TPTP Problem File: ARI628=1.p

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% File     : ARI628=1 : TPTP v7.4.0. Released v6.3.0.
% Domain   : Arithmetic
% Problem  : Example 0
% Version  : Especial.
% English  :

% Refs     : [ALR14] Avigad et al. (2014), A Heuristic Prover for Real Ineq
%          : [LAR14] Lewis et al. (2014), A Heuristic Prover for Real Inequ
%          : [Lew14] Lewis (2014), Email to Geoff Sutcliffe
% Source   : [Lew14]
% Names    : Example 0 [Lew14]

% Status   : Theorem
% Rating   : 0.40 v7.4.0, 0.50 v7.3.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.67 v6.4.0, 1.00 v6.3.0
% Syntax   : Number of formulae    :   10 (   6 unit;   4 type)
%            Number of atoms       :    6 (   0 equality)
%            Maximal formula depth :    2 (   1 average)
%            Number of connectives :    0 (   0   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   5 propositional; 0-2 arity)
%            Number of functors    :    8 (   7 constant; 0-2 arity)
%            Number of variables   :    0 (   0 sgn;   0   !;   0   ?)
%                                         (   0   :;   0  !>;   0  ?*)
%            Maximal term depth    :    4 (   1 average)
%            Arithmetic symbols    :    8 (   4 prd;   1 fun;   3 num;   0 var)
% SPC      : TF0_THM_NEQ_ARI

% Comments :
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tff(y_type,type,(
    y: $real )).

tff(x_type,type,(
    x: $real )).

tff(v_type,type,(
    v: $real )).

tff(u_type,type,(
    u: $real )).

tff(hypothesis_00,hypothesis,(
    $greater(u,0.0) )).

tff(hypothesis_01,hypothesis,(
    $less(u,v) )).

tff(hypothesis_02,hypothesis,(
    $less(v,1.0) )).

tff(hypothesis_03,hypothesis,(
    $greatereq(x,2.0) )).

tff(hypothesis_04,hypothesis,(
    $lesseq(x,y) )).

tff(conclusion,conjecture,(
    $less($product($product(2.0,$product(u,u)),x),$product($product(y,y),v)) )).

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