%------------------------------------------------------------------------------
% File     : SWW469_1 : TPTP v9.0.0. 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_tff_l112 [Bla11]

% Status   : Theorem
% Rating   : 0.00 v5.3.0
% Syntax   : Number of formulae    :   10 (   5 unt;   4 typ;   0 def)
%            Number of atoms       :    7 (   2 equ)
%            Maximal formula atoms :    2 (   0 avg)
%            Number of connectives :    4 (   3   ~;   0   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    4 (   2   !;   2   ?;   4   :)
% SPC      : TF0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 15:18:09
%------------------------------------------------------------------------------
%----Should-be-implicit typings (1)
tff(ty_ty_tc__Com__Ostate,type,
    state: $tType ).

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

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

tff(sy_c_Hoare__Mirabelle__yiemogtkbg_Ostate__not__singleton,type,
    hoare_1310879719gleton: $o ).

%----Relevant facts (4)
tff(fact_0_state__not__singleton__def,axiom,
    ( hoare_1310879719gleton
  <=> ? [S: state,T: state] : ( S != T ) ) ).

tff(fact_1_induct__false__def,axiom,
    ~ induct_false ).

tff(fact_2_induct__trueI,axiom,
    induct_true ).

tff(fact_3_induct__true__def,axiom,
    induct_true ).

%----Conjectures (2)
tff(conj_0,hypothesis,
    hoare_1310879719gleton ).

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

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