TPTP Problem File: MSC008-1.010.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : MSC008-1.010 : TPTP v8.2.0. Released v1.0.0.
% Domain : Miscellaneous
% Problem : The (in)constructability of Graeco-Latin Squares
% Version : [Rob63] axioms : Especial.
% English : The constructibility of Graeco-Latin squares of order 4t+2.
% This is impossible for t=0,1, but possible for all other
% cases. The size is the size of the squares.
% Refs : [Rob63] Robinson (1963), Theorem Proving on the Computer
% Source : [TPTP]
% Names :
% Status : Satisfiable
% Rating : 1.00 v2.1.0
% Syntax : Number of clauses : 61 ( 46 unt; 6 nHn; 54 RR)
% Number of literals : 136 ( 0 equ; 66 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 3 usr; 0 prp; 2-3 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 51 ( 0 sgn)
% SPC : CNF_SAT_EPR_NEQ
% Comments :
% : tptp2X: -f tptp -s10 MSC008-1.g
%--------------------------------------------------------------------------
cnf(p_1_is_not_p_2,axiom,
~ eq(p_1,p_2) ).
cnf(p_1_is_not_p_3,axiom,
~ eq(p_1,p_3) ).
cnf(p_1_is_not_p_4,axiom,
~ eq(p_1,p_4) ).
cnf(p_1_is_not_p_5,axiom,
~ eq(p_1,p_5) ).
cnf(p_1_is_not_p_6,axiom,
~ eq(p_1,p_6) ).
cnf(p_1_is_not_p_7,axiom,
~ eq(p_1,p_7) ).
cnf(p_1_is_not_p_8,axiom,
~ eq(p_1,p_8) ).
cnf(p_1_is_not_p_9,axiom,
~ eq(p_1,p_9) ).
cnf(p_1_is_not_p_10,axiom,
~ eq(p_1,p_10) ).
cnf(p_2_is_not_p_3,axiom,
~ eq(p_2,p_3) ).
cnf(p_2_is_not_p_4,axiom,
~ eq(p_2,p_4) ).
cnf(p_2_is_not_p_5,axiom,
~ eq(p_2,p_5) ).
cnf(p_2_is_not_p_6,axiom,
~ eq(p_2,p_6) ).
cnf(p_2_is_not_p_7,axiom,
~ eq(p_2,p_7) ).
cnf(p_2_is_not_p_8,axiom,
~ eq(p_2,p_8) ).
cnf(p_2_is_not_p_9,axiom,
~ eq(p_2,p_9) ).
cnf(p_2_is_not_p_10,axiom,
~ eq(p_2,p_10) ).
cnf(p_3_is_not_p_4,axiom,
~ eq(p_3,p_4) ).
cnf(p_3_is_not_p_5,axiom,
~ eq(p_3,p_5) ).
cnf(p_3_is_not_p_6,axiom,
~ eq(p_3,p_6) ).
cnf(p_3_is_not_p_7,axiom,
~ eq(p_3,p_7) ).
cnf(p_3_is_not_p_8,axiom,
~ eq(p_3,p_8) ).
cnf(p_3_is_not_p_9,axiom,
~ eq(p_3,p_9) ).
cnf(p_3_is_not_p_10,axiom,
~ eq(p_3,p_10) ).
cnf(p_4_is_not_p_5,axiom,
~ eq(p_4,p_5) ).
cnf(p_4_is_not_p_6,axiom,
~ eq(p_4,p_6) ).
cnf(p_4_is_not_p_7,axiom,
~ eq(p_4,p_7) ).
cnf(p_4_is_not_p_8,axiom,
~ eq(p_4,p_8) ).
cnf(p_4_is_not_p_9,axiom,
~ eq(p_4,p_9) ).
cnf(p_4_is_not_p_10,axiom,
~ eq(p_4,p_10) ).
cnf(p_5_is_not_p_6,axiom,
~ eq(p_5,p_6) ).
cnf(p_5_is_not_p_7,axiom,
~ eq(p_5,p_7) ).
cnf(p_5_is_not_p_8,axiom,
~ eq(p_5,p_8) ).
cnf(p_5_is_not_p_9,axiom,
~ eq(p_5,p_9) ).
cnf(p_5_is_not_p_10,axiom,
~ eq(p_5,p_10) ).
cnf(p_6_is_not_p_7,axiom,
~ eq(p_6,p_7) ).
cnf(p_6_is_not_p_8,axiom,
~ eq(p_6,p_8) ).
cnf(p_6_is_not_p_9,axiom,
~ eq(p_6,p_9) ).
cnf(p_6_is_not_p_10,axiom,
~ eq(p_6,p_10) ).
cnf(p_7_is_not_p_8,axiom,
~ eq(p_7,p_8) ).
cnf(p_7_is_not_p_9,axiom,
~ eq(p_7,p_9) ).
cnf(p_7_is_not_p_10,axiom,
~ eq(p_7,p_10) ).
cnf(p_8_is_not_p_9,axiom,
~ eq(p_8,p_9) ).
cnf(p_8_is_not_p_10,axiom,
~ eq(p_8,p_10) ).
cnf(p_9_is_not_p_10,axiom,
~ eq(p_9,p_10) ).
cnf(reflexivity,axiom,
eq(X,X) ).
cnf(symmetry,axiom,
( ~ eq(X,Y)
| eq(Y,X) ) ).
cnf(latin_element_is_unique,axiom,
( ~ latin(Row,Column,Label1)
| ~ latin(Row,Column,Label2)
| eq(Label1,Label2) ) ).
cnf(latin_column_is_unique,axiom,
( ~ latin(Row,Column1,Label)
| ~ latin(Row,Column2,Label)
| eq(Column1,Column2) ) ).
cnf(latin_row_is_unique,axiom,
( ~ latin(Row1,Column,Label)
| ~ latin(Row2,Column,Label)
| eq(Row1,Row2) ) ).
cnf(greek_element_is_unique,axiom,
( ~ greek(Row,Column,Label1)
| ~ greek(Row,Column,Label2)
| eq(Label1,Label2) ) ).
cnf(greek_column_is_unique,axiom,
( ~ greek(Row,Column1,Label)
| ~ greek(Row,Column2,Label)
| eq(Column1,Column2) ) ).
cnf(greek_row_is_unique,axiom,
( ~ greek(Row1,Column,Label)
| ~ greek(Row2,Column,Label)
| eq(Row1,Row2) ) ).
cnf(latin_cell_element,axiom,
( latin(Row,Column,p_1)
| latin(Row,Column,p_2)
| latin(Row,Column,p_3)
| latin(Row,Column,p_4)
| latin(Row,Column,p_5)
| latin(Row,Column,p_6)
| latin(Row,Column,p_7)
| latin(Row,Column,p_8)
| latin(Row,Column,p_9)
| latin(Row,Column,p_10) ) ).
cnf(latin_column_required,axiom,
( latin(Row,p_1,Label)
| latin(Row,p_2,Label)
| latin(Row,p_3,Label)
| latin(Row,p_4,Label)
| latin(Row,p_5,Label)
| latin(Row,p_6,Label)
| latin(Row,p_7,Label)
| latin(Row,p_8,Label)
| latin(Row,p_9,Label)
| latin(Row,p_10,Label) ) ).
cnf(latin_row_required,axiom,
( latin(p_1,Column,Label)
| latin(p_2,Column,Label)
| latin(p_3,Column,Label)
| latin(p_4,Column,Label)
| latin(p_5,Column,Label)
| latin(p_6,Column,Label)
| latin(p_7,Column,Label)
| latin(p_8,Column,Label)
| latin(p_9,Column,Label)
| latin(p_10,Column,Label) ) ).
cnf(greek_cell_element,axiom,
( greek(Row,Column,p_1)
| greek(Row,Column,p_2)
| greek(Row,Column,p_3)
| greek(Row,Column,p_4)
| greek(Row,Column,p_5)
| greek(Row,Column,p_6)
| greek(Row,Column,p_7)
| greek(Row,Column,p_8)
| greek(Row,Column,p_9)
| greek(Row,Column,p_10) ) ).
cnf(greek_column_required,axiom,
( greek(Row,p_1,Label)
| greek(Row,p_2,Label)
| greek(Row,p_3,Label)
| greek(Row,p_4,Label)
| greek(Row,p_5,Label)
| greek(Row,p_6,Label)
| greek(Row,p_7,Label)
| greek(Row,p_8,Label)
| greek(Row,p_9,Label)
| greek(Row,p_10,Label) ) ).
cnf(greek_row_required,axiom,
( greek(p_1,Column,Label)
| greek(p_2,Column,Label)
| greek(p_3,Column,Label)
| greek(p_4,Column,Label)
| greek(p_5,Column,Label)
| greek(p_6,Column,Label)
| greek(p_7,Column,Label)
| greek(p_8,Column,Label)
| greek(p_9,Column,Label)
| greek(p_10,Column,Label) ) ).
cnf(no_two_same1,negated_conjecture,
( ~ greek(Row1,Column1,Label1)
| ~ latin(Row1,Column1,Label2)
| ~ greek(Row2,Column2,Label1)
| ~ latin(Row2,Column2,Label2)
| eq(Column1,Column2) ) ).
cnf(no_two_same2,negated_conjecture,
( ~ greek(Row1,Column1,Label1)
| ~ latin(Row1,Column1,Label2)
| ~ greek(Row2,Column2,Label1)
| ~ latin(Row2,Column2,Label2)
| eq(Row1,Row2) ) ).
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