TPTP Problem File: SYO070^4.002.p

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% File     : SYO070^4.002 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Logic Calculi (Intuitionistic logic)
% Problem  : ILTP Problem SYJ211+1.002
% 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    : SYJ211+1.002 [ROK06]

% Status   : CounterSatisfiable
% Rating   : 0.75 v7.2.0, 0.67 v6.2.0, 0.33 v5.4.0, 1.00 v4.1.0, 0.50 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :   53 (   0 unit;  27 type;  19 defn)
%            Number of atoms       :  153 (  19 equality;  48 variable)
%            Maximal formula depth :    9 (   5 average)
%            Number of connectives :   92 (   3   ~;   1   |;   2   &;  84   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  102 ( 102   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   30 (  27   :;   0   =)
%            Number of variables   :   40 (   1 sgn;   7   !;   2   ?;  31   ^)
%                                         (  40   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

% Comments : This is an ILTP problem embedded in TH0
%          : In classical logic this is a Theorem.
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include('Axioms/LCL010^0.ax').
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thf(a0_type,type,(
    a0: $i > $o )).

thf(a1_type,type,(
    a1: $i > $o )).

thf(a2_type,type,(
    a2: $i > $o )).

thf(b0_type,type,(
    b0: $i > $o )).

thf(b1_type,type,(
    b1: $i > $o )).

thf(b2_type,type,(
    b2: $i > $o )).

thf(f_type,type,(
    f: $i > $o )).

thf(axiom1,axiom,
    ( ivalid @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) )).

thf(axiom2,axiom,
    ( ivalid @ ( iimplies @ ( iimplies @ ( inot @ ( inot @ ( iatom @ b2 ) ) ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) )).

thf(axiom3,axiom,
    ( ivalid @ ( iimplies @ ( iimplies @ ( inot @ ( inot @ ( iatom @ b0 ) ) ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) )).

thf(axiom4,axiom,
    ( ivalid @ ( iimplies @ ( iimplies @ ( inot @ ( inot @ ( iatom @ b1 ) ) ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) )).

thf(con,conjecture,
    ( ivalid @ ( iatom @ f ) )).

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