TPTP Problem File: NUN034^1.p
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% File : NUN034^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Number Theory
% Problem : International Mathematical Olympiad, 1966, Problem 1
% Version : [Mat16] axioms : Especial.
% English : In a mathematical contest, three problems, A, B, C were posed.
% Among the participants there were 25 students who solved at
% least one problem each. Of all the contestants who did not
% solve problem A, the number who solved B was twice the number
% who solved C. The number of students who solved only problem A
% was one more than the number of students who solved A and at
% least one other problem. Of all students who solved just one
% problem, half did not solve problem A. How many students solved
% only problem B?
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1966-1.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3485 ( 728 unt;1199 typ; 0 def)
% Number of atoms : 6510 (2235 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 39847 ( 105 ~; 243 |;1183 &;36189 @)
% (1095 <=>;1032 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4526 ( 374 atm;1206 fun;1006 num;1940 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1214 (1170 usr; 68 con; 0-9 aty)
% Number of variables : 8069 ( 414 ^;7086 !; 433 ?;8069 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: PA; Score: 6; Author: Takuya Matsuzaki;
% Generated: 2015-01-24
% : Answer
% ^ [V_numOnlyB_dot_0: $int] : ( V_numOnlyB_dot_0 = 6 ) )
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include('Axioms/MAT001^0.ax').
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thf(p_qustion,conjecture,
( 'find/1' @ $int
@ ^ [V_numOnlyB: $int] :
? [V_Students: 'ListOf' @ ( 'Triple' @ $int @ $int @ $int )] :
( ! [V_ABC_dot_7: 'Triple' @ $int @ $int @ $int] :
( ( 'member/2' @ ( 'Triple' @ $int @ $int @ $int ) @ V_ABC_dot_7 @ V_Students )
=> ? [V_A: $int,V_B: $int,V_C: $int] :
( ( V_ABC_dot_7
= ( 'triple/3' @ $int @ $int @ $int @ V_A @ V_B @ V_C ) )
& ( $is_int @ V_A )
& ( $is_int @ V_B )
& ( $is_int @ V_C )
& ( ( V_A = 0 )
| ( V_A = 1 ) )
& ( ( V_B = 0 )
| ( V_B = 1 ) )
& ( ( V_C = 0 )
| ( V_C = 1 ) ) ) )
& ( 25
= ( 'list-len/1' @ ( 'Triple' @ $int @ $int @ $int )
@ ( 'filter/2' @ ( 'Triple' @ $int @ $int @ $int )
@ ^ [V_ABC_dot_6: 'Triple' @ $int @ $int @ $int] :
( V_ABC_dot_6
!= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 0 @ 0 ) )
@ V_Students ) ) )
& ( ( 'list-len/1' @ ( 'Triple' @ $int @ $int @ $int )
@ ( 'filter/2' @ ( 'Triple' @ $int @ $int @ $int )
@ ^ [V_ABC_dot_5: 'Triple' @ $int @ $int @ $int] :
( ( V_ABC_dot_5
= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 1 @ 0 ) )
| ( V_ABC_dot_5
= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 1 @ 1 ) ) )
@ V_Students ) )
= ( $product @ 2
@ ( 'list-len/1' @ ( 'Triple' @ $int @ $int @ $int )
@ ( 'filter/2' @ ( 'Triple' @ $int @ $int @ $int )
@ ^ [V_ABC_dot_4: 'Triple' @ $int @ $int @ $int] :
( ( V_ABC_dot_4
= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 0 @ 1 ) )
| ( V_ABC_dot_4
= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 1 @ 1 ) ) )
@ V_Students ) ) ) )
& ( ( 'list-len/1' @ ( 'Triple' @ $int @ $int @ $int )
@ ( 'filter/2' @ ( 'Triple' @ $int @ $int @ $int )
@ ^ [V_ABC_dot_3: 'Triple' @ $int @ $int @ $int] :
( V_ABC_dot_3
= ( 'triple/3' @ $int @ $int @ $int @ 1 @ 0 @ 0 ) )
@ V_Students ) )
= ( $sum @ 1
@ ( 'list-len/1' @ ( 'Triple' @ $int @ $int @ $int )
@ ( 'filter/2' @ ( 'Triple' @ $int @ $int @ $int )
@ ^ [V_ABC_dot_2: 'Triple' @ $int @ $int @ $int] :
( ( V_ABC_dot_2
= ( 'triple/3' @ $int @ $int @ $int @ 1 @ 0 @ 1 ) )
| ( V_ABC_dot_2
= ( 'triple/3' @ $int @ $int @ $int @ 1 @ 0 @ 1 ) )
| ( V_ABC_dot_2
= ( 'triple/3' @ $int @ $int @ $int @ 1 @ 1 @ 1 ) ) )
@ V_Students ) ) ) )
& ( ( 'list-len/1' @ ( 'Triple' @ $int @ $int @ $int )
@ ( 'filter/2' @ ( 'Triple' @ $int @ $int @ $int )
@ ^ [V_ABC_dot_1: 'Triple' @ $int @ $int @ $int] :
( ( V_ABC_dot_1
= ( 'triple/3' @ $int @ $int @ $int @ 1 @ 0 @ 0 ) )
| ( V_ABC_dot_1
= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 1 @ 0 ) )
| ( V_ABC_dot_1
= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 0 @ 1 ) ) )
@ V_Students ) )
= ( $product @ 2
@ ( 'list-len/1' @ ( 'Triple' @ $int @ $int @ $int )
@ ( 'filter/2' @ ( 'Triple' @ $int @ $int @ $int )
@ ^ [V_ABC_dot_0: 'Triple' @ $int @ $int @ $int] :
( ( V_ABC_dot_0
= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 1 @ 0 ) )
| ( V_ABC_dot_0
= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 0 @ 1 ) ) )
@ V_Students ) ) ) )
& ( V_numOnlyB
= ( 'list-len/1' @ ( 'Triple' @ $int @ $int @ $int )
@ ( 'filter/2' @ ( 'Triple' @ $int @ $int @ $int )
@ ^ [V_ABC: 'Triple' @ $int @ $int @ $int] :
( V_ABC
= ( 'triple/3' @ $int @ $int @ $int @ 0 @ 1 @ 0 ) )
@ V_Students ) ) ) ) ) ).
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