## TPTP Problem File: SYO072^4.003.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO072^4.003 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Logic Calculi (Intuitionistic logic)
% Problem  : ILTP Problem SYJ208+1.003
% 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    : SYJ208+1.003 [ROK06]

% Status   : CounterSatisfiable
% Rating   : 0.67 v5.4.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :   58 (   0 unit;  32 type;  19 defn)
%            Number of atoms       :  263 (  19 equality;  48 variable)
%            Maximal formula depth :   23 (   5 average)
%            Number of connectives :  202 (   3   ~;   1   |;   2   &; 194   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  107 ( 107   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   35 (  32   :;   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.
%------------------------------------------------------------------------------
include('Axioms/LCL010^0.ax').
%------------------------------------------------------------------------------
thf(o11_type,type,(
o11: \$i > \$o )).

thf(o12_type,type,(
o12: \$i > \$o )).

thf(o13_type,type,(
o13: \$i > \$o )).

thf(o21_type,type,(
o21: \$i > \$o )).

thf(o22_type,type,(
o22: \$i > \$o )).

thf(o23_type,type,(
o23: \$i > \$o )).

thf(o31_type,type,(
o31: \$i > \$o )).

thf(o32_type,type,(
o32: \$i > \$o )).

thf(o33_type,type,(
o33: \$i > \$o )).

thf(o41_type,type,(
o41: \$i > \$o )).

thf(o42_type,type,(
o42: \$i > \$o )).

thf(o43_type,type,(
o43: \$i > \$o )).

thf(axiom1,axiom,
( ivalid @ ( ior @ ( iatom @ o11 ) @ ( ior @ ( iatom @ o12 ) @ ( inot @ ( inot @ ( iatom @ o13 ) ) ) ) ) )).

thf(axiom2,axiom,
( ivalid @ ( ior @ ( iatom @ o21 ) @ ( ior @ ( iatom @ o22 ) @ ( inot @ ( inot @ ( iatom @ o23 ) ) ) ) ) )).

thf(axiom3,axiom,
( ivalid @ ( ior @ ( iatom @ o31 ) @ ( ior @ ( iatom @ o32 ) @ ( inot @ ( inot @ ( iatom @ o33 ) ) ) ) ) )).

thf(axiom4,axiom,
( ivalid @ ( ior @ ( iatom @ o41 ) @ ( ior @ ( iatom @ o42 ) @ ( inot @ ( inot @ ( iatom @ o43 ) ) ) ) ) )).

thf(con,conjecture,
( ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o41 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o41 ) ) @ ( ior @ ( iand @ ( iatom @ o31 ) @ ( iatom @ o41 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o42 ) ) @ ( ior @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) @ ( ior @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o42 ) ) @ ( ior @ ( iand @ ( iatom @ o32 ) @ ( iatom @ o42 ) ) @ ( ior @ ( iand @ ( iatom @ o13 ) @ ( iatom @ o23 ) ) @ ( ior @ ( iand @ ( iatom @ o13 ) @ ( iatom @ o33 ) ) @ ( ior @ ( iand @ ( iatom @ o13 ) @ ( iatom @ o43 ) ) @ ( ior @ ( iand @ ( iatom @ o23 ) @ ( iatom @ o33 ) ) @ ( ior @ ( iand @ ( iatom @ o23 ) @ ( iatom @ o43 ) ) @ ( iand @ ( iatom @ o33 ) @ ( iatom @ o43 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

%------------------------------------------------------------------------------
```