TSTP Solution File: NUM638^4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM638^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 10:45:56 EDT 2023
% Result : Theorem 1.59s 1.79s
% Output : Proof 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : NUM638^4 : TPTP v8.1.2. Released v7.1.0.
% 0.15/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 16:34:35 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.52 %----Proving TH0
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 % File : NUM638^4 : TPTP v8.1.2. Released v7.1.0.
% 0.22/0.52 % Domain : Number theory
% 0.22/0.52 % Problem : Grundlagen problem satz3a
% 0.22/0.52 % Version : [Bro17] axioms : Especial.
% 0.22/0.52 % English :
% 0.22/0.52
% 0.22/0.52 % Refs : [Bro17] Brown (2017), Email to G. Sutcliffe
% 0.22/0.52 % Source : [Br017]
% 0.22/0.52 % Names :
% 0.22/0.52
% 0.22/0.52 % Status : Theorem
% 0.22/0.52 % Rating : 0.77 v8.1.0, 0.82 v7.5.0, 1.00 v7.1.0
% 0.22/0.52 % Syntax : Number of formulae : 291 ( 121 unt; 114 typ; 107 def)
% 0.22/0.52 % Number of atoms : 580 ( 137 equ; 0 cnn)
% 0.22/0.52 % Maximal formula atoms : 10 ( 3 avg)
% 0.22/0.52 % Number of connectives : 1284 ( 7 ~; 4 |; 14 &;1174 @)
% 0.22/0.52 % ( 3 <=>; 82 =>; 0 <=; 0 <~>)
% 0.22/0.52 % Maximal formula depth : 14 ( 4 avg)
% 0.22/0.52 % Number of types : 2 ( 0 usr)
% 0.22/0.52 % Number of type conns : 409 ( 409 >; 0 *; 0 +; 0 <<)
% 0.22/0.52 % Number of symbols : 126 ( 124 usr; 16 con; 0-7 aty)
% 0.22/0.52 % Number of variables : 521 ( 364 ^; 149 !; 8 ?; 521 :)
% 0.22/0.52 % SPC : TH0_THM_EQU_NAR
% 0.22/0.52
% 0.22/0.52 % Comments :
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 thf(typ_is_of,type,
% 0.22/0.52 is_of: $i > ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_is_of,definition,
% 0.22/0.52 ( is_of
% 0.22/0.52 = ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_all_of,type,
% 0.22/0.52 all_of: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_all_of,definition,
% 0.22/0.52 ( all_of
% 0.22/0.52 = ( ^ [X0: $i > $o,X1: $i > $o] :
% 0.22/0.52 ! [X2: $i] :
% 0.22/0.52 ( ( is_of @ X2 @ X0 )
% 0.22/0.52 => ( X1 @ X2 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_eps,type,
% 0.22/0.52 eps: ( $i > $o ) > $i ).
% 0.22/0.52
% 0.22/0.52 thf(typ_in,type,
% 0.22/0.52 in: $i > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Subq,type,
% 0.22/0.52 d_Subq: $i > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Subq,definition,
% 0.22/0.52 ( d_Subq
% 0.22/0.52 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.52 ! [X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ X0 )
% 0.22/0.52 => ( in @ X2 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(set_ext,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i] :
% 0.22/0.52 ( ( d_Subq @ X0 @ X1 )
% 0.22/0.52 => ( ( d_Subq @ X1 @ X0 )
% 0.22/0.52 => ( X0 = X1 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_In_ind,axiom,
% 0.22/0.52 ! [X0: $i > $o] :
% 0.22/0.52 ( ! [X1: $i] :
% 0.22/0.52 ( ! [X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ X1 )
% 0.22/0.52 => ( X0 @ X2 ) )
% 0.22/0.52 => ( X0 @ X1 ) )
% 0.22/0.52 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_emptyset,type,
% 0.22/0.52 emptyset: $i ).
% 0.22/0.52
% 0.22/0.52 thf(k_EmptyAx,axiom,
% 0.22/0.52 ~ ? [X0: $i] : ( in @ X0 @ emptyset ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_union,type,
% 0.22/0.52 union: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(k_UnionEq,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i] :
% 0.22/0.52 ( ( in @ X1 @ ( union @ X0 ) )
% 0.22/0.52 <=> ? [X2: $i] :
% 0.22/0.52 ( ( in @ X1 @ X2 )
% 0.22/0.52 & ( in @ X2 @ X0 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_power,type,
% 0.22/0.52 power: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(k_PowerEq,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i] :
% 0.22/0.52 ( ( in @ X1 @ ( power @ X0 ) )
% 0.22/0.52 <=> ( d_Subq @ X1 @ X0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_repl,type,
% 0.22/0.52 repl: $i > ( $i > $i ) > $i ).
% 0.22/0.52
% 0.22/0.52 thf(k_ReplEq,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ ( repl @ X0 @ X1 ) )
% 0.22/0.52 <=> ? [X3: $i] :
% 0.22/0.52 ( ( in @ X3 @ X0 )
% 0.22/0.52 & ( X2
% 0.22/0.52 = ( X1 @ X3 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Union_closed,type,
% 0.22/0.52 d_Union_closed: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Union_closed,definition,
% 0.22/0.52 ( d_Union_closed
% 0.22/0.52 = ( ^ [X0: $i] :
% 0.22/0.52 ! [X1: $i] :
% 0.22/0.52 ( ( in @ X1 @ X0 )
% 0.22/0.52 => ( in @ ( union @ X1 ) @ X0 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Power_closed,type,
% 0.22/0.52 d_Power_closed: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Power_closed,definition,
% 0.22/0.52 ( d_Power_closed
% 0.22/0.52 = ( ^ [X0: $i] :
% 0.22/0.52 ! [X1: $i] :
% 0.22/0.52 ( ( in @ X1 @ X0 )
% 0.22/0.52 => ( in @ ( power @ X1 ) @ X0 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Repl_closed,type,
% 0.22/0.52 d_Repl_closed: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Repl_closed,definition,
% 0.22/0.52 ( d_Repl_closed
% 0.22/0.52 = ( ^ [X0: $i] :
% 0.22/0.52 ! [X1: $i] :
% 0.22/0.52 ( ( in @ X1 @ X0 )
% 0.22/0.52 => ! [X2: $i > $i] :
% 0.22/0.52 ( ! [X3: $i] :
% 0.22/0.52 ( ( in @ X3 @ X1 )
% 0.22/0.52 => ( in @ ( X2 @ X3 ) @ X0 ) )
% 0.22/0.52 => ( in @ ( repl @ X1 @ X2 ) @ X0 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_ZF_closed,type,
% 0.22/0.52 d_ZF_closed: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_ZF_closed,definition,
% 0.22/0.52 ( d_ZF_closed
% 0.22/0.52 = ( ^ [X0: $i] :
% 0.22/0.52 ( ( d_Union_closed @ X0 )
% 0.22/0.52 & ( d_Power_closed @ X0 )
% 0.22/0.52 & ( d_Repl_closed @ X0 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_univof,type,
% 0.22/0.52 univof: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(k_UnivOf_In,axiom,
% 0.22/0.52 ! [X0: $i] : ( in @ X0 @ ( univof @ X0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_UnivOf_ZF_closed,axiom,
% 0.22/0.52 ! [X0: $i] : ( d_ZF_closed @ ( univof @ X0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_if,type,
% 0.22/0.52 if: $o > $i > $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_if,definition,
% 0.22/0.52 ( if
% 0.22/0.52 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.22/0.52 ( eps
% 0.22/0.52 @ ^ [X3: $i] :
% 0.22/0.52 ( ( X0
% 0.22/0.52 & ( X3 = X1 ) )
% 0.22/0.52 | ( ~ X0
% 0.22/0.52 & ( X3 = X2 ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(if_i_correct,axiom,
% 0.22/0.52 ! [X0: $o,X1: $i,X2: $i] :
% 0.22/0.52 ( ( X0
% 0.22/0.52 & ( ( if @ X0 @ X1 @ X2 )
% 0.22/0.52 = X1 ) )
% 0.22/0.52 | ( ~ X0
% 0.22/0.52 & ( ( if @ X0 @ X1 @ X2 )
% 0.22/0.52 = X2 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(if_i_0,axiom,
% 0.22/0.52 ! [X0: $o,X1: $i,X2: $i] :
% 0.22/0.52 ( ~ X0
% 0.22/0.52 => ( ( if @ X0 @ X1 @ X2 )
% 0.22/0.52 = X2 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(if_i_1,axiom,
% 0.22/0.52 ! [X0: $o,X1: $i,X2: $i] :
% 0.22/0.52 ( X0
% 0.22/0.52 => ( ( if @ X0 @ X1 @ X2 )
% 0.22/0.52 = X1 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(if_i_or,axiom,
% 0.22/0.52 ! [X0: $o,X1: $i,X2: $i] :
% 0.22/0.52 ( ( ( if @ X0 @ X1 @ X2 )
% 0.22/0.52 = X1 )
% 0.22/0.52 | ( ( if @ X0 @ X1 @ X2 )
% 0.22/0.52 = X2 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_nIn,type,
% 0.22/0.52 nIn: $i > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_nIn,definition,
% 0.22/0.52 ( nIn
% 0.22/0.52 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.52 ~ ( in @ X0 @ X1 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_PowerE,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i] :
% 0.22/0.52 ( ( in @ X1 @ ( power @ X0 ) )
% 0.22/0.52 => ( d_Subq @ X1 @ X0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_PowerI,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i] :
% 0.22/0.52 ( ( d_Subq @ X1 @ X0 )
% 0.22/0.52 => ( in @ X1 @ ( power @ X0 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_Self_In_Power,axiom,
% 0.22/0.52 ! [X0: $i] : ( in @ X0 @ ( power @ X0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_UPair,type,
% 0.22/0.52 d_UPair: $i > $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_UPair,definition,
% 0.22/0.52 ( d_UPair
% 0.22/0.52 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.52 ( repl @ ( power @ ( power @ emptyset ) )
% 0.22/0.52 @ ^ [X2: $i] : ( if @ ( in @ emptyset @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Sing,type,
% 0.22/0.52 d_Sing: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Sing,definition,
% 0.22/0.52 ( d_Sing
% 0.22/0.52 = ( ^ [X0: $i] : ( d_UPair @ X0 @ X0 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_binunion,type,
% 0.22/0.52 binunion: $i > $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_binunion,definition,
% 0.22/0.52 ( binunion
% 0.22/0.52 = ( ^ [X0: $i,X1: $i] : ( union @ ( d_UPair @ X0 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_famunion,type,
% 0.22/0.52 famunion: $i > ( $i > $i ) > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_famunion,definition,
% 0.22/0.52 ( famunion
% 0.22/0.52 = ( ^ [X0: $i,X1: $i > $i] : ( union @ ( repl @ X0 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Sep,type,
% 0.22/0.52 d_Sep: $i > ( $i > $o ) > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Sep,definition,
% 0.22/0.52 ( d_Sep
% 0.22/0.52 = ( ^ [X0: $i,X1: $i > $o] :
% 0.22/0.52 ( if
% 0.22/0.52 @ ? [X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ X0 )
% 0.22/0.52 & ( X1 @ X2 ) )
% 0.22/0.52 @ ( repl @ X0
% 0.22/0.52 @ ^ [X2: $i] :
% 0.22/0.52 ( if @ ( X1 @ X2 ) @ X2
% 0.22/0.52 @ ( eps
% 0.22/0.52 @ ^ [X3: $i] :
% 0.22/0.52 ( ( in @ X3 @ X0 )
% 0.22/0.52 & ( X1 @ X3 ) ) ) ) )
% 0.22/0.52 @ emptyset ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_SepI,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $o,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ X0 )
% 0.22/0.52 => ( ( X1 @ X2 )
% 0.22/0.52 => ( in @ X2 @ ( d_Sep @ X0 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_SepE1,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $o,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.22/0.52 => ( in @ X2 @ X0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_SepE2,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $o,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.22/0.52 => ( X1 @ X2 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_ReplSep,type,
% 0.22/0.52 d_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_ReplSep,definition,
% 0.22/0.52 ( d_ReplSep
% 0.22/0.52 = ( ^ [X0: $i,X1: $i > $o] : ( repl @ ( d_Sep @ X0 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_setminus,type,
% 0.22/0.52 setminus: $i > $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_setminus,definition,
% 0.22/0.52 ( setminus
% 0.22/0.52 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.52 ( d_Sep @ X0
% 0.22/0.52 @ ^ [X2: $i] : ( nIn @ X2 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_In_rec_G,type,
% 0.22/0.52 d_In_rec_G: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_In_rec_G,definition,
% 0.22/0.52 ( d_In_rec_G
% 0.22/0.52 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.22/0.52 ! [X3: $i > $i > $o] :
% 0.22/0.52 ( ! [X4: $i,X5: $i > $i] :
% 0.22/0.52 ( ! [X6: $i] :
% 0.22/0.52 ( ( in @ X6 @ X4 )
% 0.22/0.52 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.22/0.52 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.22/0.52 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_In_rec,type,
% 0.22/0.52 d_In_rec: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_In_rec,definition,
% 0.22/0.52 ( d_In_rec
% 0.22/0.52 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] : ( eps @ ( d_In_rec_G @ X0 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_ordsucc,type,
% 0.22/0.52 ordsucc: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_ordsucc,definition,
% 0.22/0.52 ( ordsucc
% 0.22/0.52 = ( ^ [X0: $i] : ( binunion @ X0 @ ( d_Sing @ X0 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(neq_ordsucc_0,axiom,
% 0.22/0.52 ! [X0: $i] :
% 0.22/0.52 ( ( ordsucc @ X0 )
% 0.22/0.52 != emptyset ) ).
% 0.22/0.52
% 0.22/0.52 thf(ordsucc_inj,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i] :
% 0.22/0.52 ( ( ( ordsucc @ X0 )
% 0.22/0.52 = ( ordsucc @ X1 ) )
% 0.22/0.52 => ( X0 = X1 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_In_0_1,axiom,
% 0.22/0.52 in @ emptyset @ ( ordsucc @ emptyset ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_nat_p,type,
% 0.22/0.52 nat_p: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_nat_p,definition,
% 0.22/0.52 ( nat_p
% 0.22/0.52 = ( ^ [X0: $i] :
% 0.22/0.52 ! [X1: $i > $o] :
% 0.22/0.52 ( ( X1 @ emptyset )
% 0.22/0.52 => ( ! [X2: $i] :
% 0.22/0.52 ( ( X1 @ X2 )
% 0.22/0.52 => ( X1 @ ( ordsucc @ X2 ) ) )
% 0.22/0.52 => ( X1 @ X0 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(nat_ordsucc,axiom,
% 0.22/0.52 ! [X0: $i] :
% 0.22/0.52 ( ( nat_p @ X0 )
% 0.22/0.52 => ( nat_p @ ( ordsucc @ X0 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(nat_1,axiom,
% 0.22/0.52 nat_p @ ( ordsucc @ emptyset ) ).
% 0.22/0.52
% 0.22/0.52 thf(nat_ind,axiom,
% 0.22/0.52 ! [X0: $i > $o] :
% 0.22/0.52 ( ( X0 @ emptyset )
% 0.22/0.52 => ( ! [X1: $i] :
% 0.22/0.52 ( ( nat_p @ X1 )
% 0.22/0.52 => ( ( X0 @ X1 )
% 0.22/0.52 => ( X0 @ ( ordsucc @ X1 ) ) ) )
% 0.22/0.52 => ! [X1: $i] :
% 0.22/0.52 ( ( nat_p @ X1 )
% 0.22/0.52 => ( X0 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(nat_inv,axiom,
% 0.22/0.52 ! [X0: $i] :
% 0.22/0.52 ( ( nat_p @ X0 )
% 0.22/0.52 => ( ( X0 = emptyset )
% 0.22/0.52 | ? [X1: $i] :
% 0.22/0.52 ( ( nat_p @ X1 )
% 0.22/0.52 & ( X0
% 0.22/0.52 = ( ordsucc @ X1 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_omega,type,
% 0.22/0.52 omega: $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_omega,definition,
% 0.22/0.52 ( omega
% 0.22/0.52 = ( d_Sep @ ( univof @ emptyset ) @ nat_p ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(omega_nat_p,axiom,
% 0.22/0.52 ! [X0: $i] :
% 0.22/0.52 ( ( in @ X0 @ omega )
% 0.22/0.52 => ( nat_p @ X0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(nat_p_omega,axiom,
% 0.22/0.52 ! [X0: $i] :
% 0.22/0.52 ( ( nat_p @ X0 )
% 0.22/0.52 => ( in @ X0 @ omega ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Inj1,type,
% 0.22/0.52 d_Inj1: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Inj1,definition,
% 0.22/0.52 ( d_Inj1
% 0.22/0.52 = ( d_In_rec
% 0.22/0.52 @ ^ [X0: $i,X1: $i > $i] : ( binunion @ ( d_Sing @ emptyset ) @ ( repl @ X0 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Inj0,type,
% 0.22/0.52 d_Inj0: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Inj0,definition,
% 0.22/0.52 ( d_Inj0
% 0.22/0.52 = ( ^ [X0: $i] : ( repl @ X0 @ d_Inj1 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Unj,type,
% 0.22/0.52 d_Unj: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Unj,definition,
% 0.22/0.52 ( d_Unj
% 0.22/0.52 = ( d_In_rec
% 0.22/0.52 @ ^ [X0: $i] : ( repl @ ( setminus @ X0 @ ( d_Sing @ emptyset ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_pair,type,
% 0.22/0.52 pair: $i > $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_pair,definition,
% 0.22/0.52 ( pair
% 0.22/0.52 = ( ^ [X0: $i,X1: $i] : ( binunion @ ( repl @ X0 @ d_Inj0 ) @ ( repl @ X1 @ d_Inj1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_proj0,type,
% 0.22/0.52 proj0: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_proj0,definition,
% 0.22/0.52 ( proj0
% 0.22/0.52 = ( ^ [X0: $i] :
% 0.22/0.52 ( d_ReplSep @ X0
% 0.22/0.52 @ ^ [X1: $i] :
% 0.22/0.52 ? [X2: $i] :
% 0.22/0.52 ( ( d_Inj0 @ X2 )
% 0.22/0.52 = X1 )
% 0.22/0.52 @ d_Unj ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_proj1,type,
% 0.22/0.52 proj1: $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_proj1,definition,
% 0.22/0.52 ( proj1
% 0.22/0.52 = ( ^ [X0: $i] :
% 0.22/0.52 ( d_ReplSep @ X0
% 0.22/0.52 @ ^ [X1: $i] :
% 0.22/0.52 ? [X2: $i] :
% 0.22/0.52 ( ( d_Inj1 @ X2 )
% 0.22/0.52 = X1 )
% 0.22/0.52 @ d_Unj ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(proj0_pair_eq,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i] :
% 0.22/0.52 ( ( proj0 @ ( pair @ X0 @ X1 ) )
% 0.22/0.52 = X0 ) ).
% 0.22/0.52
% 0.22/0.52 thf(proj1_pair_eq,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i] :
% 0.22/0.52 ( ( proj1 @ ( pair @ X0 @ X1 ) )
% 0.22/0.52 = X1 ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Sigma,type,
% 0.22/0.52 d_Sigma: $i > ( $i > $i ) > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Sigma,definition,
% 0.22/0.52 ( d_Sigma
% 0.22/0.52 = ( ^ [X0: $i,X1: $i > $i] :
% 0.22/0.52 ( famunion @ X0
% 0.22/0.52 @ ^ [X2: $i] : ( repl @ ( X1 @ X2 ) @ ( pair @ X2 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(pair_Sigma,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ X0 )
% 0.22/0.52 => ! [X3: $i] :
% 0.22/0.52 ( ( in @ X3 @ ( X1 @ X2 ) )
% 0.22/0.52 => ( in @ ( pair @ X2 @ X3 ) @ ( d_Sigma @ X0 @ X1 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_Sigma_eta_proj0_proj1,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ ( d_Sigma @ X0 @ X1 ) )
% 0.22/0.52 => ( ( ( pair @ ( proj0 @ X2 ) @ ( proj1 @ X2 ) )
% 0.22/0.52 = X2 )
% 0.22/0.52 & ( in @ ( proj0 @ X2 ) @ X0 )
% 0.22/0.52 & ( in @ ( proj1 @ X2 ) @ ( X1 @ ( proj0 @ X2 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(proj_Sigma_eta,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ ( d_Sigma @ X0 @ X1 ) )
% 0.22/0.52 => ( ( pair @ ( proj0 @ X2 ) @ ( proj1 @ X2 ) )
% 0.22/0.52 = X2 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(proj0_Sigma,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ ( d_Sigma @ X0 @ X1 ) )
% 0.22/0.52 => ( in @ ( proj0 @ X2 ) @ X0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(proj1_Sigma,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ ( d_Sigma @ X0 @ X1 ) )
% 0.22/0.52 => ( in @ ( proj1 @ X2 ) @ ( X1 @ ( proj0 @ X2 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_setprod,type,
% 0.22/0.52 setprod: $i > $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_setprod,definition,
% 0.22/0.52 ( setprod
% 0.22/0.52 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.52 ( d_Sigma @ X0
% 0.22/0.52 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_ap,type,
% 0.22/0.52 ap: $i > $i > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_ap,definition,
% 0.22/0.52 ( ap
% 0.22/0.52 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.52 ( d_ReplSep @ X0
% 0.22/0.52 @ ^ [X2: $i] :
% 0.22/0.52 ? [X3: $i] :
% 0.22/0.52 ( X2
% 0.22/0.52 = ( pair @ X1 @ X3 ) )
% 0.22/0.52 @ proj1 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(beta,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ X0 )
% 0.22/0.52 => ( ( ap @ ( d_Sigma @ X0 @ X1 ) @ X2 )
% 0.22/0.52 = ( X1 @ X2 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_pair_p,type,
% 0.22/0.52 pair_p: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_pair_p,definition,
% 0.22/0.52 ( pair_p
% 0.22/0.52 = ( ^ [X0: $i] :
% 0.22/0.52 ( ( pair @ ( ap @ X0 @ emptyset ) @ ( ap @ X0 @ ( ordsucc @ emptyset ) ) )
% 0.22/0.52 = X0 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_d_Pi,type,
% 0.22/0.52 d_Pi: $i > ( $i > $i ) > $i ).
% 0.22/0.52
% 0.22/0.52 thf(def_d_Pi,definition,
% 0.22/0.52 ( d_Pi
% 0.22/0.52 = ( ^ [X0: $i,X1: $i > $i] :
% 0.22/0.52 ( d_Sep
% 0.22/0.52 @ ( power
% 0.22/0.52 @ ( d_Sigma @ X0
% 0.22/0.52 @ ^ [X2: $i] : ( union @ ( X1 @ X2 ) ) ) )
% 0.22/0.52 @ ^ [X2: $i] :
% 0.22/0.52 ! [X3: $i] :
% 0.22/0.52 ( ( in @ X3 @ X0 )
% 0.22/0.52 => ( in @ ( ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(lam_Pi,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i > $i] :
% 0.22/0.52 ( ! [X3: $i] :
% 0.22/0.52 ( ( in @ X3 @ X0 )
% 0.22/0.52 => ( in @ ( X2 @ X3 ) @ ( X1 @ X3 ) ) )
% 0.22/0.52 => ( in @ ( d_Sigma @ X0 @ X2 ) @ ( d_Pi @ X0 @ X1 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(ap_Pi,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i,X3: $i] :
% 0.22/0.52 ( ( in @ X2 @ ( d_Pi @ X0 @ X1 ) )
% 0.22/0.52 => ( ( in @ X3 @ X0 )
% 0.22/0.52 => ( in @ ( ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_Pi_ext,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.22/0.52 ( ( in @ X2 @ ( d_Pi @ X0 @ X1 ) )
% 0.22/0.52 => ! [X3: $i] :
% 0.22/0.52 ( ( in @ X3 @ ( d_Pi @ X0 @ X1 ) )
% 0.22/0.52 => ( ! [X4: $i] :
% 0.22/0.52 ( ( in @ X4 @ X0 )
% 0.22/0.52 => ( ( ap @ X2 @ X4 )
% 0.22/0.52 = ( ap @ X3 @ X4 ) ) )
% 0.22/0.52 => ( X2 = X3 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(xi_ext,axiom,
% 0.22/0.52 ! [X0: $i,X1: $i > $i,X2: $i > $i] :
% 0.22/0.52 ( ! [X3: $i] :
% 0.22/0.52 ( ( in @ X3 @ X0 )
% 0.22/0.52 => ( ( X1 @ X3 )
% 0.22/0.52 = ( X2 @ X3 ) ) )
% 0.22/0.52 => ( ( d_Sigma @ X0 @ X1 )
% 0.22/0.52 = ( d_Sigma @ X0 @ X2 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_If_In_01,axiom,
% 0.22/0.52 ! [X0: $o,X1: $i,X2: $i] :
% 0.22/0.52 ( ( X0
% 0.22/0.52 => ( in @ X1 @ X2 ) )
% 0.22/0.52 => ( in @ ( if @ X0 @ X1 @ emptyset ) @ ( if @ X0 @ X2 @ ( ordsucc @ emptyset ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(k_If_In_then_E,axiom,
% 0.22/0.52 ! [X0: $o,X1: $i,X2: $i,X3: $i] :
% 0.22/0.52 ( X0
% 0.22/0.52 => ( ( in @ X1 @ ( if @ X0 @ X2 @ X3 ) )
% 0.22/0.52 => ( in @ X1 @ X2 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(typ_imp,type,
% 0.22/0.52 imp: $o > $o > $o ).
% 0.22/0.52
% 0.22/0.52 thf(def_imp,definition,
% 0.22/0.53 ( imp
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] :
% 0.22/0.53 ( X0
% 0.22/0.53 => X1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_d_not,type,
% 0.22/0.53 d_not: $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_d_not,definition,
% 0.22/0.53 ( d_not
% 0.22/0.53 = ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_wel,type,
% 0.22/0.53 wel: $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_wel,definition,
% 0.22/0.53 ( wel
% 0.22/0.53 = ( ^ [X0: $o] : ( d_not @ ( d_not @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(l_et,axiom,
% 0.22/0.53 ! [X0: $o] :
% 0.22/0.53 ( ( wel @ X0 )
% 0.22/0.53 => X0 ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_obvious,type,
% 0.22/0.53 obvious: $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_obvious,definition,
% 0.22/0.53 ( obvious
% 0.22/0.53 = ( imp @ $false @ $false ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_l_ec,type,
% 0.22/0.53 l_ec: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_l_ec,definition,
% 0.22/0.53 ( l_ec
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] : ( imp @ X0 @ ( d_not @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_d_and,type,
% 0.22/0.53 d_and: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_d_and,definition,
% 0.22/0.53 ( d_and
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] : ( d_not @ ( l_ec @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_l_or,type,
% 0.22/0.53 l_or: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_l_or,definition,
% 0.22/0.53 ( l_or
% 0.22/0.53 = ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_orec,type,
% 0.22/0.53 orec: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_orec,definition,
% 0.22/0.53 ( orec
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] : ( d_and @ ( l_or @ X0 @ X1 ) @ ( l_ec @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_l_iff,type,
% 0.22/0.53 l_iff: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_l_iff,definition,
% 0.22/0.53 ( l_iff
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] : ( d_and @ ( imp @ X0 @ X1 ) @ ( imp @ X1 @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_all,type,
% 0.22/0.53 all: $i > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_all,definition,
% 0.22/0.53 ( all
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X1: $i] : ( in @ X1 @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_non,type,
% 0.22/0.53 non: $i > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_non,definition,
% 0.22/0.53 ( non
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_l_some,type,
% 0.22/0.53 l_some: $i > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_l_some,definition,
% 0.22/0.53 ( l_some
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( d_not
% 0.22/0.53 @ ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ( non @ X0 @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_or3,type,
% 0.22/0.53 or3: $o > $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_or3,definition,
% 0.22/0.53 ( or3
% 0.22/0.53 = ( ^ [X0: $o,X1: $o,X2: $o] : ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_and3,type,
% 0.22/0.53 and3: $o > $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_and3,definition,
% 0.22/0.53 ( and3
% 0.22/0.53 = ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_ec3,type,
% 0.22/0.53 ec3: $o > $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_ec3,definition,
% 0.22/0.53 ( ec3
% 0.22/0.53 = ( ^ [X0: $o,X1: $o,X2: $o] : ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_orec3,type,
% 0.22/0.53 orec3: $o > $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_orec3,definition,
% 0.22/0.53 ( orec3
% 0.22/0.53 = ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_e_is,type,
% 0.22/0.53 e_is: $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_e_is,definition,
% 0.22/0.53 ( e_is
% 0.22/0.53 = ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(refis,axiom,
% 0.22/0.53 ! [X0: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X1: $i] : ( in @ X1 @ X0 )
% 0.22/0.53 @ ^ [X1: $i] : ( e_is @ X0 @ X1 @ X1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(e_isp,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X3: $i] : ( in @ X3 @ X0 )
% 0.22/0.53 @ ^ [X3: $i] :
% 0.22/0.53 ( ( X1 @ X2 )
% 0.22/0.53 => ( ( e_is @ X0 @ X2 @ X3 )
% 0.22/0.53 => ( X1 @ X3 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_amone,type,
% 0.22/0.53 amone: $i > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_amone,definition,
% 0.22/0.53 ( amone
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X3: $i] : ( in @ X3 @ X0 )
% 0.22/0.53 @ ^ [X3: $i] :
% 0.22/0.53 ( ( X1 @ X2 )
% 0.22/0.53 => ( ( X1 @ X3 )
% 0.22/0.53 => ( e_is @ X0 @ X2 @ X3 ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_one,type,
% 0.22/0.53 one: $i > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_one,definition,
% 0.22/0.53 ( one
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o] : ( d_and @ ( amone @ X0 @ X1 ) @ ( l_some @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_ind,type,
% 0.22/0.53 ind: $i > ( $i > $o ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_ind,definition,
% 0.22/0.53 ( ind
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( eps
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( ( in @ X2 @ X0 )
% 0.22/0.53 & ( X1 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ind_p,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( ( one @ X0 @ X1 )
% 0.22/0.53 => ( is_of @ ( ind @ X0 @ X1 )
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(oneax,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( ( one @ X0 @ X1 )
% 0.22/0.53 => ( X1 @ ( ind @ X0 @ X1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_injective,type,
% 0.22/0.53 injective: $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_injective,definition,
% 0.22/0.53 ( injective
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.22/0.53 ( all @ X0
% 0.22/0.53 @ ^ [X3: $i] :
% 0.22/0.53 ( all @ X0
% 0.22/0.53 @ ^ [X4: $i] : ( imp @ ( e_is @ X1 @ ( ap @ X2 @ X3 ) @ ( ap @ X2 @ X4 ) ) @ ( e_is @ X0 @ X3 @ X4 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_image,type,
% 0.22/0.53 image: $i > $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_image,definition,
% 0.22/0.53 ( image
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
% 0.22/0.53 ( l_some @ X0
% 0.22/0.53 @ ^ [X4: $i] : ( e_is @ X1 @ X3 @ ( ap @ X2 @ X4 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_tofs,type,
% 0.22/0.53 tofs: $i > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_tofs,definition,
% 0.22/0.53 ( tofs
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : ap ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_soft,type,
% 0.22/0.53 soft: $i > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_soft,definition,
% 0.22/0.53 ( soft
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
% 0.22/0.53 ( ind @ X0
% 0.22/0.53 @ ^ [X4: $i] : ( e_is @ X1 @ X3 @ ( ap @ X2 @ X4 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_inverse,type,
% 0.22/0.53 inverse: $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_inverse,definition,
% 0.22/0.53 ( inverse
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.22/0.53 ( d_Sigma @ X1
% 0.22/0.53 @ ^ [X3: $i] : ( if @ ( image @ X0 @ X1 @ X2 @ X3 ) @ ( soft @ X0 @ X1 @ X2 @ X3 ) @ emptyset ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_surjective,type,
% 0.22/0.53 surjective: $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_surjective,definition,
% 0.22/0.53 ( surjective
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] : ( all @ X1 @ ( image @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_bijective,type,
% 0.22/0.53 bijective: $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_bijective,definition,
% 0.22/0.53 ( bijective
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] : ( d_and @ ( injective @ X0 @ X1 @ X2 ) @ ( surjective @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_invf,type,
% 0.22/0.53 invf: $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_invf,definition,
% 0.22/0.53 ( invf
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] : ( d_Sigma @ X1 @ ( soft @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_inj_h,type,
% 0.22/0.53 inj_h: $i > $i > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_inj_h,definition,
% 0.22/0.53 ( inj_h
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
% 0.22/0.53 ( d_Sigma @ X0
% 0.22/0.53 @ ^ [X5: $i] : ( ap @ X4 @ ( ap @ X3 @ X5 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(e_fisi,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( in @ X2
% 0.22/0.53 @ ( d_Pi @ X0
% 0.22/0.53 @ ^ [X3: $i] : X1 ) )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X3: $i] :
% 0.22/0.53 ( in @ X3
% 0.22/0.53 @ ( d_Pi @ X0
% 0.22/0.53 @ ^ [X4: $i] : X1 ) )
% 0.22/0.53 @ ^ [X3: $i] :
% 0.22/0.53 ( ( all_of
% 0.22/0.53 @ ^ [X4: $i] : ( in @ X4 @ X0 )
% 0.22/0.53 @ ^ [X4: $i] : ( e_is @ X1 @ ( ap @ X2 @ X4 ) @ ( ap @ X3 @ X4 ) ) )
% 0.22/0.53 => ( e_is
% 0.22/0.53 @ ( d_Pi @ X0
% 0.22/0.53 @ ^ [X4: $i] : X1 )
% 0.22/0.53 @ X2
% 0.22/0.53 @ X3 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_e_in,type,
% 0.22/0.53 e_in: $i > ( $i > $o ) > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_e_in,definition,
% 0.22/0.53 ( e_in
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o,X2: $i] : X2 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(e_in_p,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( is_of @ ( e_in @ X0 @ X1 @ X2 )
% 0.22/0.53 @ ^ [X3: $i] : ( in @ X3 @ X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(e_inp,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.22/0.53 @ ^ [X2: $i] : ( X1 @ ( e_in @ X0 @ X1 @ X2 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(otax1,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] : ( injective @ ( d_Sep @ X0 @ X1 ) @ X0 @ ( d_Sigma @ ( d_Sep @ X0 @ X1 ) @ ( e_in @ X0 @ X1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(otax2,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( ( X1 @ X2 )
% 0.22/0.53 => ( image @ ( d_Sep @ X0 @ X1 ) @ X0 @ ( d_Sigma @ ( d_Sep @ X0 @ X1 ) @ ( e_in @ X0 @ X1 ) ) @ X2 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_out,type,
% 0.22/0.53 out: $i > ( $i > $o ) > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_out,definition,
% 0.22/0.53 ( out
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o] : ( soft @ ( d_Sep @ X0 @ X1 ) @ X0 @ ( d_Sigma @ ( d_Sep @ X0 @ X1 ) @ ( e_in @ X0 @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_d_pair,type,
% 0.22/0.53 d_pair: $i > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_d_pair,definition,
% 0.22/0.53 ( d_pair
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : pair ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(e_pair_p,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X3: $i] : ( in @ X3 @ X1 )
% 0.22/0.53 @ ^ [X3: $i] :
% 0.22/0.53 ( is_of @ ( d_pair @ X0 @ X1 @ X2 @ X3 )
% 0.22/0.53 @ ^ [X4: $i] : ( in @ X4 @ ( setprod @ X0 @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_first,type,
% 0.22/0.53 first: $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_first,definition,
% 0.22/0.53 ( first
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : proj0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(first_p,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ ( setprod @ X0 @ X1 ) )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( is_of @ ( first @ X0 @ X1 @ X2 )
% 0.22/0.53 @ ^ [X3: $i] : ( in @ X3 @ X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_second,type,
% 0.22/0.53 second: $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_second,definition,
% 0.22/0.53 ( second
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : proj1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(second_p,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ ( setprod @ X0 @ X1 ) )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( is_of @ ( second @ X0 @ X1 @ X2 )
% 0.22/0.53 @ ^ [X3: $i] : ( in @ X3 @ X1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pairis1,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ ( setprod @ X0 @ X1 ) )
% 0.22/0.53 @ ^ [X2: $i] : ( e_is @ ( setprod @ X0 @ X1 ) @ ( d_pair @ X0 @ X1 @ ( first @ X0 @ X1 @ X2 ) @ ( second @ X0 @ X1 @ X2 ) ) @ X2 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(firstis1,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X3: $i] : ( in @ X3 @ X1 )
% 0.22/0.53 @ ^ [X3: $i] : ( e_is @ X0 @ ( first @ X0 @ X1 @ ( d_pair @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(secondis1,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X3: $i] : ( in @ X3 @ X1 )
% 0.22/0.53 @ ^ [X3: $i] : ( e_is @ X1 @ ( second @ X0 @ X1 @ ( d_pair @ X0 @ X1 @ X2 @ X3 ) ) @ X3 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_prop1,type,
% 0.22/0.53 prop1: $o > $i > $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_prop1,definition,
% 0.22/0.53 ( prop1
% 0.22/0.53 = ( ^ [X0: $o,X1: $i,X2: $i,X3: $i,X4: $i] : ( d_and @ ( imp @ X0 @ ( e_is @ X1 @ X4 @ X2 ) ) @ ( imp @ ( d_not @ X0 ) @ ( e_is @ X1 @ X4 @ X3 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_ite,type,
% 0.22/0.53 ite: $o > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_ite,definition,
% 0.22/0.53 ( ite
% 0.22/0.53 = ( ^ [X0: $o,X1: $i,X2: $i,X3: $i] : ( ind @ X1 @ ( prop1 @ X0 @ X1 @ X2 @ X3 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_wissel_wa,type,
% 0.22/0.53 wissel_wa: $i > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_wissel_wa,definition,
% 0.22/0.53 ( wissel_wa
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] : ( ite @ ( e_is @ X0 @ X3 @ X1 ) @ X0 @ X2 @ X3 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_wissel_wb,type,
% 0.22/0.53 wissel_wb: $i > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_wissel_wb,definition,
% 0.22/0.53 ( wissel_wb
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] : ( ite @ ( e_is @ X0 @ X3 @ X2 ) @ X0 @ X1 @ ( wissel_wa @ X0 @ X1 @ X2 @ X3 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_wissel,type,
% 0.22/0.53 wissel: $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_wissel,definition,
% 0.22/0.53 ( wissel
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] : ( d_Sigma @ X0 @ ( wissel_wb @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_changef,type,
% 0.22/0.53 changef: $i > $i > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_changef,definition,
% 0.22/0.53 ( changef
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
% 0.22/0.53 ( d_Sigma @ X0
% 0.22/0.53 @ ^ [X5: $i] : ( ap @ X2 @ ( ap @ ( wissel @ X0 @ X3 @ X4 ) @ X5 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_r_ec,type,
% 0.22/0.53 r_ec: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_r_ec,definition,
% 0.22/0.53 ( r_ec
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] :
% 0.22/0.53 ( X0
% 0.22/0.53 => ( d_not @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_esti,type,
% 0.22/0.53 esti: $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_esti,definition,
% 0.22/0.53 ( esti
% 0.22/0.53 = ( ^ [X0: $i] : in ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(setof_p,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( is_of @ ( d_Sep @ X0 @ X1 )
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ ( power @ X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(estii,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( ( X1 @ X2 )
% 0.22/0.53 => ( esti @ X0 @ X2 @ ( d_Sep @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(estie,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( ( esti @ X0 @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.22/0.53 => ( X1 @ X2 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_empty,type,
% 0.22/0.53 empty: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_empty,definition,
% 0.22/0.53 ( empty
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.22/0.53 @ ( non @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( esti @ X0 @ X2 @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_nonempty,type,
% 0.22/0.53 nonempty: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_nonempty,definition,
% 0.22/0.53 ( nonempty
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( l_some @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( esti @ X0 @ X2 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_incl,type,
% 0.22/0.53 incl: $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_incl,definition,
% 0.22/0.53 ( incl
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.22/0.53 ( all @ X0
% 0.22/0.53 @ ^ [X3: $i] : ( imp @ ( esti @ X0 @ X3 @ X1 ) @ ( esti @ X0 @ X3 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_st_disj,type,
% 0.22/0.53 st_disj: $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_st_disj,definition,
% 0.22/0.53 ( st_disj
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.22/0.53 ( all @ X0
% 0.22/0.53 @ ^ [X3: $i] : ( l_ec @ ( esti @ X0 @ X3 @ X1 ) @ ( esti @ X0 @ X3 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(isseti,axiom,
% 0.22/0.53 ! [X0: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X1: $i] : ( in @ X1 @ ( power @ X0 ) )
% 0.22/0.53 @ ^ [X1: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X2: $i] : ( in @ X2 @ ( power @ X0 ) )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( ( incl @ X0 @ X1 @ X2 )
% 0.22/0.53 => ( ( incl @ X0 @ X2 @ X1 )
% 0.22/0.53 => ( e_is @ ( power @ X0 ) @ X1 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_nissetprop,type,
% 0.22/0.53 nissetprop: $i > $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_nissetprop,definition,
% 0.22/0.53 ( nissetprop
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] : ( d_and @ ( esti @ X0 @ X3 @ X1 ) @ ( d_not @ ( esti @ X0 @ X3 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_unmore,type,
% 0.22/0.53 unmore: $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_unmore,definition,
% 0.22/0.53 ( unmore
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.22/0.53 ( d_Sep @ X0
% 0.22/0.53 @ ^ [X3: $i] :
% 0.22/0.53 ( l_some @ X1
% 0.22/0.53 @ ^ [X4: $i] : ( esti @ X0 @ X3 @ ( ap @ X2 @ X4 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_ecelt,type,
% 0.22/0.53 ecelt: $i > ( $i > $i > $o ) > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_ecelt,definition,
% 0.22/0.53 ( ecelt
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i] : ( d_Sep @ X0 @ ( X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_ecp,type,
% 0.22/0.53 ecp: $i > ( $i > $i > $o ) > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_ecp,definition,
% 0.22/0.53 ( ecp
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] : ( e_is @ ( power @ X0 ) @ X2 @ ( ecelt @ X0 @ X1 @ X3 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_anec,type,
% 0.22/0.53 anec: $i > ( $i > $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_anec,definition,
% 0.22/0.53 ( anec
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i] : ( l_some @ X0 @ ( ecp @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_ect,type,
% 0.22/0.53 ect: $i > ( $i > $i > $o ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_ect,definition,
% 0.22/0.53 ( ect
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o] : ( d_Sep @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_ectset,type,
% 0.22/0.53 ectset: $i > ( $i > $i > $o ) > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_ectset,definition,
% 0.22/0.53 ( ectset
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o] : ( out @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_ectelt,type,
% 0.22/0.53 ectelt: $i > ( $i > $i > $o ) > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_ectelt,definition,
% 0.22/0.53 ( ectelt
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i] : ( ectset @ X0 @ X1 @ ( ecelt @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_ecect,type,
% 0.22/0.53 ecect: $i > ( $i > $i > $o ) > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_ecect,definition,
% 0.22/0.53 ( ecect
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o] : ( e_in @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_fixfu,type,
% 0.22/0.53 fixfu: $i > ( $i > $i > $o ) > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_fixfu,definition,
% 0.22/0.53 ( fixfu
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X4: $i] : ( in @ X4 @ X0 )
% 0.22/0.53 @ ^ [X4: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X5: $i] : ( in @ X5 @ X0 )
% 0.22/0.53 @ ^ [X5: $i] :
% 0.22/0.53 ( ( X1 @ X4 @ X5 )
% 0.22/0.53 => ( e_is @ X2 @ ( ap @ X3 @ X4 ) @ ( ap @ X3 @ X5 ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_d_10_prop1,type,
% 0.22/0.53 d_10_prop1: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_d_10_prop1,definition,
% 0.22/0.53 ( d_10_prop1
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : ( d_and @ ( esti @ X0 @ X6 @ ( ecect @ X0 @ X1 @ X4 ) ) @ ( e_is @ X2 @ ( ap @ X3 @ X6 ) @ X5 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_prop2,type,
% 0.22/0.53 prop2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_prop2,definition,
% 0.22/0.53 ( prop2
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i,X5: $i] : ( l_some @ X0 @ ( d_10_prop1 @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_indeq,type,
% 0.22/0.53 indeq: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_indeq,definition,
% 0.22/0.53 ( indeq
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] : ( ind @ X2 @ ( prop2 @ X0 @ X1 @ X2 @ X3 @ X4 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_fixfu2,type,
% 0.22/0.53 fixfu2: $i > ( $i > $i > $o ) > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_fixfu2,definition,
% 0.22/0.53 ( fixfu2
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X4: $i] : ( in @ X4 @ X0 )
% 0.22/0.53 @ ^ [X4: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X5: $i] : ( in @ X5 @ X0 )
% 0.22/0.53 @ ^ [X5: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X6: $i] : ( in @ X6 @ X0 )
% 0.22/0.53 @ ^ [X6: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X7: $i] : ( in @ X7 @ X0 )
% 0.22/0.53 @ ^ [X7: $i] :
% 0.22/0.53 ( ( X1 @ X4 @ X5 )
% 0.22/0.53 => ( ( X1 @ X6 @ X7 )
% 0.22/0.53 => ( e_is @ X2 @ ( ap @ ( ap @ X3 @ X4 ) @ X6 ) @ ( ap @ ( ap @ X3 @ X5 ) @ X7 ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_d_11_i,type,
% 0.22/0.53 d_11_i: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_d_11_i,definition,
% 0.22/0.53 ( d_11_i
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i] :
% 0.22/0.53 ( indeq @ X0 @ X1
% 0.22/0.53 @ ( d_Pi @ X0
% 0.22/0.53 @ ^ [X3: $i] : X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_indeq2,type,
% 0.22/0.53 indeq2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_indeq2,definition,
% 0.22/0.53 ( indeq2
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] : ( indeq @ X0 @ X1 @ X2 @ ( d_11_i @ X0 @ X1 @ X2 @ X3 @ X4 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_nat,type,
% 0.22/0.53 nat: $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_nat,definition,
% 0.22/0.53 ( nat
% 0.22/0.53 = ( d_Sep @ omega
% 0.22/0.53 @ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_n_is,type,
% 0.22/0.53 n_is: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_n_is,definition,
% 0.22/0.53 ( n_is
% 0.22/0.53 = ( e_is @ nat ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_nis,type,
% 0.22/0.53 nis: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_nis,definition,
% 0.22/0.53 ( nis
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_n_in,type,
% 0.22/0.53 n_in: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_n_in,definition,
% 0.22/0.53 ( n_in
% 0.22/0.53 = ( esti @ nat ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_n_some,type,
% 0.22/0.53 n_some: ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_n_some,definition,
% 0.22/0.53 ( n_some
% 0.22/0.53 = ( l_some @ nat ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_n_all,type,
% 0.22/0.53 n_all: ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_n_all,definition,
% 0.22/0.53 ( n_all
% 0.22/0.53 = ( all @ nat ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_n_one,type,
% 0.22/0.53 n_one: ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_n_one,definition,
% 0.22/0.53 ( n_one
% 0.22/0.53 = ( one @ nat ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_n_1,type,
% 0.22/0.53 n_1: $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_n_1,definition,
% 0.22/0.53 ( n_1
% 0.22/0.53 = ( ordsucc @ emptyset ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(n_1_p,axiom,
% 0.22/0.53 ( is_of @ n_1
% 0.22/0.53 @ ^ [X0: $i] : ( in @ X0 @ nat ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(suc_p,axiom,
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.22/0.53 @ ^ [X0: $i] :
% 0.22/0.53 ( is_of @ ( ordsucc @ X0 )
% 0.22/0.53 @ ^ [X1: $i] : ( in @ X1 @ nat ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(n_ax3,axiom,
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.22/0.53 @ ^ [X0: $i] : ( nis @ ( ordsucc @ X0 ) @ n_1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(n_ax4,axiom,
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.22/0.53 @ ^ [X0: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.22/0.53 @ ^ [X1: $i] :
% 0.22/0.53 ( ( n_is @ ( ordsucc @ X0 ) @ ( ordsucc @ X1 ) )
% 0.22/0.53 => ( n_is @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_cond1,type,
% 0.22/0.53 cond1: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_cond1,definition,
% 0.22/0.53 ( cond1
% 0.22/0.53 = ( n_in @ n_1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_cond2,type,
% 0.22/0.53 cond2: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_cond2,definition,
% 0.22/0.53 ( cond2
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( n_all
% 0.22/0.53 @ ^ [X1: $i] : ( imp @ ( n_in @ X1 @ X0 ) @ ( n_in @ ( ordsucc @ X1 ) @ X0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(n_ax5,axiom,
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X0: $i] : ( in @ X0 @ ( power @ nat ) )
% 0.22/0.53 @ ^ [X0: $i] :
% 0.22/0.53 ( ( cond1 @ X0 )
% 0.22/0.53 => ( ( cond2 @ X0 )
% 0.22/0.53 => ( all_of
% 0.22/0.53 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.22/0.53 @ ^ [X1: $i] : ( n_in @ X1 @ X0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_i1_s,type,
% 0.22/0.53 i1_s: ( $i > $o ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(def_i1_s,definition,
% 0.22/0.53 ( i1_s
% 0.22/0.53 = ( d_Sep @ nat ) ) ).
% 0.22/0.53
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 thf(satz1,axiom,
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.22/0.53 @ ^ [X0: $i] :
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.22/0.53 @ ^ [X1: $i] :
% 0.22/0.53 ( ( nis @ X0 @ X1 )
% 0.22/0.53 => ( nis @ ( ordsucc @ X0 ) @ ( ordsucc @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_d_22_prop1,type,
% 0.22/0.53 d_22_prop1: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_d_22_prop1,definition,
% 0.22/0.53 ( d_22_prop1
% 0.22/0.53 = ( ^ [X0: $i] : ( nis @ ( ordsucc @ X0 ) @ X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(satz2,axiom,
% 0.22/0.53 ( all_of
% 0.22/0.53 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.22/0.53 @ ^ [X0: $i] : ( nis @ ( ordsucc @ X0 ) @ X0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(typ_d_23_prop1,type,
% 0.22/0.53 d_23_prop1: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(def_d_23_prop1,definition,
% 0.22/0.53 ( d_23_prop1
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( l_or @ ( n_is @ X0 @ n_1 )
% 0.22/0.57 @ ( n_some
% 0.22/0.57 @ ^ [X1: $i] : ( n_is @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ) ).
% 0.22/0.57
% 0.22/0.57 thf(satz3,axiom,
% 0.22/0.57 ( all_of
% 0.22/0.57 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.22/0.57 @ ^ [X0: $i] :
% 0.22/0.57 ( ( nis @ X0 @ n_1 )
% 0.22/0.57 => ( n_some
% 0.22/0.57 @ ^ [X1: $i] : ( n_is @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ).
% 0.22/0.57
% 0.22/0.57 thf(satz3a,conjecture,
% 0.22/0.57 ( all_of
% 0.22/0.57 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.22/0.57 @ ^ [X0: $i] :
% 0.22/0.57 ( ( nis @ X0 @ n_1 )
% 0.22/0.57 => ( n_one
% 0.22/0.57 @ ^ [X1: $i] : ( n_is @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ).
% 0.22/0.57
% 0.22/0.57 %------------------------------------------------------------------------------
% 0.22/0.57 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ElPdY6bTMO/cvc5---1.0.5_21001.p...
% 0.22/0.57 (declare-sort $$unsorted 0)
% 0.22/0.57 (declare-fun tptp.is_of ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.57 (assert (= tptp.is_of (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ X1 X0))))
% 0.22/0.57 (declare-fun tptp.all_of ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.22/0.57 (assert (= tptp.all_of (lambda ((X0 (-> $$unsorted Bool)) (X1 (-> $$unsorted Bool))) (forall ((X2 $$unsorted)) (=> (@ (@ tptp.is_of X2) X0) (@ X1 X2))))))
% 0.22/0.57 (declare-fun tptp.eps ((-> $$unsorted Bool)) $$unsorted)
% 0.22/0.57 (declare-fun tptp.in ($$unsorted $$unsorted) Bool)
% 0.22/0.57 (declare-fun tptp.d_Subq ($$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.d_Subq (lambda ((X0 $$unsorted) (X1 $$unsorted)) (forall ((X2 $$unsorted)) (let ((_let_1 (@ tptp.in X2))) (=> (@ _let_1 X0) (@ _let_1 X1)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.d_Subq X0) X1) (=> (@ (@ tptp.d_Subq X1) X0) (= X0 X1)))))
% 0.22/0.57 (assert (forall ((X0 (-> $$unsorted Bool))) (=> (forall ((X1 $$unsorted)) (=> (forall ((X2 $$unsorted)) (=> (@ (@ tptp.in X2) X1) (@ X0 X2))) (@ X0 X1))) (forall ((X1 $$unsorted)) (@ X0 X1)))))
% 0.22/0.57 (declare-fun tptp.emptyset () $$unsorted)
% 0.22/0.57 (assert (not (exists ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.emptyset))))
% 0.22/0.57 (declare-fun tptp.union ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ (@ tptp.in X1) (@ tptp.union X0)) (exists ((X2 $$unsorted)) (and (@ (@ tptp.in X1) X2) (@ (@ tptp.in X2) X0))))))
% 0.22/0.57 (declare-fun tptp.power ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ (@ tptp.in X1) (@ tptp.power X0)) (@ (@ tptp.d_Subq X1) X0))))
% 0.22/0.57 (declare-fun tptp.repl ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (= (@ (@ tptp.in X2) (@ (@ tptp.repl X0) X1)) (exists ((X3 $$unsorted)) (and (@ (@ tptp.in X3) X0) (= X2 (@ X1 X3)))))))
% 0.22/0.57 (declare-fun tptp.d_Union_closed ($$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.d_Union_closed (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.in X1) X0) (@ (@ tptp.in (@ tptp.union X1)) X0))))))
% 0.22/0.57 (declare-fun tptp.d_Power_closed ($$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.d_Power_closed (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.in X1) X0) (@ (@ tptp.in (@ tptp.power X1)) X0))))))
% 0.22/0.57 (declare-fun tptp.d_Repl_closed ($$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.d_Repl_closed (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.in X1) X0) (forall ((X2 (-> $$unsorted $$unsorted))) (=> (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X1) (@ (@ tptp.in (@ X2 X3)) X0))) (@ (@ tptp.in (@ (@ tptp.repl X1) X2)) X0))))))))
% 0.22/0.57 (declare-fun tptp.d_ZF_closed ($$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.d_ZF_closed (lambda ((X0 $$unsorted)) (and (@ tptp.d_Union_closed X0) (@ tptp.d_Power_closed X0) (@ tptp.d_Repl_closed X0)))))
% 0.22/0.57 (declare-fun tptp.univof ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (@ (@ tptp.in X0) (@ tptp.univof X0))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (@ tptp.d_ZF_closed (@ tptp.univof X0))))
% 0.22/0.57 (declare-fun tptp.if (Bool $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.if (lambda ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (@ tptp.eps (lambda ((X3 $$unsorted)) (or (and X0 (= X3 X1)) (and (not X0) (= X3 X2))))))))
% 0.22/0.57 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ (@ (@ tptp.if X0) X1) X2))) (or (and X0 (= _let_1 X1)) (and (not X0) (= _let_1 X2))))))
% 0.22/0.57 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (=> (not X0) (= (@ (@ (@ tptp.if X0) X1) X2) X2))))
% 0.22/0.57 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (=> X0 (= (@ (@ (@ tptp.if X0) X1) X2) X1))))
% 0.22/0.57 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ (@ (@ tptp.if X0) X1) X2))) (or (= _let_1 X1) (= _let_1 X2)))))
% 0.22/0.57 (declare-fun tptp.nIn ($$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.nIn (lambda ((X0 $$unsorted) (X1 $$unsorted)) (not (@ (@ tptp.in X0) X1)))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.in X1) (@ tptp.power X0)) (@ (@ tptp.d_Subq X1) X0))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.d_Subq X1) X0) (@ (@ tptp.in X1) (@ tptp.power X0)))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (@ (@ tptp.in X0) (@ tptp.power X0))))
% 0.22/0.57 (declare-fun tptp.d_UPair ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_UPair (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.if (@ (@ tptp.in tptp.emptyset) X2)) X0) X1))))))
% 0.22/0.57 (declare-fun tptp.d_Sing ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_Sing (lambda ((X0 $$unsorted)) (@ (@ tptp.d_UPair X0) X0))))
% 0.22/0.57 (declare-fun tptp.binunion ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.binunion (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.union (@ (@ tptp.d_UPair X0) X1)))))
% 0.22/0.57 (declare-fun tptp.famunion ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.57 (assert (= tptp.famunion (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ tptp.union (@ (@ tptp.repl X0) X1)))))
% 0.22/0.57 (declare-fun tptp.d_Sep ($$unsorted (-> $$unsorted Bool)) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_Sep (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ (@ tptp.if (exists ((X2 $$unsorted)) (and (@ (@ tptp.in X2) X0) (@ X1 X2)))) (@ (@ tptp.repl X0) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.if (@ X1 X2)) X2) (@ tptp.eps (lambda ((X3 $$unsorted)) (and (@ (@ tptp.in X3) X0) (@ X1 X3)))))))) tptp.emptyset))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (let ((_let_1 (@ tptp.in X2))) (=> (@ _let_1 X0) (=> (@ X1 X2) (@ _let_1 (@ (@ tptp.d_Sep X0) X1)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (let ((_let_1 (@ tptp.in X2))) (=> (@ _let_1 (@ (@ tptp.d_Sep X0) X1)) (@ _let_1 X0)))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sep X0) X1)) (@ X1 X2))))
% 0.22/0.57 (declare-fun tptp.d_ReplSep ($$unsorted (-> $$unsorted Bool) (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_ReplSep (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (__flatten_var_0 (-> $$unsorted $$unsorted))) (@ (@ tptp.repl (@ (@ tptp.d_Sep X0) X1)) __flatten_var_0))))
% 0.22/0.57 (declare-fun tptp.setminus ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.setminus (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.d_Sep X0) (lambda ((X2 $$unsorted)) (@ (@ tptp.nIn X2) X1))))))
% 0.22/0.57 (declare-fun tptp.d_In_rec_G ((-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted) $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.d_In_rec_G (lambda ((X0 (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)) (X1 $$unsorted) (X2 $$unsorted)) (forall ((X3 (-> $$unsorted $$unsorted Bool))) (=> (forall ((X4 $$unsorted) (X5 (-> $$unsorted $$unsorted))) (=> (forall ((X6 $$unsorted)) (=> (@ (@ tptp.in X6) X4) (@ (@ X3 X6) (@ X5 X6)))) (@ (@ X3 X4) (@ (@ X0 X4) X5)))) (@ (@ X3 X1) X2))))))
% 0.22/0.57 (declare-fun tptp.d_In_rec ((-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted) $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_In_rec (lambda ((X0 (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)) (X1 $$unsorted)) (@ tptp.eps (@ (@ tptp.d_In_rec_G X0) X1)))))
% 0.22/0.57 (declare-fun tptp.ordsucc ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.ordsucc (lambda ((X0 $$unsorted)) (@ (@ tptp.binunion X0) (@ tptp.d_Sing X0)))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (not (= (@ tptp.ordsucc X0) tptp.emptyset))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (= (@ tptp.ordsucc X0) (@ tptp.ordsucc X1)) (= X0 X1))))
% 0.22/0.57 (assert (@ (@ tptp.in tptp.emptyset) (@ tptp.ordsucc tptp.emptyset)))
% 0.22/0.57 (declare-fun tptp.nat_p ($$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.nat_p (lambda ((X0 $$unsorted)) (forall ((X1 (-> $$unsorted Bool))) (=> (@ X1 tptp.emptyset) (=> (forall ((X2 $$unsorted)) (=> (@ X1 X2) (@ X1 (@ tptp.ordsucc X2)))) (@ X1 X0)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (=> (@ tptp.nat_p X0) (@ tptp.nat_p (@ tptp.ordsucc X0)))))
% 0.22/0.57 (assert (@ tptp.nat_p (@ tptp.ordsucc tptp.emptyset)))
% 0.22/0.57 (assert (forall ((X0 (-> $$unsorted Bool))) (=> (@ X0 tptp.emptyset) (=> (forall ((X1 $$unsorted)) (=> (@ tptp.nat_p X1) (=> (@ X0 X1) (@ X0 (@ tptp.ordsucc X1))))) (forall ((X1 $$unsorted)) (=> (@ tptp.nat_p X1) (@ X0 X1)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (=> (@ tptp.nat_p X0) (or (= X0 tptp.emptyset) (exists ((X1 $$unsorted)) (and (@ tptp.nat_p X1) (= X0 (@ tptp.ordsucc X1))))))))
% 0.22/0.57 (declare-fun tptp.omega () $$unsorted)
% 0.22/0.57 (assert (= tptp.omega (@ (@ tptp.d_Sep (@ tptp.univof tptp.emptyset)) tptp.nat_p)))
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (=> (@ (@ tptp.in X0) tptp.omega) (@ tptp.nat_p X0))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (=> (@ tptp.nat_p X0) (@ (@ tptp.in X0) tptp.omega))))
% 0.22/0.57 (declare-fun tptp.d_Inj1 ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_Inj1 (@ tptp.d_In_rec (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.binunion (@ tptp.d_Sing tptp.emptyset)) (@ (@ tptp.repl X0) X1))))))
% 0.22/0.57 (declare-fun tptp.d_Inj0 ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_Inj0 (lambda ((X0 $$unsorted)) (@ (@ tptp.repl X0) tptp.d_Inj1))))
% 0.22/0.57 (declare-fun tptp.d_Unj ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_Unj (@ tptp.d_In_rec (lambda ((X0 $$unsorted) (__flatten_var_0 (-> $$unsorted $$unsorted))) (@ (@ tptp.repl (@ (@ tptp.setminus X0) (@ tptp.d_Sing tptp.emptyset))) __flatten_var_0)))))
% 0.22/0.57 (declare-fun tptp.pair ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.pair (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.binunion (@ (@ tptp.repl X0) tptp.d_Inj0)) (@ (@ tptp.repl X1) tptp.d_Inj1)))))
% 0.22/0.57 (declare-fun tptp.proj0 ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.proj0 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X1 $$unsorted)) (exists ((X2 $$unsorted)) (= (@ tptp.d_Inj0 X2) X1)))) tptp.d_Unj))))
% 0.22/0.57 (declare-fun tptp.proj1 ($$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.proj1 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X1 $$unsorted)) (exists ((X2 $$unsorted)) (= (@ tptp.d_Inj1 X2) X1)))) tptp.d_Unj))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ tptp.proj0 (@ (@ tptp.pair X0) X1)) X0)))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ tptp.proj1 (@ (@ tptp.pair X0) X1)) X1)))
% 0.22/0.57 (declare-fun tptp.d_Sigma ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_Sigma (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.famunion X0) (lambda ((X2 $$unsorted)) (@ (@ tptp.repl (@ X1 X2)) (@ tptp.pair X2)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) X0) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) (@ X1 X2)) (@ (@ tptp.in (@ (@ tptp.pair X2) X3)) (@ (@ tptp.d_Sigma X0) X1)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (let ((_let_1 (@ tptp.proj0 X2))) (let ((_let_2 (@ tptp.proj1 X2))) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sigma X0) X1)) (and (= (@ (@ tptp.pair _let_1) _let_2) X2) (@ (@ tptp.in _let_1) X0) (@ (@ tptp.in _let_2) (@ X1 _let_1))))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sigma X0) X1)) (= (@ (@ tptp.pair (@ tptp.proj0 X2)) (@ tptp.proj1 X2)) X2))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sigma X0) X1)) (@ (@ tptp.in (@ tptp.proj0 X2)) X0))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sigma X0) X1)) (@ (@ tptp.in (@ tptp.proj1 X2)) (@ X1 (@ tptp.proj0 X2))))))
% 0.22/0.57 (declare-fun tptp.setprod ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.setprod (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.d_Sigma X0) (lambda ((X2 $$unsorted)) X1)))))
% 0.22/0.57 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.ap (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X2 $$unsorted)) (exists ((X3 $$unsorted)) (= X2 (@ (@ tptp.pair X1) X3))))) tptp.proj1))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) X0) (= (@ (@ tptp.ap (@ (@ tptp.d_Sigma X0) X1)) X2) (@ X1 X2)))))
% 0.22/0.57 (declare-fun tptp.pair_p ($$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.pair_p (lambda ((X0 $$unsorted)) (let ((_let_1 (@ tptp.ap X0))) (= (@ (@ tptp.pair (@ _let_1 tptp.emptyset)) (@ _let_1 (@ tptp.ordsucc tptp.emptyset))) X0)))))
% 0.22/0.57 (declare-fun tptp.d_Pi ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_Pi (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.d_Sep (@ tptp.power (@ (@ tptp.d_Sigma X0) (lambda ((X2 $$unsorted)) (@ tptp.union (@ X1 X2)))))) (lambda ((X2 $$unsorted)) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X0) (@ (@ tptp.in (@ (@ tptp.ap X2) X3)) (@ X1 X3)))))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted))) (=> (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X0) (@ (@ tptp.in (@ X2 X3)) (@ X1 X3)))) (@ (@ tptp.in (@ (@ tptp.d_Sigma X0) X2)) (@ (@ tptp.d_Pi X0) X1)))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted) (X3 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Pi X0) X1)) (=> (@ (@ tptp.in X3) X0) (@ (@ tptp.in (@ (@ tptp.ap X2) X3)) (@ X1 X3))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Pi X0) X1)) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) (@ (@ tptp.d_Pi X0) X1)) (=> (forall ((X4 $$unsorted)) (=> (@ (@ tptp.in X4) X0) (= (@ (@ tptp.ap X2) X4) (@ (@ tptp.ap X3) X4)))) (= X2 X3)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted))) (let ((_let_1 (@ tptp.d_Sigma X0))) (=> (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X0) (= (@ X1 X3) (@ X2 X3)))) (= (@ _let_1 X1) (@ _let_1 X2))))))
% 0.22/0.57 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ tptp.if X0))) (=> (=> X0 (@ (@ tptp.in X1) X2)) (@ (@ tptp.in (@ (@ _let_1 X1) tptp.emptyset)) (@ (@ _let_1 X2) (@ tptp.ordsucc tptp.emptyset)))))))
% 0.22/0.57 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (let ((_let_1 (@ tptp.in X1))) (=> X0 (=> (@ _let_1 (@ (@ (@ tptp.if X0) X2) X3)) (@ _let_1 X2))))))
% 0.22/0.57 (declare-fun tptp.imp (Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.imp (lambda ((X0 Bool) (X1 Bool)) (=> X0 X1))))
% 0.22/0.57 (declare-fun tptp.d_not (Bool) Bool)
% 0.22/0.57 (assert (= tptp.d_not (lambda ((X0 Bool)) (@ (@ tptp.imp X0) false))))
% 0.22/0.57 (declare-fun tptp.wel (Bool) Bool)
% 0.22/0.57 (assert (= tptp.wel (lambda ((X0 Bool)) (@ tptp.d_not (@ tptp.d_not X0)))))
% 0.22/0.57 (assert (forall ((X0 Bool)) (=> (@ tptp.wel X0) X0)))
% 0.22/0.57 (declare-fun tptp.obvious () Bool)
% 0.22/0.57 (assert (= tptp.obvious (@ (@ tptp.imp false) false)))
% 0.22/0.57 (declare-fun tptp.l_ec (Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.l_ec (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.imp X0) (@ tptp.d_not X1)))))
% 0.22/0.57 (declare-fun tptp.d_and (Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.d_and (lambda ((X0 Bool) (X1 Bool)) (@ tptp.d_not (@ (@ tptp.l_ec X0) X1)))))
% 0.22/0.57 (declare-fun tptp.l_or (Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.l_or (lambda ((X0 Bool) (__flatten_var_0 Bool)) (@ (@ tptp.imp (@ tptp.d_not X0)) __flatten_var_0))))
% 0.22/0.57 (declare-fun tptp.orec (Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.orec (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.d_and (@ (@ tptp.l_or X0) X1)) (@ (@ tptp.l_ec X0) X1)))))
% 0.22/0.57 (declare-fun tptp.l_iff (Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.l_iff (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.d_and (@ (@ tptp.imp X0) X1)) (@ (@ tptp.imp X1) X0)))))
% 0.22/0.57 (declare-fun tptp.all ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.57 (assert (= tptp.all (lambda ((X0 $$unsorted) (__flatten_var_0 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) X0))) __flatten_var_0))))
% 0.22/0.57 (declare-fun tptp.non ($$unsorted (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.non (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (@ tptp.d_not (@ X1 X2)))))
% 0.22/0.57 (declare-fun tptp.l_some ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.57 (assert (= tptp.l_some (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ tptp.d_not (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (@ (@ tptp.non X0) X1))))))
% 0.22/0.57 (declare-fun tptp.or3 (Bool Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.or3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.l_or X0) (@ (@ tptp.l_or X1) X2)))))
% 0.22/0.57 (declare-fun tptp.and3 (Bool Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.and3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.d_and X0) (@ (@ tptp.d_and X1) X2)))))
% 0.22/0.57 (declare-fun tptp.ec3 (Bool Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.ec3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ (@ tptp.and3 (@ (@ tptp.l_ec X0) X1)) (@ (@ tptp.l_ec X1) X2)) (@ (@ tptp.l_ec X2) X0)))))
% 0.22/0.57 (declare-fun tptp.orec3 (Bool Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.orec3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.d_and (@ (@ (@ tptp.or3 X0) X1) X2)) (@ (@ (@ tptp.ec3 X0) X1) X2)))))
% 0.22/0.57 (declare-fun tptp.e_is ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.e_is (lambda ((X0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (= X Y))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) X0))) (lambda ((X1 $$unsorted)) (@ (@ (@ tptp.e_is X0) X1) X1)))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X0))) (lambda ((X3 $$unsorted)) (=> (@ X1 X2) (=> (@ (@ (@ tptp.e_is X0) X2) X3) (@ X1 X3)))))))))
% 0.22/0.57 (declare-fun tptp.amone ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.57 (assert (= tptp.amone (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X0))) (lambda ((X3 $$unsorted)) (=> (@ X1 X2) (=> (@ X1 X3) (@ (@ (@ tptp.e_is X0) X2) X3))))))))))
% 0.22/0.57 (declare-fun tptp.one ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.57 (assert (= tptp.one (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.d_and (@ (@ tptp.amone X0) X1)) (@ (@ tptp.l_some X0) X1)))))
% 0.22/0.57 (declare-fun tptp.ind ($$unsorted (-> $$unsorted Bool)) $$unsorted)
% 0.22/0.57 (assert (= tptp.ind (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ tptp.eps (lambda ((X2 $$unsorted)) (and (@ (@ tptp.in X2) X0) (@ X1 X2)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (=> (@ (@ tptp.one X0) X1) (@ (@ tptp.is_of (@ (@ tptp.ind X0) X1)) (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (=> (@ (@ tptp.one X0) X1) (@ X1 (@ (@ tptp.ind X0) X1)))))
% 0.22/0.57 (declare-fun tptp.injective ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.injective (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X3 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X4 $$unsorted)) (let ((_let_1 (@ tptp.ap X2))) (@ (@ tptp.imp (@ (@ (@ tptp.e_is X1) (@ _let_1 X3)) (@ _let_1 X4))) (@ (@ (@ tptp.e_is X0) X3) X4))))))))))
% 0.22/0.57 (declare-fun tptp.image ($$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.image (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.l_some X0) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.e_is X1) X3) (@ (@ tptp.ap X2) X4)))))))
% 0.22/0.57 (declare-fun tptp.tofs ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.tofs (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ tptp.ap __flatten_var_0) __flatten_var_1))))
% 0.22/0.57 (declare-fun tptp.soft ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.soft (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.ind X0) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.e_is X1) X3) (@ (@ tptp.ap X2) X4)))))))
% 0.22/0.57 (declare-fun tptp.inverse ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.inverse (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sigma X1) (lambda ((X3 $$unsorted)) (@ (@ (@ tptp.if (@ (@ (@ (@ tptp.image X0) X1) X2) X3)) (@ (@ (@ (@ tptp.soft X0) X1) X2) X3)) tptp.emptyset))))))
% 0.22/0.57 (declare-fun tptp.surjective ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.surjective (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X1) (@ (@ (@ tptp.image X0) X1) X2)))))
% 0.22/0.57 (declare-fun tptp.bijective ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.bijective (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_and (@ (@ (@ tptp.injective X0) X1) X2)) (@ (@ (@ tptp.surjective X0) X1) X2)))))
% 0.22/0.57 (declare-fun tptp.invf ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.invf (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sigma X1) (@ (@ (@ tptp.soft X0) X1) X2)))))
% 0.22/0.57 (declare-fun tptp.inj_h ($$unsorted $$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.inj_h (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (@ (@ tptp.d_Sigma X0) (lambda ((X5 $$unsorted)) (@ (@ tptp.ap X4) (@ (@ tptp.ap X3) X5)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.d_Pi X0) (lambda ((X3 $$unsorted)) X1))))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) (@ (@ tptp.d_Pi X0) (lambda ((X4 $$unsorted)) X1))))) (lambda ((X3 $$unsorted)) (=> (@ (@ tptp.all_of (lambda ((X4 $$unsorted)) (@ (@ tptp.in X4) X0))) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.e_is X1) (@ (@ tptp.ap X2) X4)) (@ (@ tptp.ap X3) X4)))) (@ (@ (@ tptp.e_is (@ (@ tptp.d_Pi X0) (lambda ((X4 $$unsorted)) X1))) X2) X3))))))))
% 0.22/0.57 (declare-fun tptp.e_in ($$unsorted (-> $$unsorted Bool) $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.e_in (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) X2)))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.d_Sep X0) X1)))) (lambda ((X2 $$unsorted)) (@ (@ tptp.is_of (@ (@ (@ tptp.e_in X0) X1) X2)) (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X0)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.d_Sep X0) X1)))) (lambda ((X2 $$unsorted)) (@ X1 (@ (@ (@ tptp.e_in X0) X1) X2))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (let ((_let_1 (@ (@ tptp.d_Sep X0) X1))) (@ (@ (@ tptp.injective _let_1) X0) (@ (@ tptp.d_Sigma _let_1) (@ (@ tptp.e_in X0) X1))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ (@ tptp.d_Sep X0) X1))) (=> (@ X1 X2) (@ (@ (@ (@ tptp.image _let_1) X0) (@ (@ tptp.d_Sigma _let_1) (@ (@ tptp.e_in X0) X1))) X2)))))))
% 0.22/0.57 (declare-fun tptp.out ($$unsorted (-> $$unsorted Bool) $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.out (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.d_Sep X0) X1))) (@ (@ (@ (@ tptp.soft _let_1) X0) (@ (@ tptp.d_Sigma _let_1) (@ (@ tptp.e_in X0) X1))) __flatten_var_0)))))
% 0.22/0.57 (declare-fun tptp.d_pair ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_pair (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ tptp.pair __flatten_var_0) __flatten_var_1))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X1))) (lambda ((X3 $$unsorted)) (@ (@ tptp.is_of (@ (@ (@ (@ tptp.d_pair X0) X1) X2) X3)) (lambda ((X4 $$unsorted)) (@ (@ tptp.in X4) (@ (@ tptp.setprod X0) X1))))))))))
% 0.22/0.57 (declare-fun tptp.first ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.first (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted)) (@ tptp.proj0 __flatten_var_0))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.setprod X0) X1)))) (lambda ((X2 $$unsorted)) (@ (@ tptp.is_of (@ (@ (@ tptp.first X0) X1) X2)) (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X0)))))))
% 0.22/0.57 (declare-fun tptp.second ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.second (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted)) (@ tptp.proj1 __flatten_var_0))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.setprod X0) X1)))) (lambda ((X2 $$unsorted)) (@ (@ tptp.is_of (@ (@ (@ tptp.second X0) X1) X2)) (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X1)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.setprod X0) X1)))) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.e_is (@ (@ tptp.setprod X0) X1)) (@ (@ (@ (@ tptp.d_pair X0) X1) (@ (@ (@ tptp.first X0) X1) X2)) (@ (@ (@ tptp.second X0) X1) X2))) X2)))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X1))) (lambda ((X3 $$unsorted)) (@ (@ (@ tptp.e_is X0) (@ (@ (@ tptp.first X0) X1) (@ (@ (@ (@ tptp.d_pair X0) X1) X2) X3))) X2)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X1))) (lambda ((X3 $$unsorted)) (@ (@ (@ tptp.e_is X1) (@ (@ (@ tptp.second X0) X1) (@ (@ (@ (@ tptp.d_pair X0) X1) X2) X3))) X3)))))))
% 0.22/0.57 (declare-fun tptp.prop1 (Bool $$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.prop1 (lambda ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (let ((_let_1 (@ (@ tptp.e_is X1) X4))) (@ (@ tptp.d_and (@ (@ tptp.imp X0) (@ _let_1 X2))) (@ (@ tptp.imp (@ tptp.d_not X0)) (@ _let_1 X3)))))))
% 0.22/0.57 (declare-fun tptp.ite (Bool $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.ite (lambda ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.ind X1) (@ (@ (@ (@ tptp.prop1 X0) X1) X2) X3)))))
% 0.22/0.57 (declare-fun tptp.wissel_wa ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.wissel_wa (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ (@ (@ tptp.ite (@ (@ (@ tptp.e_is X0) X3) X1)) X0) X2) X3))))
% 0.22/0.57 (declare-fun tptp.wissel_wb ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.wissel_wb (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ (@ (@ tptp.ite (@ (@ (@ tptp.e_is X0) X3) X2)) X0) X1) (@ (@ (@ (@ tptp.wissel_wa X0) X1) X2) X3)))))
% 0.22/0.57 (declare-fun tptp.wissel ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.wissel (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sigma X0) (@ (@ (@ tptp.wissel_wb X0) X1) X2)))))
% 0.22/0.57 (declare-fun tptp.changef ($$unsorted $$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.changef (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (@ (@ tptp.d_Sigma X0) (lambda ((X5 $$unsorted)) (@ (@ tptp.ap X2) (@ (@ tptp.ap (@ (@ (@ tptp.wissel X0) X3) X4)) X5)))))))
% 0.22/0.57 (declare-fun tptp.r_ec (Bool Bool) Bool)
% 0.22/0.57 (assert (= tptp.r_ec (lambda ((X0 Bool) (X1 Bool)) (=> X0 (@ tptp.d_not X1)))))
% 0.22/0.57 (declare-fun tptp.esti ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.esti (lambda ((X0 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ tptp.in __flatten_var_0) __flatten_var_1))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.is_of (@ (@ tptp.d_Sep X0) X1)) (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ tptp.power X0))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (=> (@ X1 X2) (@ (@ (@ tptp.esti X0) X2) (@ (@ tptp.d_Sep X0) X1)))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (=> (@ (@ (@ tptp.esti X0) X2) (@ (@ tptp.d_Sep X0) X1)) (@ X1 X2))))))
% 0.22/0.57 (declare-fun tptp.empty ($$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.empty (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (@ (@ tptp.non X0) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.esti X0) X2) X1)))))))
% 0.22/0.57 (declare-fun tptp.nonempty ($$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.nonempty (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.l_some X0) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.esti X0) X2) X1))))))
% 0.22/0.57 (declare-fun tptp.incl ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.incl (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X3 $$unsorted)) (let ((_let_1 (@ (@ tptp.esti X0) X3))) (@ (@ tptp.imp (@ _let_1 X1)) (@ _let_1 X2))))))))
% 0.22/0.57 (declare-fun tptp.st_disj ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.st_disj (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X3 $$unsorted)) (let ((_let_1 (@ (@ tptp.esti X0) X3))) (@ (@ tptp.l_ec (@ _let_1 X1)) (@ _let_1 X2))))))))
% 0.22/0.57 (assert (forall ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) (@ tptp.power X0)))) (lambda ((X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ tptp.power X0)))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ tptp.incl X0))) (=> (@ (@ _let_1 X1) X2) (=> (@ (@ _let_1 X2) X1) (@ (@ (@ tptp.e_is (@ tptp.power X0)) X1) X2))))))))))
% 0.22/0.57 (declare-fun tptp.nissetprop ($$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.nissetprop (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (let ((_let_1 (@ (@ tptp.esti X0) X3))) (@ (@ tptp.d_and (@ _let_1 X1)) (@ tptp.d_not (@ _let_1 X2)))))))
% 0.22/0.57 (declare-fun tptp.unmore ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.unmore (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sep X0) (lambda ((X3 $$unsorted)) (@ (@ tptp.l_some X1) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.esti X0) X3) (@ (@ tptp.ap X2) X4)))))))))
% 0.22/0.57 (declare-fun tptp.ecelt ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.ecelt (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted)) (@ (@ tptp.d_Sep X0) (@ X1 X2)))))
% 0.22/0.57 (declare-fun tptp.ecp ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.ecp (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ (@ tptp.e_is (@ tptp.power X0)) X2) (@ (@ (@ tptp.ecelt X0) X1) X3)))))
% 0.22/0.57 (declare-fun tptp.anec ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.anec (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted)) (@ (@ tptp.l_some X0) (@ (@ (@ tptp.ecp X0) X1) X2)))))
% 0.22/0.57 (declare-fun tptp.ect ($$unsorted (-> $$unsorted $$unsorted Bool)) $$unsorted)
% 0.22/0.57 (assert (= tptp.ect (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.d_Sep (@ tptp.power X0)) (@ (@ tptp.anec X0) X1)))))
% 0.22/0.57 (declare-fun tptp.ectset ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.ectset (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.out (@ tptp.power X0)) (@ (@ tptp.anec X0) X1)) __flatten_var_0))))
% 0.22/0.57 (declare-fun tptp.ectelt ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.ectelt (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted)) (@ (@ (@ tptp.ectset X0) X1) (@ (@ (@ tptp.ecelt X0) X1) X2)))))
% 0.22/0.57 (declare-fun tptp.ecect ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.ecect (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.e_in (@ tptp.power X0)) (@ (@ tptp.anec X0) X1)) __flatten_var_0))))
% 0.22/0.57 (declare-fun tptp.fixfu ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.fixfu (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.all_of (lambda ((X4 $$unsorted)) (@ (@ tptp.in X4) X0))) (lambda ((X4 $$unsorted)) (@ (@ tptp.all_of (lambda ((X5 $$unsorted)) (@ (@ tptp.in X5) X0))) (lambda ((X5 $$unsorted)) (let ((_let_1 (@ tptp.ap X3))) (=> (@ (@ X1 X4) X5) (@ (@ (@ tptp.e_is X2) (@ _let_1 X4)) (@ _let_1 X5)))))))))))
% 0.22/0.57 (declare-fun tptp.d_10_prop1 ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.d_10_prop1 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (X5 $$unsorted) (X6 $$unsorted)) (@ (@ tptp.d_and (@ (@ (@ tptp.esti X0) X6) (@ (@ (@ tptp.ecect X0) X1) X4))) (@ (@ (@ tptp.e_is X2) (@ (@ tptp.ap X3) X6)) X5)))))
% 0.22/0.57 (declare-fun tptp.prop2 ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.prop2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (X5 $$unsorted)) (@ (@ tptp.l_some X0) (@ (@ (@ (@ (@ (@ tptp.d_10_prop1 X0) X1) X2) X3) X4) X5)))))
% 0.22/0.57 (declare-fun tptp.indeq ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.indeq (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (@ (@ tptp.ind X2) (@ (@ (@ (@ (@ tptp.prop2 X0) X1) X2) X3) X4)))))
% 0.22/0.57 (declare-fun tptp.fixfu2 ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.fixfu2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.all_of (lambda ((X4 $$unsorted)) (@ (@ tptp.in X4) X0))) (lambda ((X4 $$unsorted)) (@ (@ tptp.all_of (lambda ((X5 $$unsorted)) (@ (@ tptp.in X5) X0))) (lambda ((X5 $$unsorted)) (@ (@ tptp.all_of (lambda ((X6 $$unsorted)) (@ (@ tptp.in X6) X0))) (lambda ((X6 $$unsorted)) (@ (@ tptp.all_of (lambda ((X7 $$unsorted)) (@ (@ tptp.in X7) X0))) (lambda ((X7 $$unsorted)) (let ((_let_1 (@ tptp.ap X3))) (=> (@ (@ X1 X4) X5) (=> (@ (@ X1 X6) X7) (@ (@ (@ tptp.e_is X2) (@ (@ tptp.ap (@ _let_1 X4)) X6)) (@ (@ tptp.ap (@ _let_1 X5)) X7))))))))))))))))
% 0.22/0.57 (declare-fun tptp.d_11_i ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.d_11_i (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ (@ (@ (@ tptp.indeq X0) X1) (@ (@ tptp.d_Pi X0) (lambda ((X3 $$unsorted)) X2))) __flatten_var_0) __flatten_var_1))))
% 0.22/0.57 (declare-fun tptp.indeq2 ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.22/0.57 (assert (= tptp.indeq2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (__flatten_var_0 $$unsorted)) (@ (@ (@ (@ (@ tptp.indeq X0) X1) X2) (@ (@ (@ (@ (@ tptp.d_11_i X0) X1) X2) X3) X4)) __flatten_var_0))))
% 0.22/0.57 (declare-fun tptp.nat () $$unsorted)
% 0.22/0.57 (assert (= tptp.nat (@ (@ tptp.d_Sep tptp.omega) (lambda ((X0 $$unsorted)) (not (= X0 tptp.emptyset))))))
% 0.22/0.57 (declare-fun tptp.n_is ($$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.n_is (@ tptp.e_is tptp.nat)))
% 0.22/0.57 (declare-fun tptp.nis ($$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.nis (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.d_not (@ (@ tptp.n_is X0) X1)))))
% 0.22/0.57 (declare-fun tptp.n_in ($$unsorted $$unsorted) Bool)
% 0.22/0.57 (assert (= tptp.n_in (@ tptp.esti tptp.nat)))
% 0.22/0.57 (declare-fun tptp.n_some ((-> $$unsorted Bool)) Bool)
% 0.22/0.57 (assert (= tptp.n_some (@ tptp.l_some tptp.nat)))
% 0.22/0.57 (declare-fun tptp.n_all ((-> $$unsorted Bool)) Bool)
% 0.22/0.57 (assert (= tptp.n_all (@ tptp.all tptp.nat)))
% 0.22/0.57 (declare-fun tptp.n_one ((-> $$unsorted Bool)) Bool)
% 0.22/0.57 (assert (= tptp.n_one (@ tptp.one tptp.nat)))
% 0.22/0.57 (declare-fun tptp.n_1 () $$unsorted)
% 0.22/0.57 (assert (= tptp.n_1 (@ tptp.ordsucc tptp.emptyset)))
% 0.22/0.57 (assert (@ (@ tptp.is_of tptp.n_1) (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))))
% 1.59/1.79 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.is_of (@ tptp.ordsucc X0)) (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))))))
% 1.59/1.79 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.nis (@ tptp.ordsucc X0)) tptp.n_1))))
% 1.59/1.79 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.n_is (@ tptp.ordsucc X0)) (@ tptp.ordsucc X1)) (@ (@ tptp.n_is X0) X1)))))))
% 1.59/1.79 (declare-fun tptp.cond1 ($$unsorted) Bool)
% 1.59/1.79 (assert (= tptp.cond1 (@ tptp.n_in tptp.n_1)))
% 1.59/1.79 (declare-fun tptp.cond2 ($$unsorted) Bool)
% 1.59/1.79 (assert (= tptp.cond2 (lambda ((X0 $$unsorted)) (@ tptp.n_all (lambda ((X1 $$unsorted)) (@ (@ tptp.imp (@ (@ tptp.n_in X1) X0)) (@ (@ tptp.n_in (@ tptp.ordsucc X1)) X0)))))))
% 1.59/1.79 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) (@ tptp.power tptp.nat)))) (lambda ((X0 $$unsorted)) (=> (@ tptp.cond1 X0) (=> (@ tptp.cond2 X0) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ tptp.n_in X1) X0))))))))
% 1.59/1.79 (declare-fun tptp.i1_s ((-> $$unsorted Bool)) $$unsorted)
% 1.59/1.79 (assert (= tptp.i1_s (@ tptp.d_Sep tptp.nat)))
% 1.59/1.79 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.nis X0) X1) (@ (@ tptp.nis (@ tptp.ordsucc X0)) (@ tptp.ordsucc X1))))))))
% 1.59/1.79 (declare-fun tptp.d_22_prop1 ($$unsorted) Bool)
% 1.59/1.79 (assert (= tptp.d_22_prop1 (lambda ((X0 $$unsorted)) (@ (@ tptp.nis (@ tptp.ordsucc X0)) X0))))
% 1.59/1.79 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.nis (@ tptp.ordsucc X0)) X0))))
% 1.59/1.79 (declare-fun tptp.d_23_prop1 ($$unsorted) Bool)
% 1.59/1.79 (assert (= tptp.d_23_prop1 (lambda ((X0 $$unsorted)) (@ (@ tptp.l_or (@ (@ tptp.n_is X0) tptp.n_1)) (@ tptp.n_some (lambda ((X1 $$unsorted)) (@ (@ tptp.n_is X0) (@ tptp.ordsucc X1))))))))
% 1.59/1.79 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (=> (@ (@ tptp.nis X0) tptp.n_1) (@ tptp.n_some (lambda ((X1 $$unsorted)) (@ (@ tptp.n_is X0) (@ tptp.ordsucc X1))))))))
% 1.59/1.79 (assert (not (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (=> (@ (@ tptp.nis X0) tptp.n_1) (@ tptp.n_one (lambda ((X1 $$unsorted)) (@ (@ tptp.n_is X0) (@ tptp.ordsucc X1)))))))))
% 1.59/1.79 (set-info :filename cvc5---1.0.5_21001)
% 1.59/1.79 (check-sat-assuming ( true ))
% 1.59/1.79 ------- get file name : TPTP file name is NUM638^4
% 1.59/1.79 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21001.smt2...
% 1.59/1.79 --- Run --ho-elim --full-saturate-quant at 10...
% 1.59/1.79 % SZS status Theorem for NUM638^4
% 1.59/1.79 % SZS output start Proof for NUM638^4
% 1.59/1.79 (
% 1.59/1.79 (let ((_let_1 (not (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (=> (@ (@ tptp.nis X0) tptp.n_1) (@ tptp.n_one (lambda ((X1 $$unsorted)) (@ (@ tptp.n_is X0) (@ tptp.ordsucc X1)))))))))) (let ((_let_2 (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (=> (@ (@ tptp.nis X0) tptp.n_1) (@ tptp.n_some (lambda ((X1 $$unsorted)) (@ (@ tptp.n_is X0) (@ tptp.ordsucc X1))))))))) (let ((_let_3 (= tptp.d_23_prop1 (lambda ((X0 $$unsorted)) (@ (@ tptp.l_or (@ (@ tptp.n_is X0) tptp.n_1)) (@ tptp.n_some (lambda ((X1 $$unsorted)) (@ (@ tptp.n_is X0) (@ tptp.ordsucc X1))))))))) (let ((_let_4 (= tptp.d_22_prop1 (lambda ((X0 $$unsorted)) (@ (@ tptp.nis (@ tptp.ordsucc X0)) X0))))) (let ((_let_5 (= tptp.i1_s (@ tptp.d_Sep tptp.nat)))) (let ((_let_6 (= tptp.cond2 (lambda ((X0 $$unsorted)) (@ tptp.n_all (lambda ((X1 $$unsorted)) (@ (@ tptp.imp (@ (@ tptp.n_in X1) X0)) (@ (@ tptp.n_in (@ tptp.ordsucc X1)) X0)))))))) (let ((_let_7 (= tptp.cond1 (@ tptp.n_in tptp.n_1)))) (let ((_let_8 (@ tptp.ordsucc tptp.emptyset))) (let ((_let_9 (= tptp.n_1 _let_8))) (let ((_let_10 (= tptp.n_one (@ tptp.one tptp.nat)))) (let ((_let_11 (= tptp.n_all (@ tptp.all tptp.nat)))) (let ((_let_12 (= tptp.n_some (@ tptp.l_some tptp.nat)))) (let ((_let_13 (= tptp.n_in (@ tptp.esti tptp.nat)))) (let ((_let_14 (= tptp.nis (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.d_not (@ (@ tptp.n_is X0) X1)))))) (let ((_let_15 (= tptp.n_is (@ tptp.e_is tptp.nat)))) (let ((_let_16 (@ tptp.d_Sep tptp.omega))) (let ((_let_17 (= tptp.nat (@ _let_16 (lambda ((X0 $$unsorted)) (not (= X0 tptp.emptyset))))))) (let ((_let_18 (= tptp.indeq2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (__flatten_var_0 $$unsorted)) (@ (@ (@ (@ (@ tptp.indeq X0) X1) X2) (@ (@ (@ (@ (@ tptp.d_11_i X0) X1) X2) X3) X4)) __flatten_var_0))))) (let ((_let_19 (= tptp.d_11_i (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ (@ (@ (@ tptp.indeq X0) X1) (@ (@ tptp.d_Pi X0) (lambda ((X3 $$unsorted)) X2))) __flatten_var_0) __flatten_var_1))))) (let ((_let_20 (= tptp.fixfu2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.all_of (lambda ((X4 $$unsorted)) (@ (@ tptp.in X4) X0))) (lambda ((X4 $$unsorted)) (@ (@ tptp.all_of (lambda ((X5 $$unsorted)) (@ (@ tptp.in X5) X0))) (lambda ((X5 $$unsorted)) (@ (@ tptp.all_of (lambda ((X6 $$unsorted)) (@ (@ tptp.in X6) X0))) (lambda ((X6 $$unsorted)) (@ (@ tptp.all_of (lambda ((X7 $$unsorted)) (@ (@ tptp.in X7) X0))) (lambda ((X7 $$unsorted)) (let ((_let_1 (@ tptp.ap X3))) (=> (@ (@ X1 X4) X5) (=> (@ (@ X1 X6) X7) (@ (@ (@ tptp.e_is X2) (@ (@ tptp.ap (@ _let_1 X4)) X6)) (@ (@ tptp.ap (@ _let_1 X5)) X7))))))))))))))))) (let ((_let_21 (= tptp.indeq (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (@ (@ tptp.ind X2) (@ (@ (@ (@ (@ tptp.prop2 X0) X1) X2) X3) X4)))))) (let ((_let_22 (= tptp.prop2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (X5 $$unsorted)) (@ (@ tptp.l_some X0) (@ (@ (@ (@ (@ (@ tptp.d_10_prop1 X0) X1) X2) X3) X4) X5)))))) (let ((_let_23 (= tptp.d_10_prop1 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (X5 $$unsorted) (X6 $$unsorted)) (@ (@ tptp.d_and (@ (@ (@ tptp.esti X0) X6) (@ (@ (@ tptp.ecect X0) X1) X4))) (@ (@ (@ tptp.e_is X2) (@ (@ tptp.ap X3) X6)) X5)))))) (let ((_let_24 (= tptp.fixfu (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.all_of (lambda ((X4 $$unsorted)) (@ (@ tptp.in X4) X0))) (lambda ((X4 $$unsorted)) (@ (@ tptp.all_of (lambda ((X5 $$unsorted)) (@ (@ tptp.in X5) X0))) (lambda ((X5 $$unsorted)) (let ((_let_1 (@ tptp.ap X3))) (=> (@ (@ X1 X4) X5) (@ (@ (@ tptp.e_is X2) (@ _let_1 X4)) (@ _let_1 X5)))))))))))) (let ((_let_25 (= tptp.ecect (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.e_in (@ tptp.power X0)) (@ (@ tptp.anec X0) X1)) __flatten_var_0))))) (let ((_let_26 (= tptp.ectelt (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted)) (@ (@ (@ tptp.ectset X0) X1) (@ (@ (@ tptp.ecelt X0) X1) X2)))))) (let ((_let_27 (= tptp.ectset (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.out (@ tptp.power X0)) (@ (@ tptp.anec X0) X1)) __flatten_var_0))))) (let ((_let_28 (= tptp.ect (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.d_Sep (@ tptp.power X0)) (@ (@ tptp.anec X0) X1)))))) (let ((_let_29 (= tptp.anec (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted)) (@ (@ tptp.l_some X0) (@ (@ (@ tptp.ecp X0) X1) X2)))))) (let ((_let_30 (= tptp.ecp (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ (@ tptp.e_is (@ tptp.power X0)) X2) (@ (@ (@ tptp.ecelt X0) X1) X3)))))) (let ((_let_31 (= tptp.ecelt (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted)) (@ (@ tptp.d_Sep X0) (@ X1 X2)))))) (let ((_let_32 (= tptp.unmore (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sep X0) (lambda ((X3 $$unsorted)) (@ (@ tptp.l_some X1) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.esti X0) X3) (@ (@ tptp.ap X2) X4)))))))))) (let ((_let_33 (= tptp.nissetprop (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (let ((_let_1 (@ (@ tptp.esti X0) X3))) (@ (@ tptp.d_and (@ _let_1 X1)) (@ tptp.d_not (@ _let_1 X2)))))))) (let ((_let_34 (= tptp.st_disj (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X3 $$unsorted)) (let ((_let_1 (@ (@ tptp.esti X0) X3))) (@ (@ tptp.l_ec (@ _let_1 X1)) (@ _let_1 X2))))))))) (let ((_let_35 (= tptp.incl (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X3 $$unsorted)) (let ((_let_1 (@ (@ tptp.esti X0) X3))) (@ (@ tptp.imp (@ _let_1 X1)) (@ _let_1 X2))))))))) (let ((_let_36 (= tptp.nonempty (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.l_some X0) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.esti X0) X2) X1))))))) (let ((_let_37 (= tptp.empty (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (@ (@ tptp.non X0) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.esti X0) X2) X1)))))))) (let ((_let_38 (= tptp.esti (lambda ((X0 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ tptp.in __flatten_var_0) __flatten_var_1))))) (let ((_let_39 (= tptp.r_ec (lambda ((X0 Bool) (X1 Bool)) (=> X0 (@ tptp.d_not X1)))))) (let ((_let_40 (= tptp.changef (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (@ (@ tptp.d_Sigma X0) (lambda ((X5 $$unsorted)) (@ (@ tptp.ap X2) (@ (@ tptp.ap (@ (@ (@ tptp.wissel X0) X3) X4)) X5)))))))) (let ((_let_41 (= tptp.wissel (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sigma X0) (@ (@ (@ tptp.wissel_wb X0) X1) X2)))))) (let ((_let_42 (= tptp.wissel_wb (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ (@ (@ tptp.ite (@ (@ (@ tptp.e_is X0) X3) X2)) X0) X1) (@ (@ (@ (@ tptp.wissel_wa X0) X1) X2) X3)))))) (let ((_let_43 (= tptp.wissel_wa (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ (@ (@ tptp.ite (@ (@ (@ tptp.e_is X0) X3) X1)) X0) X2) X3))))) (let ((_let_44 (= tptp.ite (lambda ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.ind X1) (@ (@ (@ (@ tptp.prop1 X0) X1) X2) X3)))))) (let ((_let_45 (= tptp.prop1 (lambda ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (let ((_let_1 (@ (@ tptp.e_is X1) X4))) (@ (@ tptp.d_and (@ (@ tptp.imp X0) (@ _let_1 X2))) (@ (@ tptp.imp (@ tptp.d_not X0)) (@ _let_1 X3)))))))) (let ((_let_46 (= tptp.second (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted)) (@ tptp.proj1 __flatten_var_0))))) (let ((_let_47 (= tptp.first (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted)) (@ tptp.proj0 __flatten_var_0))))) (let ((_let_48 (= tptp.d_pair (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ tptp.pair __flatten_var_0) __flatten_var_1))))) (let ((_let_49 (= tptp.out (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.d_Sep X0) X1))) (@ (@ (@ (@ tptp.soft _let_1) X0) (@ (@ tptp.d_Sigma _let_1) (@ (@ tptp.e_in X0) X1))) __flatten_var_0)))))) (let ((_let_50 (= tptp.e_in (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) X2)))) (let ((_let_51 (= tptp.inj_h (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (@ (@ tptp.d_Sigma X0) (lambda ((X5 $$unsorted)) (@ (@ tptp.ap X4) (@ (@ tptp.ap X3) X5)))))))) (let ((_let_52 (= tptp.invf (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sigma X1) (@ (@ (@ tptp.soft X0) X1) X2)))))) (let ((_let_53 (= tptp.bijective (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_and (@ (@ (@ tptp.injective X0) X1) X2)) (@ (@ (@ tptp.surjective X0) X1) X2)))))) (let ((_let_54 (= tptp.surjective (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X1) (@ (@ (@ tptp.image X0) X1) X2)))))) (let ((_let_55 (= tptp.inverse (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sigma X1) (lambda ((X3 $$unsorted)) (@ (@ (@ tptp.if (@ (@ (@ (@ tptp.image X0) X1) X2) X3)) (@ (@ (@ (@ tptp.soft X0) X1) X2) X3)) tptp.emptyset))))))) (let ((_let_56 (= tptp.soft (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.ind X0) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.e_is X1) X3) (@ (@ tptp.ap X2) X4)))))))) (let ((_let_57 (= tptp.tofs (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ tptp.ap __flatten_var_0) __flatten_var_1))))) (let ((_let_58 (= tptp.image (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.l_some X0) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.e_is X1) X3) (@ (@ tptp.ap X2) X4)))))))) (let ((_let_59 (= tptp.injective (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X3 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X4 $$unsorted)) (let ((_let_1 (@ tptp.ap X2))) (@ (@ tptp.imp (@ (@ (@ tptp.e_is X1) (@ _let_1 X3)) (@ _let_1 X4))) (@ (@ (@ tptp.e_is X0) X3) X4))))))))))) (let ((_let_60 (= tptp.ind (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ tptp.eps (lambda ((X2 $$unsorted)) (and (@ (@ tptp.in X2) X0) (@ X1 X2)))))))) (let ((_let_61 (= tptp.one (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.d_and (@ (@ tptp.amone X0) X1)) (@ (@ tptp.l_some X0) X1)))))) (let ((_let_62 (= tptp.amone (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X0))) (lambda ((X3 $$unsorted)) (=> (@ X1 X2) (=> (@ X1 X3) (@ (@ (@ tptp.e_is X0) X2) X3))))))))))) (let ((_let_63 (= tptp.e_is (lambda ((X0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (= X Y))))) (let ((_let_64 (= tptp.orec3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.d_and (@ (@ (@ tptp.or3 X0) X1) X2)) (@ (@ (@ tptp.ec3 X0) X1) X2)))))) (let ((_let_65 (= tptp.ec3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ (@ tptp.and3 (@ (@ tptp.l_ec X0) X1)) (@ (@ tptp.l_ec X1) X2)) (@ (@ tptp.l_ec X2) X0)))))) (let ((_let_66 (= tptp.and3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.d_and X0) (@ (@ tptp.d_and X1) X2)))))) (let ((_let_67 (= tptp.or3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.l_or X0) (@ (@ tptp.l_or X1) X2)))))) (let ((_let_68 (= tptp.l_some (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ tptp.d_not (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (@ (@ tptp.non X0) X1))))))) (let ((_let_69 (= tptp.non (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (@ tptp.d_not (@ X1 X2)))))) (let ((_let_70 (= tptp.all (lambda ((X0 $$unsorted) (__flatten_var_0 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) X0))) __flatten_var_0))))) (let ((_let_71 (= tptp.l_iff (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.d_and (@ (@ tptp.imp X0) X1)) (@ (@ tptp.imp X1) X0)))))) (let ((_let_72 (= tptp.orec (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.d_and (@ (@ tptp.l_or X0) X1)) (@ (@ tptp.l_ec X0) X1)))))) (let ((_let_73 (= tptp.l_or (lambda ((X0 Bool) (__flatten_var_0 Bool)) (@ (@ tptp.imp (@ tptp.d_not X0)) __flatten_var_0))))) (let ((_let_74 (= tptp.d_and (lambda ((X0 Bool) (X1 Bool)) (@ tptp.d_not (@ (@ tptp.l_ec X0) X1)))))) (let ((_let_75 (= tptp.l_ec (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.imp X0) (@ tptp.d_not X1)))))) (let ((_let_76 (= tptp.obvious (@ (@ tptp.imp false) false)))) (let ((_let_77 (= tptp.wel (lambda ((X0 Bool)) (@ tptp.d_not (@ tptp.d_not X0)))))) (let ((_let_78 (= tptp.d_not (lambda ((X0 Bool)) (@ (@ tptp.imp X0) false))))) (let ((_let_79 (= tptp.imp (lambda ((X0 Bool) (X1 Bool)) (=> X0 X1))))) (let ((_let_80 (= tptp.d_Pi (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.d_Sep (@ tptp.power (@ (@ tptp.d_Sigma X0) (lambda ((X2 $$unsorted)) (@ tptp.union (@ X1 X2)))))) (lambda ((X2 $$unsorted)) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X0) (@ (@ tptp.in (@ (@ tptp.ap X2) X3)) (@ X1 X3)))))))))) (let ((_let_81 (= tptp.pair_p (lambda ((X0 $$unsorted)) (let ((_let_1 (@ tptp.ap X0))) (= (@ (@ tptp.pair (@ _let_1 tptp.emptyset)) (@ _let_1 (@ tptp.ordsucc tptp.emptyset))) X0)))))) (let ((_let_82 (= tptp.ap (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X2 $$unsorted)) (exists ((X3 $$unsorted)) (= X2 (@ (@ tptp.pair X1) X3))))) tptp.proj1))))) (let ((_let_83 (= tptp.setprod (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.d_Sigma X0) (lambda ((X2 $$unsorted)) X1)))))) (let ((_let_84 (= tptp.d_Sigma (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.famunion X0) (lambda ((X2 $$unsorted)) (@ (@ tptp.repl (@ X1 X2)) (@ tptp.pair X2)))))))) (let ((_let_85 (= tptp.proj1 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X1 $$unsorted)) (exists ((X2 $$unsorted)) (= (@ tptp.d_Inj1 X2) X1)))) tptp.d_Unj))))) (let ((_let_86 (= tptp.proj0 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X1 $$unsorted)) (exists ((X2 $$unsorted)) (= (@ tptp.d_Inj0 X2) X1)))) tptp.d_Unj))))) (let ((_let_87 (= tptp.pair (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.binunion (@ (@ tptp.repl X0) tptp.d_Inj0)) (@ (@ tptp.repl X1) tptp.d_Inj1)))))) (let ((_let_88 (= tptp.d_Unj (@ tptp.d_In_rec (lambda ((X0 $$unsorted) (__flatten_var_0 (-> $$unsorted $$unsorted))) (@ (@ tptp.repl (@ (@ tptp.setminus X0) (@ tptp.d_Sing tptp.emptyset))) __flatten_var_0)))))) (let ((_let_89 (= tptp.d_Inj0 (lambda ((X0 $$unsorted)) (@ (@ tptp.repl X0) tptp.d_Inj1))))) (let ((_let_90 (= tptp.d_Inj1 (@ tptp.d_In_rec (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.binunion (@ tptp.d_Sing tptp.emptyset)) (@ (@ tptp.repl X0) X1))))))) (let ((_let_91 (= tptp.omega (@ (@ tptp.d_Sep (@ tptp.univof tptp.emptyset)) tptp.nat_p)))) (let ((_let_92 (= tptp.nat_p (lambda ((X0 $$unsorted)) (forall ((X1 (-> $$unsorted Bool))) (=> (@ X1 tptp.emptyset) (=> (forall ((X2 $$unsorted)) (=> (@ X1 X2) (@ X1 (@ tptp.ordsucc X2)))) (@ X1 X0)))))))) (let ((_let_93 (= tptp.ordsucc (lambda ((X0 $$unsorted)) (@ (@ tptp.binunion X0) (@ tptp.d_Sing X0)))))) (let ((_let_94 (= tptp.d_In_rec (lambda ((X0 (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)) (X1 $$unsorted)) (@ tptp.eps (@ (@ tptp.d_In_rec_G X0) X1)))))) (let ((_let_95 (= tptp.d_In_rec_G (lambda ((X0 (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)) (X1 $$unsorted) (X2 $$unsorted)) (forall ((X3 (-> $$unsorted $$unsorted Bool))) (=> (forall ((X4 $$unsorted) (X5 (-> $$unsorted $$unsorted))) (=> (forall ((X6 $$unsorted)) (=> (@ (@ tptp.in X6) X4) (@ (@ X3 X6) (@ X5 X6)))) (@ (@ X3 X4) (@ (@ X0 X4) X5)))) (@ (@ X3 X1) X2))))))) (let ((_let_96 (= tptp.setminus (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.d_Sep X0) (lambda ((X2 $$unsorted)) (@ (@ tptp.nIn X2) X1))))))) (let ((_let_97 (= tptp.d_ReplSep (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (__flatten_var_0 (-> $$unsorted $$unsorted))) (@ (@ tptp.repl (@ (@ tptp.d_Sep X0) X1)) __flatten_var_0))))) (let ((_let_98 (= tptp.d_Sep (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ (@ tptp.if (exists ((X2 $$unsorted)) (and (@ (@ tptp.in X2) X0) (@ X1 X2)))) (@ (@ tptp.repl X0) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.if (@ X1 X2)) X2) (@ tptp.eps (lambda ((X3 $$unsorted)) (and (@ (@ tptp.in X3) X0) (@ X1 X3)))))))) tptp.emptyset))))) (let ((_let_99 (= tptp.famunion (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ tptp.union (@ (@ tptp.repl X0) X1)))))) (let ((_let_100 (= tptp.binunion (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.union (@ (@ tptp.d_UPair X0) X1)))))) (let ((_let_101 (= tptp.d_Sing (lambda ((X0 $$unsorted)) (@ (@ tptp.d_UPair X0) X0))))) (let ((_let_102 (= tptp.d_UPair (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.if (@ (@ tptp.in tptp.emptyset) X2)) X0) X1))))))) (let ((_let_103 (= tptp.nIn (lambda ((X0 $$unsorted) (X1 $$unsorted)) (not (@ (@ tptp.in X0) X1)))))) (let ((_let_104 (= tptp.if (lambda ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (@ tptp.eps (lambda ((X3 $$unsorted)) (or (and X0 (= X3 X1)) (and (not X0) (= X3 X2))))))))) (let ((_let_105 (= tptp.d_ZF_closed (lambda ((X0 $$unsorted)) (and (@ tptp.d_Union_closed X0) (@ tptp.d_Power_closed X0) (@ tptp.d_Repl_closed X0)))))) (let ((_let_106 (= tptp.d_Repl_closed (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.in X1) X0) (forall ((X2 (-> $$unsorted $$unsorted))) (=> (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X1) (@ (@ tptp.in (@ X2 X3)) X0))) (@ (@ tptp.in (@ (@ tptp.repl X1) X2)) X0))))))))) (let ((_let_107 (= tptp.d_Power_closed (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.in X1) X0) (@ (@ tptp.in (@ tptp.power X1)) X0))))))) (let ((_let_108 (= tptp.d_Union_closed (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.in X1) X0) (@ (@ tptp.in (@ tptp.union X1)) X0))))))) (let ((_let_109 (= tptp.d_Subq (lambda ((X0 $$unsorted) (X1 $$unsorted)) (forall ((X2 $$unsorted)) (let ((_let_1 (@ tptp.in X2))) (=> (@ _let_1 X0) (@ _let_1 X1)))))))) (let ((_let_110 (= tptp.all_of (lambda ((X0 (-> $$unsorted Bool)) (X1 (-> $$unsorted Bool))) (forall ((X2 $$unsorted)) (=> (@ (@ tptp.is_of X2) X0) (@ X1 X2))))))) (let ((_let_111 (= tptp.is_of (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ X1 X0))))) (let ((_let_112 (forall ((X2 $$unsorted)) (or (not (ho_580 (ho_579 k_578 X2) (ho_591 k_590 k_1108))) (= X2 (ho_573 k_609 (ho_577 (ho_576 k_575 (ho_573 k_574 (ho_573 k_574 tptp.emptyset))) k_1167))))))) (let ((_let_113 (forall ((BOUND_VARIABLE_37648 $$unsorted)) (or (not (ho_580 (ho_579 k_578 BOUND_VARIABLE_37648) (ho_591 k_590 k_1108))) (not (= BOUND_VARIABLE_37648 (ho_573 k_609 (ho_577 (ho_576 k_575 (ho_573 k_574 (ho_573 k_574 tptp.emptyset))) (ho_597 k_1105 BOUND_VARIABLE_37648))))))))) (let ((_let_114 (not _let_113))) (let ((_let_115 (or _let_114 _let_112))) (let ((_let_116 (or (not (forall ((BOUND_VARIABLE_37648 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_37648) (@ tptp.eps ll_71))) (not (= BOUND_VARIABLE_37648 (@ tptp.union (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (@ ll_74 BOUND_VARIABLE_37648)))))))) (forall ((X2 $$unsorted)) (or (not (@ (@ tptp.in X2) (@ tptp.eps ll_71))) (= X2 (@ tptp.union (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) ll_14)))))))) (let ((_let_117 (not _let_116))) (let ((_let_118 (or (not (forall ((BOUND_VARIABLE_37648 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_37648) (@ tptp.eps (lambda ((X3 $$unsorted)) (let ((_let_1 (forall ((X2 $$unsorted)) (or (not (@ (@ tptp.in X2) (@ tptp.eps (lambda ((BOUND_VARIABLE_36145 $$unsorted)) (let ((_let_1 (forall ((BOUND_VARIABLE_35985 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_35985) (@ tptp.univof tptp.emptyset))) (not (forall ((X1 (-> $$unsorted Bool))) (or (not (@ X1 tptp.emptyset)) (not (forall ((X2 $$unsorted)) (or (not (@ X1 X2)) (@ X1 (@ tptp.union (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((X2 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5724 $$unsorted)) (let ((_let_1 (@ (@ tptp.in tptp.emptyset) X2))) (or (and _let_1 (= X2 BOUND_VARIABLE_5724)) (and (not _let_1) (= (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((BOUND_VARIABLE_5319 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5290 $$unsorted)) (let ((_let_1 (= X2 BOUND_VARIABLE_5290))) (let ((_let_2 (@ (@ tptp.in tptp.emptyset) BOUND_VARIABLE_5319))) (or (and _let_2 _let_1) (and (not _let_2) _let_1)))))))) BOUND_VARIABLE_5724))))))))))))) (@ X1 BOUND_VARIABLE_35985)))))))) (or (and (not _let_1) (= (@ (@ tptp.repl (@ tptp.univof tptp.emptyset)) (lambda ((X2 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_4786 $$unsorted)) (let ((_let_1 (forall ((X1 (-> $$unsorted Bool))) (or (not (@ X1 tptp.emptyset)) (not (forall ((X2 $$unsorted)) (or (not (@ X1 X2)) (@ X1 (@ tptp.union (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((X2 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5724 $$unsorted)) (let ((_let_1 (@ (@ tptp.in tptp.emptyset) X2))) (or (and _let_1 (= X2 BOUND_VARIABLE_5724)) (and (not _let_1) (= (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((BOUND_VARIABLE_5319 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5290 $$unsorted)) (let ((_let_1 (= X2 BOUND_VARIABLE_5290))) (let ((_let_2 (@ (@ tptp.in tptp.emptyset) BOUND_VARIABLE_5319))) (or (and _let_2 _let_1) (and (not _let_2) _let_1)))))))) BOUND_VARIABLE_5724))))))))))))) (@ X1 X2))))) (or (and _let_1 (= X2 BOUND_VARIABLE_4786)) (and (not _let_1) (= BOUND_VARIABLE_4786 (@ tptp.eps (lambda ((X3 $$unsorted)) (and (@ (@ tptp.in X3) (@ tptp.univof tptp.emptyset)) (forall ((X1 (-> $$unsorted Bool))) (or (not (@ X1 tptp.emptyset)) (not (forall ((X2 $$unsorted)) (or (not (@ X1 X2)) (@ X1 (@ tptp.union (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((X2 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5724 $$unsorted)) (let ((_let_1 (@ (@ tptp.in tptp.emptyset) X2))) (or (and _let_1 (= X2 BOUND_VARIABLE_5724)) (and (not _let_1) (= (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((BOUND_VARIABLE_5319 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5290 $$unsorted)) (let ((_let_1 (= X2 BOUND_VARIABLE_5290))) (let ((_let_2 (@ (@ tptp.in tptp.emptyset) BOUND_VARIABLE_5319))) (or (and _let_2 _let_1) (and (not _let_2) _let_1)))))))) BOUND_VARIABLE_5724))))))))))))) (@ X1 X3)))))))))))))) BOUND_VARIABLE_36145)) (and _let_1 (= tptp.emptyset BOUND_VARIABLE_36145)))))))) (= tptp.emptyset X2))))) (or (and (not _let_1) (= X3 (@ (@ tptp.repl (@ tptp.eps (lambda ((BOUND_VARIABLE_36180 $$unsorted)) (let ((_let_1 (forall ((X2 $$unsorted)) (or (not (@ (@ tptp.in X2) (@ tptp.univof tptp.emptyset))) (not (forall ((X1 (-> $$unsorted Bool))) (or (not (@ X1 tptp.emptyset)) (not (forall ((X2 $$unsorted)) (or (not (@ X1 X2)) (@ X1 (@ tptp.union (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((X2 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5724 $$unsorted)) (let ((_let_1 (@ (@ tptp.in tptp.emptyset) X2))) (or (and _let_1 (= X2 BOUND_VARIABLE_5724)) (and (not _let_1) (= (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((BOUND_VARIABLE_5319 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5290 $$unsorted)) (let ((_let_1 (= X2 BOUND_VARIABLE_5290))) (let ((_let_2 (@ (@ tptp.in tptp.emptyset) BOUND_VARIABLE_5319))) (or (and _let_2 _let_1) (and (not _let_2) _let_1)))))))) BOUND_VARIABLE_5724))))))))))))) (@ X1 X2)))))))) (or (and (not _let_1) (= (@ (@ tptp.repl (@ tptp.univof tptp.emptyset)) (lambda ((X2 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_4786 $$unsorted)) (let ((_let_1 (forall ((X1 (-> $$unsorted Bool))) (or (not (@ X1 tptp.emptyset)) (not (forall ((X2 $$unsorted)) (or (not (@ X1 X2)) (@ X1 (@ tptp.union (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((X2 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5724 $$unsorted)) (let ((_let_1 (@ (@ tptp.in tptp.emptyset) X2))) (or (and _let_1 (= X2 BOUND_VARIABLE_5724)) (and (not _let_1) (= (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((BOUND_VARIABLE_5319 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5290 $$unsorted)) (let ((_let_1 (= X2 BOUND_VARIABLE_5290))) (let ((_let_2 (@ (@ tptp.in tptp.emptyset) BOUND_VARIABLE_5319))) (or (and _let_2 _let_1) (and (not _let_2) _let_1)))))))) BOUND_VARIABLE_5724))))))))))))) (@ X1 X2))))) (or (and _let_1 (= X2 BOUND_VARIABLE_4786)) (and (not _let_1) (= BOUND_VARIABLE_4786 (@ tptp.eps (lambda ((X3 $$unsorted)) (and (@ (@ tptp.in X3) (@ tptp.univof tptp.emptyset)) (forall ((X1 (-> $$unsorted Bool))) (or (not (@ X1 tptp.emptyset)) (not (forall ((X2 $$unsorted)) (or (not (@ X1 X2)) (@ X1 (@ tptp.union (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((X2 $$unsorted)) (@ tptp.eps (lambda ((BOUND_VARIABLE_5724 $$unsorted)) (let ((_let_1 (@ (@ tptp.in tptp.emptyset) X2))) (or (and _let_1 (= X2 BOUND_VARIABLE_5724)) (and (not _let_1) (= (@ (@ 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(EQ_RESOLVE (ASSUME :args (_let_101)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_101 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_130 (EQ_RESOLVE (ASSUME :args (_let_100)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_100 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_131 (ASSUME :args (_let_99)))) (let ((_let_132 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_98)) (MACRO_SR_EQ_INTRO :args (_let_98 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args ((= tptp.d_Sep (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ (@ tptp.if (not (forall ((X2 $$unsorted)) (or (not (@ (@ tptp.in X2) X0)) (not (@ X1 X2)))))) (@ (@ tptp.repl X0) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.if (@ X1 X2)) X2) (@ tptp.eps (lambda ((X3 $$unsorted)) (and (@ (@ tptp.in X3) X0) (@ X1 X3)))))))) tptp.emptyset))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (EQ_RESOLVE (ASSUME :args (_let_97)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_97 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_134 (EQ_RESOLVE (ASSUME :args (_let_96)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_96 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_135 (EQ_RESOLVE (ASSUME :args (_let_95)) (MACRO_SR_EQ_INTRO :args (_let_95 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_136 (EQ_RESOLVE (ASSUME :args (_let_94)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_94 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_137 (EQ_RESOLVE (ASSUME :args (_let_93)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_93 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_138 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_92)) (MACRO_SR_EQ_INTRO :args (_let_92 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args ((= tptp.nat_p (lambda ((X0 $$unsorted)) (forall ((X1 (-> $$unsorted Bool))) (or (not (@ X1 tptp.emptyset)) (not (forall ((X2 $$unsorted)) (or (not (@ X1 X2)) (@ X1 (@ tptp.ordsucc X2))))) (@ X1 X0))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_139 (EQ_RESOLVE (ASSUME :args (_let_91)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_91 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_140 (EQ_RESOLVE (ASSUME :args (_let_90)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_90 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_141 (EQ_RESOLVE (ASSUME :args (_let_89)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_89 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_142 (EQ_RESOLVE (ASSUME :args (_let_88)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_88 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_143 (EQ_RESOLVE (ASSUME :args (_let_87)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_87 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_144 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_86)) (MACRO_SR_EQ_INTRO :args (_let_86 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args ((= tptp.proj0 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X1 $$unsorted)) (not (forall ((X2 $$unsorted)) (not (= X1 (@ tptp.d_Inj0 X2))))))) tptp.d_Unj))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_145 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_85)) (MACRO_SR_EQ_INTRO :args (_let_85 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args ((= tptp.proj1 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X1 $$unsorted)) (not (forall ((X2 $$unsorted)) (not (= X1 (@ tptp.d_Inj1 X2))))))) tptp.d_Unj))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_146 (EQ_RESOLVE (ASSUME :args (_let_84)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_84 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_147 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_148 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_82)) (MACRO_SR_EQ_INTRO :args (_let_82 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args ((= tptp.ap (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X2 $$unsorted)) (not (forall ((X3 $$unsorted)) (not (= X2 (@ (@ tptp.pair X1) X3))))))) tptp.proj1))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_149 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_81)) (MACRO_SR_EQ_INTRO :args (_let_81 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args ((= tptp.pair_p (lambda ((X0 $$unsorted)) (let ((_let_1 (@ tptp.ap X0))) (= X0 (@ (@ tptp.pair (@ _let_1 tptp.emptyset)) (@ _let_1 (@ tptp.ordsucc tptp.emptyset))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_150 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_80)) (MACRO_SR_EQ_INTRO :args (_let_80 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args ((= tptp.d_Pi (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.d_Sep (@ tptp.power (@ (@ tptp.d_Sigma X0) (lambda ((X2 $$unsorted)) (@ tptp.union (@ X1 X2)))))) (lambda ((X2 $$unsorted)) (forall ((X3 $$unsorted)) (or (not (@ (@ tptp.in X3) X0)) (@ (@ tptp.in (@ (@ tptp.ap X2) X3)) (@ X1 X3)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_151 (ASSUME :args (_let_79)))) (let ((_let_152 (EQ_RESOLVE (ASSUME :args (_let_78)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_78 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_153 (EQ_RESOLVE (ASSUME :args (_let_77)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_77 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_154 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_76)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_76 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.obvious true))))) (let ((_let_155 (EQ_RESOLVE (ASSUME :args (_let_75)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_75 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_156 (EQ_RESOLVE (ASSUME :args (_let_74)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_74 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_157 (EQ_RESOLVE (ASSUME :args (_let_73)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_73 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_158 (EQ_RESOLVE (ASSUME :args (_let_72)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_72 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_159 (EQ_RESOLVE (ASSUME :args (_let_71)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_71 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_160 (EQ_RESOLVE (ASSUME :args (_let_70)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_70 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_161 (EQ_RESOLVE (ASSUME :args (_let_69)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_69 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_162 (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_68 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_163 (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_67 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_164 (EQ_RESOLVE (ASSUME :args (_let_66)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_66 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_165 (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_65 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_166 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_167 (ASSUME :args (_let_63)))) (let ((_let_168 (EQ_RESOLVE (ASSUME :args (_let_62)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_62 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_169 (EQ_RESOLVE (ASSUME :args (_let_61)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_61 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_170 (ASSUME :args (_let_60)))) (let ((_let_171 (EQ_RESOLVE (ASSUME :args (_let_59)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_59 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_172 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_173 (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_57 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_174 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_175 (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_55 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_176 (EQ_RESOLVE (ASSUME :args (_let_54)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_54 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_177 (EQ_RESOLVE (ASSUME :args (_let_53)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_53 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_178 (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_52 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_179 (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_51 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_180 (ASSUME :args (_let_50)))) (let ((_let_181 (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_49 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_182 (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_48 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_183 (EQ_RESOLVE (ASSUME :args (_let_47)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_47 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_184 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_185 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_186 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_187 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_188 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_189 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_190 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_191 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_192 (ASSUME :args (_let_38)))) (let ((_let_193 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_194 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_195 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_196 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_197 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_198 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_199 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_200 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_201 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_202 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_203 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_204 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_205 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_206 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_207 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_208 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_209 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_210 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_211 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_212 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_213 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args ((= tptp.nat (@ _let_16 (lambda ((X0 $$unsorted)) (not (= tptp.emptyset X0))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_214 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_215 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_216 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_217 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_218 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_219 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_220 (EQ_RESOLVE (SYMM (ASSUME :args (_let_9))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args ((= _let_8 tptp.n_1) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_221 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_222 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_223 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_224 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_225 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119) :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119))) (let ((_let_226 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_225 :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not _let_118) _let_117))) (PREPROCESS :args ((= _let_117 (not _let_115)))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_OR_ELIM _let_226 :args (1)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_225 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_118 _let_116))) (PREPROCESS :args ((= _let_116 _let_115))))) :args ((or _let_112 _let_114))) (NOT_NOT_ELIM (NOT_OR_ELIM _let_226 :args (0))) :args (_let_112 false _let_113)) :args (false false _let_112)) :args (_let_111 _let_110 _let_109 (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.d_Subq X0) X1) (=> (@ (@ tptp.d_Subq X1) X0) (= X0 X1)))) (forall ((X0 (-> $$unsorted Bool))) (=> (forall ((X1 $$unsorted)) (=> (forall ((X2 $$unsorted)) (=> (@ (@ tptp.in X2) X1) (@ X0 X2))) (@ X0 X1))) (forall ((X1 $$unsorted)) (@ X0 X1)))) (not (exists ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.emptyset))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ (@ tptp.in X1) (@ tptp.union X0)) (exists ((X2 $$unsorted)) (and (@ (@ tptp.in X1) X2) (@ (@ tptp.in X2) X0))))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ (@ tptp.in X1) (@ tptp.power X0)) (@ (@ tptp.d_Subq X1) X0))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (= (@ (@ tptp.in X2) (@ (@ tptp.repl X0) X1)) (exists ((X3 $$unsorted)) (and (@ (@ tptp.in X3) X0) (= X2 (@ X1 X3)))))) _let_108 _let_107 _let_106 _let_105 (forall ((X0 $$unsorted)) (@ (@ tptp.in X0) (@ tptp.univof X0))) (forall ((X0 $$unsorted)) (@ tptp.d_ZF_closed (@ tptp.univof X0))) _let_104 (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ (@ (@ tptp.if X0) X1) X2))) (or (and X0 (= _let_1 X1)) (and (not X0) (= _let_1 X2))))) (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (=> (not X0) (= (@ (@ (@ tptp.if X0) X1) X2) X2))) (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (=> X0 (= (@ (@ (@ tptp.if X0) X1) X2) X1))) (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ (@ (@ tptp.if X0) X1) X2))) (or (= _let_1 X1) (= _let_1 X2)))) _let_103 (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.in X1) (@ tptp.power X0)) (@ (@ tptp.d_Subq X1) X0))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.d_Subq X1) X0) (@ (@ tptp.in X1) (@ tptp.power X0)))) (forall ((X0 $$unsorted)) (@ (@ tptp.in X0) (@ tptp.power X0))) _let_102 _let_101 _let_100 _let_99 _let_98 (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (let ((_let_1 (@ tptp.in X2))) (=> (@ _let_1 X0) (=> (@ X1 X2) (@ _let_1 (@ (@ tptp.d_Sep X0) X1)))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (let ((_let_1 (@ tptp.in X2))) (=> (@ _let_1 (@ (@ tptp.d_Sep X0) X1)) (@ _let_1 X0)))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sep X0) X1)) (@ X1 X2))) _let_97 _let_96 _let_95 _let_94 _let_93 (forall ((X0 $$unsorted)) (not (= (@ tptp.ordsucc X0) tptp.emptyset))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (= (@ tptp.ordsucc X0) (@ tptp.ordsucc X1)) (= X0 X1))) (@ (@ tptp.in tptp.emptyset) _let_8) _let_92 (forall ((X0 $$unsorted)) (=> (@ tptp.nat_p X0) (@ tptp.nat_p (@ tptp.ordsucc X0)))) (@ tptp.nat_p _let_8) (forall ((X0 (-> $$unsorted Bool))) (=> (@ X0 tptp.emptyset) (=> (forall ((X1 $$unsorted)) (=> (@ tptp.nat_p X1) (=> (@ X0 X1) (@ X0 (@ tptp.ordsucc X1))))) (forall ((X1 $$unsorted)) (=> (@ tptp.nat_p X1) (@ X0 X1)))))) (forall ((X0 $$unsorted)) (=> (@ tptp.nat_p X0) (or (= X0 tptp.emptyset) (exists ((X1 $$unsorted)) (and (@ tptp.nat_p X1) (= X0 (@ tptp.ordsucc X1))))))) _let_91 (forall ((X0 $$unsorted)) (=> (@ (@ tptp.in X0) tptp.omega) (@ tptp.nat_p X0))) (forall ((X0 $$unsorted)) (=> (@ tptp.nat_p X0) (@ (@ tptp.in X0) tptp.omega))) _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ tptp.proj0 (@ (@ tptp.pair X0) X1)) X0)) (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ tptp.proj1 (@ (@ tptp.pair X0) X1)) X1)) _let_84 (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) X0) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) (@ X1 X2)) (@ (@ tptp.in (@ (@ tptp.pair X2) X3)) (@ (@ tptp.d_Sigma X0) X1)))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (let ((_let_1 (@ tptp.proj0 X2))) (let ((_let_2 (@ tptp.proj1 X2))) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sigma X0) X1)) (and (= (@ (@ tptp.pair _let_1) _let_2) X2) (@ (@ tptp.in _let_1) X0) (@ (@ tptp.in _let_2) (@ X1 _let_1))))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sigma X0) X1)) (= (@ (@ tptp.pair (@ tptp.proj0 X2)) (@ tptp.proj1 X2)) X2))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sigma X0) X1)) (@ (@ tptp.in (@ tptp.proj0 X2)) X0))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sigma X0) X1)) (@ (@ tptp.in (@ tptp.proj1 X2)) (@ X1 (@ tptp.proj0 X2))))) _let_83 _let_82 (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) X0) (= (@ (@ tptp.ap (@ (@ tptp.d_Sigma X0) X1)) X2) (@ X1 X2)))) _let_81 _let_80 (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted))) (=> (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X0) (@ (@ tptp.in (@ X2 X3)) (@ X1 X3)))) (@ (@ tptp.in (@ (@ tptp.d_Sigma X0) X2)) (@ (@ tptp.d_Pi X0) X1)))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted) (X3 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Pi X0) X1)) (=> (@ (@ tptp.in X3) X0) (@ (@ tptp.in (@ (@ tptp.ap X2) X3)) (@ X1 X3))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Pi X0) X1)) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) (@ (@ tptp.d_Pi X0) X1)) (=> (forall ((X4 $$unsorted)) (=> (@ (@ tptp.in X4) X0) (= (@ (@ tptp.ap X2) X4) (@ (@ tptp.ap X3) X4)))) (= X2 X3)))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted))) (let ((_let_1 (@ tptp.d_Sigma X0))) (=> (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X0) (= (@ X1 X3) (@ X2 X3)))) (= (@ _let_1 X1) (@ _let_1 X2))))) (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ tptp.if X0))) (=> (=> X0 (@ (@ tptp.in X1) X2)) (@ (@ tptp.in (@ (@ _let_1 X1) tptp.emptyset)) (@ (@ _let_1 X2) (@ tptp.ordsucc tptp.emptyset)))))) (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (let ((_let_1 (@ tptp.in X1))) (=> X0 (=> (@ _let_1 (@ (@ (@ tptp.if X0) X2) X3)) (@ _let_1 X2))))) _let_79 _let_78 _let_77 (forall ((X0 Bool)) (=> (@ tptp.wel X0) X0)) _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 (forall ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) X0))) (lambda ((X1 $$unsorted)) (@ (@ (@ tptp.e_is X0) X1) X1)))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X0))) (lambda ((X3 $$unsorted)) (=> (@ X1 X2) (=> (@ (@ (@ tptp.e_is X0) X2) X3) (@ X1 X3)))))))) _let_62 _let_61 _let_60 (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (=> (@ (@ tptp.one X0) X1) (@ (@ tptp.is_of (@ (@ tptp.ind X0) X1)) (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (=> (@ (@ tptp.one X0) X1) (@ X1 (@ (@ tptp.ind X0) X1)))) _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.d_Pi X0) (lambda ((X3 $$unsorted)) X1))))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) (@ (@ tptp.d_Pi X0) (lambda ((X4 $$unsorted)) X1))))) (lambda ((X3 $$unsorted)) (=> (@ (@ tptp.all_of (lambda ((X4 $$unsorted)) (@ (@ tptp.in X4) X0))) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.e_is X1) (@ (@ tptp.ap X2) X4)) (@ (@ tptp.ap X3) X4)))) (@ (@ (@ tptp.e_is (@ (@ tptp.d_Pi X0) (lambda ((X4 $$unsorted)) X1))) X2) X3))))))) _let_50 (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.d_Sep X0) X1)))) (lambda ((X2 $$unsorted)) (@ (@ tptp.is_of (@ (@ (@ tptp.e_in X0) X1) X2)) (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X0)))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.d_Sep X0) X1)))) (lambda ((X2 $$unsorted)) (@ X1 (@ (@ (@ tptp.e_in X0) X1) X2))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (let ((_let_1 (@ (@ tptp.d_Sep X0) X1))) (@ (@ (@ tptp.injective _let_1) X0) (@ (@ tptp.d_Sigma _let_1) (@ (@ tptp.e_in X0) X1))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ (@ tptp.d_Sep X0) X1))) (=> (@ X1 X2) (@ (@ (@ (@ tptp.image _let_1) X0) (@ (@ tptp.d_Sigma _let_1) (@ (@ tptp.e_in X0) X1))) X2)))))) _let_49 _let_48 (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X1))) (lambda ((X3 $$unsorted)) (@ (@ tptp.is_of (@ (@ (@ (@ tptp.d_pair X0) X1) X2) X3)) (lambda ((X4 $$unsorted)) (@ (@ tptp.in X4) (@ (@ tptp.setprod X0) X1))))))))) _let_47 (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.setprod X0) X1)))) (lambda ((X2 $$unsorted)) (@ (@ tptp.is_of (@ (@ (@ tptp.first X0) X1) X2)) (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X0)))))) _let_46 (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.setprod X0) X1)))) (lambda ((X2 $$unsorted)) (@ (@ tptp.is_of (@ (@ (@ tptp.second X0) X1) X2)) (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X1)))))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.setprod X0) X1)))) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.e_is (@ (@ tptp.setprod X0) X1)) (@ (@ (@ (@ tptp.d_pair X0) X1) (@ (@ (@ tptp.first X0) X1) X2)) (@ (@ (@ tptp.second X0) X1) X2))) X2)))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X1))) (lambda ((X3 $$unsorted)) (@ (@ (@ tptp.e_is X0) (@ (@ (@ tptp.first X0) X1) (@ (@ (@ (@ tptp.d_pair X0) X1) X2) X3))) X2)))))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (@ (@ tptp.all_of (lambda ((X3 $$unsorted)) (@ (@ tptp.in X3) X1))) (lambda ((X3 $$unsorted)) (@ (@ (@ tptp.e_is X1) (@ (@ (@ tptp.second X0) X1) (@ (@ (@ (@ tptp.d_pair X0) X1) X2) X3))) X3)))))) _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.is_of (@ (@ tptp.d_Sep X0) X1)) (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ tptp.power X0))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (=> (@ X1 X2) (@ (@ (@ tptp.esti X0) X2) (@ (@ tptp.d_Sep X0) X1)))))) (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (=> (@ (@ (@ tptp.esti X0) X2) (@ (@ tptp.d_Sep X0) X1)) (@ X1 X2))))) _let_37 _let_36 _let_35 _let_34 (forall ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) (@ tptp.power X0)))) (lambda ((X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ tptp.power X0)))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ tptp.incl X0))) (=> (@ (@ _let_1 X1) X2) (=> (@ (@ _let_1 X2) X1) (@ (@ (@ tptp.e_is (@ tptp.power X0)) X1) X2))))))))) _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 (@ (@ tptp.is_of tptp.n_1) (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.is_of (@ tptp.ordsucc X0)) (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))))) (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.nis (@ tptp.ordsucc X0)) tptp.n_1))) (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.n_is (@ tptp.ordsucc X0)) (@ tptp.ordsucc X1)) (@ (@ tptp.n_is X0) X1)))))) _let_7 _let_6 (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) (@ tptp.power tptp.nat)))) (lambda ((X0 $$unsorted)) (=> (@ tptp.cond1 X0) (=> (@ tptp.cond2 X0) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ tptp.n_in X1) X0))))))) _let_5 (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.nis X0) X1) (@ (@ tptp.nis (@ tptp.ordsucc X0)) (@ tptp.ordsucc X1))))))) _let_4 (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.nis (@ tptp.ordsucc X0)) X0))) _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.59/1.80 )
% 1.59/1.80 % SZS output end Proof for NUM638^4
% 1.59/1.80 % cvc5---1.0.5 exiting
% 1.59/1.80 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------