%------------------------------------------------------------------------------
% File     : SWW469^1 : TPTP v8.2.0. Released v5.3.0.
% Domain   : Software Verification
% Problem  : Hoare's Logic with Procedures line 112, 100 axioms selected
% Version  : Especial.
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [Bla11]
% Names    : hoare_100_thf_l112 [Bla11]

% Status   : Theorem
% Rating   : 0.30 v8.2.0, 0.15 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0
% Syntax   : Number of formulae    :   10 (   5 unt;   4 typ;   0 def)
%            Number of atoms       :    7 (   2 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    4 (   3   ~;   0   |;   0   &;   0   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :    4 (   0   ^;   2   !;   2   ?;   4   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 18:59:06
%------------------------------------------------------------------------------
%----Should-be-implicit typings (1)
thf(ty_ty_tc__Com__Ostate,type,
    state: $tType ).

%----Explicit typings (3)
thf(sy_c_HOL_Oinduct__false,type,
    induct_false: $o ).

thf(sy_c_HOL_Oinduct__true,type,
    induct_true: $o ).

thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ostate__not__singleton,type,
    hoare_1821564147gleton: $o ).

%----Relevant facts (4)
thf(fact_0_state__not__singleton__def,axiom,
    ( hoare_1821564147gleton
  <=> ? [S: state,T: state] : S != T ) ).

thf(fact_1_induct__false__def,axiom,
    ~ induct_false ).

thf(fact_2_induct__trueI,axiom,
    induct_true ).

thf(fact_3_induct__true__def,axiom,
    induct_true ).

%----Conjectures (2)
thf(conj_0,hypothesis,
    hoare_1821564147gleton ).

thf(conj_1,conjecture,
    ! [T: state] :
      ~ ! [S: state] : S = T ).

%------------------------------------------------------------------------------