## TPTP Problem File: RAL050^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : RAL050^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Functions and their graphs)
% Problem  : Hokkaido University, 1999, Humanities Course, Problem 2
% 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    : Univ-Hokkaido-1999-Bun-2.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3486 (   0 unit;1200 type;   0 defn)
%            Number of atoms       : 45360 (2211 equality;22710 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39651 ( 104   ~; 233   |;1181   &;36007   @)
%                                         (1095 <=>;1031  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1247 (1200   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8060 (  66 sgn;7085   !; 433   ?; 406   ^)
%                                         (8060   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1974 (   6 prd;   9 fun;  23 num;1936 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: RCF; Author: Hidenao Iwane; Generated: 2014-01-09
%            ^ [V_B_dot_0: '2d.Point'] :
%              ( ( \$less @ 0.0 @ 'a/0' )
%              & ( \$less @ 'a/0' @ 1.0 )
%              & ( V_B_dot_0
%                = ( '2d.point/2' @ 'a/0' @ 0.0 ) ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf('a/0_type',type,(
'a/0': \$real )).

thf(p1_simpl_qustion,conjecture,
( 'find/1' @ '2d.Point'
@ ( ^ [V_B: '2d.Point'] :
? [V_A: '2d.Point',V_F: '2d.Shape',V_G: '2d.Shape',V_O: '2d.Point'] :
( ( \$less @ 0.0 @ 'a/0' )
& ( \$less @ 'a/0' @ 1.0 )
& ( V_F
= ( '2d.graph-of/1' @ ( 'poly-fun/1' @ ( 'cons/2' @ \$real @ 1.0 @ ( 'cons/2' @ \$real @ 0.0 @ ( 'cons/2' @ \$real @ ( \$uminus @ 1.0 ) @ ( 'nil/0' @ \$real ) ) ) ) ) ) )
& ( V_G
= ( '2d.graph-of/1' @ ( 'poly-fun/1' @ ( 'cons/2' @ \$real @ 0.0 @ ( 'cons/2' @ \$real @ 0.0 @ ( 'cons/2' @ \$real @ ( \$sum @ ( \$quotient @ 1.0 @ ( '^/2' @ 'a/0' @ 2.0 ) ) @ ( \$uminus @ 1.0 ) ) @ ( 'nil/0' @ \$real ) ) ) ) ) ) )
& ( '2d.on/2' @ V_A @ V_F )
& ( '2d.on/2' @ V_A @ V_G )
& ( '2d.on/2' @ V_A @ '2d.1st-quadrant/0' )
& ( '2d.on/2' @ V_B @ '2d.x-axis/0' )
& ( '2d.perpendicular/2' @ ( '2d.line/2' @ V_A @ V_B ) @ '2d.x-axis/0' )
& ( V_O = '2d.origin/0' ) ) ) )).
%------------------------------------------------------------------------------
```