TSTP Solution File: ITP074^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP074^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 03:18:00 EDT 2023
% Result : Theorem 0.59s 0.85s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.16 % Problem : ITP074^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.18 % Command : do_cvc5 %s %d
% 0.17/0.39 % Computer : n017.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Sun Aug 27 15:34:27 EDT 2023
% 0.17/0.39 % CPUTime :
% 0.24/0.56 %----Proving TH0
% 0.24/0.57 %------------------------------------------------------------------------------
% 0.24/0.57 % File : ITP074^1 : TPTP v8.1.2. Released v7.5.0.
% 0.24/0.57 % Domain : Interactive Theorem Proving
% 0.24/0.57 % Problem : Sledgehammer HF problem prob_612__5334652_1
% 0.24/0.57 % Version : Especial.
% 0.24/0.57 % English :
% 0.24/0.57
% 0.24/0.57 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.24/0.57 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.24/0.57 % Source : [Des21]
% 0.24/0.57 % Names : HF/prob_612__5334652_1 [Des21]
% 0.24/0.57
% 0.24/0.57 % Status : Theorem
% 0.24/0.57 % Rating : 0.46 v8.1.0, 0.36 v7.5.0
% 0.24/0.57 % Syntax : Number of formulae : 376 ( 220 unt; 32 typ; 0 def)
% 0.24/0.57 % Number of atoms : 708 ( 335 equ; 0 cnn)
% 0.24/0.57 % Maximal formula atoms : 6 ( 2 avg)
% 0.24/0.57 % Number of connectives : 2286 ( 42 ~; 7 |; 34 &;1996 @)
% 0.24/0.57 % ( 0 <=>; 207 =>; 0 <=; 0 <~>)
% 0.24/0.57 % Maximal formula depth : 16 ( 5 avg)
% 0.24/0.57 % Number of types : 4 ( 3 usr)
% 0.24/0.57 % Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% 0.24/0.57 % Number of symbols : 30 ( 29 usr; 4 con; 0-2 aty)
% 0.24/0.57 % Number of variables : 876 ( 79 ^; 782 !; 15 ?; 876 :)
% 0.24/0.57 % SPC : TH0_THM_EQU_NAR
% 0.24/0.57
% 0.24/0.57 % Comments : This file was generated by Sledgehammer 2021-02-23 15:37:44.587
% 0.24/0.57 %------------------------------------------------------------------------------
% 0.24/0.57 % Could-be-implicit typings (3)
% 0.24/0.57 thf(ty_n_t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J,type,
% 0.24/0.57 set_HF_Mirabelle_hf: $tType ).
% 0.24/0.57
% 0.24/0.57 thf(ty_n_t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.57 hF_Mirabelle_hf: $tType ).
% 0.24/0.57
% 0.24/0.57 thf(ty_n_t__Nat__Onat,type,
% 0.24/0.57 nat: $tType ).
% 0.24/0.57
% 0.24/0.57 % Explicit typings (29)
% 0.24/0.57 thf(sy_c_Groups_Ominus__class_Ominus_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.57 minus_1232880740lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.24/0.57 minus_minus_nat: nat > nat > nat ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Groups_Ozero__class_Ozero_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.57 zero_z189798548lle_hf: hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.24/0.57 zero_zero_nat: nat ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_OHCollect,type,
% 0.24/0.57 hF_Mir818139703ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_OHF,type,
% 0.24/0.57 hF_Mirabelle_HF: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_OHInter,type,
% 0.24/0.57 hF_Mirabelle_HInter: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_OHUnion,type,
% 0.24/0.57 hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_OPrimReplace,type,
% 0.24/0.57 hF_Mir1248913145eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_ORepFun,type,
% 0.24/0.57 hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_OReplace,type,
% 0.24/0.57 hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohf_OAbs__hf,type,
% 0.24/0.57 hF_Mirabelle_Abs_hf: nat > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohfset,type,
% 0.24/0.57 hF_Mirabelle_hfset: hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohfst,type,
% 0.24/0.57 hF_Mirabelle_hfst: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohinsert,type,
% 0.24/0.57 hF_Mirabelle_hinsert: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohmem,type,
% 0.24/0.57 hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohpair,type,
% 0.24/0.57 hF_Mirabelle_hpair: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_HF__Mirabelle__glliljednj_Ohsnd,type,
% 0.24/0.57 hF_Mirabelle_hsnd: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Lattices_Oinf__class_Oinf_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.57 inf_in956532509lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 0.24/0.57 inf_inf_nat: nat > nat > nat ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Lattices_Osup__class_Osup_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.57 sup_su638957495lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 0.24/0.57 sup_sup_nat: nat > nat > nat ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.24/0.57 semiri1382578993at_nat: nat > nat ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.57 ord_le976219883lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.24/0.57 ord_less_eq_nat: nat > nat > $o ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_Set_OCollect_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.57 collec2046588256lle_hf: ( hF_Mirabelle_hf > $o ) > set_HF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_c_member_001t__HF____Mirabelle____glliljednj__Ohf,type,
% 0.24/0.57 member1367349282lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
% 0.24/0.57
% 0.24/0.57 thf(sy_v_x,type,
% 0.24/0.57 x: hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 thf(sy_v_y,type,
% 0.24/0.57 y: hF_Mirabelle_hf ).
% 0.24/0.57
% 0.24/0.57 % Relevant facts (343)
% 0.24/0.57 thf(fact_0_hpair__iff,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A2: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ( hF_Mirabelle_hpair @ A @ B )
% 0.24/0.57 = ( hF_Mirabelle_hpair @ A2 @ B2 ) )
% 0.24/0.57 = ( ( A = A2 )
% 0.24/0.57 & ( B = B2 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hpair_iff
% 0.24/0.57 thf(fact_1_hpair__inject,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A2: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ( hF_Mirabelle_hpair @ A @ B )
% 0.24/0.57 = ( hF_Mirabelle_hpair @ A2 @ B2 ) )
% 0.24/0.57 => ~ ( ( A = A2 )
% 0.24/0.57 => ( B != B2 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hpair_inject
% 0.24/0.57 thf(fact_2_hpair__neq__fst,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hpair @ A @ B )
% 0.24/0.57 != A ) ).
% 0.24/0.57
% 0.24/0.57 % hpair_neq_fst
% 0.24/0.57 thf(fact_3_hpair__neq__snd,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hpair @ A @ B )
% 0.24/0.57 != B ) ).
% 0.24/0.57
% 0.24/0.57 % hpair_neq_snd
% 0.24/0.57 thf(fact_4_hfst__conv,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % hfst_conv
% 0.24/0.57 thf(fact_5_hsnd__conv,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
% 0.24/0.57 = B ) ).
% 0.24/0.57
% 0.24/0.57 % hsnd_conv
% 0.24/0.57 thf(fact_6_HInter__hempty,axiom,
% 0.24/0.57 ( ( hF_Mirabelle_HInter @ zero_z189798548lle_hf )
% 0.24/0.57 = zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % HInter_hempty
% 0.24/0.57 thf(fact_7_HCollect__hempty,axiom,
% 0.24/0.57 ! [P: hF_Mirabelle_hf > $o] :
% 0.24/0.57 ( ( hF_Mir818139703ollect @ P @ zero_z189798548lle_hf )
% 0.24/0.57 = zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % HCollect_hempty
% 0.24/0.57 thf(fact_8_Replace__0,axiom,
% 0.24/0.57 ! [R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.57 ( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ R )
% 0.24/0.57 = zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % Replace_0
% 0.24/0.57 thf(fact_9_HUnion__hempty,axiom,
% 0.24/0.57 ( ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf )
% 0.24/0.57 = zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % HUnion_hempty
% 0.24/0.57 thf(fact_10_zero__reorient,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( zero_z189798548lle_hf = X )
% 0.24/0.57 = ( X = zero_z189798548lle_hf ) ) ).
% 0.24/0.57
% 0.24/0.57 % zero_reorient
% 0.24/0.57 thf(fact_11_zero__reorient,axiom,
% 0.24/0.57 ! [X: nat] :
% 0.24/0.57 ( ( zero_zero_nat = X )
% 0.24/0.57 = ( X = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % zero_reorient
% 0.24/0.57 thf(fact_12_RepFun__0,axiom,
% 0.24/0.57 ! [F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_RepFun @ zero_z189798548lle_hf @ F )
% 0.24/0.57 = zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % RepFun_0
% 0.24/0.57 thf(fact_13_hpair__def,axiom,
% 0.24/0.57 ( hF_Mirabelle_hpair
% 0.24/0.57 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A3 @ zero_z189798548lle_hf ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A3 @ ( hF_Mirabelle_hinsert @ B3 @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hpair_def
% 0.24/0.57 thf(fact_14_hpair__def_H,axiom,
% 0.24/0.57 ( hF_Mirabelle_hpair
% 0.24/0.57 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A3 @ ( hF_Mirabelle_hinsert @ A3 @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A3 @ ( hF_Mirabelle_hinsert @ B3 @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hpair_def'
% 0.24/0.57 thf(fact_15_singleton__eq__iff,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf )
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) )
% 0.24/0.57 = ( A = B ) ) ).
% 0.24/0.57
% 0.24/0.57 % singleton_eq_iff
% 0.24/0.57 thf(fact_16_RepFun__hinsert,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_RepFun @ ( hF_Mirabelle_hinsert @ A @ B ) @ F )
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ ( F @ A ) @ ( hF_Mirabelle_RepFun @ B @ F ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % RepFun_hinsert
% 0.24/0.57 thf(fact_17_hinsert__commute,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hinsert @ X @ ( hF_Mirabelle_hinsert @ Y @ Z ) )
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ Y @ ( hF_Mirabelle_hinsert @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hinsert_commute
% 0.24/0.57 thf(fact_18_hinsert__nonempty,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hinsert @ A @ A4 )
% 0.24/0.57 != zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % hinsert_nonempty
% 0.24/0.57 thf(fact_19_HF__Mirabelle__glliljednj_Odoubleton__eq__iff,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) )
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ C @ ( hF_Mirabelle_hinsert @ D @ zero_z189798548lle_hf ) ) )
% 0.24/0.57 = ( ( ( A = C )
% 0.24/0.57 & ( B = D ) )
% 0.24/0.57 | ( ( A = D )
% 0.24/0.57 & ( B = C ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % HF_Mirabelle_glliljednj.doubleton_eq_iff
% 0.24/0.57 thf(fact_20_hf__induct__ax,axiom,
% 0.24/0.57 ! [P: hF_Mirabelle_hf > $o,X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( P @ zero_z189798548lle_hf )
% 0.24/0.57 => ( ! [X2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( P @ X2 )
% 0.24/0.57 => ! [Y2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( P @ Y2 )
% 0.24/0.57 => ( P @ ( hF_Mirabelle_hinsert @ Y2 @ X2 ) ) ) )
% 0.24/0.57 => ( P @ X ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hf_induct_ax
% 0.24/0.57 thf(fact_21_HInter__hinsert,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( A4 != zero_z189798548lle_hf )
% 0.24/0.57 => ( ( hF_Mirabelle_HInter @ ( hF_Mirabelle_hinsert @ A @ A4 ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ A @ ( hF_Mirabelle_HInter @ A4 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % HInter_hinsert
% 0.24/0.57 thf(fact_22_Abs__hf__0,axiom,
% 0.24/0.57 ( ( hF_Mirabelle_Abs_hf @ zero_zero_nat )
% 0.24/0.57 = zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % Abs_hf_0
% 0.24/0.57 thf(fact_23_HInter__iff,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( A4 != zero_z189798548lle_hf )
% 0.24/0.57 => ( ( hF_Mirabelle_hmem @ X @ ( hF_Mirabelle_HInter @ A4 ) )
% 0.24/0.57 = ( ! [Y3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ Y3 @ A4 )
% 0.24/0.57 => ( hF_Mirabelle_hmem @ X @ Y3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % HInter_iff
% 0.24/0.57 thf(fact_24_HUnion__hinsert,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hinsert @ A @ A4 ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ A @ ( hF_Mirabelle_HUnion @ A4 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % HUnion_hinsert
% 0.24/0.57 thf(fact_25_hdiff__insert,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,A: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( minus_1232880740lle_hf @ A4 @ ( hF_Mirabelle_hinsert @ A @ B4 ) )
% 0.24/0.57 = ( minus_1232880740lle_hf @ ( minus_1232880740lle_hf @ A4 @ B4 ) @ ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hdiff_insert
% 0.24/0.57 thf(fact_26_hinsert__eq__sup,axiom,
% 0.24/0.57 ( hF_Mirabelle_hinsert
% 0.24/0.57 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B3 @ ( hF_Mirabelle_hinsert @ A3 @ zero_z189798548lle_hf ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hinsert_eq_sup
% 0.24/0.57 thf(fact_27_hf__induct,axiom,
% 0.24/0.57 ! [P: hF_Mirabelle_hf > $o,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( P @ zero_z189798548lle_hf )
% 0.24/0.57 => ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( P @ X2 )
% 0.24/0.57 => ( ( P @ Y2 )
% 0.24/0.57 => ( ~ ( hF_Mirabelle_hmem @ X2 @ Y2 )
% 0.24/0.57 => ( P @ ( hF_Mirabelle_hinsert @ X2 @ Y2 ) ) ) ) )
% 0.24/0.57 => ( P @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hf_induct
% 0.24/0.57 thf(fact_28_hf__cases,axiom,
% 0.24/0.57 ! [Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( Y != zero_z189798548lle_hf )
% 0.24/0.57 => ~ ! [A5: hF_Mirabelle_hf,B5: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( Y
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ A5 @ B5 ) )
% 0.24/0.57 => ( hF_Mirabelle_hmem @ A5 @ B5 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hf_cases
% 0.24/0.57 thf(fact_29_Replace__hunion,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.57 ( ( hF_Mirabelle_Replace @ ( sup_su638957495lle_hf @ A4 @ B4 ) @ R )
% 0.24/0.57 = ( sup_su638957495lle_hf @ ( hF_Mirabelle_Replace @ A4 @ R ) @ ( hF_Mirabelle_Replace @ B4 @ R ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Replace_hunion
% 0.24/0.57 thf(fact_30_HCollect__iff,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o,A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X @ ( hF_Mir818139703ollect @ P @ A4 ) )
% 0.24/0.57 = ( ( P @ X )
% 0.24/0.57 & ( hF_Mirabelle_hmem @ X @ A4 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % HCollect_iff
% 0.24/0.57 thf(fact_31_hf__equalityI,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ! [X2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X2 @ A )
% 0.24/0.57 = ( hF_Mirabelle_hmem @ X2 @ B ) )
% 0.24/0.57 => ( A = B ) ) ).
% 0.24/0.57
% 0.24/0.57 % hf_equalityI
% 0.24/0.57 thf(fact_32_zero__diff,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.24/0.57 = zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % zero_diff
% 0.24/0.57 thf(fact_33_diff__zero,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % diff_zero
% 0.24/0.57 thf(fact_34_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( minus_minus_nat @ A @ A )
% 0.24/0.57 = zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % cancel_comm_monoid_add_class.diff_cancel
% 0.24/0.57 thf(fact_35_hmem__hinsert,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
% 0.24/0.57 = ( ( A = B )
% 0.24/0.57 | ( hF_Mirabelle_hmem @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hmem_hinsert
% 0.24/0.57 thf(fact_36_hunion__iff,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X @ ( sup_su638957495lle_hf @ A @ B ) )
% 0.24/0.57 = ( ( hF_Mirabelle_hmem @ X @ A )
% 0.24/0.57 | ( hF_Mirabelle_hmem @ X @ B ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hunion_iff
% 0.24/0.57 thf(fact_37_hinter__iff,axiom,
% 0.24/0.57 ! [U: hF_Mirabelle_hf,X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U @ ( inf_in956532509lle_hf @ X @ Y ) )
% 0.24/0.57 = ( ( hF_Mirabelle_hmem @ U @ X )
% 0.24/0.57 & ( hF_Mirabelle_hmem @ U @ Y ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hinter_iff
% 0.24/0.57 thf(fact_38_RepFun__iff,axiom,
% 0.24/0.57 ! [V: hF_Mirabelle_hf,A4: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ V @ ( hF_Mirabelle_RepFun @ A4 @ F ) )
% 0.24/0.57 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U2 @ A4 )
% 0.24/0.57 & ( V
% 0.24/0.57 = ( F @ U2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % RepFun_iff
% 0.24/0.57 thf(fact_39_hunion__hempty__left,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ zero_z189798548lle_hf @ A4 )
% 0.24/0.57 = A4 ) ).
% 0.24/0.57
% 0.24/0.57 % hunion_hempty_left
% 0.24/0.57 thf(fact_40_hunion__hempty__right,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ A4 @ zero_z189798548lle_hf )
% 0.24/0.57 = A4 ) ).
% 0.24/0.57
% 0.24/0.57 % hunion_hempty_right
% 0.24/0.57 thf(fact_41_HUnion__iff,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X @ ( hF_Mirabelle_HUnion @ A4 ) )
% 0.24/0.57 = ( ? [Y3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ Y3 @ A4 )
% 0.24/0.57 & ( hF_Mirabelle_hmem @ X @ Y3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % HUnion_iff
% 0.24/0.57 thf(fact_42_mem__Collect__eq,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o] :
% 0.24/0.57 ( ( member1367349282lle_hf @ A @ ( collec2046588256lle_hf @ P ) )
% 0.24/0.57 = ( P @ A ) ) ).
% 0.24/0.57
% 0.24/0.57 % mem_Collect_eq
% 0.24/0.57 thf(fact_43_Collect__mem__eq,axiom,
% 0.24/0.57 ! [A4: set_HF_Mirabelle_hf] :
% 0.24/0.57 ( ( collec2046588256lle_hf
% 0.24/0.57 @ ^ [X3: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X3 @ A4 ) )
% 0.24/0.57 = A4 ) ).
% 0.24/0.57
% 0.24/0.57 % Collect_mem_eq
% 0.24/0.57 thf(fact_44_Collect__cong,axiom,
% 0.24/0.57 ! [P: hF_Mirabelle_hf > $o,Q: hF_Mirabelle_hf > $o] :
% 0.24/0.57 ( ! [X2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( P @ X2 )
% 0.24/0.57 = ( Q @ X2 ) )
% 0.24/0.57 => ( ( collec2046588256lle_hf @ P )
% 0.24/0.57 = ( collec2046588256lle_hf @ Q ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Collect_cong
% 0.24/0.57 thf(fact_45_hdiff__iff,axiom,
% 0.24/0.57 ! [U: hF_Mirabelle_hf,X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U @ ( minus_1232880740lle_hf @ X @ Y ) )
% 0.24/0.57 = ( ( hF_Mirabelle_hmem @ U @ X )
% 0.24/0.57 & ~ ( hF_Mirabelle_hmem @ U @ Y ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hdiff_iff
% 0.24/0.57 thf(fact_46_hinter__hempty__left,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ zero_z189798548lle_hf @ A4 )
% 0.24/0.57 = zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % hinter_hempty_left
% 0.24/0.57 thf(fact_47_hinter__hempty__right,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ A4 @ zero_z189798548lle_hf )
% 0.24/0.57 = zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % hinter_hempty_right
% 0.24/0.57 thf(fact_48_Replace__iff,axiom,
% 0.24/0.57 ! [V: hF_Mirabelle_hf,A4: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ V @ ( hF_Mirabelle_Replace @ A4 @ R ) )
% 0.24/0.57 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U2 @ A4 )
% 0.24/0.57 & ( R @ U2 @ V )
% 0.24/0.57 & ! [Y3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( R @ U2 @ Y3 )
% 0.24/0.57 => ( Y3 = V ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Replace_iff
% 0.24/0.57 thf(fact_49_hdiff__zero,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( minus_1232880740lle_hf @ X @ zero_z189798548lle_hf )
% 0.24/0.57 = X ) ).
% 0.24/0.57
% 0.24/0.57 % hdiff_zero
% 0.24/0.57 thf(fact_50_zero__hdiff,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( minus_1232880740lle_hf @ zero_z189798548lle_hf @ X )
% 0.24/0.57 = zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % zero_hdiff
% 0.24/0.57 thf(fact_51_RepFun__hunion,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_RepFun @ ( sup_su638957495lle_hf @ A4 @ B4 ) @ F )
% 0.24/0.57 = ( sup_su638957495lle_hf @ ( hF_Mirabelle_RepFun @ A4 @ F ) @ ( hF_Mirabelle_RepFun @ B4 @ F ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % RepFun_hunion
% 0.24/0.57 thf(fact_52_HUnion__hunion,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A4 @ B4 ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A4 ) @ ( hF_Mirabelle_HUnion @ B4 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % HUnion_hunion
% 0.24/0.57 thf(fact_53_diff__right__commute,axiom,
% 0.24/0.57 ! [A: nat,C: nat,B: nat] :
% 0.24/0.57 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.24/0.57 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.24/0.57
% 0.24/0.57 % diff_right_commute
% 0.24/0.57 thf(fact_54_replacement__fun,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.57 ? [Z2: hF_Mirabelle_hf] :
% 0.24/0.57 ! [V2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ V2 @ Z2 )
% 0.24/0.57 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U2 @ X )
% 0.24/0.57 & ( V2
% 0.24/0.57 = ( F @ U2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % replacement_fun
% 0.24/0.57 thf(fact_55_hmem__not__refl,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf] :
% 0.24/0.57 ~ ( hF_Mirabelle_hmem @ X @ X ) ).
% 0.24/0.57
% 0.24/0.57 % hmem_not_refl
% 0.24/0.57 thf(fact_56_comprehension,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o] :
% 0.24/0.57 ? [Z2: hF_Mirabelle_hf] :
% 0.24/0.57 ! [U3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U3 @ Z2 )
% 0.24/0.57 = ( ( hF_Mirabelle_hmem @ U3 @ X )
% 0.24/0.57 & ( P @ U3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % comprehension
% 0.24/0.57 thf(fact_57_union__of__set,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf] :
% 0.24/0.57 ? [Z2: hF_Mirabelle_hf] :
% 0.24/0.57 ! [U3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U3 @ Z2 )
% 0.24/0.57 = ( ? [Y3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ Y3 @ X )
% 0.24/0.57 & ( hF_Mirabelle_hmem @ U3 @ Y3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % union_of_set
% 0.24/0.57 thf(fact_58_hmem__not__sym,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ~ ( ( hF_Mirabelle_hmem @ X @ Y )
% 0.24/0.57 & ( hF_Mirabelle_hmem @ Y @ X ) ) ).
% 0.24/0.57
% 0.24/0.57 % hmem_not_sym
% 0.24/0.57 thf(fact_59_binary__union,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ? [Z2: hF_Mirabelle_hf] :
% 0.24/0.57 ! [U3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U3 @ Z2 )
% 0.24/0.57 = ( ( hF_Mirabelle_hmem @ U3 @ X )
% 0.24/0.57 | ( hF_Mirabelle_hmem @ U3 @ Y ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % binary_union
% 0.24/0.57 thf(fact_60_replacement,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.57 ( ! [U4: hF_Mirabelle_hf,V3: hF_Mirabelle_hf,V4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U4 @ X )
% 0.24/0.57 => ( ( R @ U4 @ V3 )
% 0.24/0.57 => ( ( R @ U4 @ V4 )
% 0.24/0.57 => ( V4 = V3 ) ) ) )
% 0.24/0.57 => ? [Z2: hF_Mirabelle_hf] :
% 0.24/0.57 ! [V2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ V2 @ Z2 )
% 0.24/0.57 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U2 @ X )
% 0.24/0.57 & ( R @ U2 @ V2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % replacement
% 0.24/0.57 thf(fact_61_hmem__ne,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X @ Y )
% 0.24/0.57 => ( X != Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % hmem_ne
% 0.24/0.57 thf(fact_62_hf__ext,axiom,
% 0.24/0.57 ( ( ^ [Y4: hF_Mirabelle_hf,Z3: hF_Mirabelle_hf] : ( Y4 = Z3 ) )
% 0.24/0.57 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.24/0.57 ! [X3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X3 @ A3 )
% 0.24/0.57 = ( hF_Mirabelle_hmem @ X3 @ B3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hf_ext
% 0.24/0.57 thf(fact_63_hinter__hinsert__right,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ B4 @ ( hF_Mirabelle_hinsert @ X @ A4 ) )
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ X @ ( inf_in956532509lle_hf @ B4 @ A4 ) ) ) )
% 0.24/0.57 & ( ~ ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ B4 @ ( hF_Mirabelle_hinsert @ X @ A4 ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ B4 @ A4 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hinter_hinsert_right
% 0.24/0.57 thf(fact_64_hinter__hinsert__left,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ ( hF_Mirabelle_hinsert @ X @ A4 ) @ B4 )
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ X @ ( inf_in956532509lle_hf @ A4 @ B4 ) ) ) )
% 0.24/0.57 & ( ~ ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ ( hF_Mirabelle_hinsert @ X @ A4 ) @ B4 )
% 0.24/0.57 = ( inf_in956532509lle_hf @ A4 @ B4 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hinter_hinsert_left
% 0.24/0.57 thf(fact_65_foundation,axiom,
% 0.24/0.57 ! [Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( Z != zero_z189798548lle_hf )
% 0.24/0.57 => ? [W: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ W @ Z )
% 0.24/0.57 & ( ( inf_in956532509lle_hf @ W @ Z )
% 0.24/0.57 = zero_z189798548lle_hf ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % foundation
% 0.24/0.57 thf(fact_66_hinsert__hdiff__if,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.57 => ( ( minus_1232880740lle_hf @ ( hF_Mirabelle_hinsert @ X @ A4 ) @ B4 )
% 0.24/0.57 = ( minus_1232880740lle_hf @ A4 @ B4 ) ) )
% 0.24/0.57 & ( ~ ( hF_Mirabelle_hmem @ X @ B4 )
% 0.24/0.57 => ( ( minus_1232880740lle_hf @ ( hF_Mirabelle_hinsert @ X @ A4 ) @ B4 )
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ X @ ( minus_1232880740lle_hf @ A4 @ B4 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hinsert_hdiff_if
% 0.24/0.57 thf(fact_67_hinsert__iff,axiom,
% 0.24/0.57 ! [Z: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( Z
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ Y @ X ) )
% 0.24/0.57 = ( ! [U2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U2 @ Z )
% 0.24/0.57 = ( ( hF_Mirabelle_hmem @ U2 @ X )
% 0.24/0.57 | ( U2 = Y ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hinsert_iff
% 0.24/0.57 thf(fact_68_hemptyE,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf] :
% 0.24/0.57 ~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % hemptyE
% 0.24/0.57 thf(fact_69_hempty__iff,axiom,
% 0.24/0.57 ! [Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( Z = zero_z189798548lle_hf )
% 0.24/0.57 = ( ! [X3: hF_Mirabelle_hf] :
% 0.24/0.57 ~ ( hF_Mirabelle_hmem @ X3 @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hempty_iff
% 0.24/0.57 thf(fact_70_hmem__hempty,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf] :
% 0.24/0.57 ~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ).
% 0.24/0.57
% 0.24/0.57 % hmem_hempty
% 0.24/0.57 thf(fact_71_hunion__hinsert__right,axiom,
% 0.24/0.57 ! [B4: hF_Mirabelle_hf,X: hF_Mirabelle_hf,A4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ B4 @ ( hF_Mirabelle_hinsert @ X @ A4 ) )
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ X @ ( sup_su638957495lle_hf @ B4 @ A4 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hunion_hinsert_right
% 0.24/0.57 thf(fact_72_hunion__hinsert__left,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_hinsert @ X @ A4 ) @ B4 )
% 0.24/0.57 = ( hF_Mirabelle_hinsert @ X @ ( sup_su638957495lle_hf @ A4 @ B4 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hunion_hinsert_left
% 0.24/0.57 thf(fact_73_RepFun__cong,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf,G: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.24/0.57 ( ( A4 = B4 )
% 0.24/0.57 => ( ! [X2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X2 @ B4 )
% 0.24/0.57 => ( ( F @ X2 )
% 0.24/0.57 = ( G @ X2 ) ) )
% 0.24/0.57 => ( ( hF_Mirabelle_RepFun @ A4 @ F )
% 0.24/0.57 = ( hF_Mirabelle_RepFun @ B4 @ G ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % RepFun_cong
% 0.24/0.57 thf(fact_74_hmem__Sup__ne,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X @ Y )
% 0.24/0.57 => ( ( hF_Mirabelle_HUnion @ X )
% 0.24/0.57 != Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % hmem_Sup_ne
% 0.24/0.57 thf(fact_75_Replace__cong,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,P: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,Q: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.24/0.57 ( ( A4 = B4 )
% 0.24/0.57 => ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X2 @ B4 )
% 0.24/0.57 => ( ( P @ X2 @ Y2 )
% 0.24/0.57 = ( Q @ X2 @ Y2 ) ) )
% 0.24/0.57 => ( ( hF_Mirabelle_Replace @ A4 @ P )
% 0.24/0.57 = ( hF_Mirabelle_Replace @ B4 @ Q ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Replace_cong
% 0.24/0.57 thf(fact_76_sup__inf__absorb,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 0.24/0.57 = X ) ).
% 0.24/0.57
% 0.24/0.57 % sup_inf_absorb
% 0.24/0.57 thf(fact_77_sup__inf__absorb,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ X @ ( inf_in956532509lle_hf @ X @ Y ) )
% 0.24/0.57 = X ) ).
% 0.24/0.57
% 0.24/0.57 % sup_inf_absorb
% 0.24/0.57 thf(fact_78_inf__sup__absorb,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 0.24/0.57 = X ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_absorb
% 0.24/0.57 thf(fact_79_inf__sup__absorb,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ X @ ( sup_su638957495lle_hf @ X @ Y ) )
% 0.24/0.57 = X ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_absorb
% 0.24/0.57 thf(fact_80_sup_Oright__idem,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ B )
% 0.24/0.57 = ( sup_sup_nat @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.right_idem
% 0.24/0.57 thf(fact_81_sup_Oright__idem,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ B )
% 0.24/0.57 = ( sup_su638957495lle_hf @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.right_idem
% 0.24/0.57 thf(fact_82_sup__left__idem,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 0.24/0.57 = ( sup_sup_nat @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_left_idem
% 0.24/0.57 thf(fact_83_sup__left__idem,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ X @ Y ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_left_idem
% 0.24/0.57 thf(fact_84_sup_Oleft__idem,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ A @ ( sup_sup_nat @ A @ B ) )
% 0.24/0.57 = ( sup_sup_nat @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.left_idem
% 0.24/0.57 thf(fact_85_sup_Oleft__idem,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.left_idem
% 0.24/0.57 thf(fact_86_sup__idem,axiom,
% 0.24/0.57 ! [X: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ X @ X )
% 0.24/0.57 = X ) ).
% 0.24/0.57
% 0.24/0.57 % sup_idem
% 0.24/0.57 thf(fact_87_sup__idem,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ X @ X )
% 0.24/0.57 = X ) ).
% 0.24/0.57
% 0.24/0.57 % sup_idem
% 0.24/0.57 thf(fact_88_sup_Oidem,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ A @ A )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % sup.idem
% 0.24/0.57 thf(fact_89_sup_Oidem,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ A @ A )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % sup.idem
% 0.24/0.57 thf(fact_90_inf__right__idem,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Y )
% 0.24/0.57 = ( inf_inf_nat @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_right_idem
% 0.24/0.57 thf(fact_91_inf__right__idem,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ Y )
% 0.24/0.57 = ( inf_in956532509lle_hf @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_right_idem
% 0.24/0.57 thf(fact_92_inf_Oidem,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ A @ A )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % inf.idem
% 0.24/0.57 thf(fact_93_inf_Oidem,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ A @ A )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % inf.idem
% 0.24/0.57 thf(fact_94_inf__idem,axiom,
% 0.24/0.57 ! [X: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ X @ X )
% 0.24/0.57 = X ) ).
% 0.24/0.57
% 0.24/0.57 % inf_idem
% 0.24/0.57 thf(fact_95_inf__idem,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ X @ X )
% 0.24/0.57 = X ) ).
% 0.24/0.57
% 0.24/0.57 % inf_idem
% 0.24/0.57 thf(fact_96_inf_Oleft__idem,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ A @ ( inf_inf_nat @ A @ B ) )
% 0.24/0.57 = ( inf_inf_nat @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.left_idem
% 0.24/0.57 thf(fact_97_inf_Oleft__idem,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ A @ B ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.left_idem
% 0.24/0.57 thf(fact_98_inf__left__idem,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 0.24/0.57 = ( inf_inf_nat @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_left_idem
% 0.24/0.57 thf(fact_99_inf__left__idem,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ X @ Y ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_left_idem
% 0.24/0.57 thf(fact_100_inf_Oright__idem,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ B )
% 0.24/0.57 = ( inf_inf_nat @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.right_idem
% 0.24/0.57 thf(fact_101_inf_Oright__idem,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ B )
% 0.24/0.57 = ( inf_in956532509lle_hf @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.right_idem
% 0.24/0.57 thf(fact_102_inf__sup__aci_I4_J,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 0.24/0.57 = ( inf_inf_nat @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(4)
% 0.24/0.57 thf(fact_103_inf__sup__aci_I4_J,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ X @ Y ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(4)
% 0.24/0.57 thf(fact_104_inf__sup__aci_I3_J,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.24/0.57 = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(3)
% 0.24/0.57 thf(fact_105_inf__sup__aci_I3_J,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ Y @ Z ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ Y @ ( inf_in956532509lle_hf @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(3)
% 0.24/0.57 thf(fact_106_inf__sup__aci_I2_J,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 0.24/0.57 = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(2)
% 0.24/0.57 thf(fact_107_inf__sup__aci_I2_J,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ Z )
% 0.24/0.57 = ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(2)
% 0.24/0.57 thf(fact_108_inf__sup__aci_I1_J,axiom,
% 0.24/0.57 ( inf_inf_nat
% 0.24/0.57 = ( ^ [X3: nat,Y3: nat] : ( inf_inf_nat @ Y3 @ X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(1)
% 0.24/0.57 thf(fact_109_inf__sup__aci_I1_J,axiom,
% 0.24/0.57 ( inf_in956532509lle_hf
% 0.24/0.57 = ( ^ [X3: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ Y3 @ X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(1)
% 0.24/0.57 thf(fact_110_boolean__algebra__cancel_Oinf1,axiom,
% 0.24/0.57 ! [A4: nat,K: nat,A: nat,B: nat] :
% 0.24/0.57 ( ( A4
% 0.24/0.57 = ( inf_inf_nat @ K @ A ) )
% 0.24/0.57 => ( ( inf_inf_nat @ A4 @ B )
% 0.24/0.57 = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % boolean_algebra_cancel.inf1
% 0.24/0.57 thf(fact_111_boolean__algebra__cancel_Oinf1,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,K: hF_Mirabelle_hf,A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( A4
% 0.24/0.57 = ( inf_in956532509lle_hf @ K @ A ) )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ A4 @ B )
% 0.24/0.57 = ( inf_in956532509lle_hf @ K @ ( inf_in956532509lle_hf @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % boolean_algebra_cancel.inf1
% 0.24/0.57 thf(fact_112_boolean__algebra__cancel_Oinf2,axiom,
% 0.24/0.57 ! [B4: nat,K: nat,B: nat,A: nat] :
% 0.24/0.57 ( ( B4
% 0.24/0.57 = ( inf_inf_nat @ K @ B ) )
% 0.24/0.57 => ( ( inf_inf_nat @ A @ B4 )
% 0.24/0.57 = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % boolean_algebra_cancel.inf2
% 0.24/0.57 thf(fact_113_boolean__algebra__cancel_Oinf2,axiom,
% 0.24/0.57 ! [B4: hF_Mirabelle_hf,K: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( B4
% 0.24/0.57 = ( inf_in956532509lle_hf @ K @ B ) )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ A @ B4 )
% 0.24/0.57 = ( inf_in956532509lle_hf @ K @ ( inf_in956532509lle_hf @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % boolean_algebra_cancel.inf2
% 0.24/0.57 thf(fact_114_inf_Oassoc,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ C )
% 0.24/0.57 = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.assoc
% 0.24/0.57 thf(fact_115_inf_Oassoc,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ C )
% 0.24/0.57 = ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.assoc
% 0.24/0.57 thf(fact_116_inf__assoc,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 0.24/0.57 = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_assoc
% 0.24/0.57 thf(fact_117_inf__assoc,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ Z )
% 0.24/0.57 = ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_assoc
% 0.24/0.57 thf(fact_118_inf_Ocommute,axiom,
% 0.24/0.57 ( inf_inf_nat
% 0.24/0.57 = ( ^ [A3: nat,B3: nat] : ( inf_inf_nat @ B3 @ A3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.commute
% 0.24/0.57 thf(fact_119_inf_Ocommute,axiom,
% 0.24/0.57 ( inf_in956532509lle_hf
% 0.24/0.57 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ B3 @ A3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.commute
% 0.24/0.57 thf(fact_120_inf__commute,axiom,
% 0.24/0.57 ( inf_inf_nat
% 0.24/0.57 = ( ^ [X3: nat,Y3: nat] : ( inf_inf_nat @ Y3 @ X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_commute
% 0.24/0.57 thf(fact_121_inf__commute,axiom,
% 0.24/0.57 ( inf_in956532509lle_hf
% 0.24/0.57 = ( ^ [X3: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ Y3 @ X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_commute
% 0.24/0.57 thf(fact_122_inf_Oleft__commute,axiom,
% 0.24/0.57 ! [B: nat,A: nat,C: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ B @ ( inf_inf_nat @ A @ C ) )
% 0.24/0.57 = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.left_commute
% 0.24/0.57 thf(fact_123_inf_Oleft__commute,axiom,
% 0.24/0.57 ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ A @ C ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.left_commute
% 0.24/0.57 thf(fact_124_inf__left__commute,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.24/0.57 = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_left_commute
% 0.24/0.57 thf(fact_125_inf__left__commute,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ X @ ( inf_in956532509lle_hf @ Y @ Z ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ Y @ ( inf_in956532509lle_hf @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_left_commute
% 0.24/0.57 thf(fact_126_inf__sup__aci_I8_J,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 0.24/0.57 = ( sup_sup_nat @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(8)
% 0.24/0.57 thf(fact_127_inf__sup__aci_I8_J,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ X @ Y ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ X @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(8)
% 0.24/0.57 thf(fact_128_inf__sup__aci_I7_J,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 0.24/0.57 = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(7)
% 0.24/0.57 thf(fact_129_inf__sup__aci_I7_J,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ Y @ Z ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ Y @ ( sup_su638957495lle_hf @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(7)
% 0.24/0.57 thf(fact_130_inf__sup__aci_I6_J,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 0.24/0.57 = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(6)
% 0.24/0.57 thf(fact_131_inf__sup__aci_I6_J,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ X @ Y ) @ Z )
% 0.24/0.57 = ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(6)
% 0.24/0.57 thf(fact_132_inf__sup__aci_I5_J,axiom,
% 0.24/0.57 ( sup_sup_nat
% 0.24/0.57 = ( ^ [X3: nat,Y3: nat] : ( sup_sup_nat @ Y3 @ X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(5)
% 0.24/0.57 thf(fact_133_inf__sup__aci_I5_J,axiom,
% 0.24/0.57 ( sup_su638957495lle_hf
% 0.24/0.57 = ( ^ [X3: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ Y3 @ X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_aci(5)
% 0.24/0.57 thf(fact_134_boolean__algebra__cancel_Osup1,axiom,
% 0.24/0.57 ! [A4: nat,K: nat,A: nat,B: nat] :
% 0.24/0.57 ( ( A4
% 0.24/0.57 = ( sup_sup_nat @ K @ A ) )
% 0.24/0.57 => ( ( sup_sup_nat @ A4 @ B )
% 0.24/0.57 = ( sup_sup_nat @ K @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % boolean_algebra_cancel.sup1
% 0.24/0.57 thf(fact_135_boolean__algebra__cancel_Osup1,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,K: hF_Mirabelle_hf,A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( A4
% 0.24/0.57 = ( sup_su638957495lle_hf @ K @ A ) )
% 0.24/0.57 => ( ( sup_su638957495lle_hf @ A4 @ B )
% 0.24/0.57 = ( sup_su638957495lle_hf @ K @ ( sup_su638957495lle_hf @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % boolean_algebra_cancel.sup1
% 0.24/0.57 thf(fact_136_boolean__algebra__cancel_Osup2,axiom,
% 0.24/0.57 ! [B4: nat,K: nat,B: nat,A: nat] :
% 0.24/0.57 ( ( B4
% 0.24/0.57 = ( sup_sup_nat @ K @ B ) )
% 0.24/0.57 => ( ( sup_sup_nat @ A @ B4 )
% 0.24/0.57 = ( sup_sup_nat @ K @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % boolean_algebra_cancel.sup2
% 0.24/0.57 thf(fact_137_boolean__algebra__cancel_Osup2,axiom,
% 0.24/0.57 ! [B4: hF_Mirabelle_hf,K: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( B4
% 0.24/0.57 = ( sup_su638957495lle_hf @ K @ B ) )
% 0.24/0.57 => ( ( sup_su638957495lle_hf @ A @ B4 )
% 0.24/0.57 = ( sup_su638957495lle_hf @ K @ ( sup_su638957495lle_hf @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % boolean_algebra_cancel.sup2
% 0.24/0.57 thf(fact_138_sup_Oassoc,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ C )
% 0.24/0.57 = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.assoc
% 0.24/0.57 thf(fact_139_sup_Oassoc,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
% 0.24/0.57 = ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.assoc
% 0.24/0.57 thf(fact_140_sup__assoc,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 0.24/0.57 = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_assoc
% 0.24/0.57 thf(fact_141_sup__assoc,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ X @ Y ) @ Z )
% 0.24/0.57 = ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_assoc
% 0.24/0.57 thf(fact_142_sup_Ocommute,axiom,
% 0.24/0.57 ( sup_sup_nat
% 0.24/0.57 = ( ^ [A3: nat,B3: nat] : ( sup_sup_nat @ B3 @ A3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.commute
% 0.24/0.57 thf(fact_143_sup_Ocommute,axiom,
% 0.24/0.57 ( sup_su638957495lle_hf
% 0.24/0.57 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B3 @ A3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.commute
% 0.24/0.57 thf(fact_144_sup__commute,axiom,
% 0.24/0.57 ( sup_sup_nat
% 0.24/0.57 = ( ^ [X3: nat,Y3: nat] : ( sup_sup_nat @ Y3 @ X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_commute
% 0.24/0.57 thf(fact_145_sup__commute,axiom,
% 0.24/0.57 ( sup_su638957495lle_hf
% 0.24/0.57 = ( ^ [X3: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ Y3 @ X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_commute
% 0.24/0.57 thf(fact_146_sup_Oleft__commute,axiom,
% 0.24/0.57 ! [B: nat,A: nat,C: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ B @ ( sup_sup_nat @ A @ C ) )
% 0.24/0.57 = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.left_commute
% 0.24/0.57 thf(fact_147_sup_Oleft__commute,axiom,
% 0.24/0.57 ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.left_commute
% 0.24/0.57 thf(fact_148_sup__left__commute,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 0.24/0.57 = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_left_commute
% 0.24/0.57 thf(fact_149_sup__left__commute,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ X @ ( sup_su638957495lle_hf @ Y @ Z ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ Y @ ( sup_su638957495lle_hf @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_left_commute
% 0.24/0.57 thf(fact_150_distrib__imp1,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ! [X2: nat,Y2: nat,Z2: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ X2 @ ( sup_sup_nat @ Y2 @ Z2 ) )
% 0.24/0.57 = ( sup_sup_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ ( inf_inf_nat @ X2 @ Z2 ) ) )
% 0.24/0.57 => ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.24/0.57 = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % distrib_imp1
% 0.24/0.57 thf(fact_151_distrib__imp1,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf,Z2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ X2 @ ( sup_su638957495lle_hf @ Y2 @ Z2 ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ X2 @ Y2 ) @ ( inf_in956532509lle_hf @ X2 @ Z2 ) ) )
% 0.24/0.57 => ( ( sup_su638957495lle_hf @ X @ ( inf_in956532509lle_hf @ Y @ Z ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ X @ Y ) @ ( sup_su638957495lle_hf @ X @ Z ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % distrib_imp1
% 0.24/0.57 thf(fact_152_distrib__imp2,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ! [X2: nat,Y2: nat,Z2: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ X2 @ ( inf_inf_nat @ Y2 @ Z2 ) )
% 0.24/0.57 = ( inf_inf_nat @ ( sup_sup_nat @ X2 @ Y2 ) @ ( sup_sup_nat @ X2 @ Z2 ) ) )
% 0.24/0.57 => ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 0.24/0.57 = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % distrib_imp2
% 0.24/0.57 thf(fact_153_distrib__imp2,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf,Z2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ X2 @ ( inf_in956532509lle_hf @ Y2 @ Z2 ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ X2 @ Y2 ) @ ( sup_su638957495lle_hf @ X2 @ Z2 ) ) )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ X @ ( sup_su638957495lle_hf @ Y @ Z ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ ( inf_in956532509lle_hf @ X @ Z ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % distrib_imp2
% 0.24/0.57 thf(fact_154_inf__sup__distrib1,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 0.24/0.57 = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_distrib1
% 0.24/0.57 thf(fact_155_inf__sup__distrib1,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ X @ ( sup_su638957495lle_hf @ Y @ Z ) )
% 0.24/0.57 = ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ ( inf_in956532509lle_hf @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_distrib1
% 0.24/0.57 thf(fact_156_inf__sup__distrib2,axiom,
% 0.24/0.57 ! [Y: nat,Z: nat,X: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ ( sup_sup_nat @ Y @ Z ) @ X )
% 0.24/0.57 = ( sup_sup_nat @ ( inf_inf_nat @ Y @ X ) @ ( inf_inf_nat @ Z @ X ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_distrib2
% 0.24/0.57 thf(fact_157_inf__sup__distrib2,axiom,
% 0.24/0.57 ! [Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ Y @ Z ) @ X )
% 0.24/0.57 = ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ Y @ X ) @ ( inf_in956532509lle_hf @ Z @ X ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_distrib2
% 0.24/0.57 thf(fact_158_sup__inf__distrib1,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.24/0.57 = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_inf_distrib1
% 0.24/0.57 thf(fact_159_sup__inf__distrib1,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ X @ ( inf_in956532509lle_hf @ Y @ Z ) )
% 0.24/0.57 = ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ X @ Y ) @ ( sup_su638957495lle_hf @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_inf_distrib1
% 0.24/0.57 thf(fact_160_sup__inf__distrib2,axiom,
% 0.24/0.57 ! [Y: nat,Z: nat,X: nat] :
% 0.24/0.57 ( ( sup_sup_nat @ ( inf_inf_nat @ Y @ Z ) @ X )
% 0.24/0.57 = ( inf_inf_nat @ ( sup_sup_nat @ Y @ X ) @ ( sup_sup_nat @ Z @ X ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_inf_distrib2
% 0.24/0.57 thf(fact_161_sup__inf__distrib2,axiom,
% 0.24/0.57 ! [Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ Y @ Z ) @ X )
% 0.24/0.57 = ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ Y @ X ) @ ( sup_su638957495lle_hf @ Z @ X ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup_inf_distrib2
% 0.24/0.57 thf(fact_162_diff__self__eq__0,axiom,
% 0.24/0.57 ! [M: nat] :
% 0.24/0.57 ( ( minus_minus_nat @ M @ M )
% 0.24/0.57 = zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % diff_self_eq_0
% 0.24/0.57 thf(fact_163_diff__0__eq__0,axiom,
% 0.24/0.57 ! [N: nat] :
% 0.24/0.57 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.24/0.57 = zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % diff_0_eq_0
% 0.24/0.57 thf(fact_164_PrimReplace__iff,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,V: hF_Mirabelle_hf] :
% 0.24/0.57 ( ! [U4: hF_Mirabelle_hf,V3: hF_Mirabelle_hf,V4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U4 @ A4 )
% 0.24/0.57 => ( ( R @ U4 @ V3 )
% 0.24/0.57 => ( ( R @ U4 @ V4 )
% 0.24/0.57 => ( V4 = V3 ) ) ) )
% 0.24/0.57 => ( ( hF_Mirabelle_hmem @ V @ ( hF_Mir1248913145eplace @ A4 @ R ) )
% 0.24/0.57 = ( ? [U2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ U2 @ A4 )
% 0.24/0.57 & ( R @ U2 @ V ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % PrimReplace_iff
% 0.24/0.57 thf(fact_165_diffs0__imp__equal,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( ( minus_minus_nat @ M @ N )
% 0.24/0.57 = zero_zero_nat )
% 0.24/0.57 => ( ( ( minus_minus_nat @ N @ M )
% 0.24/0.57 = zero_zero_nat )
% 0.24/0.57 => ( M = N ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % diffs0_imp_equal
% 0.24/0.57 thf(fact_166_minus__nat_Odiff__0,axiom,
% 0.24/0.57 ! [M: nat] :
% 0.24/0.57 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.24/0.57 = M ) ).
% 0.24/0.57
% 0.24/0.57 % minus_nat.diff_0
% 0.24/0.57 thf(fact_167_zero__natural_Orsp,axiom,
% 0.24/0.57 zero_zero_nat = zero_zero_nat ).
% 0.24/0.57
% 0.24/0.57 % zero_natural.rsp
% 0.24/0.57 thf(fact_168_diff__commute,axiom,
% 0.24/0.57 ! [I: nat,J: nat,K: nat] :
% 0.24/0.57 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.24/0.57 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.24/0.57
% 0.24/0.57 % diff_commute
% 0.24/0.57 thf(fact_169_less__eq__insert1__iff,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ ( hF_Mirabelle_hinsert @ X @ Y ) @ Z )
% 0.24/0.57 = ( ( hF_Mirabelle_hmem @ X @ Z )
% 0.24/0.57 & ( ord_le976219883lle_hf @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_eq_insert1_iff
% 0.24/0.57 thf(fact_170_hmem__def,axiom,
% 0.24/0.57 ( hF_Mirabelle_hmem
% 0.24/0.57 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A3 @ ( hF_Mirabelle_hfset @ B3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % hmem_def
% 0.24/0.57 thf(fact_171_diff__is__0__eq,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( ( minus_minus_nat @ M @ N )
% 0.24/0.57 = zero_zero_nat )
% 0.24/0.57 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.24/0.57
% 0.24/0.57 % diff_is_0_eq
% 0.24/0.57 thf(fact_172_le__zero__eq,axiom,
% 0.24/0.57 ! [N: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.24/0.57 = ( N = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_zero_eq
% 0.24/0.57 thf(fact_173_inf_Obounded__iff,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) )
% 0.24/0.57 = ( ( ord_le976219883lle_hf @ A @ B )
% 0.24/0.57 & ( ord_le976219883lle_hf @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.bounded_iff
% 0.24/0.57 thf(fact_174_inf_Obounded__iff,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 0.24/0.57 = ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.57 & ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.bounded_iff
% 0.24/0.57 thf(fact_175_le__inf__iff,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ X @ ( inf_in956532509lle_hf @ Y @ Z ) )
% 0.24/0.57 = ( ( ord_le976219883lle_hf @ X @ Y )
% 0.24/0.57 & ( ord_le976219883lle_hf @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_inf_iff
% 0.24/0.57 thf(fact_176_le__inf__iff,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.24/0.57 = ( ( ord_less_eq_nat @ X @ Y )
% 0.24/0.57 & ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_inf_iff
% 0.24/0.57 thf(fact_177_sup_Obounded__iff,axiom,
% 0.24/0.57 ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A )
% 0.24/0.57 = ( ( ord_le976219883lle_hf @ B @ A )
% 0.24/0.57 & ( ord_le976219883lle_hf @ C @ A ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.bounded_iff
% 0.24/0.57 thf(fact_178_sup_Obounded__iff,axiom,
% 0.24/0.57 ! [B: nat,C: nat,A: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 0.24/0.57 = ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.57 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.bounded_iff
% 0.24/0.57 thf(fact_179_le__sup__iff,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ X @ Y ) @ Z )
% 0.24/0.57 = ( ( ord_le976219883lle_hf @ X @ Z )
% 0.24/0.57 & ( ord_le976219883lle_hf @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_sup_iff
% 0.24/0.57 thf(fact_180_le__sup__iff,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 0.24/0.57 = ( ( ord_less_eq_nat @ X @ Z )
% 0.24/0.57 & ( ord_less_eq_nat @ Y @ Z ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_sup_iff
% 0.24/0.57 thf(fact_181_bot__nat__0_Oextremum,axiom,
% 0.24/0.57 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.24/0.57
% 0.24/0.57 % bot_nat_0.extremum
% 0.24/0.57 thf(fact_182_le0,axiom,
% 0.24/0.57 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.24/0.57
% 0.24/0.57 % le0
% 0.24/0.57 thf(fact_183_diff__diff__cancel,axiom,
% 0.24/0.57 ! [I: nat,N: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ I @ N )
% 0.24/0.57 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.24/0.57 = I ) ) ).
% 0.24/0.57
% 0.24/0.57 % diff_diff_cancel
% 0.24/0.57 thf(fact_184_hsubsetI,axiom,
% 0.24/0.57 ! [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.24/0.57 ( ! [X2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( hF_Mirabelle_hmem @ X2 @ A4 )
% 0.24/0.57 => ( hF_Mirabelle_hmem @ X2 @ B4 ) )
% 0.24/0.57 => ( ord_le976219883lle_hf @ A4 @ B4 ) ) ).
% 0.24/0.57
% 0.24/0.57 % hsubsetI
% 0.24/0.57 thf(fact_185_less__eq__hempty,axiom,
% 0.24/0.57 ! [U: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ U @ zero_z189798548lle_hf )
% 0.24/0.57 = ( U = zero_z189798548lle_hf ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_eq_hempty
% 0.24/0.57 thf(fact_186_diff__is__0__eq_H,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ M @ N )
% 0.24/0.57 => ( ( minus_minus_nat @ M @ N )
% 0.24/0.57 = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % diff_is_0_eq'
% 0.24/0.57 thf(fact_187_diff__le__mono2,axiom,
% 0.24/0.57 ! [M: nat,N: nat,L: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ M @ N )
% 0.24/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % diff_le_mono2
% 0.24/0.57 thf(fact_188_le__diff__iff_H,axiom,
% 0.24/0.57 ! [A: nat,C: nat,B: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ C )
% 0.24/0.57 => ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.57 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.24/0.57 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_diff_iff'
% 0.24/0.57 thf(fact_189_diff__le__self,axiom,
% 0.24/0.57 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.24/0.57
% 0.24/0.57 % diff_le_self
% 0.24/0.57 thf(fact_190_diff__le__mono,axiom,
% 0.24/0.57 ! [M: nat,N: nat,L: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ M @ N )
% 0.24/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % diff_le_mono
% 0.24/0.57 thf(fact_191_Nat_Odiff__diff__eq,axiom,
% 0.24/0.57 ! [K: nat,M: nat,N: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ K @ M )
% 0.24/0.57 => ( ( ord_less_eq_nat @ K @ N )
% 0.24/0.57 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.24/0.57 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Nat.diff_diff_eq
% 0.24/0.57 thf(fact_192_le__diff__iff,axiom,
% 0.24/0.57 ! [K: nat,M: nat,N: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ K @ M )
% 0.24/0.57 => ( ( ord_less_eq_nat @ K @ N )
% 0.24/0.57 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.24/0.57 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_diff_iff
% 0.24/0.57 thf(fact_193_eq__diff__iff,axiom,
% 0.24/0.57 ! [K: nat,M: nat,N: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ K @ M )
% 0.24/0.57 => ( ( ord_less_eq_nat @ K @ N )
% 0.24/0.57 => ( ( ( minus_minus_nat @ M @ K )
% 0.24/0.57 = ( minus_minus_nat @ N @ K ) )
% 0.24/0.57 = ( M = N ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % eq_diff_iff
% 0.24/0.57 thf(fact_194_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.24/0.57 => ( A = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % bot_nat_0.extremum_uniqueI
% 0.24/0.57 thf(fact_195_bot__nat__0_Oextremum__unique,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.24/0.57 = ( A = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % bot_nat_0.extremum_unique
% 0.24/0.57 thf(fact_196_le__0__eq,axiom,
% 0.24/0.57 ! [N: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.24/0.57 = ( N = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_0_eq
% 0.24/0.57 thf(fact_197_less__eq__nat_Osimps_I1_J,axiom,
% 0.24/0.57 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.24/0.57
% 0.24/0.57 % less_eq_nat.simps(1)
% 0.24/0.57 thf(fact_198_Nat_Oex__has__greatest__nat,axiom,
% 0.24/0.57 ! [P: nat > $o,K: nat,B: nat] :
% 0.24/0.57 ( ( P @ K )
% 0.24/0.57 => ( ! [Y2: nat] :
% 0.24/0.57 ( ( P @ Y2 )
% 0.24/0.57 => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.24/0.57 => ? [X2: nat] :
% 0.24/0.57 ( ( P @ X2 )
% 0.24/0.57 & ! [Y5: nat] :
% 0.24/0.57 ( ( P @ Y5 )
% 0.24/0.57 => ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Nat.ex_has_greatest_nat
% 0.24/0.57 thf(fact_199_nat__le__linear,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ M @ N )
% 0.24/0.57 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.24/0.57
% 0.24/0.57 % nat_le_linear
% 0.24/0.57 thf(fact_200_le__antisym,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ M @ N )
% 0.24/0.57 => ( ( ord_less_eq_nat @ N @ M )
% 0.24/0.57 => ( M = N ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_antisym
% 0.24/0.57 thf(fact_201_eq__imp__le,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( M = N )
% 0.24/0.57 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.24/0.57
% 0.24/0.57 % eq_imp_le
% 0.24/0.57 thf(fact_202_le__trans,axiom,
% 0.24/0.57 ! [I: nat,J: nat,K: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ I @ J )
% 0.24/0.57 => ( ( ord_less_eq_nat @ J @ K )
% 0.24/0.57 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_trans
% 0.24/0.57 thf(fact_203_le__refl,axiom,
% 0.24/0.57 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.24/0.57
% 0.24/0.57 % le_refl
% 0.24/0.57 thf(fact_204_canonically__ordered__monoid__add__class_Ozero__le,axiom,
% 0.24/0.57 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.24/0.57
% 0.24/0.57 % canonically_ordered_monoid_add_class.zero_le
% 0.24/0.57 thf(fact_205_inf_OcoboundedI2,axiom,
% 0.24/0.57 ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ B @ C )
% 0.24/0.57 => ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ C ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.coboundedI2
% 0.24/0.57 thf(fact_206_inf_OcoboundedI2,axiom,
% 0.24/0.57 ! [B: nat,C: nat,A: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.coboundedI2
% 0.24/0.57 thf(fact_207_inf_OcoboundedI1,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ A @ C )
% 0.24/0.57 => ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ C ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.coboundedI1
% 0.24/0.57 thf(fact_208_inf_OcoboundedI1,axiom,
% 0.24/0.57 ! [A: nat,C: nat,B: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ C )
% 0.24/0.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.coboundedI1
% 0.24/0.57 thf(fact_209_inf_Oabsorb__iff2,axiom,
% 0.24/0.57 ( ord_le976219883lle_hf
% 0.24/0.57 = ( ^ [B3: hF_Mirabelle_hf,A3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ A3 @ B3 )
% 0.24/0.57 = B3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.absorb_iff2
% 0.24/0.57 thf(fact_210_inf_Oabsorb__iff2,axiom,
% 0.24/0.57 ( ord_less_eq_nat
% 0.24/0.57 = ( ^ [B3: nat,A3: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ A3 @ B3 )
% 0.24/0.57 = B3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.absorb_iff2
% 0.24/0.57 thf(fact_211_inf_Oabsorb__iff1,axiom,
% 0.24/0.57 ( ord_le976219883lle_hf
% 0.24/0.57 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ A3 @ B3 )
% 0.24/0.57 = A3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.absorb_iff1
% 0.24/0.57 thf(fact_212_inf_Oabsorb__iff1,axiom,
% 0.24/0.57 ( ord_less_eq_nat
% 0.24/0.57 = ( ^ [A3: nat,B3: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ A3 @ B3 )
% 0.24/0.57 = A3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.absorb_iff1
% 0.24/0.57 thf(fact_213_inf_Ocobounded2,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ B ) ).
% 0.24/0.57
% 0.24/0.57 % inf.cobounded2
% 0.24/0.57 thf(fact_214_inf_Ocobounded2,axiom,
% 0.24/0.57 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ B ) ).
% 0.24/0.57
% 0.24/0.57 % inf.cobounded2
% 0.24/0.57 thf(fact_215_inf_Ocobounded1,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ A ) ).
% 0.24/0.57
% 0.24/0.57 % inf.cobounded1
% 0.24/0.57 thf(fact_216_inf_Ocobounded1,axiom,
% 0.24/0.57 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ A ) ).
% 0.24/0.57
% 0.24/0.57 % inf.cobounded1
% 0.24/0.57 thf(fact_217_inf_Oorder__iff,axiom,
% 0.24/0.57 ( ord_le976219883lle_hf
% 0.24/0.57 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.24/0.57 ( A3
% 0.24/0.57 = ( inf_in956532509lle_hf @ A3 @ B3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.order_iff
% 0.24/0.57 thf(fact_218_inf_Oorder__iff,axiom,
% 0.24/0.57 ( ord_less_eq_nat
% 0.24/0.57 = ( ^ [A3: nat,B3: nat] :
% 0.24/0.57 ( A3
% 0.24/0.57 = ( inf_inf_nat @ A3 @ B3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.order_iff
% 0.24/0.57 thf(fact_219_inf__greatest,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ X @ Y )
% 0.24/0.57 => ( ( ord_le976219883lle_hf @ X @ Z )
% 0.24/0.57 => ( ord_le976219883lle_hf @ X @ ( inf_in956532509lle_hf @ Y @ Z ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_greatest
% 0.24/0.57 thf(fact_220_inf__greatest,axiom,
% 0.24/0.57 ! [X: nat,Y: nat,Z: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ X @ Y )
% 0.24/0.57 => ( ( ord_less_eq_nat @ X @ Z )
% 0.24/0.57 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_greatest
% 0.24/0.57 thf(fact_221_inf_OboundedI,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ A @ B )
% 0.24/0.57 => ( ( ord_le976219883lle_hf @ A @ C )
% 0.24/0.57 => ( ord_le976219883lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.boundedI
% 0.24/0.57 thf(fact_222_inf_OboundedI,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.57 => ( ( ord_less_eq_nat @ A @ C )
% 0.24/0.57 => ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.boundedI
% 0.24/0.57 thf(fact_223_inf_OboundedE,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) )
% 0.24/0.57 => ~ ( ( ord_le976219883lle_hf @ A @ B )
% 0.24/0.57 => ~ ( ord_le976219883lle_hf @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.boundedE
% 0.24/0.57 thf(fact_224_inf_OboundedE,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 0.24/0.57 => ~ ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.57 => ~ ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.boundedE
% 0.24/0.57 thf(fact_225_inf__absorb2,axiom,
% 0.24/0.57 ! [Y: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ Y @ X )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ X @ Y )
% 0.24/0.57 = Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_absorb2
% 0.24/0.57 thf(fact_226_inf__absorb2,axiom,
% 0.24/0.57 ! [Y: nat,X: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ Y @ X )
% 0.24/0.57 => ( ( inf_inf_nat @ X @ Y )
% 0.24/0.57 = Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_absorb2
% 0.24/0.57 thf(fact_227_inf__absorb1,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ X @ Y )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ X @ Y )
% 0.24/0.57 = X ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_absorb1
% 0.24/0.57 thf(fact_228_inf__absorb1,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ X @ Y )
% 0.24/0.57 => ( ( inf_inf_nat @ X @ Y )
% 0.24/0.57 = X ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_absorb1
% 0.24/0.57 thf(fact_229_inf_Oabsorb2,axiom,
% 0.24/0.57 ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ B @ A )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ A @ B )
% 0.24/0.57 = B ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.absorb2
% 0.24/0.57 thf(fact_230_inf_Oabsorb2,axiom,
% 0.24/0.57 ! [B: nat,A: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.57 => ( ( inf_inf_nat @ A @ B )
% 0.24/0.57 = B ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.absorb2
% 0.24/0.57 thf(fact_231_inf_Oabsorb1,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ A @ B )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ A @ B )
% 0.24/0.57 = A ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.absorb1
% 0.24/0.57 thf(fact_232_inf_Oabsorb1,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.57 => ( ( inf_inf_nat @ A @ B )
% 0.24/0.57 = A ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.absorb1
% 0.24/0.57 thf(fact_233_le__iff__inf,axiom,
% 0.24/0.57 ( ord_le976219883lle_hf
% 0.24/0.57 = ( ^ [X3: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( inf_in956532509lle_hf @ X3 @ Y3 )
% 0.24/0.57 = X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_iff_inf
% 0.24/0.57 thf(fact_234_le__iff__inf,axiom,
% 0.24/0.57 ( ord_less_eq_nat
% 0.24/0.57 = ( ^ [X3: nat,Y3: nat] :
% 0.24/0.57 ( ( inf_inf_nat @ X3 @ Y3 )
% 0.24/0.57 = X3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_iff_inf
% 0.24/0.57 thf(fact_235_inf__unique,axiom,
% 0.24/0.57 ! [F: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf,X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.57 ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( F @ X2 @ Y2 ) @ X2 )
% 0.24/0.57 => ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( F @ X2 @ Y2 ) @ Y2 )
% 0.24/0.57 => ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf,Z2: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ X2 @ Y2 )
% 0.24/0.57 => ( ( ord_le976219883lle_hf @ X2 @ Z2 )
% 0.24/0.57 => ( ord_le976219883lle_hf @ X2 @ ( F @ Y2 @ Z2 ) ) ) )
% 0.24/0.57 => ( ( inf_in956532509lle_hf @ X @ Y )
% 0.24/0.57 = ( F @ X @ Y ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_unique
% 0.24/0.57 thf(fact_236_inf__unique,axiom,
% 0.24/0.57 ! [F: nat > nat > nat,X: nat,Y: nat] :
% 0.24/0.57 ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( F @ X2 @ Y2 ) @ X2 )
% 0.24/0.57 => ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( F @ X2 @ Y2 ) @ Y2 )
% 0.24/0.57 => ( ! [X2: nat,Y2: nat,Z2: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.24/0.57 => ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.24/0.57 => ( ord_less_eq_nat @ X2 @ ( F @ Y2 @ Z2 ) ) ) )
% 0.24/0.57 => ( ( inf_inf_nat @ X @ Y )
% 0.24/0.57 = ( F @ X @ Y ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_unique
% 0.24/0.57 thf(fact_237_inf_OorderI,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( A
% 0.24/0.57 = ( inf_in956532509lle_hf @ A @ B ) )
% 0.24/0.57 => ( ord_le976219883lle_hf @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.orderI
% 0.24/0.57 thf(fact_238_inf_OorderI,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( A
% 0.24/0.57 = ( inf_inf_nat @ A @ B ) )
% 0.24/0.57 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.orderI
% 0.24/0.57 thf(fact_239_inf_OorderE,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ A @ B )
% 0.24/0.57 => ( A
% 0.24/0.57 = ( inf_in956532509lle_hf @ A @ B ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.orderE
% 0.24/0.57 thf(fact_240_inf_OorderE,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.57 => ( A
% 0.24/0.57 = ( inf_inf_nat @ A @ B ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf.orderE
% 0.24/0.57 thf(fact_241_le__infI2,axiom,
% 0.24/0.57 ! [B: hF_Mirabelle_hf,X: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ B @ X )
% 0.24/0.57 => ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ X ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_infI2
% 0.24/0.57 thf(fact_242_le__infI2,axiom,
% 0.24/0.57 ! [B: nat,X: nat,A: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ B @ X )
% 0.24/0.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_infI2
% 0.24/0.57 thf(fact_243_le__infI1,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,X: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ A @ X )
% 0.24/0.57 => ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ X ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_infI1
% 0.24/0.57 thf(fact_244_le__infI1,axiom,
% 0.24/0.57 ! [A: nat,X: nat,B: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ X )
% 0.24/0.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_infI1
% 0.24/0.57 thf(fact_245_inf__mono,axiom,
% 0.24/0.57 ! [A: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ A @ C )
% 0.24/0.57 => ( ( ord_le976219883lle_hf @ B @ D )
% 0.24/0.57 => ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ ( inf_in956532509lle_hf @ C @ D ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_mono
% 0.24/0.57 thf(fact_246_inf__mono,axiom,
% 0.24/0.57 ! [A: nat,C: nat,B: nat,D: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ C )
% 0.24/0.57 => ( ( ord_less_eq_nat @ B @ D )
% 0.24/0.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ ( inf_inf_nat @ C @ D ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % inf_mono
% 0.24/0.57 thf(fact_247_le__infI,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ X @ A )
% 0.24/0.57 => ( ( ord_le976219883lle_hf @ X @ B )
% 0.24/0.57 => ( ord_le976219883lle_hf @ X @ ( inf_in956532509lle_hf @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_infI
% 0.24/0.57 thf(fact_248_le__infI,axiom,
% 0.24/0.57 ! [X: nat,A: nat,B: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ X @ A )
% 0.24/0.57 => ( ( ord_less_eq_nat @ X @ B )
% 0.24/0.57 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_infI
% 0.24/0.57 thf(fact_249_le__infE,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ X @ ( inf_in956532509lle_hf @ A @ B ) )
% 0.24/0.57 => ~ ( ( ord_le976219883lle_hf @ X @ A )
% 0.24/0.57 => ~ ( ord_le976219883lle_hf @ X @ B ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_infE
% 0.24/0.57 thf(fact_250_le__infE,axiom,
% 0.24/0.57 ! [X: nat,A: nat,B: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) )
% 0.24/0.57 => ~ ( ( ord_less_eq_nat @ X @ A )
% 0.24/0.57 => ~ ( ord_less_eq_nat @ X @ B ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_infE
% 0.24/0.57 thf(fact_251_inf__le2,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ Y ) ).
% 0.24/0.57
% 0.24/0.57 % inf_le2
% 0.24/0.57 thf(fact_252_inf__le2,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 0.24/0.57
% 0.24/0.57 % inf_le2
% 0.24/0.57 thf(fact_253_inf__le1,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ X ) ).
% 0.24/0.57
% 0.24/0.57 % inf_le1
% 0.24/0.57 thf(fact_254_inf__le1,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 0.24/0.57
% 0.24/0.57 % inf_le1
% 0.24/0.57 thf(fact_255_inf__sup__ord_I1_J,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ X ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_ord(1)
% 0.24/0.57 thf(fact_256_inf__sup__ord_I1_J,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_ord(1)
% 0.24/0.57 thf(fact_257_inf__sup__ord_I2_J,axiom,
% 0.24/0.57 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ Y ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_ord(2)
% 0.24/0.57 thf(fact_258_inf__sup__ord_I2_J,axiom,
% 0.24/0.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 0.24/0.57
% 0.24/0.57 % inf_sup_ord(2)
% 0.24/0.57 thf(fact_259_sup_OcoboundedI2,axiom,
% 0.24/0.57 ! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ C @ B )
% 0.24/0.57 => ( ord_le976219883lle_hf @ C @ ( sup_su638957495lle_hf @ A @ B ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.coboundedI2
% 0.24/0.57 thf(fact_260_sup_OcoboundedI2,axiom,
% 0.24/0.57 ! [C: nat,B: nat,A: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ C @ B )
% 0.24/0.57 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % sup.coboundedI2
% 0.24/0.57 thf(fact_261_sup_OcoboundedI1,axiom,
% 0.24/0.57 ! [C: hF_Mirabelle_hf,A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.57 ( ( ord_le976219883lle_hf @ C @ A )
% 0.24/0.57 => ( ord_le976219883lle_hf @ C @ ( sup_su638957495lle_hf @ A @ B ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.coboundedI1
% 0.24/0.58 thf(fact_262_sup_OcoboundedI1,axiom,
% 0.24/0.58 ! [C: nat,A: nat,B: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ C @ A )
% 0.24/0.58 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.coboundedI1
% 0.24/0.58 thf(fact_263_sup_Oabsorb__iff2,axiom,
% 0.24/0.58 ( ord_le976219883lle_hf
% 0.24/0.58 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( sup_su638957495lle_hf @ A3 @ B3 )
% 0.24/0.58 = B3 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.absorb_iff2
% 0.24/0.58 thf(fact_264_sup_Oabsorb__iff2,axiom,
% 0.24/0.58 ( ord_less_eq_nat
% 0.24/0.58 = ( ^ [A3: nat,B3: nat] :
% 0.24/0.58 ( ( sup_sup_nat @ A3 @ B3 )
% 0.24/0.58 = B3 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.absorb_iff2
% 0.24/0.58 thf(fact_265_sup_Oabsorb__iff1,axiom,
% 0.24/0.58 ( ord_le976219883lle_hf
% 0.24/0.58 = ( ^ [B3: hF_Mirabelle_hf,A3: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( sup_su638957495lle_hf @ A3 @ B3 )
% 0.24/0.58 = A3 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.absorb_iff1
% 0.24/0.58 thf(fact_266_sup_Oabsorb__iff1,axiom,
% 0.24/0.58 ( ord_less_eq_nat
% 0.24/0.58 = ( ^ [B3: nat,A3: nat] :
% 0.24/0.58 ( ( sup_sup_nat @ A3 @ B3 )
% 0.24/0.58 = A3 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.absorb_iff1
% 0.24/0.58 thf(fact_267_sup_Ocobounded2,axiom,
% 0.24/0.58 ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ B @ ( sup_su638957495lle_hf @ A @ B ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.cobounded2
% 0.24/0.58 thf(fact_268_sup_Ocobounded2,axiom,
% 0.24/0.58 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.cobounded2
% 0.24/0.58 thf(fact_269_sup_Ocobounded1,axiom,
% 0.24/0.58 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.cobounded1
% 0.24/0.58 thf(fact_270_sup_Ocobounded1,axiom,
% 0.24/0.58 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.cobounded1
% 0.24/0.58 thf(fact_271_sup_Oorder__iff,axiom,
% 0.24/0.58 ( ord_le976219883lle_hf
% 0.24/0.58 = ( ^ [B3: hF_Mirabelle_hf,A3: hF_Mirabelle_hf] :
% 0.24/0.58 ( A3
% 0.24/0.58 = ( sup_su638957495lle_hf @ A3 @ B3 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.order_iff
% 0.24/0.58 thf(fact_272_sup_Oorder__iff,axiom,
% 0.24/0.58 ( ord_less_eq_nat
% 0.24/0.58 = ( ^ [B3: nat,A3: nat] :
% 0.24/0.58 ( A3
% 0.24/0.58 = ( sup_sup_nat @ A3 @ B3 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.order_iff
% 0.24/0.58 thf(fact_273_sup_OboundedI,axiom,
% 0.24/0.58 ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ B @ A )
% 0.24/0.58 => ( ( ord_le976219883lle_hf @ C @ A )
% 0.24/0.58 => ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.boundedI
% 0.24/0.58 thf(fact_274_sup_OboundedI,axiom,
% 0.24/0.58 ! [B: nat,A: nat,C: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.58 => ( ( ord_less_eq_nat @ C @ A )
% 0.24/0.58 => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.boundedI
% 0.24/0.58 thf(fact_275_sup_OboundedE,axiom,
% 0.24/0.58 ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A )
% 0.24/0.58 => ~ ( ( ord_le976219883lle_hf @ B @ A )
% 0.24/0.58 => ~ ( ord_le976219883lle_hf @ C @ A ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.boundedE
% 0.24/0.58 thf(fact_276_sup_OboundedE,axiom,
% 0.24/0.58 ! [B: nat,C: nat,A: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 0.24/0.58 => ~ ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.58 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.boundedE
% 0.24/0.58 thf(fact_277_sup__absorb2,axiom,
% 0.24/0.58 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ X @ Y )
% 0.24/0.58 => ( ( sup_su638957495lle_hf @ X @ Y )
% 0.24/0.58 = Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_absorb2
% 0.24/0.58 thf(fact_278_sup__absorb2,axiom,
% 0.24/0.58 ! [X: nat,Y: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ X @ Y )
% 0.24/0.58 => ( ( sup_sup_nat @ X @ Y )
% 0.24/0.58 = Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_absorb2
% 0.24/0.58 thf(fact_279_sup__absorb1,axiom,
% 0.24/0.58 ! [Y: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ Y @ X )
% 0.24/0.58 => ( ( sup_su638957495lle_hf @ X @ Y )
% 0.24/0.58 = X ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_absorb1
% 0.24/0.58 thf(fact_280_sup__absorb1,axiom,
% 0.24/0.58 ! [Y: nat,X: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ Y @ X )
% 0.24/0.58 => ( ( sup_sup_nat @ X @ Y )
% 0.24/0.58 = X ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_absorb1
% 0.24/0.58 thf(fact_281_sup_Oabsorb2,axiom,
% 0.24/0.58 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ A @ B )
% 0.24/0.58 => ( ( sup_su638957495lle_hf @ A @ B )
% 0.24/0.58 = B ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.absorb2
% 0.24/0.58 thf(fact_282_sup_Oabsorb2,axiom,
% 0.24/0.58 ! [A: nat,B: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.58 => ( ( sup_sup_nat @ A @ B )
% 0.24/0.58 = B ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.absorb2
% 0.24/0.58 thf(fact_283_sup_Oabsorb1,axiom,
% 0.24/0.58 ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ B @ A )
% 0.24/0.58 => ( ( sup_su638957495lle_hf @ A @ B )
% 0.24/0.58 = A ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.absorb1
% 0.24/0.58 thf(fact_284_sup_Oabsorb1,axiom,
% 0.24/0.58 ! [B: nat,A: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.58 => ( ( sup_sup_nat @ A @ B )
% 0.24/0.58 = A ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.absorb1
% 0.24/0.58 thf(fact_285_sup__unique,axiom,
% 0.24/0.58 ! [F: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf,X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.58 ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ X2 @ ( F @ X2 @ Y2 ) )
% 0.24/0.58 => ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ Y2 @ ( F @ X2 @ Y2 ) )
% 0.24/0.58 => ( ! [X2: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf,Z2: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ Y2 @ X2 )
% 0.24/0.58 => ( ( ord_le976219883lle_hf @ Z2 @ X2 )
% 0.24/0.58 => ( ord_le976219883lle_hf @ ( F @ Y2 @ Z2 ) @ X2 ) ) )
% 0.24/0.58 => ( ( sup_su638957495lle_hf @ X @ Y )
% 0.24/0.58 = ( F @ X @ Y ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_unique
% 0.24/0.58 thf(fact_286_sup__unique,axiom,
% 0.24/0.58 ! [F: nat > nat > nat,X: nat,Y: nat] :
% 0.24/0.58 ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ X2 @ ( F @ X2 @ Y2 ) )
% 0.24/0.58 => ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ Y2 @ ( F @ X2 @ Y2 ) )
% 0.24/0.58 => ( ! [X2: nat,Y2: nat,Z2: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.24/0.58 => ( ( ord_less_eq_nat @ Z2 @ X2 )
% 0.24/0.58 => ( ord_less_eq_nat @ ( F @ Y2 @ Z2 ) @ X2 ) ) )
% 0.24/0.58 => ( ( sup_sup_nat @ X @ Y )
% 0.24/0.58 = ( F @ X @ Y ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_unique
% 0.24/0.58 thf(fact_287_sup_OorderI,axiom,
% 0.24/0.58 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( A
% 0.24/0.58 = ( sup_su638957495lle_hf @ A @ B ) )
% 0.24/0.58 => ( ord_le976219883lle_hf @ B @ A ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.orderI
% 0.24/0.58 thf(fact_288_sup_OorderI,axiom,
% 0.24/0.58 ! [A: nat,B: nat] :
% 0.24/0.58 ( ( A
% 0.24/0.58 = ( sup_sup_nat @ A @ B ) )
% 0.24/0.58 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.orderI
% 0.24/0.58 thf(fact_289_sup_OorderE,axiom,
% 0.24/0.58 ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ B @ A )
% 0.24/0.58 => ( A
% 0.24/0.58 = ( sup_su638957495lle_hf @ A @ B ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.orderE
% 0.24/0.58 thf(fact_290_sup_OorderE,axiom,
% 0.24/0.58 ! [B: nat,A: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.58 => ( A
% 0.24/0.58 = ( sup_sup_nat @ A @ B ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.orderE
% 0.24/0.58 thf(fact_291_le__iff__sup,axiom,
% 0.24/0.58 ( ord_le976219883lle_hf
% 0.24/0.58 = ( ^ [X3: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( sup_su638957495lle_hf @ X3 @ Y3 )
% 0.24/0.58 = Y3 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_iff_sup
% 0.24/0.58 thf(fact_292_le__iff__sup,axiom,
% 0.24/0.58 ( ord_less_eq_nat
% 0.24/0.58 = ( ^ [X3: nat,Y3: nat] :
% 0.24/0.58 ( ( sup_sup_nat @ X3 @ Y3 )
% 0.24/0.58 = Y3 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_iff_sup
% 0.24/0.58 thf(fact_293_sup__least,axiom,
% 0.24/0.58 ! [Y: hF_Mirabelle_hf,X: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ Y @ X )
% 0.24/0.58 => ( ( ord_le976219883lle_hf @ Z @ X )
% 0.24/0.58 => ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ Y @ Z ) @ X ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_least
% 0.24/0.58 thf(fact_294_sup__least,axiom,
% 0.24/0.58 ! [Y: nat,X: nat,Z: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ Y @ X )
% 0.24/0.58 => ( ( ord_less_eq_nat @ Z @ X )
% 0.24/0.58 => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z ) @ X ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_least
% 0.24/0.58 thf(fact_295_sup__mono,axiom,
% 0.24/0.58 ! [A: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ A @ C )
% 0.24/0.58 => ( ( ord_le976219883lle_hf @ B @ D )
% 0.24/0.58 => ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ ( sup_su638957495lle_hf @ C @ D ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_mono
% 0.24/0.58 thf(fact_296_sup__mono,axiom,
% 0.24/0.58 ! [A: nat,C: nat,B: nat,D: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ A @ C )
% 0.24/0.58 => ( ( ord_less_eq_nat @ B @ D )
% 0.24/0.58 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C @ D ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_mono
% 0.24/0.58 thf(fact_297_sup_Omono,axiom,
% 0.24/0.58 ! [C: hF_Mirabelle_hf,A: hF_Mirabelle_hf,D: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ C @ A )
% 0.24/0.58 => ( ( ord_le976219883lle_hf @ D @ B )
% 0.24/0.58 => ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ C @ D ) @ ( sup_su638957495lle_hf @ A @ B ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.mono
% 0.24/0.58 thf(fact_298_sup_Omono,axiom,
% 0.24/0.58 ! [C: nat,A: nat,D: nat,B: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ C @ A )
% 0.24/0.58 => ( ( ord_less_eq_nat @ D @ B )
% 0.24/0.58 => ( ord_less_eq_nat @ ( sup_sup_nat @ C @ D ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup.mono
% 0.24/0.58 thf(fact_299_le__supI2,axiom,
% 0.24/0.58 ! [X: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ X @ B )
% 0.24/0.58 => ( ord_le976219883lle_hf @ X @ ( sup_su638957495lle_hf @ A @ B ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_supI2
% 0.24/0.58 thf(fact_300_le__supI2,axiom,
% 0.24/0.58 ! [X: nat,B: nat,A: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ X @ B )
% 0.24/0.58 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_supI2
% 0.24/0.58 thf(fact_301_le__supI1,axiom,
% 0.24/0.58 ! [X: hF_Mirabelle_hf,A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ X @ A )
% 0.24/0.58 => ( ord_le976219883lle_hf @ X @ ( sup_su638957495lle_hf @ A @ B ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_supI1
% 0.24/0.58 thf(fact_302_le__supI1,axiom,
% 0.24/0.58 ! [X: nat,A: nat,B: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ X @ A )
% 0.24/0.58 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_supI1
% 0.24/0.58 thf(fact_303_sup__ge2,axiom,
% 0.24/0.58 ! [Y: hF_Mirabelle_hf,X: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ Y @ ( sup_su638957495lle_hf @ X @ Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_ge2
% 0.24/0.58 thf(fact_304_sup__ge2,axiom,
% 0.24/0.58 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_ge2
% 0.24/0.58 thf(fact_305_sup__ge1,axiom,
% 0.24/0.58 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ X @ ( sup_su638957495lle_hf @ X @ Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_ge1
% 0.24/0.58 thf(fact_306_sup__ge1,axiom,
% 0.24/0.58 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % sup_ge1
% 0.24/0.58 thf(fact_307_le__supI,axiom,
% 0.24/0.58 ! [A: hF_Mirabelle_hf,X: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ A @ X )
% 0.24/0.58 => ( ( ord_le976219883lle_hf @ B @ X )
% 0.24/0.58 => ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ X ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_supI
% 0.24/0.58 thf(fact_308_le__supI,axiom,
% 0.24/0.58 ! [A: nat,X: nat,B: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ A @ X )
% 0.24/0.58 => ( ( ord_less_eq_nat @ B @ X )
% 0.24/0.58 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_supI
% 0.24/0.58 thf(fact_309_le__supE,axiom,
% 0.24/0.58 ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,X: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ X )
% 0.24/0.58 => ~ ( ( ord_le976219883lle_hf @ A @ X )
% 0.24/0.58 => ~ ( ord_le976219883lle_hf @ B @ X ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_supE
% 0.24/0.58 thf(fact_310_le__supE,axiom,
% 0.24/0.58 ! [A: nat,B: nat,X: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
% 0.24/0.58 => ~ ( ( ord_less_eq_nat @ A @ X )
% 0.24/0.58 => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % le_supE
% 0.24/0.58 thf(fact_311_inf__sup__ord_I3_J,axiom,
% 0.24/0.58 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ X @ ( sup_su638957495lle_hf @ X @ Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % inf_sup_ord(3)
% 0.24/0.58 thf(fact_312_inf__sup__ord_I3_J,axiom,
% 0.24/0.58 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % inf_sup_ord(3)
% 0.24/0.58 thf(fact_313_inf__sup__ord_I4_J,axiom,
% 0.24/0.58 ! [Y: hF_Mirabelle_hf,X: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ Y @ ( sup_su638957495lle_hf @ X @ Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % inf_sup_ord(4)
% 0.24/0.58 thf(fact_314_inf__sup__ord_I4_J,axiom,
% 0.24/0.58 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.24/0.58
% 0.24/0.58 % inf_sup_ord(4)
% 0.24/0.58 thf(fact_315_less__eq__hf__def,axiom,
% 0.24/0.58 ( ord_le976219883lle_hf
% 0.24/0.58 = ( ^ [A6: hF_Mirabelle_hf,B6: hF_Mirabelle_hf] :
% 0.24/0.58 ! [X3: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( hF_Mirabelle_hmem @ X3 @ A6 )
% 0.24/0.58 => ( hF_Mirabelle_hmem @ X3 @ B6 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % less_eq_hf_def
% 0.24/0.58 thf(fact_316_rev__hsubsetD,axiom,
% 0.24/0.58 ! [C: hF_Mirabelle_hf,A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( hF_Mirabelle_hmem @ C @ A4 )
% 0.24/0.58 => ( ( ord_le976219883lle_hf @ A4 @ B4 )
% 0.24/0.58 => ( hF_Mirabelle_hmem @ C @ B4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % rev_hsubsetD
% 0.24/0.58 thf(fact_317_hsubsetCE,axiom,
% 0.24/0.58 ! [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ A4 @ B4 )
% 0.24/0.58 => ( ( hF_Mirabelle_hmem @ C @ A4 )
% 0.24/0.58 => ( hF_Mirabelle_hmem @ C @ B4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % hsubsetCE
% 0.24/0.58 thf(fact_318_hsubsetD,axiom,
% 0.24/0.58 ! [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ A4 @ B4 )
% 0.24/0.58 => ( ( hF_Mirabelle_hmem @ C @ A4 )
% 0.24/0.58 => ( hF_Mirabelle_hmem @ C @ B4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % hsubsetD
% 0.24/0.58 thf(fact_319_HF__Mirabelle__glliljednj_Ozero__le,axiom,
% 0.24/0.58 ! [X: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ zero_z189798548lle_hf @ X ) ).
% 0.24/0.58
% 0.24/0.58 % HF_Mirabelle_glliljednj.zero_le
% 0.24/0.58 thf(fact_320_hf__equalityE,axiom,
% 0.24/0.58 ! [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( A4 = B4 )
% 0.24/0.58 => ~ ( ( ord_le976219883lle_hf @ A4 @ B4 )
% 0.24/0.58 => ~ ( ord_le976219883lle_hf @ B4 @ A4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % hf_equalityE
% 0.24/0.58 thf(fact_321_distrib__inf__le,axiom,
% 0.24/0.58 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ ( inf_in956532509lle_hf @ X @ Y ) @ ( inf_in956532509lle_hf @ X @ Z ) ) @ ( inf_in956532509lle_hf @ X @ ( sup_su638957495lle_hf @ Y @ Z ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % distrib_inf_le
% 0.24/0.58 thf(fact_322_distrib__inf__le,axiom,
% 0.24/0.58 ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % distrib_inf_le
% 0.24/0.58 thf(fact_323_distrib__sup__le,axiom,
% 0.24/0.58 ! [X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ ( sup_su638957495lle_hf @ X @ ( inf_in956532509lle_hf @ Y @ Z ) ) @ ( inf_in956532509lle_hf @ ( sup_su638957495lle_hf @ X @ Y ) @ ( sup_su638957495lle_hf @ X @ Z ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % distrib_sup_le
% 0.24/0.58 thf(fact_324_distrib__sup__le,axiom,
% 0.24/0.58 ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % distrib_sup_le
% 0.24/0.58 thf(fact_325_less__eq__insert2__iff,axiom,
% 0.24/0.58 ! [Z: hF_Mirabelle_hf,X: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ord_le976219883lle_hf @ Z @ ( hF_Mirabelle_hinsert @ X @ Y ) )
% 0.24/0.58 = ( ( ord_le976219883lle_hf @ Z @ Y )
% 0.24/0.58 | ? [U2: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( ( hF_Mirabelle_hinsert @ X @ U2 )
% 0.24/0.58 = Z )
% 0.24/0.58 & ~ ( hF_Mirabelle_hmem @ X @ U2 )
% 0.24/0.58 & ( ord_le976219883lle_hf @ U2 @ Y ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % less_eq_insert2_iff
% 0.24/0.58 thf(fact_326_order__refl,axiom,
% 0.24/0.58 ! [X: hF_Mirabelle_hf] : ( ord_le976219883lle_hf @ X @ X ) ).
% 0.24/0.58
% 0.24/0.58 % order_refl
% 0.24/0.58 thf(fact_327_order__refl,axiom,
% 0.24/0.58 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.24/0.58
% 0.24/0.58 % order_refl
% 0.24/0.58 thf(fact_328_le__numeral__extra_I3_J,axiom,
% 0.24/0.58 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.24/0.58
% 0.24/0.58 % le_numeral_extra(3)
% 0.24/0.58 thf(fact_329_HF__hfset,axiom,
% 0.24/0.58 ! [A: hF_Mirabelle_hf] :
% 0.24/0.58 ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
% 0.24/0.58 = A ) ).
% 0.24/0.58
% 0.24/0.58 % HF_hfset
% 0.24/0.58 thf(fact_330_of__nat__le__0__iff,axiom,
% 0.24/0.58 ! [M: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
% 0.24/0.58 = ( M = zero_zero_nat ) ) ).
% 0.24/0.58
% 0.24/0.58 % of_nat_le_0_iff
% 0.24/0.58 thf(fact_331_of__nat__eq__iff,axiom,
% 0.24/0.58 ! [M: nat,N: nat] :
% 0.24/0.58 ( ( ( semiri1382578993at_nat @ M )
% 0.24/0.58 = ( semiri1382578993at_nat @ N ) )
% 0.24/0.58 = ( M = N ) ) ).
% 0.24/0.58
% 0.24/0.58 % of_nat_eq_iff
% 0.24/0.58 thf(fact_332_of__nat__0,axiom,
% 0.24/0.58 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 0.24/0.58 = zero_zero_nat ) ).
% 0.24/0.58
% 0.24/0.58 % of_nat_0
% 0.24/0.58 thf(fact_333_of__nat__0__eq__iff,axiom,
% 0.24/0.58 ! [N: nat] :
% 0.24/0.58 ( ( zero_zero_nat
% 0.24/0.58 = ( semiri1382578993at_nat @ N ) )
% 0.24/0.58 = ( zero_zero_nat = N ) ) ).
% 0.24/0.58
% 0.24/0.58 % of_nat_0_eq_iff
% 0.24/0.58 thf(fact_334_of__nat__eq__0__iff,axiom,
% 0.24/0.58 ! [M: nat] :
% 0.24/0.58 ( ( ( semiri1382578993at_nat @ M )
% 0.24/0.58 = zero_zero_nat )
% 0.24/0.58 = ( M = zero_zero_nat ) ) ).
% 0.24/0.58
% 0.24/0.58 % of_nat_eq_0_iff
% 0.24/0.58 thf(fact_335_of__nat__le__iff,axiom,
% 0.24/0.58 ! [M: nat,N: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 0.24/0.58 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.24/0.58
% 0.24/0.58 % of_nat_le_iff
% 0.24/0.58 thf(fact_336_of__nat__0__le__iff,axiom,
% 0.24/0.58 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) ) ).
% 0.24/0.58
% 0.24/0.58 % of_nat_0_le_iff
% 0.24/0.58 thf(fact_337_of__nat__mono,axiom,
% 0.24/0.58 ! [I: nat,J: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ I @ J )
% 0.24/0.58 => ( ord_less_eq_nat @ ( semiri1382578993at_nat @ I ) @ ( semiri1382578993at_nat @ J ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % of_nat_mono
% 0.24/0.58 thf(fact_338_of__nat__diff,axiom,
% 0.24/0.58 ! [N: nat,M: nat] :
% 0.24/0.58 ( ( ord_less_eq_nat @ N @ M )
% 0.24/0.58 => ( ( semiri1382578993at_nat @ ( minus_minus_nat @ M @ N ) )
% 0.24/0.58 = ( minus_minus_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ) ).
% 0.24/0.64
% 0.24/0.64 % of_nat_diff
% 0.24/0.64 thf(fact_339_dual__order_Oantisym,axiom,
% 0.24/0.64 ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
% 0.24/0.64 ( ( ord_le976219883lle_hf @ B @ A )
% 0.24/0.64 => ( ( ord_le976219883lle_hf @ A @ B )
% 0.24/0.64 => ( A = B ) ) ) ).
% 0.24/0.64
% 0.24/0.64 % dual_order.antisym
% 0.24/0.64 thf(fact_340_dual__order_Oantisym,axiom,
% 0.24/0.64 ! [B: nat,A: nat] :
% 0.24/0.64 ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.64 => ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.64 => ( A = B ) ) ) ).
% 0.24/0.64
% 0.24/0.64 % dual_order.antisym
% 0.24/0.64 thf(fact_341_dual__order_Oeq__iff,axiom,
% 0.24/0.64 ( ( ^ [Y4: hF_Mirabelle_hf,Z3: hF_Mirabelle_hf] : ( Y4 = Z3 ) )
% 0.24/0.64 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.24/0.64 ( ( ord_le976219883lle_hf @ B3 @ A3 )
% 0.24/0.64 & ( ord_le976219883lle_hf @ A3 @ B3 ) ) ) ) ).
% 0.24/0.64
% 0.24/0.64 % dual_order.eq_iff
% 0.24/0.64 thf(fact_342_dual__order_Oeq__iff,axiom,
% 0.24/0.64 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.24/0.64 = ( ^ [A3: nat,B3: nat] :
% 0.24/0.64 ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.24/0.64 & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 0.24/0.64
% 0.24/0.64 % dual_order.eq_iff
% 0.24/0.64
% 0.24/0.64 % Conjectures (1)
% 0.24/0.64 thf(conj_0,conjecture,
% 0.24/0.64 ( ( hF_Mirabelle_hpair @ x @ y )
% 0.24/0.64 != zero_z189798548lle_hf ) ).
% 0.24/0.64
% 0.24/0.64 %------------------------------------------------------------------------------
% 0.24/0.64 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.WiJOECiBKG/cvc5---1.0.5_26928.p...
% 0.24/0.64 (declare-sort $$unsorted 0)
% 0.24/0.64 (declare-sort tptp.set_HF_Mirabelle_hf 0)
% 0.24/0.64 (declare-sort tptp.hF_Mirabelle_hf 0)
% 0.24/0.64 (declare-sort tptp.nat 0)
% 0.24/0.64 (declare-fun tptp.minus_1232880740lle_hf (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.24/0.64 (declare-fun tptp.zero_z189798548lle_hf () tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.24/0.64 (declare-fun tptp.hF_Mir818139703ollect ((-> tptp.hF_Mirabelle_hf Bool) tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_HF (tptp.set_HF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_HInter (tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_HUnion (tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mir1248913145eplace (tptp.hF_Mirabelle_hf (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool)) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_RepFun (tptp.hF_Mirabelle_hf (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_Replace (tptp.hF_Mirabelle_hf (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool)) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_Abs_hf (tptp.nat) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_hfset (tptp.hF_Mirabelle_hf) tptp.set_HF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_hfst (tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_hinsert (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_hmem (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) Bool)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_hpair (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.hF_Mirabelle_hsnd (tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.inf_in956532509lle_hf (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 0.24/0.64 (declare-fun tptp.sup_su638957495lle_hf (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 0.24/0.64 (declare-fun tptp.semiri1382578993at_nat (tptp.nat) tptp.nat)
% 0.24/0.64 (declare-fun tptp.ord_le976219883lle_hf (tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf) Bool)
% 0.24/0.64 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.24/0.64 (declare-fun tptp.collec2046588256lle_hf ((-> tptp.hF_Mirabelle_hf Bool)) tptp.set_HF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.member1367349282lle_hf (tptp.hF_Mirabelle_hf tptp.set_HF_Mirabelle_hf) Bool)
% 0.24/0.64 (declare-fun tptp.x () tptp.hF_Mirabelle_hf)
% 0.24/0.64 (declare-fun tptp.y () tptp.hF_Mirabelle_hf)
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B2 tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hpair A) B) (@ (@ tptp.hF_Mirabelle_hpair A2) B2)) (and (= A A2) (= B B2)))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B2 tptp.hF_Mirabelle_hf)) (=> (= (@ (@ tptp.hF_Mirabelle_hpair A) B) (@ (@ tptp.hF_Mirabelle_hpair A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hpair A) B) A))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hpair A) B) B))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_hfst (@ (@ tptp.hF_Mirabelle_hpair A) B)) A)))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_hsnd (@ (@ tptp.hF_Mirabelle_hpair A) B)) B)))
% 0.24/0.64 (assert (= (@ tptp.hF_Mirabelle_HInter tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf))
% 0.24/0.64 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mir818139703ollect P) tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf)))
% 0.24/0.64 (assert (forall ((R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_Replace tptp.zero_z189798548lle_hf) R) tptp.zero_z189798548lle_hf)))
% 0.24/0.64 (assert (= (@ tptp.hF_Mirabelle_HUnion tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (= tptp.zero_z189798548lle_hf X) (= X tptp.zero_z189798548lle_hf))))
% 0.24/0.64 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 0.24/0.64 (assert (forall ((F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_RepFun tptp.zero_z189798548lle_hf) F) tptp.zero_z189798548lle_hf)))
% 0.24/0.64 (assert (= tptp.hF_Mirabelle_hpair (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A3))) (@ (@ 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))))))
% 0.24/0.64 (assert (= tptp.hF_Mirabelle_hpair (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A3))) (@ (@ 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))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hinsert A) tptp.zero_z189798548lle_hf) (@ (@ tptp.hF_Mirabelle_hinsert B) tptp.zero_z189798548lle_hf)) (= A B))))
% 0.24/0.64 (assert (forall ((A 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 A) B)) F) (@ (@ tptp.hF_Mirabelle_hinsert (@ F A)) (@ (@ tptp.hF_Mirabelle_RepFun B) F)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hinsert A) A4) tptp.zero_z189798548lle_hf))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hinsert A) (@ (@ 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 (= A C) (= B D)) (and (= A D) (= B C))))))
% 0.24/0.64 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (X tptp.hF_Mirabelle_hf)) (=> (@ P tptp.zero_z189798548lle_hf) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (=> (@ P X2) (forall ((Y2 tptp.hF_Mirabelle_hf)) (=> (@ P Y2) (@ P (@ (@ tptp.hF_Mirabelle_hinsert Y2) X2)))))) (@ P X)))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (not (= A4 tptp.zero_z189798548lle_hf)) (= (@ tptp.hF_Mirabelle_HInter (@ (@ tptp.hF_Mirabelle_hinsert A) A4)) (@ (@ tptp.inf_in956532509lle_hf A) (@ tptp.hF_Mirabelle_HInter A4))))))
% 0.24/0.64 (assert (= (@ tptp.hF_Mirabelle_Abs_hf tptp.zero_zero_nat) tptp.zero_z189798548lle_hf))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (not (= A4 tptp.zero_z189798548lle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem X) (@ tptp.hF_Mirabelle_HInter A4)) (forall ((Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem Y3) A4) (@ (@ tptp.hF_Mirabelle_hmem X) Y3)))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HUnion (@ (@ tptp.hF_Mirabelle_hinsert A) A4)) (@ (@ tptp.sup_su638957495lle_hf A) (@ tptp.hF_Mirabelle_HUnion A4)))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A))) (let ((_let_2 (@ tptp.minus_1232880740lle_hf A4))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_1232880740lle_hf (@ _let_2 B4)) (@ _let_1 tptp.zero_z189798548lle_hf)))))))
% 0.24/0.64 (assert (= tptp.hF_Mirabelle_hinsert (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf B3) (@ (@ tptp.hF_Mirabelle_hinsert A3) tptp.zero_z189798548lle_hf)))))
% 0.24/0.64 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (Z tptp.hF_Mirabelle_hf)) (=> (@ P tptp.zero_z189798548lle_hf) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (=> (@ P X2) (=> (@ P Y2) (=> (not (@ (@ tptp.hF_Mirabelle_hmem X2) Y2)) (@ P (@ (@ tptp.hF_Mirabelle_hinsert X2) Y2)))))) (@ P Z)))))
% 0.24/0.64 (assert (forall ((Y tptp.hF_Mirabelle_hf)) (=> (not (= Y tptp.zero_z189798548lle_hf)) (not (forall ((A5 tptp.hF_Mirabelle_hf) (B5 tptp.hF_Mirabelle_hf)) (=> (= Y (@ (@ tptp.hF_Mirabelle_hinsert A5) B5)) (@ (@ tptp.hF_Mirabelle_hmem A5) B5)))))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_Replace (@ (@ tptp.sup_su638957495lle_hf A4) B4)) R) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.hF_Mirabelle_Replace A4) R)) (@ (@ tptp.hF_Mirabelle_Replace B4) R)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool)) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X))) (= (@ _let_1 (@ (@ tptp.hF_Mir818139703ollect P) A4)) (and (@ P X) (@ _let_1 A4))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X2))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))))
% 0.24/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 0.24/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 0.24/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem A))) (= (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert B) C)) (or (= A B) (@ _let_1 C))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 0.24/0.64 (assert (forall ((U tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))))
% 0.24/0.64 (assert (forall ((V tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_hmem V) (@ (@ tptp.hF_Mirabelle_RepFun A4) F)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A4) (= V (@ F U2)))))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf tptp.zero_z189798548lle_hf) A4) A4)))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A4) tptp.zero_z189798548lle_hf) A4)))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem X) (@ tptp.hF_Mirabelle_HUnion A4)) (exists ((Y3 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem Y3) A4) (@ (@ tptp.hF_Mirabelle_hmem X) Y3))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.member1367349282lle_hf A) (@ tptp.collec2046588256lle_hf P)) (@ P A))))
% 0.24/0.64 (assert (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ tptp.collec2046588256lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X3) A4))) A4)))
% 0.24/0.64 (assert (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (Q (-> tptp.hF_Mirabelle_hf Bool))) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (= (@ P X2) (@ Q X2))) (= (@ tptp.collec2046588256lle_hf P) (@ tptp.collec2046588256lle_hf Q)))))
% 0.24/0.64 (assert (forall ((U tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U))) (= (@ _let_1 (@ (@ tptp.minus_1232880740lle_hf X) Y)) (and (@ _let_1 X) (not (@ _let_1 Y)))))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf tptp.zero_z189798548lle_hf) A4) tptp.zero_z189798548lle_hf)))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A4) tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf)))
% 0.24/0.64 (assert (forall ((V tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_hmem V) (@ (@ tptp.hF_Mirabelle_Replace A4) R)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A4) (@ (@ R U2) V) (forall ((Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ R U2) Y3) (= Y3 V))))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.minus_1232880740lle_hf X) tptp.zero_z189798548lle_hf) X)))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.minus_1232880740lle_hf tptp.zero_z189798548lle_hf) X) tptp.zero_z189798548lle_hf)))
% 0.24/0.64 (assert (forall ((A4 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 A4) B4)) F) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.hF_Mirabelle_RepFun A4) F)) (@ (@ tptp.hF_Mirabelle_RepFun B4) F)))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HUnion (@ (@ tptp.sup_su638957495lle_hf A4) B4)) (@ (@ tptp.sup_su638957495lle_hf (@ tptp.hF_Mirabelle_HUnion A4)) (@ tptp.hF_Mirabelle_HUnion B4)))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((V2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem V2) Z2) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) X) (= V2 (@ F U2)))))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem X) X))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool))) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((U3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U3))) (= (@ _let_1 Z2) (and (@ _let_1 X) (@ P U3))))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf)) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((U3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem U3) Z2) (exists ((Y3 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem Y3) X) (@ (@ tptp.hF_Mirabelle_hmem U3) Y3))))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (not (and (@ (@ tptp.hF_Mirabelle_hmem X) Y) (@ (@ tptp.hF_Mirabelle_hmem Y) X)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((U3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U3))) (= (@ _let_1 Z2) (or (@ _let_1 X) (@ _let_1 Y))))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (=> (forall ((U4 tptp.hF_Mirabelle_hf) (V3 tptp.hF_Mirabelle_hf) (V4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ R U4))) (=> (@ (@ tptp.hF_Mirabelle_hmem U4) X) (=> (@ _let_1 V3) (=> (@ _let_1 V4) (= V4 V3)))))) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((V2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem V2) Z2) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) X) (@ (@ R U2) V2)))))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X) Y) (not (= X Y)))))
% 0.24/0.64 (assert (= (lambda ((Y4 tptp.hF_Mirabelle_hf) (Z3 tptp.hF_Mirabelle_hf)) (= Y4 Z3)) (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (forall ((X3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X3))) (= (@ _let_1 A3) (@ _let_1 B3)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf B4))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_4 (@ _let_1 (@ _let_3 A4)))) (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))))))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf A4) B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_3 (@ (@ tptp.inf_in956532509lle_hf (@ _let_2 A4)) 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)))))))))
% 0.24/0.64 (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))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.minus_1232880740lle_hf A4) B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_3 (@ (@ tptp.minus_1232880740lle_hf (@ _let_2 A4)) B4))) (let ((_let_4 (@ (@ tptp.hF_Mirabelle_hmem X) B4))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 0.24/0.64 (assert (forall ((Z tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (= Z (@ (@ tptp.hF_Mirabelle_hinsert Y) X)) (forall ((U2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U2))) (= (@ _let_1 Z) (or (@ _let_1 X) (= U2 Y))))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A) tptp.zero_z189798548lle_hf))))
% 0.24/0.64 (assert (forall ((Z tptp.hF_Mirabelle_hf)) (= (= Z tptp.zero_z189798548lle_hf) (forall ((X3 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem X3) Z))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A) tptp.zero_z189798548lle_hf))))
% 0.24/0.64 (assert (forall ((B4 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 A4)) B4) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A4) B4))))))
% 0.24/0.64 (assert (forall ((A4 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))) (=> (= A4 B4) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X2) B4) (= (@ F X2) (@ G X2)))) (= (@ (@ tptp.hF_Mirabelle_RepFun A4) F) (@ (@ tptp.hF_Mirabelle_RepFun B4) G))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X) Y) (not (= (@ tptp.hF_Mirabelle_HUnion X) Y)))))
% 0.24/0.64 (assert (forall ((A4 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))) (=> (= A4 B4) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X2) B4) (= (@ (@ P X2) Y2) (@ (@ Q X2) Y2)))) (= (@ (@ tptp.hF_Mirabelle_Replace A4) P) (@ (@ tptp.hF_Mirabelle_Replace B4) Q))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X) (@ (@ tptp.inf_in956532509lle_hf X) Y)) X)))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) (@ (@ tptp.sup_sup_nat X) Y)) X)))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X) (@ (@ tptp.sup_su638957495lle_hf X) Y)) X)))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.sup_sup_nat A) B))) (= (@ (@ tptp.sup_sup_nat _let_1) B) _let_1))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))) (= (@ (@ tptp.sup_su638957495lle_hf _let_1) B) _let_1))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) X) X)))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X) X) X)))
% 0.24/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.sup_sup_nat A) A) A)))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A) A) A)))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.inf_inf_nat X) Y))) (= (@ (@ tptp.inf_inf_nat _let_1) Y) _let_1))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf X) Y))) (= (@ (@ tptp.inf_in956532509lle_hf _let_1) Y) _let_1))))
% 0.24/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.inf_inf_nat A) A) A)))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A) A) A)))
% 0.24/0.64 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) X) X)))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X) X) X)))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.inf_inf_nat A) B))) (= (@ (@ tptp.inf_inf_nat _let_1) B) _let_1))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf A) B))) (= (@ (@ tptp.inf_in956532509lle_hf _let_1) B) _let_1))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ tptp.inf_inf_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z))))))
% 0.24/0.64 (assert (= tptp.inf_inf_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.inf_inf_nat Y3) X3))))
% 0.24/0.64 (assert (= tptp.inf_in956532509lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf Y3) X3))))
% 0.24/0.64 (assert (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.inf_inf_nat A4) B) (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)))))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.inf_in956532509lle_hf A4) B) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf A) B)))))))
% 0.24/0.64 (assert (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (let ((_let_2 (@ tptp.inf_inf_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.64 (assert (forall ((B4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z))))))
% 0.24/0.64 (assert (= tptp.inf_inf_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.inf_inf_nat B3) A3))))
% 0.24/0.64 (assert (= tptp.inf_in956532509lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf B3) A3))))
% 0.24/0.64 (assert (= tptp.inf_inf_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.inf_inf_nat Y3) X3))))
% 0.24/0.64 (assert (= tptp.inf_in956532509lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf Y3) X3))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat B))) (let ((_let_2 (@ tptp.inf_inf_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf B))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ tptp.inf_inf_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ tptp.sup_sup_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z))))))
% 0.24/0.64 (assert (= tptp.sup_sup_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.sup_sup_nat Y3) X3))))
% 0.24/0.64 (assert (= tptp.sup_su638957495lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf Y3) X3))))
% 0.24/0.64 (assert (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.sup_sup_nat A4) B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B)))))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.sup_su638957495lle_hf A4) B) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B)))))))
% 0.24/0.64 (assert (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (let ((_let_2 (@ tptp.sup_sup_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.64 (assert (forall ((B4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_sup_nat B) C))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf B) C))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z))))))
% 0.24/0.64 (assert (= tptp.sup_sup_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.sup_sup_nat B3) A3))))
% 0.24/0.64 (assert (= tptp.sup_su638957495lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf B3) A3))))
% 0.24/0.64 (assert (= tptp.sup_sup_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.sup_sup_nat Y3) X3))))
% 0.24/0.64 (assert (= tptp.sup_su638957495lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf Y3) X3))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat B))) (let ((_let_2 (@ tptp.sup_sup_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf B))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ tptp.sup_sup_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X2))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y2) Z2)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (Z2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X2))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y2) Z2)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y2) Z2)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (Z2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X2))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y2) Z2)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) (@ _let_1 Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) (@ _let_1 Z))))))
% 0.24/0.64 (assert (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) Z)) X) (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) X)) (@ (@ tptp.inf_inf_nat Z) X)))))
% 0.24/0.64 (assert (forall ((Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf (@ (@ tptp.sup_su638957495lle_hf Y) Z)) X) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.inf_in956532509lle_hf Y) X)) (@ (@ tptp.inf_in956532509lle_hf Z) X)))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) (@ _let_1 Z))))))
% 0.24/0.64 (assert (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) Z)) X) (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) X)) (@ (@ tptp.sup_sup_nat Z) X)))))
% 0.24/0.64 (assert (forall ((Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.inf_in956532509lle_hf Y) Z)) X) (@ (@ tptp.inf_in956532509lle_hf (@ (@ tptp.sup_su638957495lle_hf Y) X)) (@ (@ tptp.sup_su638957495lle_hf Z) X)))))
% 0.24/0.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 0.24/0.64 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool)) (V tptp.hF_Mirabelle_hf)) (=> (forall ((U4 tptp.hF_Mirabelle_hf) (V3 tptp.hF_Mirabelle_hf) (V4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ R U4))) (=> (@ (@ tptp.hF_Mirabelle_hmem U4) A4) (=> (@ _let_1 V3) (=> (@ _let_1 V4) (= V4 V3)))))) (= (@ (@ tptp.hF_Mirabelle_hmem V) (@ (@ tptp.hF_Mir1248913145eplace A4) R)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A4) (@ (@ R U2) V)))))))
% 0.24/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 0.24/0.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 0.24/0.64 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 0.24/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.hF_Mirabelle_hinsert X) Y)) Z) (and (@ (@ tptp.hF_Mirabelle_hmem X) Z) (@ (@ tptp.ord_le976219883lle_hf Y) Z)))))
% 0.24/0.64 (assert (= tptp.hF_Mirabelle_hmem (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A3) (@ tptp.hF_Mirabelle_hfset B3)))))
% 0.24/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.24/0.64 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf A))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf B) C)) A) (and (@ (@ tptp.ord_le976219883lle_hf B) A) (@ (@ tptp.ord_le976219883lle_hf C) A)))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf X) Y)) Z) (and (@ (@ tptp.ord_le976219883lle_hf X) Z) (@ (@ tptp.ord_le976219883lle_hf Y) Z)))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_nat X) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))))
% 0.24/0.64 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 0.24/0.64 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.24/0.64 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X2))) (=> (@ _let_1 A4) (@ _let_1 B4)))) (@ (@ tptp.ord_le976219883lle_hf A4) B4))))
% 0.24/0.64 (assert (forall ((U tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.ord_le976219883lle_hf U) tptp.zero_z189798548lle_hf) (= U tptp.zero_z189798548lle_hf))))
% 0.24/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 0.24/0.64 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 0.24/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 0.24/0.64 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 0.24/0.64 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 0.24/0.64 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 0.24/0.64 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 0.24/0.64 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 0.24/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 0.24/0.64 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.24/0.64 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.24/0.64 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y2 tptp.nat)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_nat Y2) B))) (exists ((X2 tptp.nat)) (and (@ P X2) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X2)))))))))
% 0.24/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.24/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.24/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.24/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.24/0.64 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.24/0.64 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) C) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) C))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) C) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) C))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 0.24/0.64 (assert (= tptp.ord_le976219883lle_hf (lambda ((B3 tptp.hF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A3) B3) B3))))
% 0.24/0.64 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A3) B3) B3))))
% 0.24/0.64 (assert (= tptp.ord_le976219883lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A3) B3) A3))))
% 0.24/0.64 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A3) B3) A3))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) B)))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) B)))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) A)))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) A)))
% 0.24/0.64 (assert (= tptp.ord_le976219883lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (= A3 (@ (@ tptp.inf_in956532509lle_hf A3) B3)))))
% 0.24/0.64 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= A3 (@ (@ tptp.inf_inf_nat A3) B3)))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C)))))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf A))) (=> (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 0.24/0.64 (assert (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf Y) X) (= (@ (@ tptp.inf_in956532509lle_hf X) Y) Y))))
% 0.24/0.64 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.inf_inf_nat X) Y) Y))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf X) Y) (= (@ (@ tptp.inf_in956532509lle_hf X) Y) X))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.inf_inf_nat X) Y) X))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (= (@ (@ tptp.inf_in956532509lle_hf A) B) B))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.inf_inf_nat A) B) B))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) B) (= (@ (@ tptp.inf_in956532509lle_hf A) B) A))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.inf_inf_nat A) B) A))))
% 0.24/0.64 (assert (= tptp.ord_le976219883lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X3) Y3) X3))))
% 0.24/0.64 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat X3) Y3) X3))))
% 0.24/0.64 (assert (forall ((F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ F X2) Y2)) X2)) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ F X2) Y2)) Y2)) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (Z2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y2) Z2)))))) (= (@ (@ tptp.inf_in956532509lle_hf X) Y) (@ (@ F X) Y)))))))
% 0.24/0.64 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F X2) Y2)) X2)) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F X2) Y2)) Y2)) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y2) Z2)))))) (= (@ (@ tptp.inf_inf_nat X) Y) (@ (@ F X) Y)))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (= A (@ (@ tptp.inf_in956532509lle_hf A) B)) (@ (@ tptp.ord_le976219883lle_hf A) B))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) B) (= A (@ (@ tptp.inf_in956532509lle_hf A) B)))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A (@ (@ tptp.inf_inf_nat A) B)))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) X) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) X))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (X tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) X) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) X))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) C) (=> (@ (@ tptp.ord_le976219883lle_hf B) D) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) (@ (@ tptp.inf_in956532509lle_hf C) D))))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.inf_inf_nat C) D))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf A) B)))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf X) Y)) Y)))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf X) Y)) X)))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf X) Y)) X)))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf X) Y)) Y)))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 0.24/0.64 (assert (forall ((C tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))))))
% 0.24/0.64 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 0.24/0.64 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))))))
% 0.24/0.64 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 0.24/0.64 (assert (= tptp.ord_le976219883lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A3) B3) B3))))
% 0.24/0.64 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A3) B3) B3))))
% 0.24/0.64 (assert (= tptp.ord_le976219883lle_hf (lambda ((B3 tptp.hF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A3) B3) A3))))
% 0.24/0.64 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A3) B3) A3))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf B) (@ (@ tptp.sup_su638957495lle_hf A) B))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.sup_sup_nat A) B))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf A) (@ (@ tptp.sup_su638957495lle_hf A) B))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.sup_sup_nat A) B))))
% 0.24/0.64 (assert (= tptp.ord_le976219883lle_hf (lambda ((B3 tptp.hF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf)) (= A3 (@ (@ tptp.sup_su638957495lle_hf A3) B3)))))
% 0.24/0.64 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.sup_sup_nat A3) B3)))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (=> (@ (@ tptp.ord_le976219883lle_hf C) A) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf B) C)) A)))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A)))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf B) C)) A) (not (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (not (@ (@ tptp.ord_le976219883lle_hf C) A)))))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf X) Y) (= (@ (@ tptp.sup_su638957495lle_hf X) Y) Y))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.sup_sup_nat X) Y) Y))))
% 0.24/0.64 (assert (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf Y) X) (= (@ (@ tptp.sup_su638957495lle_hf X) Y) X))))
% 0.24/0.64 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.sup_sup_nat X) Y) X))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) B) (= (@ (@ tptp.sup_su638957495lle_hf A) B) B))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (= (@ (@ tptp.sup_su638957495lle_hf A) B) A))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))))
% 0.24/0.64 (assert (forall ((F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf X2) (@ (@ F X2) Y2))) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf Y2) (@ (@ F X2) Y2))) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (Z2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf Y2) X2) (=> (@ (@ tptp.ord_le976219883lle_hf Z2) X2) (@ (@ tptp.ord_le976219883lle_hf (@ (@ F Y2) Z2)) X2)))) (= (@ (@ tptp.sup_su638957495lle_hf X) Y) (@ (@ F X) Y)))))))
% 0.24/0.64 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ F X2) Y2))) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y2) (@ (@ F X2) Y2))) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (=> (@ (@ tptp.ord_less_eq_nat Z2) X2) (@ (@ tptp.ord_less_eq_nat (@ (@ F Y2) Z2)) X2)))) (= (@ (@ tptp.sup_sup_nat X) Y) (@ (@ F X) Y)))))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (= A (@ (@ tptp.sup_su638957495lle_hf A) B)) (@ (@ tptp.ord_le976219883lle_hf B) A))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 0.24/0.64 (assert (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (= A (@ (@ tptp.sup_su638957495lle_hf A) B)))))
% 0.24/0.64 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.sup_sup_nat A) B)))))
% 0.24/0.64 (assert (= tptp.ord_le976219883lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X3) Y3) Y3))))
% 0.24/0.64 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat X3) Y3) Y3))))
% 0.24/0.64 (assert (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf Y) X) (=> (@ (@ tptp.ord_le976219883lle_hf Z) X) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf Y) Z)) X)))))
% 0.24/0.64 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (=> (@ (@ tptp.ord_less_eq_nat Z) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y) Z)) X)))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) C) (=> (@ (@ tptp.ord_le976219883lle_hf B) D) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf A) B)) (@ (@ tptp.sup_su638957495lle_hf C) D))))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.sup_sup_nat C) D))))))
% 0.24/0.64 (assert (forall ((C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf C) A) (=> (@ (@ tptp.ord_le976219883lle_hf D) B) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf C) D)) (@ (@ tptp.sup_su638957495lle_hf A) B))))))
% 0.24/0.64 (assert (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C) D)) (@ (@ tptp.sup_sup_nat A) B))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 0.24/0.64 (assert (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf Y) (@ (@ tptp.sup_su638957495lle_hf X) Y))))
% 0.24/0.64 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf X) (@ (@ tptp.sup_su638957495lle_hf X) Y))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) X) (=> (@ (@ tptp.ord_le976219883lle_hf B) X) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf A) B)) X)))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) X) (=> (@ (@ tptp.ord_less_eq_nat B) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X)))))
% 0.24/0.64 (assert (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf A) B)) X) (not (=> (@ (@ tptp.ord_le976219883lle_hf A) X) (not (@ (@ tptp.ord_le976219883lle_hf B) X)))))))
% 0.24/0.64 (assert (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_nat A) X) (not (@ (@ tptp.ord_less_eq_nat B) X)))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf X) (@ (@ tptp.sup_su638957495lle_hf X) Y))))
% 0.24/0.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 0.24/0.64 (assert (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf Y) (@ (@ tptp.sup_su638957495lle_hf X) Y))))
% 0.24/0.64 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 0.24/0.64 (assert (= tptp.ord_le976219883lle_hf (lambda ((A6 tptp.hF_Mirabelle_hf) (B6 tptp.hF_Mirabelle_hf)) (forall ((X3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 0.24/0.64 (assert (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem C))) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le976219883lle_hf A4) B4) (@ _let_1 B4))))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem C))) (=> (@ (@ tptp.ord_le976219883lle_hf A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem C))) (=> (@ (@ tptp.ord_le976219883lle_hf A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 0.24/0.64 (assert (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf tptp.zero_z189798548lle_hf) X)))
% 0.24/0.64 (assert (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (=> (= A4 B4) (not (=> (@ (@ tptp.ord_le976219883lle_hf A4) B4) (not (@ (@ tptp.ord_le976219883lle_hf B4) A4)))))))
% 0.24/0.65 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z))))))
% 0.24/0.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))))
% 0.24/0.65 (assert (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (@ (@ tptp.ord_le976219883lle_hf (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z))) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) (@ _let_1 Z))))))
% 0.24/0.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 0.24/0.65 (assert (forall ((Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf Z))) (= (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert X) Y)) (or (@ _let_1 Y) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (= (@ (@ tptp.hF_Mirabelle_hinsert X) U2) Z) (not (@ (@ tptp.hF_Mirabelle_hmem X) U2)) (@ (@ tptp.ord_le976219883lle_hf U2) Y))))))))
% 0.24/0.65 (assert (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf X) X)))
% 0.24/0.65 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 0.24/0.65 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 0.24/0.65 (assert (forall ((A tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HF (@ tptp.hF_Mirabelle_hfset A)) A)))
% 0.24/0.65 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1382578993at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 0.24/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1382578993at_nat M) (@ tptp.semiri1382578993at_nat N)) (= M N))))
% 0.24/0.65 (assert (= (@ tptp.semiri1382578993at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 0.24/0.65 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1382578993at_nat N)) (= tptp.zero_zero_nat N))))
% 0.24/0.65 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1382578993at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 0.24/0.65 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.24/0.65 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1382578993at_nat N))))
% 0.24/0.65 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1382578993at_nat I)) (@ tptp.semiri1382578993at_nat J)))))
% 0.24/0.65 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1382578993at_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N))))))
% 0.24/0.65 (assert (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (=> (@ (@ tptp.ord_le976219883lle_hf A) B) (= A B)))))
% 0.24/0.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 0.24/0.65 (assert (= (lambda ((Y4 tptp.hF_Mirabelle_hf) (Z3 tptp.hF_Mirabelle_hf)) (= Y4 Z3)) (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.ord_le976219883lle_hf B3) A3) (@ (@ tptp.ord_le976219883lle_hf A3) B3)))))
% 0.24/0.65 (assert (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (@ (@ tptp.ord_less_eq_nat A3) B3)))))
% 0.24/0.65 (assert (not (not (= (@ (@ tptp.hF_Mirabelle_hpair tptp.x) tptp.y) tptp.zero_z189798548lle_hf))))
% 0.24/0.65 (set-info :filename cvc5---1.0.5_26928)
% 0.24/0.65 (check-sat-assuming ( true ))
% 0.24/0.65 ------- get file name : TPTP file name is ITP074^1
% 0.24/0.65 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26928.smt2...
% 0.59/0.85 --- Run --ho-elim --full-saturate-quant at 10...
% 0.59/0.85 % SZS status Theorem for ITP074^1
% 0.59/0.85 % SZS output start Proof for ITP074^1
% 0.59/0.85 (
% 0.59/0.85 (let ((_let_1 (@ (@ tptp.hF_Mirabelle_hpair tptp.x) tptp.y))) (let ((_let_2 (not (not (= _let_1 tptp.zero_z189798548lle_hf))))) (let ((_let_3 (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A3) B3) B3))))) (let ((_let_4 (= tptp.ord_le976219883lle_hf (lambda ((B3 tptp.hF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A3) B3) B3))))) (let ((_let_5 (= tptp.hF_Mirabelle_hmem (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf A3) (@ tptp.hF_Mirabelle_hfset B3)))))) (let ((_let_6 (@ tptp.hF_Mirabelle_Abs_hf tptp.zero_zero_nat))) (let ((_let_7 (= _let_6 tptp.zero_z189798548lle_hf))) (let ((_let_8 (forall ((A tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hinsert A) A4) tptp.zero_z189798548lle_hf))))) (let ((_let_9 (= tptp.hF_Mirabelle_hpair (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A3))) (@ (@ 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 (forall ((A tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (not (= (ho_97 k_96 tptp.zero_zero_nat) (ho_54 (ho_53 k_98 A) A4)))))) (let ((_let_11 (ho_97 k_96 tptp.zero_zero_nat))) (let ((_let_12 (ho_53 k_98 tptp.x))) (let ((_let_13 (ho_54 (ho_53 k_98 (ho_54 _let_12 (ho_54 (ho_53 k_98 tptp.y) _let_11))) _let_11))) (let ((_let_14 (ho_54 _let_12 _let_11))) (let ((_let_15 (= _let_11 (ho_54 (ho_53 k_98 _let_14) _let_13)))) (let ((_let_16 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_5)) (SYMM (ASSUME :args (_let_7))) (ASSUME :args (_let_9))))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_16 :args ((forall ((A tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (not (= tptp.zero_z189798548lle_hf (@ (@ tptp.hF_Mirabelle_hinsert A) A4)))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hinsert A) A4) (@ tptp.hF_Mirabelle_Abs_hf tptp.zero_zero_nat)))) _let_10))))))) (let ((_let_18 (@ tptp.hF_Mirabelle_hinsert tptp.x))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (_let_14 _let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_10))) (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_16 :args ((= tptp.zero_z189798548lle_hf _let_1) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_6 (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_18 _let_6)) (@ (@ tptp.hF_Mirabelle_hinsert (@ _let_18 (@ (@ tptp.hF_Mirabelle_hinsert tptp.y) _let_6))) _let_6))) _let_15))))) _let_17 :args (false false _let_15 false _let_10)) :args ((forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B2 tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hpair A) B) (@ (@ tptp.hF_Mirabelle_hpair A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A2 tptp.hF_Mirabelle_hf) (B2 tptp.hF_Mirabelle_hf)) (=> (= (@ (@ tptp.hF_Mirabelle_hpair A) B) (@ (@ tptp.hF_Mirabelle_hpair A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hpair A) B) A))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (not (= (@ (@ tptp.hF_Mirabelle_hpair A) B) B))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_hfst (@ (@ tptp.hF_Mirabelle_hpair A) B)) A)) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_hsnd (@ (@ tptp.hF_Mirabelle_hpair A) B)) B)) (= (@ tptp.hF_Mirabelle_HInter tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf) (forall ((P (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mir818139703ollect P) tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf)) (forall ((R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_Replace tptp.zero_z189798548lle_hf) R) tptp.zero_z189798548lle_hf)) (= (@ tptp.hF_Mirabelle_HUnion tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf) (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 ((F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_RepFun tptp.zero_z189798548lle_hf) F) tptp.zero_z189798548lle_hf)) _let_9 (= tptp.hF_Mirabelle_hpair (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A3))) (@ (@ 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 ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hinsert A) tptp.zero_z189798548lle_hf) (@ (@ tptp.hF_Mirabelle_hinsert B) tptp.zero_z189798548lle_hf)) (= A B))) (forall ((A 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 A) B)) F) (@ (@ tptp.hF_Mirabelle_hinsert (@ F A)) (@ (@ tptp.hF_Mirabelle_RepFun B) F)))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) _let_8 (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (= (= (@ (@ tptp.hF_Mirabelle_hinsert A) (@ (@ 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 (= A C) (= B D)) (and (= A D) (= B C))))) (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (X tptp.hF_Mirabelle_hf)) (=> (@ P tptp.zero_z189798548lle_hf) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (=> (@ P X2) (forall ((Y2 tptp.hF_Mirabelle_hf)) (=> (@ P Y2) (@ P (@ (@ tptp.hF_Mirabelle_hinsert Y2) X2)))))) (@ P X)))) (forall ((A4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (not (= A4 tptp.zero_z189798548lle_hf)) (= (@ tptp.hF_Mirabelle_HInter (@ (@ tptp.hF_Mirabelle_hinsert A) A4)) (@ (@ tptp.inf_in956532509lle_hf A) (@ tptp.hF_Mirabelle_HInter A4))))) _let_7 (forall ((A4 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (not (= A4 tptp.zero_z189798548lle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem X) (@ tptp.hF_Mirabelle_HInter A4)) (forall ((Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem Y3) A4) (@ (@ tptp.hF_Mirabelle_hmem X) Y3)))))) (forall ((A tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HUnion (@ (@ tptp.hF_Mirabelle_hinsert A) A4)) (@ (@ tptp.sup_su638957495lle_hf A) (@ tptp.hF_Mirabelle_HUnion A4)))) (forall ((A4 tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert A))) (let ((_let_2 (@ tptp.minus_1232880740lle_hf A4))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_1232880740lle_hf (@ _let_2 B4)) (@ _let_1 tptp.zero_z189798548lle_hf)))))) (= tptp.hF_Mirabelle_hinsert (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf B3) (@ (@ tptp.hF_Mirabelle_hinsert A3) tptp.zero_z189798548lle_hf)))) (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (Z tptp.hF_Mirabelle_hf)) (=> (@ P tptp.zero_z189798548lle_hf) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (=> (@ P X2) (=> (@ P Y2) (=> (not (@ (@ tptp.hF_Mirabelle_hmem X2) Y2)) (@ P (@ (@ tptp.hF_Mirabelle_hinsert X2) Y2)))))) (@ P Z)))) (forall ((Y tptp.hF_Mirabelle_hf)) (=> (not (= Y tptp.zero_z189798548lle_hf)) (not (forall ((A5 tptp.hF_Mirabelle_hf) (B5 tptp.hF_Mirabelle_hf)) (=> (= Y (@ (@ tptp.hF_Mirabelle_hinsert A5) B5)) (@ (@ tptp.hF_Mirabelle_hmem A5) B5)))))) (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_Replace (@ (@ tptp.sup_su638957495lle_hf A4) B4)) R) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.hF_Mirabelle_Replace A4) R)) (@ (@ tptp.hF_Mirabelle_Replace B4) R)))) (forall ((X tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool)) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X))) (= (@ _let_1 (@ (@ tptp.hF_Mir818139703ollect P) A4)) (and (@ P X) (@ _let_1 A4))))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X2))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem A))) (= (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert B) C)) (or (= A B) (@ _let_1 C))))) (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((U tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))) (forall ((V tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (= (@ (@ tptp.hF_Mirabelle_hmem V) (@ (@ tptp.hF_Mirabelle_RepFun A4) F)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A4) (= V (@ F U2)))))) (forall ((A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf tptp.zero_z189798548lle_hf) A4) A4)) (forall ((A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A4) tptp.zero_z189798548lle_hf) A4)) (forall ((X tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem X) (@ tptp.hF_Mirabelle_HUnion A4)) (exists ((Y3 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem Y3) A4) (@ (@ tptp.hF_Mirabelle_hmem X) Y3))))) (forall ((A tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.member1367349282lle_hf A) (@ tptp.collec2046588256lle_hf P)) (@ P A))) (forall ((A4 tptp.set_HF_Mirabelle_hf)) (= (@ tptp.collec2046588256lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.member1367349282lle_hf X3) A4))) A4)) (forall ((P (-> tptp.hF_Mirabelle_hf Bool)) (Q (-> tptp.hF_Mirabelle_hf Bool))) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (= (@ P X2) (@ Q X2))) (= (@ tptp.collec2046588256lle_hf P) (@ tptp.collec2046588256lle_hf Q)))) (forall ((U tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U))) (= (@ _let_1 (@ (@ tptp.minus_1232880740lle_hf X) Y)) (and (@ _let_1 X) (not (@ _let_1 Y)))))) (forall ((A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf tptp.zero_z189798548lle_hf) A4) tptp.zero_z189798548lle_hf)) (forall ((A4 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A4) tptp.zero_z189798548lle_hf) tptp.zero_z189798548lle_hf)) (forall ((V tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (= (@ (@ tptp.hF_Mirabelle_hmem V) (@ (@ tptp.hF_Mirabelle_Replace A4) R)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A4) (@ (@ R U2) V) (forall ((Y3 tptp.hF_Mirabelle_hf)) (=> (@ (@ R U2) Y3) (= Y3 V))))))) (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.minus_1232880740lle_hf X) tptp.zero_z189798548lle_hf) X)) (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.minus_1232880740lle_hf tptp.zero_z189798548lle_hf) X) tptp.zero_z189798548lle_hf)) (forall ((A4 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 A4) B4)) F) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.hF_Mirabelle_RepFun A4) F)) (@ (@ tptp.hF_Mirabelle_RepFun B4) F)))) (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HUnion (@ (@ tptp.sup_su638957495lle_hf A4) B4)) (@ (@ tptp.sup_su638957495lle_hf (@ tptp.hF_Mirabelle_HUnion A4)) (@ tptp.hF_Mirabelle_HUnion B4)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))) (forall ((X tptp.hF_Mirabelle_hf) (F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf))) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((V2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem V2) Z2) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) X) (= V2 (@ F U2)))))))) (forall ((X tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem X) X))) (forall ((X tptp.hF_Mirabelle_hf) (P (-> tptp.hF_Mirabelle_hf Bool))) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((U3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U3))) (= (@ _let_1 Z2) (and (@ _let_1 X) (@ P U3))))))) (forall ((X tptp.hF_Mirabelle_hf)) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((U3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem U3) Z2) (exists ((Y3 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem Y3) X) (@ (@ tptp.hF_Mirabelle_hmem U3) Y3))))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (not (and (@ (@ tptp.hF_Mirabelle_hmem X) Y) (@ (@ tptp.hF_Mirabelle_hmem Y) X)))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((U3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U3))) (= (@ _let_1 Z2) (or (@ _let_1 X) (@ _let_1 Y))))))) (forall ((X tptp.hF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool))) (=> (forall ((U4 tptp.hF_Mirabelle_hf) (V3 tptp.hF_Mirabelle_hf) (V4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ R U4))) (=> (@ (@ tptp.hF_Mirabelle_hmem U4) X) (=> (@ _let_1 V3) (=> (@ _let_1 V4) (= V4 V3)))))) (exists ((Z2 tptp.hF_Mirabelle_hf)) (forall ((V2 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.hF_Mirabelle_hmem V2) Z2) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) X) (@ (@ R U2) V2)))))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X) Y) (not (= X Y)))) (= (lambda ((Y4 tptp.hF_Mirabelle_hf) (Z3 tptp.hF_Mirabelle_hf)) (= Y4 Z3)) (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (forall ((X3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X3))) (= (@ _let_1 A3) (@ _let_1 B3)))))) (forall ((X tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf B4))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_4 (@ _let_1 (@ _let_3 A4)))) (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) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf A4) B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_3 (@ (@ tptp.inf_in956532509lle_hf (@ _let_2 A4)) 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 ((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) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.minus_1232880740lle_hf A4) B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (let ((_let_3 (@ (@ tptp.minus_1232880740lle_hf (@ _let_2 A4)) B4))) (let ((_let_4 (@ (@ tptp.hF_Mirabelle_hmem X) B4))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((Z tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (= Z (@ (@ tptp.hF_Mirabelle_hinsert Y) X)) (forall ((U2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem U2))) (= (@ _let_1 Z) (or (@ _let_1 X) (= U2 Y))))))) (forall ((A tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A) tptp.zero_z189798548lle_hf))) (forall ((Z tptp.hF_Mirabelle_hf)) (= (= Z tptp.zero_z189798548lle_hf) (forall ((X3 tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem X3) Z))))) (forall ((A tptp.hF_Mirabelle_hf)) (not (@ (@ tptp.hF_Mirabelle_hmem A) tptp.zero_z189798548lle_hf))) (forall ((B4 tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf B4))) (let ((_let_2 (@ tptp.hF_Mirabelle_hinsert X))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))) (forall ((X tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hinsert X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 A4)) B4) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A4) B4))))) (forall ((A4 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))) (=> (= A4 B4) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X2) B4) (= (@ F X2) (@ G X2)))) (= (@ (@ tptp.hF_Mirabelle_RepFun A4) F) (@ (@ tptp.hF_Mirabelle_RepFun B4) G))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X) Y) (not (= (@ tptp.hF_Mirabelle_HUnion X) Y)))) (forall ((A4 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))) (=> (= A4 B4) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.hF_Mirabelle_hmem X2) B4) (= (@ (@ P X2) Y2) (@ (@ Q X2) Y2)))) (= (@ (@ tptp.hF_Mirabelle_Replace A4) P) (@ (@ tptp.hF_Mirabelle_Replace B4) Q))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) (@ (@ tptp.inf_inf_nat X) Y)) X)) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X) (@ (@ tptp.inf_in956532509lle_hf X) Y)) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) (@ (@ tptp.sup_sup_nat X) Y)) X)) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X) (@ (@ tptp.sup_su638957495lle_hf X) Y)) X)) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.sup_sup_nat A) B))) (= (@ (@ tptp.sup_sup_nat _let_1) B) _let_1))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))) (= (@ (@ tptp.sup_su638957495lle_hf _let_1) B) _let_1))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) X) X)) (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X) X) X)) (forall ((A tptp.nat)) (= (@ (@ tptp.sup_sup_nat A) A) A)) (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A) A) A)) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.inf_inf_nat X) Y))) (= (@ (@ tptp.inf_inf_nat _let_1) Y) _let_1))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf X) Y))) (= (@ (@ tptp.inf_in956532509lle_hf _let_1) Y) _let_1))) (forall ((A tptp.nat)) (= (@ (@ tptp.inf_inf_nat A) A) A)) (forall ((A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A) A) A)) (forall ((X tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) X) X)) (forall ((X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X) X) X)) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.inf_inf_nat A) B))) (= (@ (@ tptp.inf_inf_nat _let_1) B) _let_1))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ (@ tptp.inf_in956532509lle_hf A) B))) (= (@ (@ tptp.inf_in956532509lle_hf _let_1) B) _let_1))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ tptp.inf_inf_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z))))) (= tptp.inf_inf_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.inf_inf_nat Y3) X3))) (= tptp.inf_in956532509lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf Y3) X3))) (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.inf_inf_nat A4) B) (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)))))) (forall ((A4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.inf_in956532509lle_hf A4) B) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf A) B)))))) (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (let ((_let_2 (@ tptp.inf_inf_nat 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) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C))))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf A))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z))))) (= tptp.inf_inf_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.inf_inf_nat B3) A3))) (= tptp.inf_in956532509lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf B3) A3))) (= tptp.inf_inf_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.inf_inf_nat Y3) X3))) (= tptp.inf_in956532509lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.inf_in956532509lle_hf Y3) X3))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat B))) (let ((_let_2 (@ tptp.inf_inf_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf B))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ tptp.inf_inf_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (let ((_let_2 (@ tptp.inf_in956532509lle_hf Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ tptp.sup_sup_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z))))) (= tptp.sup_sup_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.sup_sup_nat Y3) X3))) (= tptp.sup_su638957495lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf Y3) X3))) (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.sup_sup_nat A4) B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B)))))) (forall ((A4 tptp.hF_Mirabelle_hf) (K tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.sup_su638957495lle_hf A4) B) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B)))))) (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (let ((_let_2 (@ tptp.sup_sup_nat 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) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_sup_nat B) C))))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf A))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf B) C))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z))))) (= tptp.sup_sup_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.sup_sup_nat B3) A3))) (= tptp.sup_su638957495lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf B3) A3))) (= tptp.sup_sup_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.sup_sup_nat Y3) X3))) (= tptp.sup_su638957495lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (@ (@ tptp.sup_su638957495lle_hf Y3) X3))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat B))) (let ((_let_2 (@ tptp.sup_sup_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf B))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ tptp.sup_sup_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (let ((_let_2 (@ tptp.sup_su638957495lle_hf Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X2))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y2) Z2)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (Z2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X2))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y2) Z2)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y2) Z2)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (Z2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X2))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y2) Z2)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (= (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z)) (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) Z)) X) (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) X)) (@ (@ tptp.inf_inf_nat Z) X)))) (forall ((Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf (@ (@ tptp.sup_su638957495lle_hf Y) Z)) X) (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.inf_in956532509lle_hf Y) X)) (@ (@ tptp.inf_in956532509lle_hf Z) X)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z)) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) Z)) X) (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) X)) (@ (@ tptp.sup_sup_nat Z) X)))) (forall ((Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf (@ (@ tptp.inf_in956532509lle_hf Y) Z)) X) (@ (@ tptp.inf_in956532509lle_hf (@ (@ tptp.sup_su638957495lle_hf Y) X)) (@ (@ tptp.sup_su638957495lle_hf Z) X)))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((A4 tptp.hF_Mirabelle_hf) (R (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf Bool)) (V tptp.hF_Mirabelle_hf)) (=> (forall ((U4 tptp.hF_Mirabelle_hf) (V3 tptp.hF_Mirabelle_hf) (V4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ R U4))) (=> (@ (@ tptp.hF_Mirabelle_hmem U4) A4) (=> (@ _let_1 V3) (=> (@ _let_1 V4) (= V4 V3)))))) (= (@ (@ tptp.hF_Mirabelle_hmem V) (@ (@ tptp.hF_Mir1248913145eplace A4) R)) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.hF_Mirabelle_hmem U2) A4) (@ (@ R U2) V)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (= tptp.zero_zero_nat tptp.zero_zero_nat) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.hF_Mirabelle_hinsert X) Y)) Z) (and (@ (@ tptp.hF_Mirabelle_hmem X) Z) (@ (@ tptp.ord_le976219883lle_hf Y) Z)))) _let_5 (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf A))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C)) (and (@ _let_1 B) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (= (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf B) C)) A) (and (@ (@ tptp.ord_le976219883lle_hf B) A) (@ (@ tptp.ord_le976219883lle_hf C) A)))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf X) Y)) Z) (and (@ (@ tptp.ord_le976219883lle_hf X) Z) (@ (@ tptp.ord_le976219883lle_hf Y) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_nat X) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))) (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (=> (forall ((X2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X2))) (=> (@ _let_1 A4) (@ _let_1 B4)))) (@ (@ tptp.ord_le976219883lle_hf A4) B4))) (forall ((U tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.ord_le976219883lle_hf U) tptp.zero_z189798548lle_hf) (= U tptp.zero_z189798548lle_hf))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)) (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))) (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y2 tptp.nat)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_nat Y2) B))) (exists ((X2 tptp.nat)) (and (@ P X2) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X2)))))))) (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (forall ((B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) C) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) C))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C))) (forall ((A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) C) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) C))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C))) _let_4 _let_3 (= tptp.ord_le976219883lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf A3) B3) A3))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A3) B3) A3))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) B)) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) B)) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) A)) (= tptp.ord_le976219883lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (= A3 (@ (@ tptp.inf_in956532509lle_hf A3) B3)))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= A3 (@ (@ tptp.inf_inf_nat A3) B3)))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)))))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)))))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf A))) (=> (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))) (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf Y) X) (= (@ (@ tptp.inf_in956532509lle_hf X) Y) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.inf_inf_nat X) Y) Y))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf X) Y) (= (@ (@ tptp.inf_in956532509lle_hf X) Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.inf_inf_nat X) Y) X))) (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (= (@ (@ tptp.inf_in956532509lle_hf A) B) B))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.inf_inf_nat A) B) B))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) B) (= (@ (@ tptp.inf_in956532509lle_hf A) B) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.inf_inf_nat A) B) A))) (= tptp.ord_le976219883lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.inf_in956532509lle_hf X3) Y3) X3))) (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat X3) Y3) X3))) (forall ((F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ F X2) Y2)) X2)) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ F X2) Y2)) Y2)) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (Z2 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y2) Z2)))))) (= (@ (@ tptp.inf_in956532509lle_hf X) Y) (@ (@ F X) Y)))))) (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F X2) Y2)) X2)) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F X2) Y2)) Y2)) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y2) Z2)))))) (= (@ (@ tptp.inf_inf_nat X) Y) (@ (@ F X) Y)))))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (= A (@ (@ tptp.inf_in956532509lle_hf A) B)) (@ (@ tptp.ord_le976219883lle_hf A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) B) (= A (@ (@ tptp.inf_in956532509lle_hf A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A (@ (@ tptp.inf_inf_nat A) B)))) (forall ((B tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) X) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) X))) (forall ((B tptp.nat) (X tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) X))) (forall ((A tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) X) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) X))) (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) X))) (forall ((A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) C) (=> (@ (@ tptp.ord_le976219883lle_hf B) D) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf A) B)) (@ (@ tptp.inf_in956532509lle_hf C) D))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.inf_inf_nat C) D))))) (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf A) B)))))) (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)))))) (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf X) Y)) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf X) Y)) X)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf X) Y)) X)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.inf_in956532509lle_hf X) Y)) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)) (forall ((C tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))) (= tptp.ord_le976219883lle_hf (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A3) B3) B3))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A3) B3) B3))) (= tptp.ord_le976219883lle_hf (lambda ((B3 tptp.hF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf A3) B3) A3))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A3) B3) A3))) (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf B) (@ (@ tptp.sup_su638957495lle_hf A) B))) (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.sup_sup_nat A) B))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf A) (@ (@ tptp.sup_su638957495lle_hf A) B))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.sup_sup_nat A) B))) (= tptp.ord_le976219883lle_hf (lambda ((B3 tptp.hF_Mirabelle_hf) (A3 tptp.hF_Mirabelle_hf)) (= A3 (@ (@ tptp.sup_su638957495lle_hf A3) B3)))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.sup_sup_nat A3) B3)))) (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (=> (@ (@ tptp.ord_le976219883lle_hf C) A) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf B) C)) A)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A)))) (forall ((B tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf B) C)) A) (not (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (not (@ (@ tptp.ord_le976219883lle_hf C) A)))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf X) Y) (= (@ (@ tptp.sup_su638957495lle_hf X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.sup_sup_nat X) Y) Y))) (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf Y) X) (= (@ (@ tptp.sup_su638957495lle_hf X) Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.sup_sup_nat X) Y) X))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) B) (= (@ (@ tptp.sup_su638957495lle_hf A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))) (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (= (@ (@ tptp.sup_su638957495lle_hf A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))) (forall ((F (-> tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf tptp.hF_Mirabelle_hf)) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf X2) (@ (@ F X2) Y2))) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf Y2) (@ (@ F X2) Y2))) (=> (forall ((X2 tptp.hF_Mirabelle_hf) (Y2 tptp.hF_Mirabelle_hf) (Z2 tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf Y2) X2) (=> (@ (@ tptp.ord_le976219883lle_hf Z2) X2) (@ (@ tptp.ord_le976219883lle_hf (@ (@ F Y2) Z2)) X2)))) (= (@ (@ tptp.sup_su638957495lle_hf X) Y) (@ (@ F X) Y)))))) (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ F X2) Y2))) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y2) (@ (@ F X2) Y2))) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (=> (@ (@ tptp.ord_less_eq_nat Z2) X2) (@ (@ tptp.ord_less_eq_nat (@ (@ F Y2) Z2)) X2)))) (= (@ (@ tptp.sup_sup_nat X) Y) (@ (@ F X) Y)))))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (= A (@ (@ tptp.sup_su638957495lle_hf A) B)) (@ (@ tptp.ord_le976219883lle_hf B) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))) (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (= A (@ (@ tptp.sup_su638957495lle_hf A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.sup_sup_nat A) B)))) (= tptp.ord_le976219883lle_hf (lambda ((X3 tptp.hF_Mirabelle_hf) (Y3 tptp.hF_Mirabelle_hf)) (= (@ (@ tptp.sup_su638957495lle_hf X3) Y3) Y3))) (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat X3) Y3) Y3))) (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf Y) X) (=> (@ (@ tptp.ord_le976219883lle_hf Z) X) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf Y) Z)) X)))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (=> (@ (@ tptp.ord_less_eq_nat Z) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y) Z)) X)))) (forall ((A tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) C) (=> (@ (@ tptp.ord_le976219883lle_hf B) D) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf A) B)) (@ (@ tptp.sup_su638957495lle_hf C) D))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.sup_sup_nat C) D))))) (forall ((C tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (D tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf C) A) (=> (@ (@ tptp.ord_le976219883lle_hf D) B) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf C) D)) (@ (@ tptp.sup_su638957495lle_hf A) B))))) (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C) D)) (@ (@ tptp.sup_sup_nat A) B))))) (forall ((X tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))))) (forall ((X tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))) (forall ((X tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf A) B))))) (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))) (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf Y) (@ (@ tptp.sup_su638957495lle_hf X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf X) (@ (@ tptp.sup_su638957495lle_hf X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((A tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf A) X) (=> (@ (@ tptp.ord_le976219883lle_hf B) X) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf A) B)) X)))) (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) X) (=> (@ (@ tptp.ord_less_eq_nat B) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X)))) (forall ((A tptp.hF_Mirabelle_hf) (B tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf A) B)) X) (not (=> (@ (@ tptp.ord_le976219883lle_hf A) X) (not (@ (@ tptp.ord_le976219883lle_hf B) X)))))) (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_nat A) X) (not (@ (@ tptp.ord_less_eq_nat B) X)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf X) (@ (@ tptp.sup_su638957495lle_hf X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((Y tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf Y) (@ (@ tptp.sup_su638957495lle_hf X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))) (= tptp.ord_le976219883lle_hf (lambda ((A6 tptp.hF_Mirabelle_hf) (B6 tptp.hF_Mirabelle_hf)) (forall ((X3 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))) (forall ((C tptp.hF_Mirabelle_hf) (A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem C))) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le976219883lle_hf A4) B4) (@ _let_1 B4))))) (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem C))) (=> (@ (@ tptp.ord_le976219883lle_hf A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))) (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf) (C tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.hF_Mirabelle_hmem C))) (=> (@ (@ tptp.ord_le976219883lle_hf A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))) (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf tptp.zero_z189798548lle_hf) X)) (forall ((A4 tptp.hF_Mirabelle_hf) (B4 tptp.hF_Mirabelle_hf)) (=> (= A4 B4) (not (=> (@ (@ tptp.ord_le976219883lle_hf A4) B4) (not (@ (@ tptp.ord_le976219883lle_hf B4) A4)))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.inf_in956532509lle_hf X))) (@ (@ tptp.ord_le976219883lle_hf (@ (@ tptp.sup_su638957495lle_hf (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su638957495lle_hf Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))) (forall ((X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf) (Z tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.sup_su638957495lle_hf X))) (@ (@ tptp.ord_le976219883lle_hf (@ _let_1 (@ (@ tptp.inf_in956532509lle_hf Y) Z))) (@ (@ tptp.inf_in956532509lle_hf (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((Z tptp.hF_Mirabelle_hf) (X tptp.hF_Mirabelle_hf) (Y tptp.hF_Mirabelle_hf)) (let ((_let_1 (@ tptp.ord_le976219883lle_hf Z))) (= (@ _let_1 (@ (@ tptp.hF_Mirabelle_hinsert X) Y)) (or (@ _let_1 Y) (exists ((U2 tptp.hF_Mirabelle_hf)) (and (= (@ (@ tptp.hF_Mirabelle_hinsert X) U2) Z) (not (@ (@ tptp.hF_Mirabelle_hmem X) U2)) (@ (@ tptp.ord_le976219883lle_hf U2) Y))))))) (forall ((X tptp.hF_Mirabelle_hf)) (@ (@ tptp.ord_le976219883lle_hf X) X)) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((A tptp.hF_Mirabelle_hf)) (= (@ tptp.hF_Mirabelle_HF (@ tptp.hF_Mirabelle_hfset A)) A)) (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1382578993at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1382578993at_nat M) (@ tptp.semiri1382578993at_nat N)) (= M N))) (= (@ tptp.semiri1382578993at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1382578993at_nat N)) (= tptp.zero_zero_nat N))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri1382578993at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1382578993at_nat N))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1382578993at_nat I)) (@ tptp.semiri1382578993at_nat J)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1382578993at_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N))))) (forall ((B tptp.hF_Mirabelle_hf) (A tptp.hF_Mirabelle_hf)) (=> (@ (@ tptp.ord_le976219883lle_hf B) A) (=> (@ (@ tptp.ord_le976219883lle_hf A) B) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))) (= (lambda ((Y4 tptp.hF_Mirabelle_hf) (Z3 tptp.hF_Mirabelle_hf)) (= Y4 Z3)) (lambda ((A3 tptp.hF_Mirabelle_hf) (B3 tptp.hF_Mirabelle_hf)) (and (@ (@ tptp.ord_le976219883lle_hf B3) A3) (@ (@ tptp.ord_le976219883lle_hf A3) B3)))) (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (@ (@ tptp.ord_less_eq_nat A3) B3)))) _let_2 true)))))))))))))))))))))
% 0.66/0.85 )
% 0.66/0.85 % SZS output end Proof for ITP074^1
% 0.66/0.85 % cvc5---1.0.5 exiting
% 0.66/0.85 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------