%------------------------------------------------------------------------------
% File     : PHI007^5 : TPTP v9.0.0. Released v6.4.0.
% Domain   : Philosophy
% Problem  : Inconsistency of the axioms in Goedel's original manuscript
% Version  : [Ben16] axioms : Biased > Reduced > Biased.
% English  : Scott's variant without the conjunct in the definition of essence.

% Refs     : [Ben16] Benzmueller (2016), Email to Geoff Sutcliffe
% Source   : [Ben16]
% Names    : Sledgehammer_Inconsistency_S5U_direct_satallax.p [Ben16]

% Status   : ContradictoryAxioms
% Rating   : 0.38 v9.0.0, 0.40 v8.2.0, 0.69 v8.1.0, 0.73 v7.5.0, 0.57 v7.4.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0, 0.71 v6.4.0
% Syntax   : Number of formulae    :   17 (   4 unt;   7 typ;   0 def)
%            Number of atoms       :   25 (   3 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   69 (   4   ~;   0   |;   1   &;  51   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   1 con; 0-3 aty)
%            Number of variables   :   32 (  11   ^;  20   !;   1   ?;  32   :)
% SPC      : TH0_CAX_EQU_NAR

% Comments : This problem file has been generated by Sledgehammer (satallax
%            translation) in default setting.
%          : The $false conjecture makes this correspond to the Isabelle
%            sources. Otherwise it could be omitted and the status would be
%            Unsatisfiable.
%------------------------------------------------------------------------------
%----Could-be-implicit typings (2)
thf(ty_n_t__QML____S5__O__092__060mu__062,type,
    qML_mu: $tType ).

thf(ty_n_t__QML____S5__Oi,type,
    qML_i: $tType ).

%----Explicit typings (5)
thf(sy_c_Inconsistency__S5_OG,type,
    inconsistency_G: qML_mu > qML_i > $o ).

thf(sy_c_Inconsistency__S5_ONE_001t__QML____S5__O__092__060mu__062,type,
    incons1905966852QML_mu: qML_mu > qML_i > $o ).

thf(sy_c_Inconsistency__S5_OP,type,
    inconsistency_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).

thf(sy_c_Inconsistency__S5_Oess_001t__QML____S5__O__092__060mu__062,type,
    incons1389517216QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).

thf(sy_c_QML__S5_Or,type,
    qML_r: qML_i > qML_i > $o ).

%----Relevant facts (9)
thf(fact_0_A1a,axiom,
    ! [W: qML_i,X: qML_mu > qML_i > $o] :
      ( ( inconsistency_P
        @ ^ [Y: qML_mu,Z: qML_i] :
            ~ ( X @ Y @ Z )
        @ W )
     => ~ ( inconsistency_P @ X @ W ) ) ).

% A1a
thf(fact_1_A1b,axiom,
    ! [W: qML_i,X: qML_mu > qML_i > $o] :
      ( ~ ( inconsistency_P @ X @ W )
     => ( inconsistency_P
        @ ^ [Y: qML_mu,Z: qML_i] :
            ~ ( X @ Y @ Z )
        @ W ) ) ).

% A1b
thf(fact_2_A2,axiom,
    ! [W: qML_i,X: qML_mu > qML_i > $o,Xa: qML_mu > qML_i > $o] :
      ( ( ( inconsistency_P @ X @ W )
        & ! [V: qML_i] :
            ( ( qML_r @ W @ V )
           => ! [Xb: qML_mu] :
                ( ( X @ Xb @ V )
               => ( Xa @ Xb @ V ) ) ) )
     => ( inconsistency_P @ Xa @ W ) ) ).

% A2
thf(fact_3_A3,axiom,
    ! [X_1: qML_i] : ( inconsistency_P @ inconsistency_G @ X_1 ) ).

% A3
thf(fact_4_A4,axiom,
    ! [W: qML_i,X: qML_mu > qML_i > $o] :
      ( ( inconsistency_P @ X @ W )
     => ! [V2: qML_i] :
          ( ( qML_r @ W @ V2 )
         => ( inconsistency_P @ X @ V2 ) ) ) ).

% A4
thf(fact_5_A5,axiom,
    ! [X_1: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ X_1 ) ).

% A5
thf(fact_6_G__def,axiom,
    ( inconsistency_G
    = ( ^ [X2: qML_mu,W2: qML_i] :
        ! [Y: qML_mu > qML_i > $o] :
          ( ( inconsistency_P @ Y @ W2 )
         => ( Y @ X2 @ W2 ) ) ) ) ).

% G_def
thf(fact_7_NE__def,axiom,
    ( incons1905966852QML_mu
    = ( ^ [X2: qML_mu,W2: qML_i] :
        ! [Y: qML_mu > qML_i > $o] :
          ( ( incons1389517216QML_mu @ Y @ X2 @ W2 )
         => ! [V3: qML_i] :
              ( ( qML_r @ W2 @ V3 )
             => ? [Z: qML_mu] : ( Y @ Z @ V3 ) ) ) ) ) ).

% NE_def
thf(fact_8_ess__def,axiom,
    ( incons1389517216QML_mu
    = ( ^ [Phi: qML_mu > qML_i > $o,X2: qML_mu,W2: qML_i] :
        ! [Y: qML_mu > qML_i > $o] :
          ( ( Y @ X2 @ W2 )
         => ! [V3: qML_i] :
              ( ( qML_r @ W2 @ V3 )
             => ! [Z: qML_mu] :
                  ( ( Phi @ Z @ V3 )
                 => ( Y @ Z @ V3 ) ) ) ) ) ) ).

% ess_def

%----Conjectures (1)
thf(conj_0,conjecture,
    $false ).