## TPTP Problem File: PUZ037-2.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : PUZ037-2 : TPTP v8.1.0. Released v2.3.0.
% Domain   : Puzzles
% Problem  : Rubik's Cube
% Version  : [HM98] axioms : Especial.
%            Theorem formulation : Rotations in two planes.
% English  : Rubik's Cube is a 3x3x3 cube consisting of 27 subcubes with
%            colored faces. The three layers perpendicular to any axis may
%            be rotated independently. The object is to take a scrambled
%            cube and unscramble it so that each side consists entirely
%            of one color(Blue, White, Green, Yellow, Orange, Red).

% Refs     : [HM98]  Huang & Myers (1998), Subgoal Strategies for Solving B
% Source   : [HM98]
% Names    : Rubik's Cube [HM98]

% Status   : Unsatisfiable
% Rating   : 0.33 v8.1.0, 0.00 v7.3.0, 0.20 v7.2.0, 0.22 v7.1.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.25 v6.2.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.33 v5.0.0, 0.17 v4.1.0, 0.20 v3.7.0, 0.25 v3.5.0, 0.00 v3.3.0, 0.33 v3.2.0, 0.00 v3.1.0, 0.22 v2.7.0, 0.00 v2.6.0, 0.22 v2.5.0, 0.25 v2.4.0, 0.33 v2.3.0
% Syntax   : Number of clauses     :   20 (   2 unt;   0 nHn;  20 RR)
%            Number of literals    :   38 (   0 equ;  19 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 54-54 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :  972 (   0 sgn)
% SPC      : CNF_UNS_EPR_NEQ_HRN

% Comments : mxy, rzx, lzx rotations to solve.
%--------------------------------------------------------------------------
cnf(make_like_this,negated_conjecture,
~ state(b,b,b,b,b,b,b,b,b,r,r,r,g,g,g,o,o,o,y,y,y,r,r,r,g,g,g,o,o,o,y,y,y,r,r,r,g,g,g,o,o,o,y,y,y,w,w,w,w,w,w,w,w,w) ).

cnf(start_with_this,hypothesis,
state(y,b,y,y,b,y,y,b,y,r,r,r,b,g,b,o,o,o,w,y,w,w,y,w,r,r,r,b,g,b,o,o,o,r,r,r,b,g,b,o,o,o,w,y,w,g,w,g,g,w,g,g,w,g) ).

cnf(txy,axiom,
( ~ state(W7,W6,W5,W8,A1,W4,W1,W2,W3,Y1,Y2,Y3,X1,X2,X3,X4,X5,X6,X7,X8,X9,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,D7)
| state(W1,W8,W7,W2,A1,W6,W3,W4,W5,X1,X2,X3,X4,X5,X6,X7,X8,X9,Y1,Y2,Y3,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,D7) ) ).

cnf(mxy,axiom,
( ~ state(A1,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,Y1,Y2,Y3,X1,X2,X3,X4,X5,X6,X7,X8,X9,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,D7,D8,D9,E1,E2,E3,E4,E5,E6)
| state(A1,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,X1,X2,X3,X4,X5,X6,X7,X8,X9,Y1,Y2,Y3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,D7,D8,D9,E1,E2,E3,E4,E5,E6) ) ).

cnf(bxy,axiom,
( ~ state(A1,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,Y1,Y2,Y3,X1,X2,X3,X4,X5,X6,X7,X8,X9,W7,W8,W1,W6,D7,W2,W5,W4,W3)
| state(A1,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,X1,X2,X3,X4,X5,X6,X7,X8,X9,Y1,Y2,Y3,W1,W2,W3,W8,D7,W4,W7,W6,W5) ) ).

cnf(fzy,axiom,
( ~ state(A1,A2,A3,A4,A5,A6,V1,U1,Y1,A7,A8,W1,V2,U2,Y2,X1,A9,B1,B2,B3,B4,B5,B6,W2,V3,U3,Y3,X2,B7,B8,B9,C1,C2,C3,C4,W3,V4,U4,Y4,X3,C5,C6,C7,C8,C9,V5,U5,Y5,D1,D2,D3,D4,D5,D6)
| state(A1,A2,A3,A4,A5,A6,X1,X2,X3,A7,A8,Y1,Y2,Y3,Y4,Y5,A9,B1,B2,B3,B4,B5,B6,U1,U2,U3,U4,U5,B7,B8,B9,C1,C2,C3,C4,V1,V2,V3,V4,V5,C5,C6,C7,C8,C9,W1,W2,W3,D1,D2,D3,D4,D5,D6) ) ).

cnf(mzy,axiom,
( ~ state(A1,A2,A3,Y1,Y2,Y3,A4,A5,A6,A7,X9,A8,A9,B1,B2,B3,X1,B4,B5,B6,B7,B8,X8,B9,C1,C2,C3,C4,X2,C5,C6,C7,C8,C9,X7,D1,D2,D3,D4,D5,X3,D6,D7,D8,D9,E1,E2,E3,X6,X5,X4,E4,E5,E6)
| state(A1,A2,A3,X1,X2,X3,A4,A5,A6,A7,Y3,A8,A9,B1,B2,B3,X4,B4,B5,B6,B7,B8,Y2,B9,C1,C2,C3,C4,X5,C5,C6,C7,C8,C9,Y1,D1,D2,D3,D4,D5,X6,D6,D7,D8,D9,E1,E2,E3,X9,X8,X7,E4,E5,E6) ) ).

cnf(bzy,axiom,
( ~ state(Y1,Y2,Y3,A1,A2,A3,A4,A5,A6,X9,A7,A8,A9,B1,B2,B3,B4,X1,W1,W8,W7,X8,B5,B6,B7,B8,B9,C1,C2,X2,W2,C3,W6,X7,C4,C5,C6,C7,C8,C9,D1,X3,W3,W4,W5,D2,D3,D4,D5,D6,D7,X6,X5,X4)
| state(X1,X2,X3,A1,A2,A3,A4,A5,A6,Y3,A7,A8,A9,B1,B2,B3,B4,X4,W3,W2,W1,Y2,B5,B6,B7,B8,B9,C1,C2,X5,W4,C3,W8,Y1,C4,C5,C6,C7,C8,C9,D1,X6,W5,W6,W7,D2,D3,D4,D5,D6,D7,X9,X8,X7) ) ).

cnf(lzx,axiom,
( ~ state(Y1,A1,A2,Y2,A3,A4,Y3,A5,A6,W7,W8,W1,X1,A7,A8,A9,B1,B2,B3,B4,X9,W6,B5,W2,X2,B6,B7,B8,B9,C1,C2,C3,X8,W5,W4,W3,X3,C4,C5,C6,C7,C8,C9,D1,X7,X4,D2,D3,X5,D4,D5,X6,D6,D7)
| state(X1,A1,A2,X2,A3,A4,X3,A5,A6,W1,W2,W3,X4,A7,A8,A9,B1,B2,B3,B4,Y3,W8,B5,W4,X5,B6,B7,B8,B9,C1,C2,C3,Y2,W7,W6,W5,X6,C4,C5,C6,C7,C8,C9,D1,Y1,X7,D2,D3,X8,D4,D5,X9,D6,D7) ) ).

cnf(mzx,axiom,
( ~ state(A1,Y1,A2,A3,Y2,A4,A5,Y3,A6,A7,A8,A9,B1,X1,B2,B3,B4,B5,B6,X9,B7,B8,B9,C1,C2,X2,C3,C4,C5,C6,C7,X8,C8,C9,D1,D2,D3,X3,D4,D5,D6,D7,D8,X7,D9,E1,X4,E2,E3,X5,E4,E5,X6,E6)
| state(A1,X1,A2,A3,X2,A4,A5,X3,A6,A7,A8,A9,B1,X4,B2,B3,B4,B5,B6,Y3,B7,B8,B9,C1,C2,X5,C3,C4,C5,C6,C7,Y2,C8,C9,D1,D2,D3,X6,D4,D5,D6,D7,D8,Y1,D9,E1,X7,E2,E3,X8,E4,E5,X9,E6) ) ).

cnf(rzx,axiom,
( ~ state(A1,A2,Y1,A3,A4,Y2,A5,A6,Y3,A7,A8,A9,B1,B2,X1,W1,W8,W7,X9,B3,B4,B5,B6,B7,B8,B9,X2,W2,C1,W6,X8,C2,C3,C4,C5,C6,C7,C8,X3,W3,W4,W5,X7,C9,D1,D2,D3,X4,D4,D5,X5,D6,D7,X6)
| state(A1,A2,X1,A3,A4,X2,A5,A6,X3,A7,A8,A9,B1,B2,X4,W3,W2,W1,Y3,B3,B4,B5,B6,B7,B8,B9,X5,W4,C1,W8,Y2,C2,C3,C4,C5,C6,C7,C8,X6,W5,W6,W7,Y1,C9,D1,D2,D3,X7,D4,D5,X8,D6,D7,X9) ) ).

cnf(tyx,axiom,
( ~ state(W1,W8,W7,W2,A1,W6,W3,W4,W5,X1,X2,X3,X4,X5,X6,X7,X8,X9,Y1,Y2,Y3,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,D7)
| state(W7,W6,W5,W8,A1,W4,W1,W2,W3,Y1,Y2,Y3,X1,X2,X3,X4,X5,X6,X7,X8,X9,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,D7) ) ).

cnf(myx,axiom,
( ~ state(A1,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,X1,X2,X3,X4,X5,X6,X7,X8,X9,Y1,Y2,Y3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,D7,D8,D9,E1,E2,E3,E4,E5,E6)
| state(A1,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,Y1,Y2,Y3,X1,X2,X3,X4,X5,X6,X7,X8,X9,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,D7,D8,D9,E1,E2,E3,E4,E5,E6) ) ).

cnf(byx,axiom,
( ~ state(A1,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,X1,X2,X3,X4,X5,X6,X7,X8,X9,Y1,Y2,Y3,W1,W2,W3,W8,D7,W4,W7,W6,W5)
| state(A1,A2,A3,A4,A5,A6,A7,A8,A9,B1,B2,B3,B4,B5,B6,B7,B8,B9,C1,C2,C3,C4,C5,C6,C7,C8,C9,D1,D2,D3,D4,D5,D6,Y1,Y2,Y3,X1,X2,X3,X4,X5,X6,X7,X8,X9,W7,W8,W1,W6,D7,W2,W5,W4,W3) ) ).

cnf(fyz,axiom,
( ~ state(A1,A2,A3,A4,A5,A6,X1,X2,X3,A7,A8,Y1,Y2,Y3,Y4,Y5,A9,B1,B2,B3,B4,B5,B6,U1,U2,U3,U4,U5,B7,B8,B9,C1,C2,C3,C4,V1,V2,V3,V4,V5,C5,C6,C7,C8,C9,W1,W2,W3,D1,D2,D3,D4,D5,D6)
| state(A1,A2,A3,A4,A5,A6,V1,U1,Y1,A7,A8,W1,V2,U2,Y2,X1,A9,B1,B2,B3,B4,B5,B6,W2,V3,U3,Y3,X2,B7,B8,B9,C1,C2,C3,C4,W3,V4,U4,Y4,X3,C5,C6,C7,C8,C9,V5,U5,Y5,D1,D2,D3,D4,D5,D6) ) ).

cnf(myz,axiom,
( ~ state(A1,A2,A3,X1,X2,X3,A4,A5,A6,A7,Y3,A8,A9,B1,B2,B3,X4,B4,B5,B6,B7,B8,Y2,B9,C1,C2,C3,C4,X5,C5,C6,C7,C8,C9,Y1,D1,D2,D3,D4,D5,X6,D6,D7,D8,D9,E1,E2,E3,X9,X8,X7,E4,E5,E6)
| state(A1,A2,A3,Y1,Y2,Y3,A4,A5,A6,A7,X9,A8,A9,B1,B2,B3,X1,B4,B5,B6,B7,B8,X8,B9,C1,C2,C3,C4,X2,C5,C6,C7,C8,C9,X7,D1,D2,D3,D4,D5,X3,D6,D7,D8,D9,E1,E2,E3,X6,X5,X4,E4,E5,E6) ) ).

cnf(byz,axiom,
( ~ state(X1,X2,X3,A1,A2,A3,A4,A5,A6,Y3,A7,A8,A9,B1,B2,B3,B4,X4,W3,W2,W1,Y2,B5,B6,B7,B8,B9,C1,C2,X5,W4,C3,W8,Y1,C4,C5,C6,C7,C8,C9,D1,X6,W5,W6,W7,D2,D3,D4,D5,D6,D7,X9,X8,X7)
| state(Y1,Y2,Y3,A1,A2,A3,A4,A5,A6,X9,A7,A8,A9,B1,B2,B3,B4,X1,W1,W8,W7,X8,B5,B6,B7,B8,B9,C1,C2,X2,W2,C3,W6,X7,C4,C5,C6,C7,C8,C9,D1,X3,W3,W4,W5,D2,D3,D4,D5,D6,D7,X6,X5,X4) ) ).

cnf(lxz,axiom,
( ~ state(X1,A1,A2,X2,A3,A4,X3,A5,A6,W1,W2,W3,X4,A7,A8,A9,B1,B2,B3,B4,Y3,W8,B5,W4,X5,B6,B7,B8,B9,C1,C2,C3,Y2,W7,W6,W5,X6,C4,C5,C6,C7,C8,C9,D1,Y1,X7,D2,D3,X8,D4,D5,X9,D6,D7)
| state(Y1,A1,A2,Y2,A3,A4,Y3,A5,A6,W7,W8,W1,X1,A7,A8,A9,B1,B2,B3,B4,X9,W6,B5,W2,X2,B6,B7,B8,B9,C1,C2,C3,X8,W5,W4,W3,X3,C4,C5,C6,C7,C8,C9,D1,X7,X4,D2,D3,X5,D4,D5,X6,D6,D7) ) ).

cnf(mxz,axiom,
( ~ state(A1,X1,A2,A3,X2,A4,A5,X3,A6,A7,A8,A9,B1,X4,B2,B3,B4,B5,B6,Y3,B7,B8,B9,C1,C2,X5,C3,C4,C5,C6,C7,Y2,C8,C9,D1,D2,D3,X6,D4,D5,D6,D7,D8,Y1,D9,E1,X7,E2,E3,X8,E4,E5,X9,E6)
| state(A1,Y1,A2,A3,Y2,A4,A5,Y3,A6,A7,A8,A9,B1,X1,B2,B3,B4,B5,B6,X9,B7,B8,B9,C1,C2,X2,C3,C4,C5,C6,C7,X8,C8,C9,D1,D2,D3,X3,D4,D5,D6,D7,D8,X7,D9,E1,X4,E2,E3,X5,E4,E5,X6,E6) ) ).

cnf(rxz,axiom,
( ~ state(A1,A2,X1,A3,A4,X2,A5,A6,X3,A7,A8,A9,B1,B2,X4,W3,W2,W1,Y3,B3,B4,B5,B6,B7,B8,B9,X5,W4,C1,W8,Y2,C2,C3,C4,C5,C6,C7,C8,X6,W5,W6,W7,Y1,C9,D1,D2,D3,X7,D4,D5,X8,D6,D7,X9)
| state(A1,A2,Y1,A3,A4,Y2,A5,A6,Y3,A7,A8,A9,B1,B2,X1,W1,W8,W7,X9,B3,B4,B5,B6,B7,B8,B9,X2,W2,C1,W6,X8,C2,C3,C4,C5,C6,C7,C8,X3,W3,W4,W5,X7,C9,D1,D2,D3,X4,D4,D5,X5,D6,D7,X6) ) ).

%--------------------------------------------------------------------------
```