TPTP Problem File: RAL005^1.p

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%------------------------------------------------------------------------------
% File     : RAL005^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Numbers and algebraic expressions)
% Problem  : Chart System Math I+A Red Book, Problem 07CR1E017
% Version  : [Mat16] axioms : Especial.
% English  : 

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : Chart-1A-Red-07CR1E017.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45363 (2209 equality;22717 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39659 ( 104   ~; 233   |;1180   &;36016   @)
%                                         (1095 <=>;1031  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1246 (1199   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8062 (  66 sgn;7085   !; 432   ?; 409   ^)
%                                         (8062   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1980 (   6 prd;   9 fun;  23 num;1942 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: PA; Level: 5; Author: Munehiro Kobayashi;
%            Generated: 2015-01-07
%          : Answer
%            ^ [V_answer_dot_0: ( ''ListOf'' @ $int )] :
%              ( V_answer_dot_0
%              = ( 'cons/2' @ $int @ 8 @ ( 'cons/2' @ $int @ 9 @ ( 'nil/0' @ $int ) ) ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p1_qustion,conjecture,
    ( 'find/1' @ ( 'ListOf' @ $int )
    @ ( ^ [V_answer: ( 'ListOf' @ $int )] : 
        ? [V_a: $int,V_b: $int] : 
          ( ( V_answer
            = ( 'cons/2' @ $int @ V_a @ ( 'cons/2' @ $int @ V_b @ ( 'nil/0' @ $int ) ) ) )
          & ( 'int.is-natural-number/1' @ V_a )
          & ( 'int.is-natural-number/1' @ V_b )
          & ( $less @ V_a @ V_b )
          & ( $less @ ( $sum @ ( $quotient @ ( $to_rat @ 1 ) @ ( $to_rat @ V_a ) ) @ ( $quotient @ ( $to_rat @ 1 ) @ ( $to_rat @ V_b ) ) ) @ ( $quotient @ ( $to_rat @ 1 ) @ ( $to_rat @ 4 ) ) )
          & ( 'minimum/3' @ $int
            @ ( 'set-by-def/1' @ $int
              @ ( ^ [V_b0: $int] : 
                    ( ( 'int.is-natural-number/1' @ V_b0 )
                    & ? [V_a0: $int] : 
                        ( ( 'int.is-natural-number/1' @ V_a0 )
                        & ( $less @ V_a0 @ V_b0 )
                        & ( $less @ ( $sum @ ( $quotient @ ( $to_rat @ 1 ) @ ( $to_rat @ V_a0 ) ) @ ( $quotient @ ( $to_rat @ 1 ) @ ( $to_rat @ V_b0 ) ) ) @ ( $quotient @ ( $to_rat @ 1 ) @ ( $to_rat @ 4 ) ) ) ) ) ) )
            @ ( ^ [V_lhs: $int,V_rhs: $int] : 
                  ( $less @ V_lhs @ V_rhs ) ) @ V_b ) ) ) )).
%------------------------------------------------------------------------------