TPTP Problem File: MSC029^1.p
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%------------------------------------------------------------------------------
% File : MSC029^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Miscellaneous (Permutation and combination)
% Problem : International Mathematical Olympiad, 1963, Problem 6
% Version : [Mat16] axioms : Especial.
% English : Five students, A, B, C, D, E, took part in a contest. One
% prediction was that the contestants would finish in the order
% ABCDE. This prediction was very poor. In fact no contestant
% finished in the position predicted, and no two contestants
% predicted to finish consecutively actually did so. A second
% prediction had the contestants finishing in the order DAECB.
% This prediction was better. Exactly two of the contestants
% finished in the places predicted, and two disjoint pairs of
% students predicted to finish consecutively actually did so.
% Determine the order in which the contestants finished.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1963-6.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3485 ( 711 unt;1199 typ; 0 def)
% Number of atoms : 7954 (2280 equ; 0 cnn)
% Maximal formula atoms : 95 ( 3 avg)
% Number of connectives : 39818 ( 149 ~; 244 |;1234 &;36065 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 8 avg)
% Number arithmetic : 4559 ( 371 atm;1219 fun;1027 num;1942 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1213 (1170 usr; 67 con; 0-9 aty)
% Number of variables : 8062 ( 407 ^;7085 !; 434 ?;8062 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: PA(comb); Score: 8; Author: Takuya Matsuzaki;
% Generated: 2015-01-24
% : Answer
% ^ [V_ABCDE_dot_0: ( 'ListOf' @ $real )] :
% ( V_ABCDE_dot_0
% = ( 'cons/2' @ $real @ 3.0 @ ( 'cons/2' @ $real @ 5.0 @ ( 'cons/2' @ $real @ 4.0 @ ( 'cons/2' @ $real @ 2.0 @ ( 'cons/2' @ $real @ 1.0 @ ( 'nil/0' @ $real ) ) ) ) ) ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p_qustion,conjecture,
( 'find/1' @ ( 'ListOf' @ $real )
@ ^ [V_ABCDE: 'ListOf' @ $real] :
? [V_A: $real,V_B: $real,V_C: $real,V_D: $real,V_E: $real] :
( ( V_ABCDE
= ( 'cons/2' @ $real @ V_A @ ( 'cons/2' @ $real @ V_B @ ( 'cons/2' @ $real @ V_C @ ( 'cons/2' @ $real @ V_D @ ( 'cons/2' @ $real @ V_E @ ( 'nil/0' @ $real ) ) ) ) ) ) )
& ( 'all/2' @ $real
@ ^ [V_x: $real] : ( 'member/2' @ $real @ V_x @ ( 'cons/2' @ $real @ 1.0 @ ( 'cons/2' @ $real @ 2.0 @ ( 'cons/2' @ $real @ 3.0 @ ( 'cons/2' @ $real @ 4.0 @ ( 'cons/2' @ $real @ 5.0 @ ( 'nil/0' @ $real ) ) ) ) ) ) )
@ ( 'cons/2' @ $real @ V_A @ ( 'cons/2' @ $real @ V_B @ ( 'cons/2' @ $real @ V_C @ ( 'cons/2' @ $real @ V_D @ ( 'cons/2' @ $real @ V_E @ ( 'nil/0' @ $real ) ) ) ) ) ) )
& ( 'pairwise-distinct/1' @ $real @ ( 'cons/2' @ $real @ V_A @ ( 'cons/2' @ $real @ V_B @ ( 'cons/2' @ $real @ V_C @ ( 'cons/2' @ $real @ V_D @ ( 'cons/2' @ $real @ V_E @ ( 'nil/0' @ $real ) ) ) ) ) ) )
& ( V_A != 1.0 )
& ( V_B != 2.0 )
& ( V_C != 3.0 )
& ( V_D != 4.0 )
& ( V_E != 5.0 )
& ( ( $sum @ V_A @ 1.0 )
!= V_B )
& ( ( $sum @ V_B @ 1.0 )
!= V_C )
& ( ( $sum @ V_C @ 1.0 )
!= V_D )
& ( ( $sum @ V_D @ 1.0 )
!= V_E )
& ( ( ( V_D = 1.0 )
& ( V_A = 2.0 )
& ( V_E != 3.0 )
& ( V_C != 4.0 )
& ( V_B != 5.0 ) )
| ( ( V_D = 1.0 )
& ( V_A != 2.0 )
& ( V_E = 3.0 )
& ( V_C != 4.0 )
& ( V_B != 5.0 ) )
| ( ( V_D = 1.0 )
& ( V_A != 2.0 )
& ( V_E != 3.0 )
& ( V_C = 4.0 )
& ( V_B != 5.0 ) )
| ( ( V_D = 1.0 )
& ( V_A != 2.0 )
& ( V_E != 3.0 )
& ( V_C != 4.0 )
& ( V_B = 5.0 ) )
| ( ( V_D != 1.0 )
& ( V_A = 2.0 )
& ( V_E = 3.0 )
& ( V_C != 4.0 )
& ( V_B != 5.0 ) )
| ( ( V_D != 1.0 )
& ( V_A = 2.0 )
& ( V_E != 3.0 )
& ( V_C = 4.0 )
& ( V_B != 5.0 ) )
| ( ( V_D != 1.0 )
& ( V_A = 2.0 )
& ( V_E != 3.0 )
& ( V_C != 4.0 )
& ( V_B = 5.0 ) )
| ( ( V_D != 1.0 )
& ( V_A != 2.0 )
& ( V_E = 3.0 )
& ( V_C = 4.0 )
& ( V_B != 5.0 ) )
| ( ( V_D != 1.0 )
& ( V_A != 2.0 )
& ( V_E = 3.0 )
& ( V_C != 4.0 )
& ( V_B = 5.0 ) )
| ( ( V_D != 1.0 )
& ( V_A != 2.0 )
& ( V_E != 3.0 )
& ( V_C = 4.0 )
& ( V_B = 5.0 ) ) )
& ( ( ( ( $sum @ V_D @ 1.0 )
= V_A )
& ( ( $sum @ V_A @ 1.0 )
!= V_E )
& ( ( $sum @ V_E @ 1.0 )
= V_C )
& ( ( $sum @ V_C @ 1.0 )
!= V_B ) )
| ( ( ( $sum @ V_D @ 1.0 )
= V_A )
& ( ( $sum @ V_A @ 1.0 )
!= V_E )
& ( ( $sum @ V_E @ 1.0 )
!= V_C )
& ( ( $sum @ V_C @ 1.0 )
= V_B ) )
| ( ( ( $sum @ V_D @ 1.0 )
!= V_A )
& ( ( $sum @ V_A @ 1.0 )
= V_E )
& ( ( $sum @ V_E @ 1.0 )
!= V_C )
& ( ( $sum @ V_C @ 1.0 )
= V_B ) ) ) ) ) ).
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