TSTP Solution File: NUM669^4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM669^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 10:46:29 EDT 2023
% Result : Timeout 299.90s 300.12s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : NUM669^4 : TPTP v8.1.2. Released v7.1.0.
% 0.14/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n023.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Aug 25 15:19:42 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.38/0.55 %----Proving TH0
% 0.38/0.56 %------------------------------------------------------------------------------
% 0.38/0.56 % File : NUM669^4 : TPTP v8.1.2. Released v7.1.0.
% 0.38/0.56 % Domain : Number theory
% 0.38/0.56 % Problem : Grundlagen problem satz18b
% 0.38/0.56 % Version : [Bro17] axioms : Especial.
% 0.38/0.56 % English :
% 0.38/0.56
% 0.38/0.56 % Refs : [Bro17] Brown (2017), Email to G. Sutcliffe
% 0.38/0.56 % Source : [Br017]
% 0.38/0.56 % Names :
% 0.38/0.56
% 0.38/0.56 % Status : Theorem
% 0.38/0.56 % Rating : 0.69 v8.1.0, 0.73 v7.5.0, 1.00 v7.4.0, 0.78 v7.2.0, 0.75 v7.1.0
% 0.38/0.56 % Syntax : Number of formulae : 367 ( 136 unt; 131 typ; 124 def)
% 0.38/0.56 % Number of atoms : 1116 ( 154 equ; 0 cnn)
% 0.38/0.56 % Maximal formula atoms : 18 ( 4 avg)
% 0.38/0.56 % Number of connectives : 2036 ( 7 ~; 4 |; 14 &;1900 @)
% 0.38/0.56 % ( 3 <=>; 108 =>; 0 <=; 0 <~>)
% 0.38/0.56 % Maximal formula depth : 14 ( 5 avg)
% 0.38/0.56 % Number of types : 2 ( 0 usr)
% 0.38/0.56 % Number of type conns : 443 ( 443 >; 0 *; 0 +; 0 <<)
% 0.38/0.56 % Number of symbols : 156 ( 154 usr; 29 con; 0-7 aty)
% 0.38/0.56 % Number of variables : 738 ( 581 ^; 149 !; 8 ?; 738 :)
% 0.38/0.56 % SPC : TH0_THM_EQU_NAR
% 0.38/0.56
% 0.38/0.56 % Comments :
% 0.38/0.56 %------------------------------------------------------------------------------
% 0.38/0.56 %------------------------------------------------------------------------------
% 0.38/0.56 thf(typ_is_of,type,
% 0.38/0.56 is_of: $i > ( $i > $o ) > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_is_of,definition,
% 0.38/0.56 ( is_of
% 0.38/0.56 = ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_all_of,type,
% 0.38/0.56 all_of: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_all_of,definition,
% 0.38/0.56 ( all_of
% 0.38/0.56 = ( ^ [X0: $i > $o,X1: $i > $o] :
% 0.38/0.56 ! [X2: $i] :
% 0.38/0.56 ( ( is_of @ X2 @ X0 )
% 0.38/0.56 => ( X1 @ X2 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_eps,type,
% 0.38/0.56 eps: ( $i > $o ) > $i ).
% 0.38/0.56
% 0.38/0.56 thf(typ_in,type,
% 0.38/0.56 in: $i > $i > $o ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Subq,type,
% 0.38/0.56 d_Subq: $i > $i > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Subq,definition,
% 0.38/0.56 ( d_Subq
% 0.38/0.56 = ( ^ [X0: $i,X1: $i] :
% 0.38/0.56 ! [X2: $i] :
% 0.38/0.56 ( ( in @ X2 @ X0 )
% 0.38/0.56 => ( in @ X2 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(set_ext,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i] :
% 0.38/0.56 ( ( d_Subq @ X0 @ X1 )
% 0.38/0.56 => ( ( d_Subq @ X1 @ X0 )
% 0.38/0.56 => ( X0 = X1 ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_In_ind,axiom,
% 0.38/0.56 ! [X0: $i > $o] :
% 0.38/0.56 ( ! [X1: $i] :
% 0.38/0.56 ( ! [X2: $i] :
% 0.38/0.56 ( ( in @ X2 @ X1 )
% 0.38/0.56 => ( X0 @ X2 ) )
% 0.38/0.56 => ( X0 @ X1 ) )
% 0.38/0.56 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_emptyset,type,
% 0.38/0.56 emptyset: $i ).
% 0.38/0.56
% 0.38/0.56 thf(k_EmptyAx,axiom,
% 0.38/0.56 ~ ? [X0: $i] : ( in @ X0 @ emptyset ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_union,type,
% 0.38/0.56 union: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(k_UnionEq,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i] :
% 0.38/0.56 ( ( in @ X1 @ ( union @ X0 ) )
% 0.38/0.56 <=> ? [X2: $i] :
% 0.38/0.56 ( ( in @ X1 @ X2 )
% 0.38/0.56 & ( in @ X2 @ X0 ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_power,type,
% 0.38/0.56 power: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(k_PowerEq,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i] :
% 0.38/0.56 ( ( in @ X1 @ ( power @ X0 ) )
% 0.38/0.56 <=> ( d_Subq @ X1 @ X0 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_repl,type,
% 0.38/0.56 repl: $i > ( $i > $i ) > $i ).
% 0.38/0.56
% 0.38/0.56 thf(k_ReplEq,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.38/0.56 ( ( in @ X2 @ ( repl @ X0 @ X1 ) )
% 0.38/0.56 <=> ? [X3: $i] :
% 0.38/0.56 ( ( in @ X3 @ X0 )
% 0.38/0.56 & ( X2
% 0.38/0.56 = ( X1 @ X3 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Union_closed,type,
% 0.38/0.56 d_Union_closed: $i > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Union_closed,definition,
% 0.38/0.56 ( d_Union_closed
% 0.38/0.56 = ( ^ [X0: $i] :
% 0.38/0.56 ! [X1: $i] :
% 0.38/0.56 ( ( in @ X1 @ X0 )
% 0.38/0.56 => ( in @ ( union @ X1 ) @ X0 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Power_closed,type,
% 0.38/0.56 d_Power_closed: $i > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Power_closed,definition,
% 0.38/0.56 ( d_Power_closed
% 0.38/0.56 = ( ^ [X0: $i] :
% 0.38/0.56 ! [X1: $i] :
% 0.38/0.56 ( ( in @ X1 @ X0 )
% 0.38/0.56 => ( in @ ( power @ X1 ) @ X0 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Repl_closed,type,
% 0.38/0.56 d_Repl_closed: $i > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Repl_closed,definition,
% 0.38/0.56 ( d_Repl_closed
% 0.38/0.56 = ( ^ [X0: $i] :
% 0.38/0.56 ! [X1: $i] :
% 0.38/0.56 ( ( in @ X1 @ X0 )
% 0.38/0.56 => ! [X2: $i > $i] :
% 0.38/0.56 ( ! [X3: $i] :
% 0.38/0.56 ( ( in @ X3 @ X1 )
% 0.38/0.56 => ( in @ ( X2 @ X3 ) @ X0 ) )
% 0.38/0.56 => ( in @ ( repl @ X1 @ X2 ) @ X0 ) ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_ZF_closed,type,
% 0.38/0.56 d_ZF_closed: $i > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_ZF_closed,definition,
% 0.38/0.56 ( d_ZF_closed
% 0.38/0.56 = ( ^ [X0: $i] :
% 0.38/0.56 ( ( d_Union_closed @ X0 )
% 0.38/0.56 & ( d_Power_closed @ X0 )
% 0.38/0.56 & ( d_Repl_closed @ X0 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_univof,type,
% 0.38/0.56 univof: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(k_UnivOf_In,axiom,
% 0.38/0.56 ! [X0: $i] : ( in @ X0 @ ( univof @ X0 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_UnivOf_ZF_closed,axiom,
% 0.38/0.56 ! [X0: $i] : ( d_ZF_closed @ ( univof @ X0 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_if,type,
% 0.38/0.56 if: $o > $i > $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_if,definition,
% 0.38/0.56 ( if
% 0.38/0.56 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.38/0.56 ( eps
% 0.38/0.56 @ ^ [X3: $i] :
% 0.38/0.56 ( ( X0
% 0.38/0.56 & ( X3 = X1 ) )
% 0.38/0.56 | ( ~ X0
% 0.38/0.56 & ( X3 = X2 ) ) ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(if_i_correct,axiom,
% 0.38/0.56 ! [X0: $o,X1: $i,X2: $i] :
% 0.38/0.56 ( ( X0
% 0.38/0.56 & ( ( if @ X0 @ X1 @ X2 )
% 0.38/0.56 = X1 ) )
% 0.38/0.56 | ( ~ X0
% 0.38/0.56 & ( ( if @ X0 @ X1 @ X2 )
% 0.38/0.56 = X2 ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(if_i_0,axiom,
% 0.38/0.56 ! [X0: $o,X1: $i,X2: $i] :
% 0.38/0.56 ( ~ X0
% 0.38/0.56 => ( ( if @ X0 @ X1 @ X2 )
% 0.38/0.56 = X2 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(if_i_1,axiom,
% 0.38/0.56 ! [X0: $o,X1: $i,X2: $i] :
% 0.38/0.56 ( X0
% 0.38/0.56 => ( ( if @ X0 @ X1 @ X2 )
% 0.38/0.56 = X1 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(if_i_or,axiom,
% 0.38/0.56 ! [X0: $o,X1: $i,X2: $i] :
% 0.38/0.56 ( ( ( if @ X0 @ X1 @ X2 )
% 0.38/0.56 = X1 )
% 0.38/0.56 | ( ( if @ X0 @ X1 @ X2 )
% 0.38/0.56 = X2 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_nIn,type,
% 0.38/0.56 nIn: $i > $i > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_nIn,definition,
% 0.38/0.56 ( nIn
% 0.38/0.56 = ( ^ [X0: $i,X1: $i] :
% 0.38/0.56 ~ ( in @ X0 @ X1 ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_PowerE,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i] :
% 0.38/0.56 ( ( in @ X1 @ ( power @ X0 ) )
% 0.38/0.56 => ( d_Subq @ X1 @ X0 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_PowerI,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i] :
% 0.38/0.56 ( ( d_Subq @ X1 @ X0 )
% 0.38/0.56 => ( in @ X1 @ ( power @ X0 ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_Self_In_Power,axiom,
% 0.38/0.56 ! [X0: $i] : ( in @ X0 @ ( power @ X0 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_UPair,type,
% 0.38/0.56 d_UPair: $i > $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_UPair,definition,
% 0.38/0.56 ( d_UPair
% 0.38/0.56 = ( ^ [X0: $i,X1: $i] :
% 0.38/0.56 ( repl @ ( power @ ( power @ emptyset ) )
% 0.38/0.56 @ ^ [X2: $i] : ( if @ ( in @ emptyset @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Sing,type,
% 0.38/0.56 d_Sing: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Sing,definition,
% 0.38/0.56 ( d_Sing
% 0.38/0.56 = ( ^ [X0: $i] : ( d_UPair @ X0 @ X0 ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_binunion,type,
% 0.38/0.56 binunion: $i > $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_binunion,definition,
% 0.38/0.56 ( binunion
% 0.38/0.56 = ( ^ [X0: $i,X1: $i] : ( union @ ( d_UPair @ X0 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_famunion,type,
% 0.38/0.56 famunion: $i > ( $i > $i ) > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_famunion,definition,
% 0.38/0.56 ( famunion
% 0.38/0.56 = ( ^ [X0: $i,X1: $i > $i] : ( union @ ( repl @ X0 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Sep,type,
% 0.38/0.56 d_Sep: $i > ( $i > $o ) > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Sep,definition,
% 0.38/0.56 ( d_Sep
% 0.38/0.56 = ( ^ [X0: $i,X1: $i > $o] :
% 0.38/0.56 ( if
% 0.38/0.56 @ ? [X2: $i] :
% 0.38/0.56 ( ( in @ X2 @ X0 )
% 0.38/0.56 & ( X1 @ X2 ) )
% 0.38/0.56 @ ( repl @ X0
% 0.38/0.56 @ ^ [X2: $i] :
% 0.38/0.56 ( if @ ( X1 @ X2 ) @ X2
% 0.38/0.56 @ ( eps
% 0.38/0.56 @ ^ [X3: $i] :
% 0.38/0.56 ( ( in @ X3 @ X0 )
% 0.38/0.56 & ( X1 @ X3 ) ) ) ) )
% 0.38/0.56 @ emptyset ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_SepI,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i > $o,X2: $i] :
% 0.38/0.56 ( ( in @ X2 @ X0 )
% 0.38/0.56 => ( ( X1 @ X2 )
% 0.38/0.56 => ( in @ X2 @ ( d_Sep @ X0 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_SepE1,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i > $o,X2: $i] :
% 0.38/0.56 ( ( in @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.38/0.56 => ( in @ X2 @ X0 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_SepE2,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i > $o,X2: $i] :
% 0.38/0.56 ( ( in @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.38/0.56 => ( X1 @ X2 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_ReplSep,type,
% 0.38/0.56 d_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_ReplSep,definition,
% 0.38/0.56 ( d_ReplSep
% 0.38/0.56 = ( ^ [X0: $i,X1: $i > $o] : ( repl @ ( d_Sep @ X0 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_setminus,type,
% 0.38/0.56 setminus: $i > $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_setminus,definition,
% 0.38/0.56 ( setminus
% 0.38/0.56 = ( ^ [X0: $i,X1: $i] :
% 0.38/0.56 ( d_Sep @ X0
% 0.38/0.56 @ ^ [X2: $i] : ( nIn @ X2 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_In_rec_G,type,
% 0.38/0.56 d_In_rec_G: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_In_rec_G,definition,
% 0.38/0.56 ( d_In_rec_G
% 0.38/0.56 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.38/0.56 ! [X3: $i > $i > $o] :
% 0.38/0.56 ( ! [X4: $i,X5: $i > $i] :
% 0.38/0.56 ( ! [X6: $i] :
% 0.38/0.56 ( ( in @ X6 @ X4 )
% 0.38/0.56 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.38/0.56 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.38/0.56 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_In_rec,type,
% 0.38/0.56 d_In_rec: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_In_rec,definition,
% 0.38/0.56 ( d_In_rec
% 0.38/0.56 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] : ( eps @ ( d_In_rec_G @ X0 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_ordsucc,type,
% 0.38/0.56 ordsucc: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_ordsucc,definition,
% 0.38/0.56 ( ordsucc
% 0.38/0.56 = ( ^ [X0: $i] : ( binunion @ X0 @ ( d_Sing @ X0 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(neq_ordsucc_0,axiom,
% 0.38/0.56 ! [X0: $i] :
% 0.38/0.56 ( ( ordsucc @ X0 )
% 0.38/0.56 != emptyset ) ).
% 0.38/0.56
% 0.38/0.56 thf(ordsucc_inj,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i] :
% 0.38/0.56 ( ( ( ordsucc @ X0 )
% 0.38/0.56 = ( ordsucc @ X1 ) )
% 0.38/0.56 => ( X0 = X1 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_In_0_1,axiom,
% 0.38/0.56 in @ emptyset @ ( ordsucc @ emptyset ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_nat_p,type,
% 0.38/0.56 nat_p: $i > $o ).
% 0.38/0.56
% 0.38/0.56 thf(def_nat_p,definition,
% 0.38/0.56 ( nat_p
% 0.38/0.56 = ( ^ [X0: $i] :
% 0.38/0.56 ! [X1: $i > $o] :
% 0.38/0.56 ( ( X1 @ emptyset )
% 0.38/0.56 => ( ! [X2: $i] :
% 0.38/0.56 ( ( X1 @ X2 )
% 0.38/0.56 => ( X1 @ ( ordsucc @ X2 ) ) )
% 0.38/0.56 => ( X1 @ X0 ) ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(nat_ordsucc,axiom,
% 0.38/0.56 ! [X0: $i] :
% 0.38/0.56 ( ( nat_p @ X0 )
% 0.38/0.56 => ( nat_p @ ( ordsucc @ X0 ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(nat_1,axiom,
% 0.38/0.56 nat_p @ ( ordsucc @ emptyset ) ).
% 0.38/0.56
% 0.38/0.56 thf(nat_ind,axiom,
% 0.38/0.56 ! [X0: $i > $o] :
% 0.38/0.56 ( ( X0 @ emptyset )
% 0.38/0.56 => ( ! [X1: $i] :
% 0.38/0.56 ( ( nat_p @ X1 )
% 0.38/0.56 => ( ( X0 @ X1 )
% 0.38/0.56 => ( X0 @ ( ordsucc @ X1 ) ) ) )
% 0.38/0.56 => ! [X1: $i] :
% 0.38/0.56 ( ( nat_p @ X1 )
% 0.38/0.56 => ( X0 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(nat_inv,axiom,
% 0.38/0.56 ! [X0: $i] :
% 0.38/0.56 ( ( nat_p @ X0 )
% 0.38/0.56 => ( ( X0 = emptyset )
% 0.38/0.56 | ? [X1: $i] :
% 0.38/0.56 ( ( nat_p @ X1 )
% 0.38/0.56 & ( X0
% 0.38/0.56 = ( ordsucc @ X1 ) ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_omega,type,
% 0.38/0.56 omega: $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_omega,definition,
% 0.38/0.56 ( omega
% 0.38/0.56 = ( d_Sep @ ( univof @ emptyset ) @ nat_p ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(omega_nat_p,axiom,
% 0.38/0.56 ! [X0: $i] :
% 0.38/0.56 ( ( in @ X0 @ omega )
% 0.38/0.56 => ( nat_p @ X0 ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(nat_p_omega,axiom,
% 0.38/0.56 ! [X0: $i] :
% 0.38/0.56 ( ( nat_p @ X0 )
% 0.38/0.56 => ( in @ X0 @ omega ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Inj1,type,
% 0.38/0.56 d_Inj1: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Inj1,definition,
% 0.38/0.56 ( d_Inj1
% 0.38/0.56 = ( d_In_rec
% 0.38/0.56 @ ^ [X0: $i,X1: $i > $i] : ( binunion @ ( d_Sing @ emptyset ) @ ( repl @ X0 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Inj0,type,
% 0.38/0.56 d_Inj0: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Inj0,definition,
% 0.38/0.56 ( d_Inj0
% 0.38/0.56 = ( ^ [X0: $i] : ( repl @ X0 @ d_Inj1 ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Unj,type,
% 0.38/0.56 d_Unj: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Unj,definition,
% 0.38/0.56 ( d_Unj
% 0.38/0.56 = ( d_In_rec
% 0.38/0.56 @ ^ [X0: $i] : ( repl @ ( setminus @ X0 @ ( d_Sing @ emptyset ) ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_pair,type,
% 0.38/0.56 pair: $i > $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_pair,definition,
% 0.38/0.56 ( pair
% 0.38/0.56 = ( ^ [X0: $i,X1: $i] : ( binunion @ ( repl @ X0 @ d_Inj0 ) @ ( repl @ X1 @ d_Inj1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_proj0,type,
% 0.38/0.56 proj0: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_proj0,definition,
% 0.38/0.56 ( proj0
% 0.38/0.56 = ( ^ [X0: $i] :
% 0.38/0.56 ( d_ReplSep @ X0
% 0.38/0.56 @ ^ [X1: $i] :
% 0.38/0.56 ? [X2: $i] :
% 0.38/0.56 ( ( d_Inj0 @ X2 )
% 0.38/0.56 = X1 )
% 0.38/0.56 @ d_Unj ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_proj1,type,
% 0.38/0.56 proj1: $i > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_proj1,definition,
% 0.38/0.56 ( proj1
% 0.38/0.56 = ( ^ [X0: $i] :
% 0.38/0.56 ( d_ReplSep @ X0
% 0.38/0.56 @ ^ [X1: $i] :
% 0.38/0.56 ? [X2: $i] :
% 0.38/0.56 ( ( d_Inj1 @ X2 )
% 0.38/0.56 = X1 )
% 0.38/0.56 @ d_Unj ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(proj0_pair_eq,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i] :
% 0.38/0.56 ( ( proj0 @ ( pair @ X0 @ X1 ) )
% 0.38/0.56 = X0 ) ).
% 0.38/0.56
% 0.38/0.56 thf(proj1_pair_eq,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i] :
% 0.38/0.56 ( ( proj1 @ ( pair @ X0 @ X1 ) )
% 0.38/0.56 = X1 ) ).
% 0.38/0.56
% 0.38/0.56 thf(typ_d_Sigma,type,
% 0.38/0.56 d_Sigma: $i > ( $i > $i ) > $i ).
% 0.38/0.56
% 0.38/0.56 thf(def_d_Sigma,definition,
% 0.38/0.56 ( d_Sigma
% 0.38/0.56 = ( ^ [X0: $i,X1: $i > $i] :
% 0.38/0.56 ( famunion @ X0
% 0.38/0.56 @ ^ [X2: $i] : ( repl @ ( X1 @ X2 ) @ ( pair @ X2 ) ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(pair_Sigma,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.38/0.56 ( ( in @ X2 @ X0 )
% 0.38/0.56 => ! [X3: $i] :
% 0.38/0.56 ( ( in @ X3 @ ( X1 @ X2 ) )
% 0.38/0.56 => ( in @ ( pair @ X2 @ X3 ) @ ( d_Sigma @ X0 @ X1 ) ) ) ) ).
% 0.38/0.56
% 0.38/0.56 thf(k_Sigma_eta_proj0_proj1,axiom,
% 0.38/0.56 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.38/0.56 ( ( in @ X2 @ ( d_Sigma @ X0 @ X1 ) )
% 0.38/0.56 => ( ( ( pair @ ( proj0 @ X2 ) @ ( proj1 @ X2 ) )
% 0.38/0.56 = X2 )
% 0.38/0.56 & ( in @ ( proj0 @ X2 ) @ X0 )
% 0.38/0.56 & ( in @ ( proj1 @ X2 ) @ ( X1 @ ( proj0 @ X2 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(proj_Sigma_eta,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.39/0.56 ( ( in @ X2 @ ( d_Sigma @ X0 @ X1 ) )
% 0.39/0.56 => ( ( pair @ ( proj0 @ X2 ) @ ( proj1 @ X2 ) )
% 0.39/0.56 = X2 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(proj0_Sigma,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.39/0.56 ( ( in @ X2 @ ( d_Sigma @ X0 @ X1 ) )
% 0.39/0.56 => ( in @ ( proj0 @ X2 ) @ X0 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(proj1_Sigma,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.39/0.56 ( ( in @ X2 @ ( d_Sigma @ X0 @ X1 ) )
% 0.39/0.56 => ( in @ ( proj1 @ X2 ) @ ( X1 @ ( proj0 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_setprod,type,
% 0.39/0.56 setprod: $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_setprod,definition,
% 0.39/0.56 ( setprod
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] :
% 0.39/0.56 ( d_Sigma @ X0
% 0.39/0.56 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ap,type,
% 0.39/0.56 ap: $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_ap,definition,
% 0.39/0.56 ( ap
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] :
% 0.39/0.56 ( d_ReplSep @ X0
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ? [X3: $i] :
% 0.39/0.56 ( X2
% 0.39/0.56 = ( pair @ X1 @ X3 ) )
% 0.39/0.56 @ proj1 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(beta,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.39/0.56 ( ( in @ X2 @ X0 )
% 0.39/0.56 => ( ( ap @ ( d_Sigma @ X0 @ X1 ) @ X2 )
% 0.39/0.56 = ( X1 @ X2 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_pair_p,type,
% 0.39/0.56 pair_p: $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_pair_p,definition,
% 0.39/0.56 ( pair_p
% 0.39/0.56 = ( ^ [X0: $i] :
% 0.39/0.56 ( ( pair @ ( ap @ X0 @ emptyset ) @ ( ap @ X0 @ ( ordsucc @ emptyset ) ) )
% 0.39/0.56 = X0 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_Pi,type,
% 0.39/0.56 d_Pi: $i > ( $i > $i ) > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_Pi,definition,
% 0.39/0.56 ( d_Pi
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i] :
% 0.39/0.56 ( d_Sep
% 0.39/0.56 @ ( power
% 0.39/0.56 @ ( d_Sigma @ X0
% 0.39/0.56 @ ^ [X2: $i] : ( union @ ( X1 @ X2 ) ) ) )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ! [X3: $i] :
% 0.39/0.56 ( ( in @ X3 @ X0 )
% 0.39/0.56 => ( in @ ( ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(lam_Pi,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $i,X2: $i > $i] :
% 0.39/0.56 ( ! [X3: $i] :
% 0.39/0.56 ( ( in @ X3 @ X0 )
% 0.39/0.56 => ( in @ ( X2 @ X3 ) @ ( X1 @ X3 ) ) )
% 0.39/0.56 => ( in @ ( d_Sigma @ X0 @ X2 ) @ ( d_Pi @ X0 @ X1 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(ap_Pi,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $i,X2: $i,X3: $i] :
% 0.39/0.56 ( ( in @ X2 @ ( d_Pi @ X0 @ X1 ) )
% 0.39/0.56 => ( ( in @ X3 @ X0 )
% 0.39/0.56 => ( in @ ( ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(k_Pi_ext,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.39/0.56 ( ( in @ X2 @ ( d_Pi @ X0 @ X1 ) )
% 0.39/0.56 => ! [X3: $i] :
% 0.39/0.56 ( ( in @ X3 @ ( d_Pi @ X0 @ X1 ) )
% 0.39/0.56 => ( ! [X4: $i] :
% 0.39/0.56 ( ( in @ X4 @ X0 )
% 0.39/0.56 => ( ( ap @ X2 @ X4 )
% 0.39/0.56 = ( ap @ X3 @ X4 ) ) )
% 0.39/0.56 => ( X2 = X3 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(xi_ext,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $i,X2: $i > $i] :
% 0.39/0.56 ( ! [X3: $i] :
% 0.39/0.56 ( ( in @ X3 @ X0 )
% 0.39/0.56 => ( ( X1 @ X3 )
% 0.39/0.56 = ( X2 @ X3 ) ) )
% 0.39/0.56 => ( ( d_Sigma @ X0 @ X1 )
% 0.39/0.56 = ( d_Sigma @ X0 @ X2 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(k_If_In_01,axiom,
% 0.39/0.56 ! [X0: $o,X1: $i,X2: $i] :
% 0.39/0.56 ( ( X0
% 0.39/0.56 => ( in @ X1 @ X2 ) )
% 0.39/0.56 => ( in @ ( if @ X0 @ X1 @ emptyset ) @ ( if @ X0 @ X2 @ ( ordsucc @ emptyset ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(k_If_In_then_E,axiom,
% 0.39/0.56 ! [X0: $o,X1: $i,X2: $i,X3: $i] :
% 0.39/0.56 ( X0
% 0.39/0.56 => ( ( in @ X1 @ ( if @ X0 @ X2 @ X3 ) )
% 0.39/0.56 => ( in @ X1 @ X2 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_imp,type,
% 0.39/0.56 imp: $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_imp,definition,
% 0.39/0.56 ( imp
% 0.39/0.56 = ( ^ [X0: $o,X1: $o] :
% 0.39/0.56 ( X0
% 0.39/0.56 => X1 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_not,type,
% 0.39/0.56 d_not: $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_not,definition,
% 0.39/0.56 ( d_not
% 0.39/0.56 = ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_wel,type,
% 0.39/0.56 wel: $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_wel,definition,
% 0.39/0.56 ( wel
% 0.39/0.56 = ( ^ [X0: $o] : ( d_not @ ( d_not @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(l_et,axiom,
% 0.39/0.56 ! [X0: $o] :
% 0.39/0.56 ( ( wel @ X0 )
% 0.39/0.56 => X0 ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_obvious,type,
% 0.39/0.56 obvious: $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_obvious,definition,
% 0.39/0.56 ( obvious
% 0.39/0.56 = ( imp @ $false @ $false ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_l_ec,type,
% 0.39/0.56 l_ec: $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_l_ec,definition,
% 0.39/0.56 ( l_ec
% 0.39/0.56 = ( ^ [X0: $o,X1: $o] : ( imp @ X0 @ ( d_not @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_and,type,
% 0.39/0.56 d_and: $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_and,definition,
% 0.39/0.56 ( d_and
% 0.39/0.56 = ( ^ [X0: $o,X1: $o] : ( d_not @ ( l_ec @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_l_or,type,
% 0.39/0.56 l_or: $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_l_or,definition,
% 0.39/0.56 ( l_or
% 0.39/0.56 = ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_orec,type,
% 0.39/0.56 orec: $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_orec,definition,
% 0.39/0.56 ( orec
% 0.39/0.56 = ( ^ [X0: $o,X1: $o] : ( d_and @ ( l_or @ X0 @ X1 ) @ ( l_ec @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_l_iff,type,
% 0.39/0.56 l_iff: $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_l_iff,definition,
% 0.39/0.56 ( l_iff
% 0.39/0.56 = ( ^ [X0: $o,X1: $o] : ( d_and @ ( imp @ X0 @ X1 ) @ ( imp @ X1 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_all,type,
% 0.39/0.56 all: $i > ( $i > $o ) > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_all,definition,
% 0.39/0.56 ( all
% 0.39/0.56 = ( ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_non,type,
% 0.39/0.56 non: $i > ( $i > $o ) > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_non,definition,
% 0.39/0.56 ( non
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_l_some,type,
% 0.39/0.56 l_some: $i > ( $i > $o ) > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_l_some,definition,
% 0.39/0.56 ( l_some
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( d_not
% 0.39/0.56 @ ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ( non @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_or3,type,
% 0.39/0.56 or3: $o > $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_or3,definition,
% 0.39/0.56 ( or3
% 0.39/0.56 = ( ^ [X0: $o,X1: $o,X2: $o] : ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_and3,type,
% 0.39/0.56 and3: $o > $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_and3,definition,
% 0.39/0.56 ( and3
% 0.39/0.56 = ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ec3,type,
% 0.39/0.56 ec3: $o > $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_ec3,definition,
% 0.39/0.56 ( ec3
% 0.39/0.56 = ( ^ [X0: $o,X1: $o,X2: $o] : ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_orec3,type,
% 0.39/0.56 orec3: $o > $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_orec3,definition,
% 0.39/0.56 ( orec3
% 0.39/0.56 = ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_e_is,type,
% 0.39/0.56 e_is: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_e_is,definition,
% 0.39/0.56 ( e_is
% 0.39/0.56 = ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(refis,axiom,
% 0.39/0.56 ! [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ X0 )
% 0.39/0.56 @ ^ [X1: $i] : ( e_is @ X0 @ X1 @ X1 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(e_isp,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X3: $i] : ( in @ X3 @ X0 )
% 0.39/0.56 @ ^ [X3: $i] :
% 0.39/0.56 ( ( X1 @ X2 )
% 0.39/0.56 => ( ( e_is @ X0 @ X2 @ X3 )
% 0.39/0.56 => ( X1 @ X3 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_amone,type,
% 0.39/0.56 amone: $i > ( $i > $o ) > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_amone,definition,
% 0.39/0.56 ( amone
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X3: $i] : ( in @ X3 @ X0 )
% 0.39/0.56 @ ^ [X3: $i] :
% 0.39/0.56 ( ( X1 @ X2 )
% 0.39/0.56 => ( ( X1 @ X3 )
% 0.39/0.56 => ( e_is @ X0 @ X2 @ X3 ) ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_one,type,
% 0.39/0.56 one: $i > ( $i > $o ) > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_one,definition,
% 0.39/0.56 ( one
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $o] : ( d_and @ ( amone @ X0 @ X1 ) @ ( l_some @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ind,type,
% 0.39/0.56 ind: $i > ( $i > $o ) > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_ind,definition,
% 0.39/0.56 ( ind
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( eps
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( ( in @ X2 @ X0 )
% 0.39/0.56 & ( X1 @ X2 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(ind_p,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( ( one @ X0 @ X1 )
% 0.39/0.56 => ( is_of @ ( ind @ X0 @ X1 )
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(oneax,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( ( one @ X0 @ X1 )
% 0.39/0.56 => ( X1 @ ( ind @ X0 @ X1 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_injective,type,
% 0.39/0.56 injective: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_injective,definition,
% 0.39/0.56 ( injective
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.39/0.56 ( all @ X0
% 0.39/0.56 @ ^ [X3: $i] :
% 0.39/0.56 ( all @ X0
% 0.39/0.56 @ ^ [X4: $i] : ( imp @ ( e_is @ X1 @ ( ap @ X2 @ X3 ) @ ( ap @ X2 @ X4 ) ) @ ( e_is @ X0 @ X3 @ X4 ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_image,type,
% 0.39/0.56 image: $i > $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_image,definition,
% 0.39/0.56 ( image
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
% 0.39/0.56 ( l_some @ X0
% 0.39/0.56 @ ^ [X4: $i] : ( e_is @ X1 @ X3 @ ( ap @ X2 @ X4 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_tofs,type,
% 0.39/0.56 tofs: $i > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_tofs,definition,
% 0.39/0.56 ( tofs
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ap ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_soft,type,
% 0.39/0.56 soft: $i > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_soft,definition,
% 0.39/0.56 ( soft
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
% 0.39/0.56 ( ind @ X0
% 0.39/0.56 @ ^ [X4: $i] : ( e_is @ X1 @ X3 @ ( ap @ X2 @ X4 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_inverse,type,
% 0.39/0.56 inverse: $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_inverse,definition,
% 0.39/0.56 ( inverse
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.39/0.56 ( d_Sigma @ X1
% 0.39/0.56 @ ^ [X3: $i] : ( if @ ( image @ X0 @ X1 @ X2 @ X3 ) @ ( soft @ X0 @ X1 @ X2 @ X3 ) @ emptyset ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_surjective,type,
% 0.39/0.56 surjective: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_surjective,definition,
% 0.39/0.56 ( surjective
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] : ( all @ X1 @ ( image @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_bijective,type,
% 0.39/0.56 bijective: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_bijective,definition,
% 0.39/0.56 ( bijective
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] : ( d_and @ ( injective @ X0 @ X1 @ X2 ) @ ( surjective @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_invf,type,
% 0.39/0.56 invf: $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_invf,definition,
% 0.39/0.56 ( invf
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] : ( d_Sigma @ X1 @ ( soft @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_inj_h,type,
% 0.39/0.56 inj_h: $i > $i > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_inj_h,definition,
% 0.39/0.56 ( inj_h
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
% 0.39/0.56 ( d_Sigma @ X0
% 0.39/0.56 @ ^ [X5: $i] : ( ap @ X4 @ ( ap @ X3 @ X5 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(e_fisi,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( in @ X2
% 0.39/0.56 @ ( d_Pi @ X0
% 0.39/0.56 @ ^ [X3: $i] : X1 ) )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X3: $i] :
% 0.39/0.56 ( in @ X3
% 0.39/0.56 @ ( d_Pi @ X0
% 0.39/0.56 @ ^ [X4: $i] : X1 ) )
% 0.39/0.56 @ ^ [X3: $i] :
% 0.39/0.56 ( ( all_of
% 0.39/0.56 @ ^ [X4: $i] : ( in @ X4 @ X0 )
% 0.39/0.56 @ ^ [X4: $i] : ( e_is @ X1 @ ( ap @ X2 @ X4 ) @ ( ap @ X3 @ X4 ) ) )
% 0.39/0.56 => ( e_is
% 0.39/0.56 @ ( d_Pi @ X0
% 0.39/0.56 @ ^ [X4: $i] : X1 )
% 0.39/0.56 @ X2
% 0.39/0.56 @ X3 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_e_in,type,
% 0.39/0.56 e_in: $i > ( $i > $o ) > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_e_in,definition,
% 0.39/0.56 ( e_in
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $o,X2: $i] : X2 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(e_in_p,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( is_of @ ( e_in @ X0 @ X1 @ X2 )
% 0.39/0.56 @ ^ [X3: $i] : ( in @ X3 @ X0 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(e_inp,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.39/0.56 @ ^ [X2: $i] : ( X1 @ ( e_in @ X0 @ X1 @ X2 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(otax1,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] : ( injective @ ( d_Sep @ X0 @ X1 ) @ X0 @ ( d_Sigma @ ( d_Sep @ X0 @ X1 ) @ ( e_in @ X0 @ X1 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(otax2,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( ( X1 @ X2 )
% 0.39/0.56 => ( image @ ( d_Sep @ X0 @ X1 ) @ X0 @ ( d_Sigma @ ( d_Sep @ X0 @ X1 ) @ ( e_in @ X0 @ X1 ) ) @ X2 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_out,type,
% 0.39/0.56 out: $i > ( $i > $o ) > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_out,definition,
% 0.39/0.56 ( out
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $o] : ( soft @ ( d_Sep @ X0 @ X1 ) @ X0 @ ( d_Sigma @ ( d_Sep @ X0 @ X1 ) @ ( e_in @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_pair,type,
% 0.39/0.56 d_pair: $i > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_pair,definition,
% 0.39/0.56 ( d_pair
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : pair ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(e_pair_p,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X3: $i] : ( in @ X3 @ X1 )
% 0.39/0.56 @ ^ [X3: $i] :
% 0.39/0.56 ( is_of @ ( d_pair @ X0 @ X1 @ X2 @ X3 )
% 0.39/0.56 @ ^ [X4: $i] : ( in @ X4 @ ( setprod @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_first,type,
% 0.39/0.56 first: $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_first,definition,
% 0.39/0.56 ( first
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : proj0 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(first_p,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ ( setprod @ X0 @ X1 ) )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( is_of @ ( first @ X0 @ X1 @ X2 )
% 0.39/0.56 @ ^ [X3: $i] : ( in @ X3 @ X0 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_second,type,
% 0.39/0.56 second: $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_second,definition,
% 0.39/0.56 ( second
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : proj1 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(second_p,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ ( setprod @ X0 @ X1 ) )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( is_of @ ( second @ X0 @ X1 @ X2 )
% 0.39/0.56 @ ^ [X3: $i] : ( in @ X3 @ X1 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(pairis1,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ ( setprod @ X0 @ X1 ) )
% 0.39/0.56 @ ^ [X2: $i] : ( e_is @ ( setprod @ X0 @ X1 ) @ ( d_pair @ X0 @ X1 @ ( first @ X0 @ X1 @ X2 ) @ ( second @ X0 @ X1 @ X2 ) ) @ X2 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(firstis1,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X3: $i] : ( in @ X3 @ X1 )
% 0.39/0.56 @ ^ [X3: $i] : ( e_is @ X0 @ ( first @ X0 @ X1 @ ( d_pair @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(secondis1,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X3: $i] : ( in @ X3 @ X1 )
% 0.39/0.56 @ ^ [X3: $i] : ( e_is @ X1 @ ( second @ X0 @ X1 @ ( d_pair @ X0 @ X1 @ X2 @ X3 ) ) @ X3 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_prop1,type,
% 0.39/0.56 prop1: $o > $i > $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_prop1,definition,
% 0.39/0.56 ( prop1
% 0.39/0.56 = ( ^ [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 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ite,type,
% 0.39/0.56 ite: $o > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_ite,definition,
% 0.39/0.56 ( ite
% 0.39/0.56 = ( ^ [X0: $o,X1: $i,X2: $i,X3: $i] : ( ind @ X1 @ ( prop1 @ X0 @ X1 @ X2 @ X3 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_wissel_wa,type,
% 0.39/0.56 wissel_wa: $i > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_wissel_wa,definition,
% 0.39/0.56 ( wissel_wa
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] : ( ite @ ( e_is @ X0 @ X3 @ X1 ) @ X0 @ X2 @ X3 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_wissel_wb,type,
% 0.39/0.56 wissel_wb: $i > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_wissel_wb,definition,
% 0.39/0.56 ( wissel_wb
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] : ( ite @ ( e_is @ X0 @ X3 @ X2 ) @ X0 @ X1 @ ( wissel_wa @ X0 @ X1 @ X2 @ X3 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_wissel,type,
% 0.39/0.56 wissel: $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_wissel,definition,
% 0.39/0.56 ( wissel
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] : ( d_Sigma @ X0 @ ( wissel_wb @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_changef,type,
% 0.39/0.56 changef: $i > $i > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_changef,definition,
% 0.39/0.56 ( changef
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
% 0.39/0.56 ( d_Sigma @ X0
% 0.39/0.56 @ ^ [X5: $i] : ( ap @ X2 @ ( ap @ ( wissel @ X0 @ X3 @ X4 ) @ X5 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_r_ec,type,
% 0.39/0.56 r_ec: $o > $o > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_r_ec,definition,
% 0.39/0.56 ( r_ec
% 0.39/0.56 = ( ^ [X0: $o,X1: $o] :
% 0.39/0.56 ( X0
% 0.39/0.56 => ( d_not @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_esti,type,
% 0.39/0.56 esti: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_esti,definition,
% 0.39/0.56 ( esti
% 0.39/0.56 = ( ^ [X0: $i] : in ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(setof_p,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( is_of @ ( d_Sep @ X0 @ X1 )
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ ( power @ X0 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(estii,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( ( X1 @ X2 )
% 0.39/0.56 => ( esti @ X0 @ X2 @ ( d_Sep @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(estie,axiom,
% 0.39/0.56 ! [X0: $i,X1: $i > $o] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( ( esti @ X0 @ X2 @ ( d_Sep @ X0 @ X1 ) )
% 0.39/0.56 => ( X1 @ X2 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_empty,type,
% 0.39/0.56 empty: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_empty,definition,
% 0.39/0.56 ( empty
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ X0 )
% 0.39/0.56 @ ( non @ X0
% 0.39/0.56 @ ^ [X2: $i] : ( esti @ X0 @ X2 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_nonempty,type,
% 0.39/0.56 nonempty: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_nonempty,definition,
% 0.39/0.56 ( nonempty
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] :
% 0.39/0.56 ( l_some @ X0
% 0.39/0.56 @ ^ [X2: $i] : ( esti @ X0 @ X2 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_incl,type,
% 0.39/0.56 incl: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_incl,definition,
% 0.39/0.56 ( incl
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.39/0.56 ( all @ X0
% 0.39/0.56 @ ^ [X3: $i] : ( imp @ ( esti @ X0 @ X3 @ X1 ) @ ( esti @ X0 @ X3 @ X2 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_st_disj,type,
% 0.39/0.56 st_disj: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_st_disj,definition,
% 0.39/0.56 ( st_disj
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.39/0.56 ( all @ X0
% 0.39/0.56 @ ^ [X3: $i] : ( l_ec @ ( esti @ X0 @ X3 @ X1 ) @ ( esti @ X0 @ X3 @ X2 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(isseti,axiom,
% 0.39/0.56 ! [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ ( power @ X0 ) )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ ( power @ X0 ) )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( ( incl @ X0 @ X1 @ X2 )
% 0.39/0.56 => ( ( incl @ X0 @ X2 @ X1 )
% 0.39/0.56 => ( e_is @ ( power @ X0 ) @ X1 @ X2 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_nissetprop,type,
% 0.39/0.56 nissetprop: $i > $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_nissetprop,definition,
% 0.39/0.56 ( nissetprop
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] : ( d_and @ ( esti @ X0 @ X3 @ X1 ) @ ( d_not @ ( esti @ X0 @ X3 @ X2 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_unmore,type,
% 0.39/0.56 unmore: $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_unmore,definition,
% 0.39/0.56 ( unmore
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.39/0.56 ( d_Sep @ X0
% 0.39/0.56 @ ^ [X3: $i] :
% 0.39/0.56 ( l_some @ X1
% 0.39/0.56 @ ^ [X4: $i] : ( esti @ X0 @ X3 @ ( ap @ X2 @ X4 ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ecelt,type,
% 0.39/0.56 ecelt: $i > ( $i > $i > $o ) > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_ecelt,definition,
% 0.39/0.56 ( ecelt
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i] : ( d_Sep @ X0 @ ( X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ecp,type,
% 0.39/0.56 ecp: $i > ( $i > $i > $o ) > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_ecp,definition,
% 0.39/0.56 ( ecp
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] : ( e_is @ ( power @ X0 ) @ X2 @ ( ecelt @ X0 @ X1 @ X3 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_anec,type,
% 0.39/0.56 anec: $i > ( $i > $i > $o ) > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_anec,definition,
% 0.39/0.56 ( anec
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i] : ( l_some @ X0 @ ( ecp @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ect,type,
% 0.39/0.56 ect: $i > ( $i > $i > $o ) > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_ect,definition,
% 0.39/0.56 ( ect
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o] : ( d_Sep @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ectset,type,
% 0.39/0.56 ectset: $i > ( $i > $i > $o ) > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_ectset,definition,
% 0.39/0.56 ( ectset
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o] : ( out @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ectelt,type,
% 0.39/0.56 ectelt: $i > ( $i > $i > $o ) > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_ectelt,definition,
% 0.39/0.56 ( ectelt
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i] : ( ectset @ X0 @ X1 @ ( ecelt @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_ecect,type,
% 0.39/0.56 ecect: $i > ( $i > $i > $o ) > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_ecect,definition,
% 0.39/0.56 ( ecect
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o] : ( e_in @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_fixfu,type,
% 0.39/0.56 fixfu: $i > ( $i > $i > $o ) > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_fixfu,definition,
% 0.39/0.56 ( fixfu
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X4: $i] : ( in @ X4 @ X0 )
% 0.39/0.56 @ ^ [X4: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X5: $i] : ( in @ X5 @ X0 )
% 0.39/0.56 @ ^ [X5: $i] :
% 0.39/0.56 ( ( X1 @ X4 @ X5 )
% 0.39/0.56 => ( e_is @ X2 @ ( ap @ X3 @ X4 ) @ ( ap @ X3 @ X5 ) ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_10_prop1,type,
% 0.39/0.56 d_10_prop1: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_10_prop1,definition,
% 0.39/0.56 ( d_10_prop1
% 0.39/0.56 = ( ^ [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 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_prop2,type,
% 0.39/0.56 prop2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_prop2,definition,
% 0.39/0.56 ( prop2
% 0.39/0.56 = ( ^ [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 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_indeq,type,
% 0.39/0.56 indeq: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_indeq,definition,
% 0.39/0.56 ( indeq
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] : ( ind @ X2 @ ( prop2 @ X0 @ X1 @ X2 @ X3 @ X4 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_fixfu2,type,
% 0.39/0.56 fixfu2: $i > ( $i > $i > $o ) > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_fixfu2,definition,
% 0.39/0.56 ( fixfu2
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X4: $i] : ( in @ X4 @ X0 )
% 0.39/0.56 @ ^ [X4: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X5: $i] : ( in @ X5 @ X0 )
% 0.39/0.56 @ ^ [X5: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X6: $i] : ( in @ X6 @ X0 )
% 0.39/0.56 @ ^ [X6: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X7: $i] : ( in @ X7 @ X0 )
% 0.39/0.56 @ ^ [X7: $i] :
% 0.39/0.56 ( ( X1 @ X4 @ X5 )
% 0.39/0.56 => ( ( X1 @ X6 @ X7 )
% 0.39/0.56 => ( e_is @ X2 @ ( ap @ ( ap @ X3 @ X4 ) @ X6 ) @ ( ap @ ( ap @ X3 @ X5 ) @ X7 ) ) ) ) ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_11_i,type,
% 0.39/0.56 d_11_i: $i > ( $i > $i > $o ) > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_11_i,definition,
% 0.39/0.56 ( d_11_i
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i] :
% 0.39/0.56 ( indeq @ X0 @ X1
% 0.39/0.56 @ ( d_Pi @ X0
% 0.39/0.56 @ ^ [X3: $i] : X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_indeq2,type,
% 0.39/0.56 indeq2: $i > ( $i > $i > $o ) > $i > $i > $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_indeq2,definition,
% 0.39/0.56 ( indeq2
% 0.39/0.56 = ( ^ [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] : ( indeq @ X0 @ X1 @ X2 @ ( d_11_i @ X0 @ X1 @ X2 @ X3 @ X4 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_nat,type,
% 0.39/0.56 nat: $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_nat,definition,
% 0.39/0.56 ( nat
% 0.39/0.56 = ( d_Sep @ omega
% 0.39/0.56 @ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_n_is,type,
% 0.39/0.56 n_is: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_n_is,definition,
% 0.39/0.56 ( n_is
% 0.39/0.56 = ( e_is @ nat ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_nis,type,
% 0.39/0.56 nis: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_nis,definition,
% 0.39/0.56 ( nis
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_n_in,type,
% 0.39/0.56 n_in: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_n_in,definition,
% 0.39/0.56 ( n_in
% 0.39/0.56 = ( esti @ nat ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_n_some,type,
% 0.39/0.56 n_some: ( $i > $o ) > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_n_some,definition,
% 0.39/0.56 ( n_some
% 0.39/0.56 = ( l_some @ nat ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_n_all,type,
% 0.39/0.56 n_all: ( $i > $o ) > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_n_all,definition,
% 0.39/0.56 ( n_all
% 0.39/0.56 = ( all @ nat ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_n_one,type,
% 0.39/0.56 n_one: ( $i > $o ) > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_n_one,definition,
% 0.39/0.56 ( n_one
% 0.39/0.56 = ( one @ nat ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_n_1,type,
% 0.39/0.56 n_1: $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_n_1,definition,
% 0.39/0.56 ( n_1
% 0.39/0.56 = ( ordsucc @ emptyset ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(n_1_p,axiom,
% 0.39/0.56 ( is_of @ n_1
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(suc_p,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( is_of @ ( ordsucc @ X0 )
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(n_ax3,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] : ( nis @ ( ordsucc @ X0 ) @ n_1 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(n_ax4,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( n_is @ ( ordsucc @ X0 ) @ ( ordsucc @ X1 ) )
% 0.39/0.56 => ( n_is @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_cond1,type,
% 0.39/0.56 cond1: $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_cond1,definition,
% 0.39/0.56 ( cond1
% 0.39/0.56 = ( n_in @ n_1 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_cond2,type,
% 0.39/0.56 cond2: $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_cond2,definition,
% 0.39/0.56 ( cond2
% 0.39/0.56 = ( ^ [X0: $i] :
% 0.39/0.56 ( n_all
% 0.39/0.56 @ ^ [X1: $i] : ( imp @ ( n_in @ X1 @ X0 ) @ ( n_in @ ( ordsucc @ X1 ) @ X0 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(n_ax5,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ ( power @ nat ) )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( ( cond1 @ X0 )
% 0.39/0.56 => ( ( cond2 @ X0 )
% 0.39/0.56 => ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( n_in @ X1 @ X0 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_i1_s,type,
% 0.39/0.56 i1_s: ( $i > $o ) > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_i1_s,definition,
% 0.39/0.56 ( i1_s
% 0.39/0.56 = ( d_Sep @ nat ) ) ).
% 0.39/0.56
% 0.39/0.56 %------------------------------------------------------------------------------
% 0.39/0.56 %------------------------------------------------------------------------------
% 0.39/0.56 thf(satz1,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( nis @ X0 @ X1 )
% 0.39/0.56 => ( nis @ ( ordsucc @ X0 ) @ ( ordsucc @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_22_prop1,type,
% 0.39/0.56 d_22_prop1: $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_22_prop1,definition,
% 0.39/0.56 ( d_22_prop1
% 0.39/0.56 = ( ^ [X0: $i] : ( nis @ ( ordsucc @ X0 ) @ X0 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz2,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] : ( nis @ ( ordsucc @ X0 ) @ X0 ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_23_prop1,type,
% 0.39/0.56 d_23_prop1: $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_23_prop1,definition,
% 0.39/0.56 ( d_23_prop1
% 0.39/0.56 = ( ^ [X0: $i] :
% 0.39/0.56 ( l_or @ ( n_is @ X0 @ n_1 )
% 0.39/0.56 @ ( n_some
% 0.39/0.56 @ ^ [X1: $i] : ( n_is @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz3,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( ( nis @ X0 @ n_1 )
% 0.39/0.56 => ( n_some
% 0.39/0.56 @ ^ [X1: $i] : ( n_is @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz3a,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( ( nis @ X0 @ n_1 )
% 0.39/0.56 => ( n_one
% 0.39/0.56 @ ^ [X1: $i] : ( n_is @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_24_prop1,type,
% 0.39/0.56 d_24_prop1: $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_24_prop1,definition,
% 0.39/0.56 ( d_24_prop1
% 0.39/0.56 = ( ^ [X0: $i] :
% 0.39/0.56 ( n_all
% 0.39/0.56 @ ^ [X1: $i] : ( n_is @ ( ap @ X0 @ ( ordsucc @ X1 ) ) @ ( ordsucc @ ( ap @ X0 @ X1 ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_24_prop2,type,
% 0.39/0.56 d_24_prop2: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_24_prop2,definition,
% 0.39/0.56 ( d_24_prop2
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ( d_and @ ( n_is @ ( ap @ X1 @ n_1 ) @ ( ordsucc @ X0 ) ) @ ( d_24_prop1 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_prop3,type,
% 0.39/0.56 prop3: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_prop3,definition,
% 0.39/0.56 ( prop3
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ ( ap @ X0 @ X2 ) @ ( ap @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_prop4,type,
% 0.39/0.56 prop4: $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_prop4,definition,
% 0.39/0.56 ( prop4
% 0.39/0.56 = ( ^ [X0: $i] :
% 0.39/0.56 ( l_some
% 0.39/0.56 @ ( d_Pi @ nat
% 0.39/0.56 @ ^ [X1: $i] : nat )
% 0.39/0.56 @ ( d_24_prop2 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_24_g,type,
% 0.39/0.56 d_24_g: $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_24_g,definition,
% 0.39/0.56 ( d_24_g
% 0.39/0.56 = ( ^ [X0: $i] :
% 0.39/0.56 ( d_Sigma @ nat
% 0.39/0.56 @ ^ [X1: $i] : ( ordsucc @ ( ap @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz4,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( one
% 0.39/0.56 @ ( d_Pi @ nat
% 0.39/0.56 @ ^ [X1: $i] : nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( d_and @ ( n_is @ ( ap @ X1 @ n_1 ) @ ( ordsucc @ X0 ) )
% 0.39/0.56 @ ( n_all
% 0.39/0.56 @ ^ [X2: $i] : ( n_is @ ( ap @ X1 @ ( ordsucc @ X2 ) ) @ ( ordsucc @ ( ap @ X1 @ X2 ) ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_plus,type,
% 0.39/0.56 plus: $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_plus,definition,
% 0.39/0.56 ( plus
% 0.39/0.56 = ( ^ [X0: $i] :
% 0.39/0.56 ( ind
% 0.39/0.56 @ ( d_Pi @ nat
% 0.39/0.56 @ ^ [X1: $i] : nat )
% 0.39/0.56 @ ( d_24_prop2 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_n_pl,type,
% 0.39/0.56 n_pl: $i > $i > $i ).
% 0.39/0.56
% 0.39/0.56 thf(def_n_pl,definition,
% 0.39/0.56 ( n_pl
% 0.39/0.56 = ( ^ [X0: $i] : ( ap @ ( plus @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz4a,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] : ( n_is @ ( n_pl @ X0 @ n_1 ) @ ( ordsucc @ X0 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz4b,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( n_is @ ( n_pl @ X0 @ ( ordsucc @ X1 ) ) @ ( ordsucc @ ( n_pl @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz4c,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] : ( n_is @ ( n_pl @ n_1 @ X0 ) @ ( ordsucc @ X0 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz4d,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( n_is @ ( n_pl @ ( ordsucc @ X0 ) @ X1 ) @ ( ordsucc @ ( n_pl @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz4e,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] : ( n_is @ ( ordsucc @ X0 ) @ ( n_pl @ X0 @ n_1 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz4f,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( n_is @ ( ordsucc @ ( n_pl @ X0 @ X1 ) ) @ ( n_pl @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz4g,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] : ( n_is @ ( ordsucc @ X0 ) @ ( n_pl @ n_1 @ X0 ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz4h,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( n_is @ ( ordsucc @ ( n_pl @ X0 @ X1 ) ) @ ( n_pl @ ( ordsucc @ X0 ) @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_25_prop1,type,
% 0.39/0.56 d_25_prop1: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_25_prop1,definition,
% 0.39/0.56 ( d_25_prop1
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ ( n_pl @ ( n_pl @ X0 @ X1 ) @ X2 ) @ ( n_pl @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz5,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ nat )
% 0.39/0.56 @ ^ [X2: $i] : ( n_is @ ( n_pl @ ( n_pl @ X0 @ X1 ) @ X2 ) @ ( n_pl @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_26_prop1,type,
% 0.39/0.56 d_26_prop1: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_26_prop1,definition,
% 0.39/0.56 ( d_26_prop1
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz6,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_27_prop1,type,
% 0.39/0.56 d_27_prop1: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_27_prop1,definition,
% 0.39/0.56 ( d_27_prop1
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ( nis @ X1 @ ( n_pl @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz7,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( nis @ X1 @ ( n_pl @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_28_prop1,type,
% 0.39/0.56 d_28_prop1: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_28_prop1,definition,
% 0.39/0.56 ( d_28_prop1
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] : ( nis @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz8,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ nat )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( ( nis @ X1 @ X2 )
% 0.39/0.56 => ( nis @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz8a,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X2: $i] : ( in @ X2 @ nat )
% 0.39/0.56 @ ^ [X2: $i] :
% 0.39/0.56 ( ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) )
% 0.39/0.56 => ( n_is @ X1 @ X2 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_diffprop,type,
% 0.39/0.56 diffprop: $i > $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_diffprop,definition,
% 0.39/0.56 ( diffprop
% 0.39/0.56 = ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz8b,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( amone @ nat
% 0.39/0.56 @ ^ [X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_29_ii,type,
% 0.39/0.56 d_29_ii: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_29_ii,definition,
% 0.39/0.56 ( d_29_ii
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_iii,type,
% 0.39/0.56 iii: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_iii,definition,
% 0.39/0.56 ( iii
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_d_29_prop1,type,
% 0.39/0.56 d_29_prop1: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_d_29_prop1,definition,
% 0.39/0.56 ( d_29_prop1
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ( or3 @ ( n_is @ X0 @ X1 ) @ ( d_29_ii @ X0 @ X1 ) @ ( iii @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz9,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( orec3 @ ( n_is @ X0 @ X1 )
% 0.39/0.56 @ ( n_some
% 0.39/0.56 @ ^ [X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) )
% 0.39/0.56 @ ( n_some
% 0.39/0.56 @ ^ [X2: $i] : ( n_is @ X1 @ ( n_pl @ X0 @ X2 ) ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz9a,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( or3 @ ( n_is @ X0 @ X1 ) @ ( n_some @ ( diffprop @ X0 @ X1 ) ) @ ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz9b,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( ec3 @ ( n_is @ X0 @ X1 ) @ ( n_some @ ( diffprop @ X0 @ X1 ) ) @ ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( orec3 @ ( n_is @ X0 @ X1 ) @ ( d_29_ii @ X0 @ X1 ) @ ( iii @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10a,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( or3 @ ( n_is @ X0 @ X1 ) @ ( d_29_ii @ X0 @ X1 ) @ ( iii @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10b,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] : ( ec3 @ ( n_is @ X0 @ X1 ) @ ( d_29_ii @ X0 @ X1 ) @ ( iii @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz11,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( d_29_ii @ X0 @ X1 )
% 0.39/0.56 => ( iii @ X1 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz12,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( iii @ X0 @ X1 )
% 0.39/0.56 => ( d_29_ii @ X1 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_moreis,type,
% 0.39/0.56 moreis: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_moreis,definition,
% 0.39/0.56 ( moreis
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(typ_lessis,type,
% 0.39/0.56 lessis: $i > $i > $o ).
% 0.39/0.56
% 0.39/0.56 thf(def_lessis,definition,
% 0.39/0.56 ( lessis
% 0.39/0.56 = ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz13,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( moreis @ X0 @ X1 )
% 0.39/0.56 => ( lessis @ X1 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz14,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( lessis @ X0 @ X1 )
% 0.39/0.56 => ( moreis @ X1 @ X0 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10c,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( moreis @ X0 @ X1 )
% 0.39/0.56 => ( d_not @ ( iii @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10d,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( lessis @ X0 @ X1 )
% 0.39/0.56 => ( d_not @ ( d_29_ii @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10e,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( d_not @ ( d_29_ii @ X0 @ X1 ) )
% 0.39/0.56 => ( lessis @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10f,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( d_not @ ( iii @ X0 @ X1 ) )
% 0.39/0.56 => ( moreis @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10g,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( d_29_ii @ X0 @ X1 )
% 0.39/0.56 => ( d_not @ ( lessis @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10h,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( iii @ X0 @ X1 )
% 0.39/0.56 => ( d_not @ ( moreis @ X0 @ X1 ) ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10j,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.56 ( ( d_not @ ( moreis @ X0 @ X1 ) )
% 0.39/0.56 => ( iii @ X0 @ X1 ) ) ) ) ).
% 0.39/0.56
% 0.39/0.56 thf(satz10k,axiom,
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.56 @ ^ [X0: $i] :
% 0.39/0.56 ( all_of
% 0.39/0.56 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.56 @ ^ [X1: $i] :
% 0.39/0.62 ( ( d_not @ ( lessis @ X0 @ X1 ) )
% 0.39/0.62 => ( d_29_ii @ X0 @ X1 ) ) ) ) ).
% 0.39/0.62
% 0.39/0.62 thf(satz15,axiom,
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.62 @ ^ [X0: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.62 @ ^ [X1: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X2: $i] : ( in @ X2 @ nat )
% 0.39/0.62 @ ^ [X2: $i] :
% 0.39/0.62 ( ( iii @ X0 @ X1 )
% 0.39/0.62 => ( ( iii @ X1 @ X2 )
% 0.39/0.62 => ( iii @ X0 @ X2 ) ) ) ) ) ) ).
% 0.39/0.62
% 0.39/0.62 thf(satz16a,axiom,
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.62 @ ^ [X0: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.62 @ ^ [X1: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X2: $i] : ( in @ X2 @ nat )
% 0.39/0.62 @ ^ [X2: $i] :
% 0.39/0.62 ( ( lessis @ X0 @ X1 )
% 0.39/0.62 => ( ( iii @ X1 @ X2 )
% 0.39/0.62 => ( iii @ X0 @ X2 ) ) ) ) ) ) ).
% 0.39/0.62
% 0.39/0.62 thf(satz16b,axiom,
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.62 @ ^ [X0: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.62 @ ^ [X1: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X2: $i] : ( in @ X2 @ nat )
% 0.39/0.62 @ ^ [X2: $i] :
% 0.39/0.62 ( ( iii @ X0 @ X1 )
% 0.39/0.62 => ( ( lessis @ X1 @ X2 )
% 0.39/0.62 => ( iii @ X0 @ X2 ) ) ) ) ) ) ).
% 0.39/0.62
% 0.39/0.62 thf(satz16c,axiom,
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.62 @ ^ [X0: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.62 @ ^ [X1: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X2: $i] : ( in @ X2 @ nat )
% 0.39/0.62 @ ^ [X2: $i] :
% 0.39/0.62 ( ( moreis @ X0 @ X1 )
% 0.39/0.62 => ( ( d_29_ii @ X1 @ X2 )
% 0.39/0.62 => ( d_29_ii @ X0 @ X2 ) ) ) ) ) ) ).
% 0.39/0.62
% 0.39/0.62 thf(satz16d,axiom,
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.62 @ ^ [X0: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.62 @ ^ [X1: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X2: $i] : ( in @ X2 @ nat )
% 0.39/0.62 @ ^ [X2: $i] :
% 0.39/0.62 ( ( d_29_ii @ X0 @ X1 )
% 0.39/0.62 => ( ( moreis @ X1 @ X2 )
% 0.39/0.62 => ( d_29_ii @ X0 @ X2 ) ) ) ) ) ) ).
% 0.39/0.62
% 0.39/0.62 thf(satz17,axiom,
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.62 @ ^ [X0: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.62 @ ^ [X1: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X2: $i] : ( in @ X2 @ nat )
% 0.39/0.62 @ ^ [X2: $i] :
% 0.39/0.62 ( ( lessis @ X0 @ X1 )
% 0.39/0.62 => ( ( lessis @ X1 @ X2 )
% 0.39/0.62 => ( lessis @ X0 @ X2 ) ) ) ) ) ) ).
% 0.39/0.62
% 0.39/0.62 thf(satz18,axiom,
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.62 @ ^ [X0: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.62 @ ^ [X1: $i] : ( d_29_ii @ ( n_pl @ X0 @ X1 ) @ X0 ) ) ) ).
% 0.39/0.62
% 0.39/0.62 thf(satz18a,axiom,
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.62 @ ^ [X0: $i] :
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X1: $i] : ( in @ X1 @ nat )
% 0.39/0.62 @ ^ [X1: $i] : ( iii @ X0 @ ( n_pl @ X0 @ X1 ) ) ) ) ).
% 0.39/0.62
% 0.39/0.62 thf(satz18b,conjecture,
% 0.39/0.62 ( all_of
% 0.39/0.62 @ ^ [X0: $i] : ( in @ X0 @ nat )
% 0.39/0.62 @ ^ [X0: $i] : ( d_29_ii @ ( ordsucc @ X0 ) @ X0 ) ) ).
% 0.39/0.62
% 0.39/0.62 %------------------------------------------------------------------------------
% 0.39/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.SJe5xAanoK/cvc5---1.0.5_27387.p...
% 0.39/0.62 (declare-sort $$unsorted 0)
% 0.39/0.62 (declare-fun tptp.is_of ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.39/0.62 (assert (= tptp.is_of (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ X1 X0))))
% 0.39/0.62 (declare-fun tptp.all_of ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.39/0.62 (assert (= tptp.all_of (lambda ((X0 (-> $$unsorted Bool)) (X1 (-> $$unsorted Bool))) (forall ((X2 $$unsorted)) (=> (@ (@ tptp.is_of X2) X0) (@ X1 X2))))))
% 0.39/0.62 (declare-fun tptp.eps ((-> $$unsorted Bool)) $$unsorted)
% 0.39/0.62 (declare-fun tptp.in ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (declare-fun tptp.d_Subq ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_Subq (lambda ((X0 $$unsorted) (X1 $$unsorted)) (forall ((X2 $$unsorted)) (let ((_let_1 (@ tptp.in X2))) (=> (@ _let_1 X0) (@ _let_1 X1)))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.d_Subq X0) X1) (=> (@ (@ tptp.d_Subq X1) X0) (= X0 X1)))))
% 0.39/0.62 (assert (forall ((X0 (-> $$unsorted Bool))) (=> (forall ((X1 $$unsorted)) (=> (forall ((X2 $$unsorted)) (=> (@ (@ tptp.in X2) X1) (@ X0 X2))) (@ X0 X1))) (forall ((X1 $$unsorted)) (@ X0 X1)))))
% 0.39/0.62 (declare-fun tptp.emptyset () $$unsorted)
% 0.39/0.62 (assert (not (exists ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.emptyset))))
% 0.39/0.62 (declare-fun tptp.union ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ (@ tptp.in X1) (@ tptp.union X0)) (exists ((X2 $$unsorted)) (and (@ (@ tptp.in X1) X2) (@ (@ tptp.in X2) X0))))))
% 0.39/0.62 (declare-fun tptp.power ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ (@ tptp.in X1) (@ tptp.power X0)) (@ (@ tptp.d_Subq X1) X0))))
% 0.39/0.62 (declare-fun tptp.repl ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (= (@ (@ tptp.in X2) (@ (@ tptp.repl X0) X1)) (exists ((X3 $$unsorted)) (and (@ (@ tptp.in X3) X0) (= X2 (@ X1 X3)))))))
% 0.39/0.62 (declare-fun tptp.d_Union_closed ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_Union_closed (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.in X1) X0) (@ (@ tptp.in (@ tptp.union X1)) X0))))))
% 0.39/0.62 (declare-fun tptp.d_Power_closed ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_Power_closed (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.in X1) X0) (@ (@ tptp.in (@ tptp.power X1)) X0))))))
% 0.39/0.62 (declare-fun tptp.d_Repl_closed ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_Repl_closed (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.in X1) X0) (forall ((X2 (-> $$unsorted $$unsorted))) (=> (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X1) (@ (@ tptp.in (@ X2 X3)) X0))) (@ (@ tptp.in (@ (@ tptp.repl X1) X2)) X0))))))))
% 0.39/0.62 (declare-fun tptp.d_ZF_closed ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_ZF_closed (lambda ((X0 $$unsorted)) (and (@ tptp.d_Union_closed X0) (@ tptp.d_Power_closed X0) (@ tptp.d_Repl_closed X0)))))
% 0.39/0.62 (declare-fun tptp.univof ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (forall ((X0 $$unsorted)) (@ (@ tptp.in X0) (@ tptp.univof X0))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted)) (@ tptp.d_ZF_closed (@ tptp.univof X0))))
% 0.39/0.62 (declare-fun tptp.if (Bool $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.if (lambda ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (@ tptp.eps (lambda ((X3 $$unsorted)) (or (and X0 (= X3 X1)) (and (not X0) (= X3 X2))))))))
% 0.39/0.62 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ (@ (@ tptp.if X0) X1) X2))) (or (and X0 (= _let_1 X1)) (and (not X0) (= _let_1 X2))))))
% 0.39/0.62 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (=> (not X0) (= (@ (@ (@ tptp.if X0) X1) X2) X2))))
% 0.39/0.62 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (=> X0 (= (@ (@ (@ tptp.if X0) X1) X2) X1))))
% 0.39/0.62 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ (@ (@ tptp.if X0) X1) X2))) (or (= _let_1 X1) (= _let_1 X2)))))
% 0.39/0.62 (declare-fun tptp.nIn ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.nIn (lambda ((X0 $$unsorted) (X1 $$unsorted)) (not (@ (@ tptp.in X0) X1)))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.in X1) (@ tptp.power X0)) (@ (@ tptp.d_Subq X1) X0))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.d_Subq X1) X0) (@ (@ tptp.in X1) (@ tptp.power X0)))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted)) (@ (@ tptp.in X0) (@ tptp.power X0))))
% 0.39/0.62 (declare-fun tptp.d_UPair ($$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_UPair (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.repl (@ tptp.power (@ tptp.power tptp.emptyset))) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.if (@ (@ tptp.in tptp.emptyset) X2)) X0) X1))))))
% 0.39/0.62 (declare-fun tptp.d_Sing ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_Sing (lambda ((X0 $$unsorted)) (@ (@ tptp.d_UPair X0) X0))))
% 0.39/0.62 (declare-fun tptp.binunion ($$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.binunion (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.union (@ (@ tptp.d_UPair X0) X1)))))
% 0.39/0.62 (declare-fun tptp.famunion ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.39/0.62 (assert (= tptp.famunion (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ tptp.union (@ (@ tptp.repl X0) X1)))))
% 0.39/0.62 (declare-fun tptp.d_Sep ($$unsorted (-> $$unsorted Bool)) $$unsorted)
% 0.39/0.62 (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 $$unsorted)) (and (@ (@ tptp.in X3) X0) (@ X1 X3)))))))) tptp.emptyset))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (let ((_let_1 (@ tptp.in X2))) (=> (@ _let_1 X0) (=> (@ X1 X2) (@ _let_1 (@ (@ tptp.d_Sep X0) X1)))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (let ((_let_1 (@ tptp.in X2))) (=> (@ _let_1 (@ (@ tptp.d_Sep X0) X1)) (@ _let_1 X0)))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sep X0) X1)) (@ X1 X2))))
% 0.39/0.62 (declare-fun tptp.d_ReplSep ($$unsorted (-> $$unsorted Bool) (-> $$unsorted $$unsorted)) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_ReplSep (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (__flatten_var_0 (-> $$unsorted $$unsorted))) (@ (@ tptp.repl (@ (@ tptp.d_Sep X0) X1)) __flatten_var_0))))
% 0.39/0.62 (declare-fun tptp.setminus ($$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.setminus (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.d_Sep X0) (lambda ((X2 $$unsorted)) (@ (@ tptp.nIn X2) X1))))))
% 0.39/0.62 (declare-fun tptp.d_In_rec_G ((-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted) $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_In_rec_G (lambda ((X0 (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)) (X1 $$unsorted) (X2 $$unsorted)) (forall ((X3 (-> $$unsorted $$unsorted Bool))) (=> (forall ((X4 $$unsorted) (X5 (-> $$unsorted $$unsorted))) (=> (forall ((X6 $$unsorted)) (=> (@ (@ tptp.in X6) X4) (@ (@ X3 X6) (@ X5 X6)))) (@ (@ X3 X4) (@ (@ X0 X4) X5)))) (@ (@ X3 X1) X2))))))
% 0.39/0.62 (declare-fun tptp.d_In_rec ((-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted) $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_In_rec (lambda ((X0 (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)) (X1 $$unsorted)) (@ tptp.eps (@ (@ tptp.d_In_rec_G X0) X1)))))
% 0.39/0.62 (declare-fun tptp.ordsucc ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.ordsucc (lambda ((X0 $$unsorted)) (@ (@ tptp.binunion X0) (@ tptp.d_Sing X0)))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted)) (not (= (@ tptp.ordsucc X0) tptp.emptyset))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (= (@ tptp.ordsucc X0) (@ tptp.ordsucc X1)) (= X0 X1))))
% 0.39/0.62 (assert (@ (@ tptp.in tptp.emptyset) (@ tptp.ordsucc tptp.emptyset)))
% 0.39/0.62 (declare-fun tptp.nat_p ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.nat_p (lambda ((X0 $$unsorted)) (forall ((X1 (-> $$unsorted Bool))) (=> (@ X1 tptp.emptyset) (=> (forall ((X2 $$unsorted)) (=> (@ X1 X2) (@ X1 (@ tptp.ordsucc X2)))) (@ X1 X0)))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted)) (=> (@ tptp.nat_p X0) (@ tptp.nat_p (@ tptp.ordsucc X0)))))
% 0.39/0.62 (assert (@ tptp.nat_p (@ tptp.ordsucc tptp.emptyset)))
% 0.39/0.62 (assert (forall ((X0 (-> $$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)))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted)) (=> (@ tptp.nat_p X0) (or (= X0 tptp.emptyset) (exists ((X1 $$unsorted)) (and (@ tptp.nat_p X1) (= X0 (@ tptp.ordsucc X1))))))))
% 0.39/0.62 (declare-fun tptp.omega () $$unsorted)
% 0.39/0.62 (assert (= tptp.omega (@ (@ tptp.d_Sep (@ tptp.univof tptp.emptyset)) tptp.nat_p)))
% 0.39/0.62 (assert (forall ((X0 $$unsorted)) (=> (@ (@ tptp.in X0) tptp.omega) (@ tptp.nat_p X0))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted)) (=> (@ tptp.nat_p X0) (@ (@ tptp.in X0) tptp.omega))))
% 0.39/0.62 (declare-fun tptp.d_Inj1 ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_Inj1 (@ tptp.d_In_rec (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.binunion (@ tptp.d_Sing tptp.emptyset)) (@ (@ tptp.repl X0) X1))))))
% 0.39/0.62 (declare-fun tptp.d_Inj0 ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_Inj0 (lambda ((X0 $$unsorted)) (@ (@ tptp.repl X0) tptp.d_Inj1))))
% 0.39/0.62 (declare-fun tptp.d_Unj ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_Unj (@ tptp.d_In_rec (lambda ((X0 $$unsorted) (__flatten_var_0 (-> $$unsorted $$unsorted))) (@ (@ tptp.repl (@ (@ tptp.setminus X0) (@ tptp.d_Sing tptp.emptyset))) __flatten_var_0)))))
% 0.39/0.62 (declare-fun tptp.pair ($$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.pair (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.binunion (@ (@ tptp.repl X0) tptp.d_Inj0)) (@ (@ tptp.repl X1) tptp.d_Inj1)))))
% 0.39/0.62 (declare-fun tptp.proj0 ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.proj0 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X1 $$unsorted)) (exists ((X2 $$unsorted)) (= (@ tptp.d_Inj0 X2) X1)))) tptp.d_Unj))))
% 0.39/0.62 (declare-fun tptp.proj1 ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.proj1 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X1 $$unsorted)) (exists ((X2 $$unsorted)) (= (@ tptp.d_Inj1 X2) X1)))) tptp.d_Unj))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ tptp.proj0 (@ (@ tptp.pair X0) X1)) X0)))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (@ tptp.proj1 (@ (@ tptp.pair X0) X1)) X1)))
% 0.39/0.62 (declare-fun tptp.d_Sigma ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_Sigma (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.famunion X0) (lambda ((X2 $$unsorted)) (@ (@ tptp.repl (@ X1 X2)) (@ tptp.pair X2)))))))
% 0.39/0.62 (assert (forall ((X0 $$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)))))))
% 0.39/0.62 (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))))))))
% 0.39/0.62 (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))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) (@ (@ tptp.d_Sigma X0) X1)) (@ (@ tptp.in (@ tptp.proj0 X2)) X0))))
% 0.39/0.62 (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))))))
% 0.39/0.62 (declare-fun tptp.setprod ($$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.setprod (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.d_Sigma X0) (lambda ((X2 $$unsorted)) X1)))))
% 0.39/0.62 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.ap (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ tptp.d_ReplSep X0) (lambda ((X2 $$unsorted)) (exists ((X3 $$unsorted)) (= X2 (@ (@ tptp.pair X1) X3))))) tptp.proj1))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (=> (@ (@ tptp.in X2) X0) (= (@ (@ tptp.ap (@ (@ tptp.d_Sigma X0) X1)) X2) (@ X1 X2)))))
% 0.39/0.62 (declare-fun tptp.pair_p ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.pair_p (lambda ((X0 $$unsorted)) (let ((_let_1 (@ tptp.ap X0))) (= (@ (@ tptp.pair (@ _let_1 tptp.emptyset)) (@ _let_1 (@ tptp.ordsucc tptp.emptyset))) X0)))))
% 0.39/0.62 (declare-fun tptp.d_Pi ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_Pi (lambda ((X0 $$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 $$unsorted)) (=> (@ (@ tptp.in X3) X0) (@ (@ tptp.in (@ (@ tptp.ap X2) X3)) (@ X1 X3)))))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted))) (=> (forall ((X3 $$unsorted)) (=> (@ (@ tptp.in X3) X0) (@ (@ tptp.in (@ X2 X3)) (@ X1 X3)))) (@ (@ tptp.in (@ (@ tptp.d_Sigma X0) X2)) (@ (@ tptp.d_Pi X0) X1)))))
% 0.39/0.62 (assert (forall ((X0 $$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))))))
% 0.39/0.62 (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)))))))
% 0.39/0.62 (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))))))
% 0.39/0.62 (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)))))))
% 0.39/0.62 (assert (forall ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (let ((_let_1 (@ tptp.in X1))) (=> X0 (=> (@ _let_1 (@ (@ (@ tptp.if X0) X2) X3)) (@ _let_1 X2))))))
% 0.39/0.62 (declare-fun tptp.imp (Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.imp (lambda ((X0 Bool) (X1 Bool)) (=> X0 X1))))
% 0.39/0.62 (declare-fun tptp.d_not (Bool) Bool)
% 0.39/0.62 (assert (= tptp.d_not (lambda ((X0 Bool)) (@ (@ tptp.imp X0) false))))
% 0.39/0.62 (declare-fun tptp.wel (Bool) Bool)
% 0.39/0.62 (assert (= tptp.wel (lambda ((X0 Bool)) (@ tptp.d_not (@ tptp.d_not X0)))))
% 0.39/0.62 (assert (forall ((X0 Bool)) (=> (@ tptp.wel X0) X0)))
% 0.39/0.62 (declare-fun tptp.obvious () Bool)
% 0.39/0.62 (assert (= tptp.obvious (@ (@ tptp.imp false) false)))
% 0.39/0.62 (declare-fun tptp.l_ec (Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.l_ec (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.imp X0) (@ tptp.d_not X1)))))
% 0.39/0.62 (declare-fun tptp.d_and (Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.d_and (lambda ((X0 Bool) (X1 Bool)) (@ tptp.d_not (@ (@ tptp.l_ec X0) X1)))))
% 0.39/0.62 (declare-fun tptp.l_or (Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.l_or (lambda ((X0 Bool) (__flatten_var_0 Bool)) (@ (@ tptp.imp (@ tptp.d_not X0)) __flatten_var_0))))
% 0.39/0.62 (declare-fun tptp.orec (Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.orec (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.d_and (@ (@ tptp.l_or X0) X1)) (@ (@ tptp.l_ec X0) X1)))))
% 0.39/0.62 (declare-fun tptp.l_iff (Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.l_iff (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.d_and (@ (@ tptp.imp X0) X1)) (@ (@ tptp.imp X1) X0)))))
% 0.39/0.62 (declare-fun tptp.all ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.39/0.62 (assert (= tptp.all (lambda ((X0 $$unsorted) (__flatten_var_0 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) X0))) __flatten_var_0))))
% 0.39/0.62 (declare-fun tptp.non ($$unsorted (-> $$unsorted Bool) $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.non (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) (@ tptp.d_not (@ X1 X2)))))
% 0.39/0.62 (declare-fun tptp.l_some ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.39/0.62 (assert (= tptp.l_some (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ tptp.d_not (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (@ (@ tptp.non X0) X1))))))
% 0.39/0.62 (declare-fun tptp.or3 (Bool Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.or3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.l_or X0) (@ (@ tptp.l_or X1) X2)))))
% 0.39/0.62 (declare-fun tptp.and3 (Bool Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.and3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.d_and X0) (@ (@ tptp.d_and X1) X2)))))
% 0.39/0.62 (declare-fun tptp.ec3 (Bool Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.ec3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ (@ tptp.and3 (@ (@ tptp.l_ec X0) X1)) (@ (@ tptp.l_ec X1) X2)) (@ (@ tptp.l_ec X2) X0)))))
% 0.39/0.62 (declare-fun tptp.orec3 (Bool Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.orec3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.d_and (@ (@ (@ tptp.or3 X0) X1) X2)) (@ (@ (@ tptp.ec3 X0) X1) X2)))))
% 0.39/0.62 (declare-fun tptp.e_is ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.e_is (lambda ((X0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (= X Y))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) X0))) (lambda ((X1 $$unsorted)) (@ (@ (@ tptp.e_is X0) X1) X1)))))
% 0.39/0.62 (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)))))))))
% 0.39/0.62 (declare-fun tptp.amone ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.39/0.62 (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))))))))))
% 0.39/0.62 (declare-fun tptp.one ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.39/0.62 (assert (= tptp.one (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.d_and (@ (@ tptp.amone X0) X1)) (@ (@ tptp.l_some X0) X1)))))
% 0.39/0.62 (declare-fun tptp.ind ($$unsorted (-> $$unsorted Bool)) $$unsorted)
% 0.39/0.62 (assert (= tptp.ind (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ tptp.eps (lambda ((X2 $$unsorted)) (and (@ (@ tptp.in X2) X0) (@ X1 X2)))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (=> (@ (@ tptp.one X0) X1) (@ (@ tptp.is_of (@ (@ tptp.ind X0) X1)) (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (=> (@ (@ tptp.one X0) X1) (@ X1 (@ (@ tptp.ind X0) X1)))))
% 0.39/0.62 (declare-fun tptp.injective ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.injective (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X3 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X4 $$unsorted)) (let ((_let_1 (@ tptp.ap X2))) (@ (@ tptp.imp (@ (@ (@ tptp.e_is X1) (@ _let_1 X3)) (@ _let_1 X4))) (@ (@ (@ tptp.e_is X0) X3) X4))))))))))
% 0.39/0.62 (declare-fun tptp.image ($$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.image (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.l_some X0) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.e_is X1) X3) (@ (@ tptp.ap X2) X4)))))))
% 0.39/0.62 (declare-fun tptp.tofs ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.tofs (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ tptp.ap __flatten_var_0) __flatten_var_1))))
% 0.39/0.62 (declare-fun tptp.soft ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.soft (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.ind X0) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.e_is X1) X3) (@ (@ tptp.ap X2) X4)))))))
% 0.39/0.62 (declare-fun tptp.inverse ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.inverse (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sigma X1) (lambda ((X3 $$unsorted)) (@ (@ (@ tptp.if (@ (@ (@ (@ tptp.image X0) X1) X2) X3)) (@ (@ (@ (@ tptp.soft X0) X1) X2) X3)) tptp.emptyset))))))
% 0.39/0.62 (declare-fun tptp.surjective ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.surjective (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X1) (@ (@ (@ tptp.image X0) X1) X2)))))
% 0.39/0.62 (declare-fun tptp.bijective ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.bijective (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_and (@ (@ (@ tptp.injective X0) X1) X2)) (@ (@ (@ tptp.surjective X0) X1) X2)))))
% 0.39/0.62 (declare-fun tptp.invf ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.invf (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sigma X1) (@ (@ (@ tptp.soft X0) X1) X2)))))
% 0.39/0.62 (declare-fun tptp.inj_h ($$unsorted $$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (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)))))))
% 0.39/0.62 (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 $$unsorted)) X1))) X2) X3))))))))
% 0.39/0.62 (declare-fun tptp.e_in ($$unsorted (-> $$unsorted Bool) $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.e_in (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted)) X2)))
% 0.39/0.62 (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 $$unsorted)) (@ (@ tptp.in X3) X0)))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ (@ tptp.d_Sep X0) X1)))) (lambda ((X2 $$unsorted)) (@ X1 (@ (@ (@ tptp.e_in X0) X1) X2))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (let ((_let_1 (@ (@ tptp.d_Sep X0) X1))) (@ (@ (@ tptp.injective _let_1) X0) (@ (@ tptp.d_Sigma _let_1) (@ (@ tptp.e_in X0) X1))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ (@ tptp.d_Sep X0) X1))) (=> (@ X1 X2) (@ (@ (@ (@ tptp.image _let_1) X0) (@ (@ tptp.d_Sigma _let_1) (@ (@ tptp.e_in X0) X1))) X2)))))))
% 0.39/0.62 (declare-fun tptp.out ($$unsorted (-> $$unsorted Bool) $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.out (lambda ((X0 $$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)))))
% 0.39/0.62 (declare-fun tptp.d_pair ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_pair (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ tptp.pair __flatten_var_0) __flatten_var_1))))
% 0.39/0.62 (assert (forall ((X0 $$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))))))))))
% 0.39/0.62 (declare-fun tptp.first ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.first (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted)) (@ tptp.proj0 __flatten_var_0))))
% 0.39/0.62 (assert (forall ((X0 $$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)))))))
% 0.39/0.62 (declare-fun tptp.second ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.second (lambda ((X0 $$unsorted) (X1 $$unsorted) (__flatten_var_0 $$unsorted)) (@ tptp.proj1 __flatten_var_0))))
% 0.39/0.62 (assert (forall ((X0 $$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)))))))
% 0.39/0.62 (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)))))
% 0.39/0.62 (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)))))))
% 0.39/0.62 (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)))))))
% 0.39/0.62 (declare-fun tptp.prop1 (Bool $$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (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)))))))
% 0.39/0.62 (declare-fun tptp.ite (Bool $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.ite (lambda ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.ind X1) (@ (@ (@ (@ tptp.prop1 X0) X1) X2) X3)))))
% 0.39/0.62 (declare-fun tptp.wissel_wa ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.wissel_wa (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ (@ (@ tptp.ite (@ (@ (@ tptp.e_is X0) X3) X1)) X0) X2) X3))))
% 0.39/0.62 (declare-fun tptp.wissel_wb ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.wissel_wb (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ (@ (@ tptp.ite (@ (@ (@ tptp.e_is X0) X3) X2)) X0) X1) (@ (@ (@ (@ tptp.wissel_wa X0) X1) X2) X3)))))
% 0.39/0.62 (declare-fun tptp.wissel ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.wissel (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.d_Sigma X0) (@ (@ (@ tptp.wissel_wb X0) X1) X2)))))
% 0.39/0.62 (declare-fun tptp.changef ($$unsorted $$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (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)))))))
% 0.39/0.62 (declare-fun tptp.r_ec (Bool Bool) Bool)
% 0.39/0.62 (assert (= tptp.r_ec (lambda ((X0 Bool) (X1 Bool)) (=> X0 (@ tptp.d_not X1)))))
% 0.39/0.62 (declare-fun tptp.esti ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.esti (lambda ((X0 $$unsorted) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ tptp.in __flatten_var_0) __flatten_var_1))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.is_of (@ (@ tptp.d_Sep X0) X1)) (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) (@ tptp.power X0))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (=> (@ X1 X2) (@ (@ (@ tptp.esti X0) X2) (@ (@ tptp.d_Sep X0) X1)))))))
% 0.39/0.62 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (lambda ((X2 $$unsorted)) (=> (@ (@ (@ tptp.esti X0) X2) (@ (@ tptp.d_Sep X0) X1)) (@ X1 X2))))))
% 0.39/0.62 (declare-fun tptp.empty ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.empty (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) X0))) (@ (@ tptp.non X0) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.esti X0) X2) X1)))))))
% 0.39/0.62 (declare-fun tptp.nonempty ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.nonempty (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.l_some X0) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.esti X0) X2) X1))))))
% 0.39/0.62 (declare-fun tptp.incl ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.incl (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.all X0) (lambda ((X3 $$unsorted)) (let ((_let_1 (@ (@ tptp.esti X0) X3))) (@ (@ tptp.imp (@ _let_1 X1)) (@ _let_1 X2))))))))
% 0.39/0.62 (declare-fun tptp.st_disj ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (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))))))))
% 0.39/0.62 (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 $$unsorted)) (let ((_let_1 (@ tptp.incl X0))) (=> (@ (@ _let_1 X1) X2) (=> (@ (@ _let_1 X2) X1) (@ (@ (@ tptp.e_is (@ tptp.power X0)) X1) X2))))))))))
% 0.39/0.62 (declare-fun tptp.nissetprop ($$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.nissetprop (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (let ((_let_1 (@ (@ tptp.esti X0) X3))) (@ (@ tptp.d_and (@ _let_1 X1)) (@ tptp.d_not (@ _let_1 X2)))))))
% 0.39/0.62 (declare-fun tptp.unmore ($$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.unmore (lambda ((X0 $$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)))))))))
% 0.39/0.62 (declare-fun tptp.ecelt ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.ecelt (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted)) (@ (@ tptp.d_Sep X0) (@ X1 X2)))))
% 0.39/0.62 (declare-fun tptp.ecp ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.ecp (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted)) (@ (@ (@ tptp.e_is (@ tptp.power X0)) X2) (@ (@ (@ tptp.ecelt X0) X1) X3)))))
% 0.39/0.62 (declare-fun tptp.anec ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.anec (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted)) (@ (@ tptp.l_some X0) (@ (@ (@ tptp.ecp X0) X1) X2)))))
% 0.39/0.62 (declare-fun tptp.ect ($$unsorted (-> $$unsorted $$unsorted Bool)) $$unsorted)
% 0.39/0.62 (assert (= tptp.ect (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.d_Sep (@ tptp.power X0)) (@ (@ tptp.anec X0) X1)))))
% 0.39/0.62 (declare-fun tptp.ectset ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.ectset (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.out (@ tptp.power X0)) (@ (@ tptp.anec X0) X1)) __flatten_var_0))))
% 0.39/0.62 (declare-fun tptp.ectelt ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.ectelt (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted)) (@ (@ (@ tptp.ectset X0) X1) (@ (@ (@ tptp.ecelt X0) X1) X2)))))
% 0.39/0.62 (declare-fun tptp.ecect ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.ecect (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.e_in (@ tptp.power X0)) (@ (@ tptp.anec X0) X1)) __flatten_var_0))))
% 0.39/0.62 (declare-fun tptp.fixfu ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.39/0.62 (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 $$unsorted)) (let ((_let_1 (@ tptp.ap X3))) (=> (@ (@ X1 X4) X5) (@ (@ (@ tptp.e_is X2) (@ _let_1 X4)) (@ _let_1 X5)))))))))))
% 0.39/0.62 (declare-fun tptp.d_10_prop1 ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_10_prop1 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (X5 $$unsorted) (X6 $$unsorted)) (@ (@ tptp.d_and (@ (@ (@ tptp.esti X0) X6) (@ (@ (@ tptp.ecect X0) X1) X4))) (@ (@ (@ tptp.e_is X2) (@ (@ tptp.ap X3) X6)) X5)))))
% 0.39/0.62 (declare-fun tptp.prop2 ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.prop2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (X5 $$unsorted)) (@ (@ tptp.l_some X0) (@ (@ (@ (@ (@ (@ tptp.d_10_prop1 X0) X1) X2) X3) X4) X5)))))
% 0.39/0.62 (declare-fun tptp.indeq ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (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)))))
% 0.39/0.62 (declare-fun tptp.fixfu2 ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.fixfu2 (lambda ((X0 $$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))))))))))))))))
% 0.39/0.62 (declare-fun tptp.d_11_i ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_11_i (lambda ((X0 $$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))))
% 0.39/0.62 (declare-fun tptp.indeq2 ($$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.indeq2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted Bool)) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (__flatten_var_0 $$unsorted)) (@ (@ (@ (@ (@ tptp.indeq X0) X1) X2) (@ (@ (@ (@ (@ tptp.d_11_i X0) X1) X2) X3) X4)) __flatten_var_0))))
% 0.39/0.62 (declare-fun tptp.nat () $$unsorted)
% 0.39/0.62 (assert (= tptp.nat (@ (@ tptp.d_Sep tptp.omega) (lambda ((X0 $$unsorted)) (not (= X0 tptp.emptyset))))))
% 0.39/0.62 (declare-fun tptp.n_is ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.n_is (@ tptp.e_is tptp.nat)))
% 0.39/0.62 (declare-fun tptp.nis ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.nis (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.d_not (@ (@ tptp.n_is X0) X1)))))
% 0.39/0.62 (declare-fun tptp.n_in ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.n_in (@ tptp.esti tptp.nat)))
% 0.39/0.62 (declare-fun tptp.n_some ((-> $$unsorted Bool)) Bool)
% 0.39/0.62 (assert (= tptp.n_some (@ tptp.l_some tptp.nat)))
% 0.39/0.62 (declare-fun tptp.n_all ((-> $$unsorted Bool)) Bool)
% 0.39/0.62 (assert (= tptp.n_all (@ tptp.all tptp.nat)))
% 0.39/0.62 (declare-fun tptp.n_one ((-> $$unsorted Bool)) Bool)
% 0.39/0.62 (assert (= tptp.n_one (@ tptp.one tptp.nat)))
% 0.39/0.62 (declare-fun tptp.n_1 () $$unsorted)
% 0.39/0.62 (assert (= tptp.n_1 (@ tptp.ordsucc tptp.emptyset)))
% 0.39/0.62 (assert (@ (@ tptp.is_of tptp.n_1) (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.is_of (@ tptp.ordsucc X0)) (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.nis (@ tptp.ordsucc X0)) tptp.n_1))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.n_is (@ tptp.ordsucc X0)) (@ tptp.ordsucc X1)) (@ (@ tptp.n_is X0) X1)))))))
% 0.39/0.62 (declare-fun tptp.cond1 ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.cond1 (@ tptp.n_in tptp.n_1)))
% 0.39/0.62 (declare-fun tptp.cond2 ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.cond2 (lambda ((X0 $$unsorted)) (@ tptp.n_all (lambda ((X1 $$unsorted)) (@ (@ tptp.imp (@ (@ tptp.n_in X1) X0)) (@ (@ tptp.n_in (@ tptp.ordsucc X1)) X0)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$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 $$unsorted)) (@ (@ tptp.n_in X1) X0))))))))
% 0.39/0.62 (declare-fun tptp.i1_s ((-> $$unsorted Bool)) $$unsorted)
% 0.39/0.62 (assert (= tptp.i1_s (@ tptp.d_Sep tptp.nat)))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.nis X0) X1) (@ (@ tptp.nis (@ tptp.ordsucc X0)) (@ tptp.ordsucc X1))))))))
% 0.39/0.62 (declare-fun tptp.d_22_prop1 ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_22_prop1 (lambda ((X0 $$unsorted)) (@ (@ tptp.nis (@ tptp.ordsucc X0)) X0))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.nis (@ tptp.ordsucc X0)) X0))))
% 0.39/0.62 (declare-fun tptp.d_23_prop1 ($$unsorted) Bool)
% 0.39/0.62 (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))))))))
% 0.39/0.62 (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 $$unsorted)) (@ (@ tptp.n_is X0) (@ tptp.ordsucc X1))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$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))))))))
% 0.39/0.62 (declare-fun tptp.d_24_prop1 ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_24_prop1 (lambda ((X0 $$unsorted)) (@ tptp.n_all (lambda ((X1 $$unsorted)) (let ((_let_1 (@ tptp.ap X0))) (@ (@ tptp.n_is (@ _let_1 (@ tptp.ordsucc X1))) (@ tptp.ordsucc (@ _let_1 X1)))))))))
% 0.39/0.62 (declare-fun tptp.d_24_prop2 ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_24_prop2 (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.d_and (@ (@ tptp.n_is (@ (@ tptp.ap X1) tptp.n_1)) (@ tptp.ordsucc X0))) (@ tptp.d_24_prop1 X1)))))
% 0.39/0.62 (declare-fun tptp.prop3 ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.prop3 (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.n_is (@ (@ tptp.ap X0) X2)) (@ (@ tptp.ap X1) X2)))))
% 0.39/0.62 (declare-fun tptp.prop4 ($$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.prop4 (lambda ((X0 $$unsorted)) (@ (@ tptp.l_some (@ (@ tptp.d_Pi tptp.nat) (lambda ((X1 $$unsorted)) tptp.nat))) (@ tptp.d_24_prop2 X0)))))
% 0.39/0.62 (declare-fun tptp.d_24_g ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.d_24_g (lambda ((X0 $$unsorted)) (@ (@ tptp.d_Sigma tptp.nat) (lambda ((X1 $$unsorted)) (@ tptp.ordsucc (@ (@ tptp.ap X0) X1)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.one (@ (@ tptp.d_Pi tptp.nat) (lambda ((X1 $$unsorted)) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ tptp.d_and (@ (@ tptp.n_is (@ (@ tptp.ap X1) tptp.n_1)) (@ tptp.ordsucc X0))) (@ tptp.n_all (lambda ((X2 $$unsorted)) (let ((_let_1 (@ tptp.ap X1))) (@ (@ tptp.n_is (@ _let_1 (@ tptp.ordsucc X2))) (@ tptp.ordsucc (@ _let_1 X2))))))))))))
% 0.39/0.62 (declare-fun tptp.plus ($$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.plus (lambda ((X0 $$unsorted)) (@ (@ tptp.ind (@ (@ tptp.d_Pi tptp.nat) (lambda ((X1 $$unsorted)) tptp.nat))) (@ tptp.d_24_prop2 X0)))))
% 0.39/0.62 (declare-fun tptp.n_pl ($$unsorted $$unsorted) $$unsorted)
% 0.39/0.62 (assert (= tptp.n_pl (lambda ((X0 $$unsorted) (__flatten_var_0 $$unsorted)) (@ (@ tptp.ap (@ tptp.plus X0)) __flatten_var_0))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.n_is (@ (@ tptp.n_pl X0) tptp.n_1)) (@ tptp.ordsucc X0)))))
% 0.39/0.62 (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)) (let ((_let_1 (@ tptp.n_pl X0))) (@ (@ tptp.n_is (@ _let_1 (@ tptp.ordsucc X1))) (@ tptp.ordsucc (@ _let_1 X1)))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.n_is (@ (@ tptp.n_pl tptp.n_1) X0)) (@ tptp.ordsucc X0)))))
% 0.39/0.62 (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.n_pl (@ tptp.ordsucc X0)) X1)) (@ tptp.ordsucc (@ (@ tptp.n_pl X0) X1))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.n_is (@ tptp.ordsucc X0)) (@ (@ tptp.n_pl X0) tptp.n_1)))))
% 0.39/0.62 (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)) (let ((_let_1 (@ tptp.n_pl X0))) (@ (@ tptp.n_is (@ tptp.ordsucc (@ _let_1 X1))) (@ _let_1 (@ tptp.ordsucc X1)))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.n_is (@ tptp.ordsucc X0)) (@ (@ tptp.n_pl tptp.n_1) X0)))))
% 0.39/0.62 (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 (@ (@ tptp.n_pl X0) X1))) (@ (@ tptp.n_pl (@ tptp.ordsucc X0)) X1)))))))
% 0.39/0.62 (declare-fun tptp.d_25_prop1 ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_25_prop1 (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ tptp.n_pl X0))) (@ (@ tptp.n_is (@ (@ tptp.n_pl (@ _let_1 X1)) X2)) (@ _let_1 (@ (@ tptp.n_pl X1) X2)))))))
% 0.39/0.62 (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.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) tptp.nat))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ tptp.n_pl X0))) (@ (@ tptp.n_is (@ (@ tptp.n_pl (@ _let_1 X1)) X2)) (@ _let_1 (@ (@ tptp.n_pl X1) X2)))))))))))
% 0.39/0.62 (declare-fun tptp.d_26_prop1 ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_26_prop1 (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.n_is (@ (@ tptp.n_pl X0) X1)) (@ (@ tptp.n_pl X1) X0)))))
% 0.39/0.62 (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.n_pl X0) X1)) (@ (@ tptp.n_pl X1) X0)))))))
% 0.39/0.62 (declare-fun tptp.d_27_prop1 ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_27_prop1 (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.nis X1) (@ (@ tptp.n_pl X0) X1)))))
% 0.39/0.62 (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 X1) (@ (@ tptp.n_pl X0) X1)))))))
% 0.39/0.62 (declare-fun tptp.d_28_prop1 ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_28_prop1 (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (@ tptp.n_pl X0))) (@ (@ tptp.nis (@ _let_1 X1)) (@ _let_1 X2))))))
% 0.39/0.62 (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.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) tptp.nat))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ tptp.n_pl X0))) (=> (@ (@ tptp.nis X1) X2) (@ (@ tptp.nis (@ _let_1 X1)) (@ _let_1 X2)))))))))))
% 0.39/0.62 (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.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) tptp.nat))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ tptp.n_pl X0))) (=> (@ (@ tptp.n_is (@ _let_1 X1)) (@ _let_1 X2)) (@ (@ tptp.n_is X1) X2))))))))))
% 0.39/0.62 (declare-fun tptp.diffprop ($$unsorted $$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.diffprop (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.n_is X0) (@ (@ tptp.n_pl X1) X2)))))
% 0.39/0.62 (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.amone tptp.nat) (lambda ((X2 $$unsorted)) (@ (@ tptp.n_is X0) (@ (@ tptp.n_pl X1) X2)))))))))
% 0.39/0.62 (declare-fun tptp.d_29_ii ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_29_ii (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.n_some (@ (@ tptp.diffprop X0) X1)))))
% 0.39/0.62 (declare-fun tptp.iii ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.iii (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.n_some (@ (@ tptp.diffprop X1) X0)))))
% 0.39/0.62 (declare-fun tptp.d_29_prop1 ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.d_29_prop1 (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ tptp.or3 (@ (@ tptp.n_is X0) X1)) (@ (@ tptp.d_29_ii X0) X1)) (@ (@ tptp.iii X0) X1)))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ (@ tptp.orec3 (@ (@ tptp.n_is X0) X1)) (@ tptp.n_some (lambda ((X2 $$unsorted)) (@ (@ tptp.n_is X0) (@ (@ tptp.n_pl X1) X2))))) (@ tptp.n_some (lambda ((X2 $$unsorted)) (@ (@ tptp.n_is X1) (@ (@ tptp.n_pl X0) X2))))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ (@ tptp.or3 (@ (@ tptp.n_is X0) X1)) (@ tptp.n_some (@ (@ tptp.diffprop X0) X1))) (@ tptp.n_some (@ (@ tptp.diffprop X1) X0))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ (@ tptp.ec3 (@ (@ tptp.n_is X0) X1)) (@ tptp.n_some (@ (@ tptp.diffprop X0) X1))) (@ tptp.n_some (@ (@ tptp.diffprop X1) X0))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ (@ tptp.orec3 (@ (@ tptp.n_is X0) X1)) (@ (@ tptp.d_29_ii X0) X1)) (@ (@ tptp.iii X0) X1)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ (@ tptp.or3 (@ (@ tptp.n_is X0) X1)) (@ (@ tptp.d_29_ii X0) X1)) (@ (@ tptp.iii X0) X1)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ (@ tptp.ec3 (@ (@ tptp.n_is X0) X1)) (@ (@ tptp.d_29_ii X0) X1)) (@ (@ tptp.iii X0) X1)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.d_29_ii X0) X1) (@ (@ tptp.iii X1) X0)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.iii X0) X1) (@ (@ tptp.d_29_ii X1) X0)))))))
% 0.39/0.62 (declare-fun tptp.moreis ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.moreis (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.l_or (@ (@ tptp.d_29_ii X0) X1)) (@ (@ tptp.n_is X0) X1)))))
% 0.39/0.62 (declare-fun tptp.lessis ($$unsorted $$unsorted) Bool)
% 0.39/0.62 (assert (= tptp.lessis (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.l_or (@ (@ tptp.iii X0) X1)) (@ (@ tptp.n_is X0) X1)))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.moreis X0) X1) (@ (@ tptp.lessis X1) X0)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.lessis X0) X1) (@ (@ tptp.moreis X1) X0)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.moreis X0) X1) (@ tptp.d_not (@ (@ tptp.iii X0) X1))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.lessis X0) X1) (@ tptp.d_not (@ (@ tptp.d_29_ii X0) X1))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ tptp.d_not (@ (@ tptp.d_29_ii X0) X1)) (@ (@ tptp.lessis X0) X1)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ tptp.d_not (@ (@ tptp.iii X0) X1)) (@ (@ tptp.moreis X0) X1)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.d_29_ii X0) X1) (@ tptp.d_not (@ (@ tptp.lessis X0) X1))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ (@ tptp.iii X0) X1) (@ tptp.d_not (@ (@ tptp.moreis X0) X1))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ tptp.d_not (@ (@ tptp.moreis X0) X1)) (@ (@ tptp.iii X0) X1)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (=> (@ tptp.d_not (@ (@ tptp.lessis X0) X1)) (@ (@ tptp.d_29_ii X0) X1)))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) tptp.nat))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ tptp.iii X0))) (=> (@ _let_1 X1) (=> (@ (@ tptp.iii X1) X2) (@ _let_1 X2)))))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) tptp.nat))) (lambda ((X2 $$unsorted)) (=> (@ (@ tptp.lessis X0) X1) (=> (@ (@ tptp.iii X1) X2) (@ (@ tptp.iii X0) X2))))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) tptp.nat))) (lambda ((X2 $$unsorted)) (let ((_let_1 (@ tptp.iii X0))) (=> (@ _let_1 X1) (=> (@ (@ tptp.lessis X1) X2) (@ _let_1 X2)))))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (lambda ((X1 $$unsorted)) (@ (@ tptp.in X1) tptp.nat))) (lambda ((X1 $$unsorted)) (@ (@ tptp.all_of (lambda ((X2 $$unsorted)) (@ (@ tptp.in X2) tptp.nat))) (lambda ((X2 $$unsorted)) (=> (@ (@ tptp.moreis X0) X1) (=> (@ (@ tptp.d_29_ii X1) X2) (@ (@ tptp.d_29_ii X0) X2))))))))))
% 0.39/0.62 (assert (@ (@ tptp.all_of (lambda ((X0 $$unsorted)) (@ (@ tptp.in X0) tptp.nat))) (lambda ((X0 $$unsorted)) (@ (@ tptp.all_of (l/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 30576 Alarm clock ( read result; case "$result" in
% 299.90/300.12 unsat)
% 299.90/300.12 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.90/300.12 ;;
% 299.90/300.12 sat)
% 299.90/300.12 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.90/300.12 ;;
% 299.90/300.12 esac; exit 1 )
% 299.90/300.13 Alarm clock
% 299.90/300.13 % cvc5---1.0.5 exiting
% 299.90/300.13 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------