TSTP Solution File: PUZ037-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : PUZ037-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 18:21:27 EDT 2022
% Result : Unsatisfiable 8.82s 8.94s
% Output : Proof 8.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : PUZ037-1 : TPTP v8.1.0. Released v2.3.0.
% 0.06/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat May 28 20:18:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 8.82/8.94 % SZS status Unsatisfiable
% 8.82/8.94 % SZS output start Proof
% 8.82/8.94 The input problem is unsatisfiable because
% 8.82/8.94
% 8.82/8.94 [1] the following set of Horn clauses is unsatisfiable:
% 8.82/8.94
% 8.82/8.94 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) ==> \bottom
% 8.82/8.94 state(b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94 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)
% 8.82/8.94
% 8.82/8.94 This holds because
% 8.82/8.94
% 8.82/8.94 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.82/8.94
% 8.82/8.94 E:
% 8.82/8.94 f1(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)) = true__
% 8.82/8.94 f1(true__) = false__
% 8.82/8.94 f10(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), 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) = true__
% 8.82/8.94 f10(true__, 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, 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)
% 8.82/8.94 f11(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), 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) = true__
% 8.82/8.94 f11(true__, 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(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)
% 8.82/8.94 f12(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), 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) = true__
% 8.82/8.94 f12(true__, 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, 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)
% 8.82/8.94 f13(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), 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) = true__
% 8.82/8.94 f13(true__, 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, Y1, Y2, Y3, X1, X2, X3, X4, X5, X6, X7, X8, X9, W7, W8, W1, W6, D7, W2, W5, W4, W3)
% 8.82/8.94 f14(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), 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) = true__
% 8.82/8.94 f14(true__, 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, 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)
% 8.82/8.94 f15(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), 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) = true__
% 8.82/8.94 f15(true__, 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, 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)
% 8.82/8.94 f16(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), 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) = true__
% 8.82/8.94 f16(true__, 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(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)
% 8.82/8.94 f17(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), 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) = true__
% 8.82/8.94 f17(true__, 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(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)
% 8.82/8.94 f18(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), 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) = true__
% 8.82/8.94 f18(true__, 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, 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)
% 8.82/8.94 f19(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), 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) = true__
% 8.82/8.94 f19(true__, 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, 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)
% 8.82/8.94 f2(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), 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) = true__
% 8.82/8.94 f2(true__, 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(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)
% 8.82/8.94 f3(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), 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) = true__
% 8.82/8.94 f3(true__, 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, 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)
% 8.82/8.94 f4(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), 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) = true__
% 8.82/8.94 f4(true__, 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, X1, X2, X3, X4, X5, X6, X7, X8, X9, Y1, Y2, Y3, W1, W2, W3, W8, D7, W4, W7, W6, W5)
% 8.82/8.94 f5(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), 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) = true__
% 8.82/8.94 f5(true__, 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, 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)
% 8.82/8.94 f6(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), 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) = true__
% 8.82/8.94 f6(true__, 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, 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)
% 8.82/8.94 f7(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), 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) = true__
% 8.82/8.94 f7(true__, 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(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)
% 8.82/8.94 f8(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), 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) = true__
% 8.82/8.94 f8(true__, 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(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)
% 8.87/9.02 f9(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), 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) = true__
% 8.87/9.02 f9(true__, 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, 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)
% 8.87/9.02 state(b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w) = true__
% 8.87/9.02 G:
% 8.87/9.02 true__ = false__
% 8.87/9.02
% 8.87/9.02 This holds because
% 8.87/9.02
% 8.87/9.02 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.87/9.02
% 8.87/9.02
% 8.87/9.02 f1(f2(true__, 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)) -> true__
% 8.87/9.02 f1(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)) -> true__
% 8.87/9.02 f1(true__) -> false__
% 8.87/9.02 f10(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), 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) -> true__
% 8.87/9.02 f10(true__, 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, 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)
% 8.87/9.02 f11(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), 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) -> true__
% 8.87/9.02 f11(true__, 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(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)
% 8.87/9.02 f12(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), 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) -> true__
% 8.87/9.02 f12(true__, 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, 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)
% 8.87/9.02 f13(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), 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) -> true__
% 8.87/9.02 f13(true__, 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, Y1, Y2, Y3, X1, X2, X3, X4, X5, X6, X7, X8, X9, W7, W8, W1, W6, D7, W2, W5, W4, W3)
% 8.87/9.02 f14(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), 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) -> true__
% 8.87/9.02 f14(true__, 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, 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)
% 8.87/9.02 f15(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), 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) -> true__
% 8.87/9.02 f15(true__, 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, 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)
% 8.87/9.02 f16(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), 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) -> true__
% 8.87/9.02 f16(true__, 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(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)
% 8.87/9.02 f17(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), 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) -> true__
% 8.87/9.02 f17(true__, 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(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)
% 8.87/9.02 f18(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), 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) -> true__
% 8.87/9.02 f18(true__, 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, 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)
% 8.87/9.02 f19(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), 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) -> true__
% 8.87/9.02 f19(true__, 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, 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)
% 8.87/9.02 f2(f2(true__, Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53), Y6, Y3, Y0, Y7, Y4, Y1, Y8, Y5, Y2, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y9, Y10, Y11, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53) -> true__
% 8.87/9.02 f2(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), 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) -> true__
% 8.87/9.02 f2(true__, b, b, b, b, b, b, b, b, b, g, g, g, o, o, o, y, y, y, r, r, r, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w) -> true__
% 8.87/9.02 f2(true__, b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, g, g, g, o, o, o, y, y, y, r, r, r, w, w, w, w, w, w, w, w, w) -> true__
% 8.87/9.02 f2(true__, b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w) -> true__
% 8.87/9.02 f2(true__, b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, y, y, y, r, r, r, g, g, g, o, o, o, w, w, w, w, w, w, w, w, w) -> true__
% 8.87/9.02 f2(true__, b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, o, o, o, y, y, y, r, r, r, g, g, g, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w) -> true__
% 8.87/9.02 f2(true__, 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) -> true__
% 8.87/9.02 f2(true__, b, b, b, b, b, b, b, b, b, y, y, y, r, r, r, g, g, g, o, o, o, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w) -> true__
% 8.87/9.02 f2(true__, b, b, b, b, b, b, o, y, o, r, r, b, g, o, g, w, o, o, y, y, y, g, g, b, g, o, g, w, y, y, r, r, r, r, r, b, g, o, g, w, o, o, y, y, y, r, g, r, w, w, w, w, w, w) -> true__
% 8.87/9.02 f2(true__, b, b, b, b, b, b, r, g, r, r, r, w, g, o, g, b, o, o, y, y, y, g, g, w, g, o, g, b, y, y, r, r, r, r, r, w, g, o, g, b, o, o, y, y, y, o, y, o, w, w, w, w, w, w) -> true__
% 8.87/9.02 f2(true__, b, b, b, o, y, o, b, b, b, r, b, r, g, g, g, o, w, o, y, y, y, g, b, g, o, o, o, y, w, y, r, r, r, r, b, r, g, g, g, o, w, o, y, y, y, w, w, w, r, g, r, w, w, w) -> true__
% 8.87/9.02 f2(true__, b, b, b, r, g, r, b, b, b, r, w, r, g, g, g, o, b, o, y, y, y, g, w, g, o, o, o, y, b, y, r, r, r, r, w, r, g, g, g, o, b, o, y, y, y, w, w, w, o, y, o, w, w, w) -> true__
% 8.87/9.02 f2(true__, b, b, g, b, b, o, b, b, g, r, r, r, g, g, w, o, y, o, b, y, y, g, g, g, o, o, w, o, y, o, b, r, r, r, r, r, g, g, w, o, y, o, b, y, y, w, w, y, w, w, r, w, w, y) -> true__
% 8.87/9.02 f2(true__, b, g, b, b, o, b, b, g, b, r, r, r, g, w, g, o, o, o, y, b, y, g, g, g, o, w, o, y, y, y, r, b, r, r, r, r, g, w, g, o, o, o, y, b, y, w, y, w, w, r, w, w, y, w) -> true__
% 8.87/9.02 f2(true__, b, y, b, b, r, b, b, y, b, r, r, r, g, b, g, o, o, o, y, w, y, g, g, g, o, b, o, y, y, y, r, w, r, r, r, r, g, b, g, o, o, o, y, w, y, w, g, w, w, o, w, w, g, w) -> true__
% 8.87/9.02 f2(true__, g, b, b, o, b, b, g, b, b, r, g, r, w, g, g, o, o, o, y, y, b, r, g, r, w, o, o, y, y, y, r, r, b, r, g, r, w, g, g, o, o, o, y, y, b, y, w, w, r, w, w, y, w, w) -> true__
% 8.87/9.02 f2(true__, o, y, o, b, b, b, b, b, b, b, r, r, g, g, g, o, o, w, y, r, y, b, g, g, o, o, o, y, y, w, y, r, y, b, r, r, g, g, g, o, o, w, y, r, y, w, w, w, w, w, w, r, g, r) -> true__
% 8.87/9.02 f2(true__, r, g, r, b, b, b, b, b, b, w, r, r, g, g, g, o, o, b, y, r, y, w, g, g, o, o, o, y, y, b, y, r, y, w, r, r, g, g, g, o, o, b, y, r, y, w, w, w, w, w, w, o, y, o) -> true__
% 8.87/9.02 f2(true__, y, b, b, r, b, b, y, b, b, r, g, r, b, g, g, o, o, o, y, y, w, r, g, r, b, o, o, y, y, y, r, r, w, r, g, r, b, g, g, o, o, o, y, y, w, g, w, w, o, w, w, g, w, w) -> true__
% 8.87/9.02 f3(f2(true__, Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53), Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y21, Y22, Y23, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53) -> true__
% 8.87/9.02 f3(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), 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) -> true__
% 8.87/9.02 f3(true__, 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, 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)
% 8.87/9.02 f4(f2(true__, Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53), Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y33, Y34, Y35, Y47, Y50, Y53, Y46, Y49, Y52, Y45, Y48, Y51) -> true__
% 8.87/9.02 f4(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), 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) -> true__
% 8.87/9.02 f4(true__, 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, X1, X2, X3, X4, X5, X6, X7, X8, X9, Y1, Y2, Y3, W1, W2, W3, W8, D7, W4, W7, W6, W5)
% 8.87/9.02 f5(f2(true__, Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53), Y0, Y1, Y2, Y3, Y4, Y5, Y15, Y27, Y39, Y9, Y10, Y8, Y14, Y26, Y38, Y47, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y7, Y13, Y25, Y37, Y46, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y6, Y12, Y24, Y36, Y45, Y40, Y41, Y42, Y43, Y44, Y11, Y23, Y35, Y48, Y49, Y50, Y51, Y52, Y53) -> true__
% 8.87/9.02 f5(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), 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) -> true__
% 8.87/9.02 f5(true__, 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, 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)
% 8.87/9.02 f6(f2(true__, Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53), Y0, Y1, Y2, Y16, Y28, Y40, Y6, Y7, Y8, Y9, Y5, Y11, Y12, Y13, Y14, Y15, Y50, Y17, Y18, Y19, Y20, Y21, Y4, Y23, Y24, Y25, Y26, Y27, Y49, Y29, Y30, Y31, Y32, Y33, Y3, Y35, Y36, Y37, Y38, Y39, Y48, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y10, Y22, Y34, Y51, Y52, Y53) -> true__
% 8.87/9.02 f6(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), 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) -> true__
% 8.87/9.02 f6(true__, 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, 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)
% 8.87/9.02 f7(f2(true__, Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53), Y17, Y29, Y41, Y3, Y4, Y5, Y6, Y7, Y8, Y2, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y53, Y42, Y30, Y18, Y1, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y52, Y43, Y31, Y19, Y0, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y51, Y44, Y32, Y20, Y45, Y46, Y47, Y48, Y49, Y50, Y9, Y21, Y33) -> true__
% 8.87/9.02 f7(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), 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) -> true__
% 8.87/9.02 f7(true__, 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(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)
% 8.87/9.02 f8(f2(true__, Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53), Y12, Y1, Y2, Y24, Y4, Y5, Y36, Y7, Y8, Y11, Y23, Y35, Y45, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y6, Y10, Y22, Y34, Y48, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y3, Y9, Y21, Y33, Y51, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y0, Y44, Y46, Y47, Y32, Y49, Y50, Y20, Y52, Y53) -> true__
% 8.87/9.02 f8(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), 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) -> true__
% 8.87/9.02 f8(true__, 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(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)
% 8.87/9.02 f9(f2(true__, Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10, Y11, Y12, Y13, Y14, Y15, Y16, Y17, Y18, Y19, Y20, Y21, Y22, Y23, Y24, Y25, Y26, Y27, Y28, Y29, Y30, Y31, Y32, Y33, Y34, Y35, Y36, Y37, Y38, Y39, Y40, Y41, Y42, Y43, Y44, Y45, Y46, Y47, Y48, Y49, Y50, Y51, Y52, Y53), Y0, Y13, Y2, Y3, Y25, Y5, Y6, Y37, Y8, Y9, Y10, Y11, Y12, Y46, Y14, Y15, Y16, Y17, Y18, Y7, Y20, Y21, Y22, Y23, Y24, Y49, Y26, Y27, Y28, Y29, Y30, Y4, Y32, Y33, Y34, Y35, Y36, Y52, Y38, Y39, Y40, Y41, Y42, Y1, Y44, Y45, Y43, Y47, Y48, Y31, Y50, Y51, Y19, Y53) -> true__
% 8.87/9.02 f9(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), 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) -> true__
% 8.87/9.02 f9(true__, 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, 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)
% 8.87/9.02 false__ -> true__
% 8.87/9.02 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) -> f2(true__, 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)
% 8.87/9.02 state(b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w) -> true__
% 8.87/9.02 with the LPO induced by
% 8.87/9.02 w > f18 > f19 > f17 > f16 > f15 > f14 > f13 > f12 > f11 > f10 > f9 > f8 > f7 > f6 > f5 > f4 > f3 > state > f2 > y > o > g > r > b > f1 > false__ > true__
% 8.87/9.02
% 8.87/9.02 % SZS output end Proof
% 8.87/9.02
%------------------------------------------------------------------------------