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.hF_Mirabelle_hmem X) B4))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((X tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf A) B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_3 (@ (@ tptp.inf_in956532509lle_hf (@ _let_2 A)) B4))) (let ((_let_4 (@ (@ tptp.hF_Mirabelle_hmem X) B4))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((X tptp.hF_Mirabelle_hf)) (= (= tptp.zero_z189798548lle_hf X) (= X tptp.zero_z189798548lle_hf))) (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))) (forall ((A tptp.set_HF_Mirabelle_hf)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X3) A)) (= tptp.top_to489427057lle_hf A))) (forall ((A tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A)) (= tptp.top_top_set_nat A))) (exists ((X3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X3) tptp.top_to489427057lle_hf)) (exists ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) tptp.top_top_set_nat)) (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) tptp.top_top_set_nat) tptp.top_top_set_nat)) (forall ((B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.top_top_set_nat) B4) tptp.top_top_set_nat)) _let_5 (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (F2 (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) tptp.top_top_set_nat) (= (exists ((X4 tptp.nat)) (@ F2 X4)) (exists ((B3 tptp.hF_Mirabelle_hf)) (@ F2 (@ Rep B3)))))) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (S tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) tptp.top_top_set_nat) (not (forall ((X3 tptp.nat)) (not (= S (@ Abs X3))))))) (forall ((A2 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HF (@ tptp.hF_Mirabelle_hfset A2)) A2)) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (@ (@ tptp.member_nat (@ Rep X)) A))) _let_4 (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.top_top_set_nat) (and (= A tptp.top_top_set_nat) (= B4 tptp.top_top_set_nat)))) (forall ((C tptp.nat) (B4 tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (=> (not (@ _let_1 B4)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))))) (forall ((C tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (=> (not (@ _let_1 B4)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4))))) (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (or (@ _let_1 A) (@ _let_1 B4))))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (= (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4)) (or (@ _let_1 A) (@ _let_1 B4))))) (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (=> (not (@ _let_1 A)) (@ _let_1 B4))))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4)) (=> (not (@ _let_1 A)) (@ _let_1 B4))))) (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4))))) (forall ((C tptp.nat) (B4 tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))))) (forall ((C tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf A) B4))))) (forall ((B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) B4) B4)) (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) tptp.top_top_set_nat) A)) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (= (@ Abs (@ Rep X)) X))) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (Y3 tptp.nat)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (@ (@ tptp.member_nat Y3) A) (= (@ Rep (@ Abs Y3)) Y3)))) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (= (= (@ Rep X) (@ Rep Y3)) (= X Y3)))) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (Y3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (@ (@ tptp.member_nat Y3) A) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ P (@ Rep X3))) (@ P Y3))))) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.nat) (Y3 tptp.nat)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (@ (@ tptp.member_nat X) A) (=> (@ (@ tptp.member_nat Y3) A) (= (= (@ Abs X) (@ Abs Y3)) (= X Y3)))))) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (P (-> tptp.hF_Mirabelle_hf Bool)) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A) (@ P (@ Abs Y5)))) (@ P X)))) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (Y3 tptp.nat)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (=> (@ (@ tptp.member_nat Y3) A) (not (forall ((X3 tptp.hF_Mirabelle_hf)) (not (= Y3 (@ Rep X3)))))))) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf)) (A tptp.set_nat) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A) (not (forall ((Y5 tptp.nat)) (=> (= X (@ Abs Y5)) (not (@ (@ tptp.member_nat Y5) A))))))) (forall ((Rep (-> tptp.hF_Mirabelle_hf tptp.nat)) (A tptp.set_nat) (Abs (-> tptp.nat tptp.hF_Mirabelle_hf))) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member_nat (@ Rep X3)) A)) (=> (forall ((X3 tptp.hF_Mirabelle_hf)) (= (@ Abs (@ Rep X3)) X3)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A) (= (@ Rep (@ Abs Y5)) Y5))) (@ (@ (@ tptp.type_d1794767497hf_nat Rep) Abs) A))))) (= tptp.top_to22270292e_hf_o (lambda ((X2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X2) tptp.top_to489427057lle_hf))) (= tptp.top_top_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) tptp.top_top_set_nat))) (= (@ tptp.hF_Mirabelle_hcard tptp.zero_z189798548lle_hf) tptp.zero_zero_nat) _let_3 (forall ((X tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.nat) (B tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (= (@ _let_1 (@ (@ tptp.insert_nat B) A)) (or (= A2 B) (@ _let_1 A))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf B) A)) (or (= A2 B) (@ _let_1 A))))) (forall ((A2 tptp.nat) (B4 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B)) (@ _let_1 (@ (@ tptp.insert_nat B) B4))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B)) (@ _let_1 (@ (@ tptp.insert9649339lle_hf B) B4))))) (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)))))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)))))) (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (= (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))) (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B4 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat A2) C2)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A2) B4)) C2) (@ (@ tptp.inf_inf_set_nat B4) C2)))) (forall ((A2 tptp.hF_Mirabelle_hf) (C2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (=> (not (@ (@ tptp.member1367349282lle_hf A2) C2)) (= (@ (@ tptp.inf_in923488851lle_hf (@ (@ tptp.insert9649339lle_hf A2) B4)) C2) (@ (@ tptp.inf_in923488851lle_hf B4) C2)))) (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) C2) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B4)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B4) C2)))))) (forall ((A2 tptp.hF_Mirabelle_hf) (C2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (=> (@ (@ tptp.member1367349282lle_hf A2) C2) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 B4)) C2) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf B4) C2)))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (= (@ (@ tptp.inf_in923488851lle_hf (@ _let_1 A)) (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (=> (not (@ (@ tptp.member_nat A2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat A2) B4)) (@ _let_1 B4))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A))) (=> (not (@ (@ tptp.member1367349282lle_hf A2) A)) (= (@ _let_1 (@ (@ tptp.insert9649339lle_hf A2) B4)) (@ _let_1 B4))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) A) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4))))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A))) (let ((_let_2 (@ tptp.insert9649339lle_hf A2))) (=> (@ (@ tptp.member1367349282lle_hf A2) A) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4))))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (C2 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf A2))) (= (@ (@ tptp.sup_su1790843629lle_hf (@ _let_1 B4)) C2) (@ _let_1 (@ (@ tptp.sup_su1790843629lle_hf B4) C2))))) (forall ((A tptp.set_HF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su1790843629lle_hf A))) (let ((_let_2 (@ tptp.insert9649339lle_hf A2))) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4)))))) (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.insert9649339lle_hf X) tptp.top_to489427057lle_hf) tptp.top_to489427057lle_hf)) (forall ((X tptp.nat)) (= (@ (@ tptp.insert_nat X) tptp.top_top_set_nat) tptp.top_top_set_nat)) (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (not (=> (@ _let_1 A) (not (@ _let_1 B4))))))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)) (not (=> (@ _let_1 A) (not (@ _let_1 B4))))))) (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (@ _let_1 A)))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)) (@ _let_1 A)))) (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (@ _let_1 B4)))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf C))) (=> (@ _let_1 (@ (@ tptp.inf_in923488851lle_hf A) B4)) (@ _let_1 B4)))) (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat B4) C2))) (let ((_let_2 (@ tptp.insert_nat A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_nat (@ _let_2 B4)) C2))) (let ((_let_4 (@ (@ tptp.member_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((A2 tptp.hF_Mirabelle_hf) (C2 tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in923488851lle_hf B4) C2))) (let ((_let_2 (@ tptp.insert9649339lle_hf A2))) (let ((_let_3 (@ (@ tptp.inf_in923488851lle_hf (@ _let_2 B4)) C2))) (let ((_let_4 (@ (@ tptp.member1367349282lle_hf A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ tptp.insert_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B4)))) (let ((_let_5 (@ (@ tptp.member_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in923488851lle_hf A))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ tptp.insert9649339lle_hf A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B4)))) (let ((_let_5 (@ (@ tptp.member1367349282lle_hf A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A) (exists ((B6 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat A2) B6)) (not (@ (@ tptp.member_nat A2) B6)))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A2) A) (exists ((B6 tptp.set_HF_Mirabelle_hf)) (and (= A (@ (@ tptp.insert9649339lle_hf A2) B6)) (not (@ (@ tptp.member1367349282lle_hf A2) B6)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X))) (let ((_let_2 (@ tptp.insert9649339lle_hf Y3))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (= A2 B))) (=> (not (@ (@ tptp.member_nat A2) A)) (=> (not (@ (@ tptp.member_nat B) B4)) (= (= (@ (@ tptp.insert_nat A2) A) (@ (@ tptp.insert_nat B) B4)) (and (=> _let_1 (= A B4)) (=> (not _let_1) (exists ((C3 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat B) C3)) (not (@ (@ tptp.member_nat B) C3)) (= B4 (@ (@ tptp.insert_nat A2) C3)) (not (@ (@ tptp.member_nat A2) C3))))))))))) (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (= A2 B))) (=> (not (@ (@ tptp.member1367349282lle_hf A2) A)) (=> (not (@ (@ tptp.member1367349282lle_hf B) B4)) (= (= (@ (@ tptp.insert9649339lle_hf A2) A) (@ (@ tptp.insert9649339lle_hf B) B4)) (and (=> _let_1 (= A B4)) (=> (not _let_1) (exists ((C3 tptp.set_HF_Mirabelle_hf)) (and (= A (@ (@ tptp.insert9649339lle_hf B) C3)) (not (@ (@ tptp.member1367349282lle_hf B) C3)) (= B4 (@ (@ tptp.insert9649339lle_hf A2) C3)) (not (@ (@ tptp.member1367349282lle_hf A2) C3))))))))))) (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A) (= (@ (@ tptp.insert_nat A2) A) A))) (forall ((A2 tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf A2) A) (= (@ (@ tptp.insert9649339lle_hf A2) A) A))) (forall ((X tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.member_nat X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A) (@ _let_1 B4)) (= A B4))))))) (forall ((X tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.insert9649339lle_hf X))) (let ((_let_2 (@ tptp.member1367349282lle_hf X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A) (@ _let_1 B4)) (= A B4))))))) (forall ((X tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A) (not (forall ((B6 tptp.set_nat)) (=> (= A (@ (@ tptp.insert_nat X) B6)) (@ (@ tptp.member_nat X) B6)))))) (forall ((X tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (=> (@ (@ tptp.member1367349282lle_hf X) A) (not (forall ((B6 tptp.set_HF_Mirabelle_hf)) (=> (= A (@ (@ tptp.insert9649339lle_hf X) B6)) (@ (@ tptp.member1367349282lle_hf X) B6)))))) (forall ((A2 tptp.nat) (B4 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_nat B) B4))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B4 tptp.set_HF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert9649339lle_hf B) B4))))) (forall ((A2 tptp.nat) (B4 tptp.set_nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat 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) (B tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert_nat B) A)) (=> (not (= A2 B)) (@ _let_1 A))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.set_HF_Mirabelle_hf)) (let ((_let_1 (@ tptp.member1367349282lle_hf A2))) (=> (@ _let_1 (@ (@ tptp.insert9649339lle_hf B) A)) (=> (not (= A2 B)) (@ _let_1 A))))) (forall ((A2 tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_hfset (@ (@ tptp.hF_Mirabelle_hinsert A2) B)) (@ (@ tptp.insert9649339lle_hf A2) (@ tptp.hF_Mirabelle_hfset B)))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.plus_plus_nat (@ tptp.hF_Mirabelle_hcard (@ (@ tptp.sup_su638957495lle_hf X) Y3))) (@ tptp.hF_Mirabelle_hcard (@ (@ tptp.inf_in956532509lle_hf X) Y3))) (@ (@ tptp.plus_plus_nat (@ tptp.hF_Mirabelle_hcard X)) (@ tptp.hF_Mirabelle_hcard Y3)))) (forall ((X tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hcard Y3))) (let ((_let_2 (@ tptp.hF_Mirabelle_hcard (@ (@ tptp.hF_Mirabelle_hinsert X) Y3)))) (let ((_let_3 (@ (@ tptp.hF_Mirabelle_hmem X) Y3))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1)))))))) (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B C))) (forall ((X tptp.nat) (Y3 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y3)) (and (= X tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y3) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))) (forall ((A2 tptp.nat) (B tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat A2) B)) (= B tptp.zero_zero_nat))) (forall ((A2 tptp.nat) (B tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat B) A2)) (= B tptp.zero_zero_nat))) (forall ((A2 tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A2) B) A2) (= B tptp.zero_zero_nat))) (forall ((B tptp.nat) (A2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A2) A2) (= B tptp.zero_zero_nat))) (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)) (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((A tptp.nat) (K tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_nat A) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B)))))) (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.69/0.93 )
% 0.69/0.93 % SZS output end Proof for ITP076^1
% 0.69/0.93 % cvc5---1.0.5 exiting
% 0.69/0.94 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------