%------------------------------------------------------------------------------
% File     : SYO065^4.004 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Logic Calculi (Intuitionistic logic)
% Problem  : ILTP Problem SYJ201+1.004
% Version  : [Goe33] axioms.
% English  :

% Refs     : [Goe33] Goedel (1933), An Interpretation of the Intuitionistic
%          : [Gol06] Goldblatt (2006), Mathematical Modal Logic: A View of
%          : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
%          : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
%          : [BP10]  Benzmueller & Paulson (2009), Exploring Properties of
% Source   : [Ben09]
% Names    : SYJ201+1.004 [ROK06]

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :   60 (  20 unt;  29 typ;  19 def)
%            Number of atoms       :  387 (  19 equ;   0 cnn)
%            Maximal formula atoms :   33 (  12 avg)
%            Number of connectives :  369 (   3   ~;   1   |;   2   &; 361   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  104 ( 104   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   36 (  34 usr;   6 con; 0-3 aty)
%            Number of variables   :   40 (  31   ^;   7   !;   2   ?;  40   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This is an ILTP problem embedded in TH0
%------------------------------------------------------------------------------
include('Axioms/LCL010^0.ax').
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thf(p1_type,type,
    p1: $i > $o ).

thf(p2_type,type,
    p2: $i > $o ).

thf(p3_type,type,
    p3: $i > $o ).

thf(p4_type,type,
    p4: $i > $o ).

thf(p5_type,type,
    p5: $i > $o ).

thf(p6_type,type,
    p6: $i > $o ).

thf(p7_type,type,
    p7: $i > $o ).

thf(p8_type,type,
    p8: $i > $o ).

thf(p9_type,type,
    p9: $i > $o ).

thf(axiom1,axiom,
    ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ) ).

thf(axiom2,axiom,
    ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p2 ) @ ( iatom @ p3 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ) ).

thf(axiom3,axiom,
    ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p3 ) @ ( iatom @ p4 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ) ).

thf(axiom4,axiom,
    ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p4 ) @ ( iatom @ p5 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ) ).

thf(axiom5,axiom,
    ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p5 ) @ ( iatom @ p6 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ) ).

thf(axiom6,axiom,
    ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ) ).

thf(axiom7,axiom,
    ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ) ).

thf(axiom8,axiom,
    ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ) ).

thf(axiom9,axiom,
    ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p9 ) @ ( iatom @ p1 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ) ).

thf(con,conjecture,
    ivalid @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iand @ ( iatom @ p8 ) @ ( iatom @ p9 ) ) ) ) ) ) ) ) ) ).

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