%------------------------------------------------------------------------------
% File     : SWC455_1 : TPTP v9.0.0. Released v9.0.0.
% Domain   : Software Creation
% Problem  : Prove equivalence of small and fast program for sequence A94390
% Version  : Especial.
% English  : Terms: 2 4 6 8 10 13 15 17 19 21 24 26 28 30 32 35 37 39 41 43
%            Small: 2+((((x-(x/((2*(2*(2*(2+2))))-2)))/(1+(2+2)))+x)+x)
%            Fast : ((((((1+(2+2))*(1+x))+x)/((2*(2*(2*(2+2))))-1))+2)+x)+x

% Refs     : [GB+23] Gauthier et al. (2023), A Mathematical Benchmark for I
%          : [Git23] https://github.com/ai4reason/oeis-atp-benchmark
% Source   : [Git23]
% Names    : A94390 [Git23]

% Status   : CounterSatisfiable
% Rating   : 1.00 v9.0.0
% Syntax   : Number of formulae    :    5 (   2 unt;   2 typ;   0 def)
%            Number of atoms       :    7 (   3 equ)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :    3 (   2   ~;   0   |;   1   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :   10 (   3 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number arithmetic     :   50 (   1 atm;  24 fun;  22 num;   3 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    8 (   2 usr;   3 con; 0-2 aty)
%            Number of variables   :    3 (;   2   !;   1   ?;   3   :)
% SPC      : TX0_CSA_EQU_ARI

% Comments : Not in an "aind_*" subset, i.e., unlikely to require induction.
%------------------------------------------------------------------------------
tff(fast,type,
    fast: $int > $int ).

tff(small,type,
    small: $int > $int ).

%----∀ x:Int (small(x) = (2 + ((((x - (x div ((2 * (2 * (2 * (2 + 2)))) - 2)))
%----div (1 + (2 + 2))) + x) + x)))
tff(formula_1,axiom,
    ! [X: $int] : ( small(X) = $sum(2,$sum($sum('div:(Int*Int)>Int'($difference(X,'div:(Int*Int)>Int'(X,$difference($product(2,$product(2,$product(2,$sum(2,2)))),2))),$sum(1,$sum(2,2))),X),X)) ) ).

%----∀ x:Int (fast(x) = (((((((1 + (2 + 2)) * (1 + x)) + x) div ((2 * (2 * (2 *
%----(2 + 2)))) - 1)) + 2) + x) + x))
tff(formula_2,axiom,
    ! [X: $int] : ( fast(X) = $sum($sum($sum('div:(Int*Int)>Int'($sum($product($sum(1,$sum(2,2)),$sum(1,X)),X),$difference($product(2,$product(2,$product(2,$sum(2,2)))),1)),2),X),X) ) ).

%----∃ c:Int ((c ≥ 0) ∧ ¬(small(c) = fast(c)))
tff(conjecture_1,conjecture,
    ~ ? [C: $int] :
        ( $greatereq(C,0)
        & ( small(C) != fast(C) ) ) ).

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