Article GATE_3, MML version 4.99.1005

:: GATE_3:th 1
theorem
for b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12 being set
      st (b1 is not empty implies AND2(NOT1 b10,NOT1 b9) is not empty) &
         (AND2(NOT1 b10,NOT1 b9) is not empty implies b1 is not empty) &
         (b2 is not empty implies AND2(NOT1 b10,b9) is not empty) &
         (AND2(NOT1 b10,b9) is not empty implies b2 is not empty) &
         (b3 is not empty implies AND2(b10,NOT1 b9) is not empty) &
         (AND2(b10,NOT1 b9) is not empty implies b3 is not empty) &
         (b4 is not empty implies AND2(b10,b9) is not empty) &
         (AND2(b10,b9) is not empty implies b4 is not empty) &
         (b5 is not empty implies AND2(NOT1 b12,NOT1 b11) is not empty) &
         (AND2(NOT1 b12,NOT1 b11) is not empty implies b5 is not empty) &
         (b6 is not empty implies AND2(NOT1 b12,b11) is not empty) &
         (AND2(NOT1 b12,b11) is not empty implies b6 is not empty) &
         (b7 is not empty implies AND2(b12,NOT1 b11) is not empty) &
         (AND2(b12,NOT1 b11) is not empty implies b7 is not empty) &
         (b8 is not empty implies AND2(b12,b11) is not empty) &
         (AND2(b12,b11) is not empty implies b8 is not empty) &
         (b11 is not empty implies NOT1 b10 is not empty) &
         (NOT1 b10 is not empty implies b11 is not empty) &
         (b12 is not empty implies b9 is not empty) &
         (b9 is not empty implies b12 is not empty)
   holds (b6 is not empty implies b1 is not empty) & (b1 is not empty implies b6 is not empty) & (b8 is not empty implies b2 is not empty) & (b2 is not empty implies b8 is not empty) & (b7 is not empty implies b4 is not empty) & (b4 is not empty implies b7 is not empty) & (b5 is not empty implies b3 is not empty) & (b3 is not empty implies b5 is not empty);

:: GATE_3:th 2
theorem
for b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13 being set
      st (b1 is not empty implies AND2(NOT1 b10,NOT1 b9) is not empty) &
         (AND2(NOT1 b10,NOT1 b9) is not empty implies b1 is not empty) &
         (b2 is not empty implies AND2(NOT1 b10,b9) is not empty) &
         (AND2(NOT1 b10,b9) is not empty implies b2 is not empty) &
         (b3 is not empty implies AND2(b10,NOT1 b9) is not empty) &
         (AND2(b10,NOT1 b9) is not empty implies b3 is not empty) &
         (b4 is not empty implies AND2(b10,b9) is not empty) &
         (AND2(b10,b9) is not empty implies b4 is not empty) &
         (b5 is not empty implies AND2(NOT1 b12,NOT1 b11) is not empty) &
         (AND2(NOT1 b12,NOT1 b11) is not empty implies b5 is not empty) &
         (b6 is not empty implies AND2(NOT1 b12,b11) is not empty) &
         (AND2(NOT1 b12,b11) is not empty implies b6 is not empty) &
         (b7 is not empty implies AND2(b12,NOT1 b11) is not empty) &
         (AND2(b12,NOT1 b11) is not empty implies b7 is not empty) &
         (b8 is not empty implies AND2(b12,b11) is not empty) &
         (AND2(b12,b11) is not empty implies b8 is not empty) &
         (b11 is not empty implies AND2(NOT1 b10,b13) is not empty) &
         (AND2(NOT1 b10,b13) is not empty implies b11 is not empty) &
         (b12 is not empty implies AND2(b9,b13) is not empty) &
         (AND2(b9,b13) is not empty implies b12 is not empty)
   holds (b6 is not empty implies AND2(b1,b13) is not empty) &
    (AND2(b1,b13) is not empty implies b6 is not empty) &
    (b8 is not empty implies AND2(b2,b13) is not empty) &
    (AND2(b2,b13) is not empty implies b8 is not empty) &
    (b7 is not empty implies AND2(b4,b13) is not empty) &
    (AND2(b4,b13) is not empty implies b7 is not empty) &
    (b5 is not empty implies OR2(AND2(b3,b13),NOT1 b13) is not empty) &
    (OR2(AND2(b3,b13),NOT1 b13) is not empty implies b5 is not empty);

:: GATE_3:th 3
theorem
for b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22 being set
      st (b1 is not empty implies AND3(NOT1 b19,NOT1 b18,NOT1 b17) is not empty) &
         (AND3(NOT1 b19,NOT1 b18,NOT1 b17) is not empty implies b1 is not empty) &
         (b2 is not empty implies AND3(NOT1 b19,NOT1 b18,b17) is not empty) &
         (AND3(NOT1 b19,NOT1 b18,b17) is not empty implies b2 is not empty) &
         (b3 is not empty implies AND3(NOT1 b19,b18,NOT1 b17) is not empty) &
         (AND3(NOT1 b19,b18,NOT1 b17) is not empty implies b3 is not empty) &
         (b4 is not empty implies AND3(NOT1 b19,b18,b17) is not empty) &
         (AND3(NOT1 b19,b18,b17) is not empty implies b4 is not empty) &
         (b5 is not empty implies AND3(b19,NOT1 b18,NOT1 b17) is not empty) &
         (AND3(b19,NOT1 b18,NOT1 b17) is not empty implies b5 is not empty) &
         (b6 is not empty implies AND3(b19,NOT1 b18,b17) is not empty) &
         (AND3(b19,NOT1 b18,b17) is not empty implies b6 is not empty) &
         (b7 is not empty implies AND3(b19,b18,NOT1 b17) is not empty) &
         (AND3(b19,b18,NOT1 b17) is not empty implies b7 is not empty) &
         (b8 is not empty implies AND3(b19,b18,b17) is not empty) &
         (AND3(b19,b18,b17) is not empty implies b8 is not empty) &
         (b9 is not empty implies AND3(NOT1 b22,NOT1 b21,NOT1 b20) is not empty) &
         (AND3(NOT1 b22,NOT1 b21,NOT1 b20) is not empty implies b9 is not empty) &
         (b10 is not empty implies AND3(NOT1 b22,NOT1 b21,b20) is not empty) &
         (AND3(NOT1 b22,NOT1 b21,b20) is not empty implies b10 is not empty) &
         (b11 is not empty implies AND3(NOT1 b22,b21,NOT1 b20) is not empty) &
         (AND3(NOT1 b22,b21,NOT1 b20) is not empty implies b11 is not empty) &
         (b12 is not empty implies AND3(NOT1 b22,b21,b20) is not empty) &
         (AND3(NOT1 b22,b21,b20) is not empty implies b12 is not empty) &
         (b13 is not empty implies AND3(b22,NOT1 b21,NOT1 b20) is not empty) &
         (AND3(b22,NOT1 b21,NOT1 b20) is not empty implies b13 is not empty) &
         (b14 is not empty implies AND3(b22,NOT1 b21,b20) is not empty) &
         (AND3(b22,NOT1 b21,b20) is not empty implies b14 is not empty) &
         (b15 is not empty implies AND3(b22,b21,NOT1 b20) is not empty) &
         (AND3(b22,b21,NOT1 b20) is not empty implies b15 is not empty) &
         (b16 is not empty implies AND3(b22,b21,b20) is not empty) &
         (AND3(b22,b21,b20) is not empty implies b16 is not empty) &
         (b20 is not empty implies NOT1 b19 is not empty) &
         (NOT1 b19 is not empty implies b20 is not empty) &
         (b21 is not empty implies b17 is not empty) &
         (b17 is not empty implies b21 is not empty) &
         (b22 is not empty implies b18 is not empty) &
         (b18 is not empty implies b22 is not empty)
   holds (b10 is not empty implies b1 is not empty) & (b1 is not empty implies b10 is not empty) & (b12 is not empty implies b2 is not empty) & (b2 is not empty implies b12 is not empty) & (b16 is not empty implies b4 is not empty) & (b4 is not empty implies b16 is not empty) & (b15 is not empty implies b8 is not empty) & (b8 is not empty implies b15 is not empty) & (b13 is not empty implies b7 is not empty) & (b7 is not empty implies b13 is not empty) & (b9 is not empty implies b5 is not empty) & (b5 is not empty implies b9 is not empty) & (b11 is not empty implies b6 is not empty) & (b6 is not empty implies b11 is not empty) & (b14 is not empty implies b3 is not empty) & (b3 is not empty implies b14 is not empty);

:: GATE_3:th 4
theorem
for b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23 being set
      st (b1 is not empty implies AND3(NOT1 b19,NOT1 b18,NOT1 b17) is not empty) &
         (AND3(NOT1 b19,NOT1 b18,NOT1 b17) is not empty implies b1 is not empty) &
         (b2 is not empty implies AND3(NOT1 b19,NOT1 b18,b17) is not empty) &
         (AND3(NOT1 b19,NOT1 b18,b17) is not empty implies b2 is not empty) &
         (b3 is not empty implies AND3(NOT1 b19,b18,NOT1 b17) is not empty) &
         (AND3(NOT1 b19,b18,NOT1 b17) is not empty implies b3 is not empty) &
         (b4 is not empty implies AND3(NOT1 b19,b18,b17) is not empty) &
         (AND3(NOT1 b19,b18,b17) is not empty implies b4 is not empty) &
         (b5 is not empty implies AND3(b19,NOT1 b18,NOT1 b17) is not empty) &
         (AND3(b19,NOT1 b18,NOT1 b17) is not empty implies b5 is not empty) &
         (b6 is not empty implies AND3(b19,NOT1 b18,b17) is not empty) &
         (AND3(b19,NOT1 b18,b17) is not empty implies b6 is not empty) &
         (b7 is not empty implies AND3(b19,b18,NOT1 b17) is not empty) &
         (AND3(b19,b18,NOT1 b17) is not empty implies b7 is not empty) &
         (b8 is not empty implies AND3(b19,b18,b17) is not empty) &
         (AND3(b19,b18,b17) is not empty implies b8 is not empty) &
         (b9 is not empty implies AND3(NOT1 b22,NOT1 b21,NOT1 b20) is not empty) &
         (AND3(NOT1 b22,NOT1 b21,NOT1 b20) is not empty implies b9 is not empty) &
         (b10 is not empty implies AND3(NOT1 b22,NOT1 b21,b20) is not empty) &
         (AND3(NOT1 b22,NOT1 b21,b20) is not empty implies b10 is not empty) &
         (b11 is not empty implies AND3(NOT1 b22,b21,NOT1 b20) is not empty) &
         (AND3(NOT1 b22,b21,NOT1 b20) is not empty implies b11 is not empty) &
         (b12 is not empty implies AND3(NOT1 b22,b21,b20) is not empty) &
         (AND3(NOT1 b22,b21,b20) is not empty implies b12 is not empty) &
         (b13 is not empty implies AND3(b22,NOT1 b21,NOT1 b20) is not empty) &
         (AND3(b22,NOT1 b21,NOT1 b20) is not empty implies b13 is not empty) &
         (b14 is not empty implies AND3(b22,NOT1 b21,b20) is not empty) &
         (AND3(b22,NOT1 b21,b20) is not empty implies b14 is not empty) &
         (b15 is not empty implies AND3(b22,b21,NOT1 b20) is not empty) &
         (AND3(b22,b21,NOT1 b20) is not empty implies b15 is not empty) &
         (b16 is not empty implies AND3(b22,b21,b20) is not empty) &
         (AND3(b22,b21,b20) is not empty implies b16 is not empty) &
         (b20 is not empty implies AND2(NOT1 b19,b23) is not empty) &
         (AND2(NOT1 b19,b23) is not empty implies b20 is not empty) &
         (b21 is not empty implies AND2(b17,b23) is not empty) &
         (AND2(b17,b23) is not empty implies b21 is not empty) &
         (b22 is not empty implies AND2(b18,b23) is not empty) &
         (AND2(b18,b23) is not empty implies b22 is not empty)
   holds (b10 is not empty implies AND2(b1,b23) is not empty) &
    (AND2(b1,b23) is not empty implies b10 is not empty) &
    (b12 is not empty implies AND2(b2,b23) is not empty) &
    (AND2(b2,b23) is not empty implies b12 is not empty) &
    (b16 is not empty implies AND2(b4,b23) is not empty) &
    (AND2(b4,b23) is not empty implies b16 is not empty) &
    (b15 is not empty implies AND2(b8,b23) is not empty) &
    (AND2(b8,b23) is not empty implies b15 is not empty) &
    (b13 is not empty implies AND2(b7,b23) is not empty) &
    (AND2(b7,b23) is not empty implies b13 is not empty) &
    (b9 is not empty implies OR2(AND2(b5,b23),NOT1 b23) is not empty) &
    (OR2(AND2(b5,b23),NOT1 b23) is not empty implies b9 is not empty) &
    (b11 is not empty implies AND2(b6,b23) is not empty) &
    (AND2(b6,b23) is not empty implies b11 is not empty) &
    (b14 is not empty implies AND2(b3,b23) is not empty) &
    (AND2(b3,b23) is not empty implies b14 is not empty);

:: GATE_3:th 5
theorem
for b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35, b36, b37, b38, b39, b40 being set
      st (b1 is not empty implies AND4(NOT1 b36,NOT1 b35,NOT1 b34,NOT1 b33) is not empty) &
         (AND4(NOT1 b36,NOT1 b35,NOT1 b34,NOT1 b33) is not empty implies b1 is not empty) &
         (b2 is not empty implies AND4(NOT1 b36,NOT1 b35,NOT1 b34,b33) is not empty) &
         (AND4(NOT1 b36,NOT1 b35,NOT1 b34,b33) is not empty implies b2 is not empty) &
         (b3 is not empty implies AND4(NOT1 b36,NOT1 b35,b34,NOT1 b33) is not empty) &
         (AND4(NOT1 b36,NOT1 b35,b34,NOT1 b33) is not empty implies b3 is not empty) &
         (b4 is not empty implies AND4(NOT1 b36,NOT1 b35,b34,b33) is not empty) &
         (AND4(NOT1 b36,NOT1 b35,b34,b33) is not empty implies b4 is not empty) &
         (b5 is not empty implies AND4(NOT1 b36,b35,NOT1 b34,NOT1 b33) is not empty) &
         (AND4(NOT1 b36,b35,NOT1 b34,NOT1 b33) is not empty implies b5 is not empty) &
         (b6 is not empty implies AND4(NOT1 b36,b35,NOT1 b34,b33) is not empty) &
         (AND4(NOT1 b36,b35,NOT1 b34,b33) is not empty implies b6 is not empty) &
         (b7 is not empty implies AND4(NOT1 b36,b35,b34,NOT1 b33) is not empty) &
         (AND4(NOT1 b36,b35,b34,NOT1 b33) is not empty implies b7 is not empty) &
         (b8 is not empty implies AND4(NOT1 b36,b35,b34,b33) is not empty) &
         (AND4(NOT1 b36,b35,b34,b33) is not empty implies b8 is not empty) &
         (b9 is not empty implies AND4(b36,NOT1 b35,NOT1 b34,NOT1 b33) is not empty) &
         (AND4(b36,NOT1 b35,NOT1 b34,NOT1 b33) is not empty implies b9 is not empty) &
         (b10 is not empty implies AND4(b36,NOT1 b35,NOT1 b34,b33) is not empty) &
         (AND4(b36,NOT1 b35,NOT1 b34,b33) is not empty implies b10 is not empty) &
         (b11 is not empty implies AND4(b36,NOT1 b35,b34,NOT1 b33) is not empty) &
         (AND4(b36,NOT1 b35,b34,NOT1 b33) is not empty implies b11 is not empty) &
         (b12 is not empty implies AND4(b36,NOT1 b35,b34,b33) is not empty) &
         (AND4(b36,NOT1 b35,b34,b33) is not empty implies b12 is not empty) &
         (b13 is not empty implies AND4(b36,b35,NOT1 b34,NOT1 b33) is not empty) &
         (AND4(b36,b35,NOT1 b34,NOT1 b33) is not empty implies b13 is not empty) &
         (b14 is not empty implies AND4(b36,b35,NOT1 b34,b33) is not empty) &
         (AND4(b36,b35,NOT1 b34,b33) is not empty implies b14 is not empty) &
         (b15 is not empty implies AND4(b36,b35,b34,NOT1 b33) is not empty) &
         (AND4(b36,b35,b34,NOT1 b33) is not empty implies b15 is not empty) &
         (b16 is not empty implies AND4(b36,b35,b34,b33) is not empty) &
         (AND4(b36,b35,b34,b33) is not empty implies b16 is not empty) &
         (b17 is not empty implies AND4(NOT1 b40,NOT1 b39,NOT1 b38,NOT1 b37) is not empty) &
         (AND4(NOT1 b40,NOT1 b39,NOT1 b38,NOT1 b37) is not empty implies b17 is not empty) &
         (b18 is not empty implies AND4(NOT1 b40,NOT1 b39,NOT1 b38,b37) is not empty) &
         (AND4(NOT1 b40,NOT1 b39,NOT1 b38,b37) is not empty implies b18 is not empty) &
         (b19 is not empty implies AND4(NOT1 b40,NOT1 b39,b38,NOT1 b37) is not empty) &
         (AND4(NOT1 b40,NOT1 b39,b38,NOT1 b37) is not empty implies b19 is not empty) &
         (b20 is not empty implies AND4(NOT1 b40,NOT1 b39,b38,b37) is not empty) &
         (AND4(NOT1 b40,NOT1 b39,b38,b37) is not empty implies b20 is not empty) &
         (b21 is not empty implies AND4(NOT1 b40,b39,NOT1 b38,NOT1 b37) is not empty) &
         (AND4(NOT1 b40,b39,NOT1 b38,NOT1 b37) is not empty implies b21 is not empty) &
         (b22 is not empty implies AND4(NOT1 b40,b39,NOT1 b38,b37) is not empty) &
         (AND4(NOT1 b40,b39,NOT1 b38,b37) is not empty implies b22 is not empty) &
         (b23 is not empty implies AND4(NOT1 b40,b39,b38,NOT1 b37) is not empty) &
         (AND4(NOT1 b40,b39,b38,NOT1 b37) is not empty implies b23 is not empty) &
         (b24 is not empty implies AND4(NOT1 b40,b39,b38,b37) is not empty) &
         (AND4(NOT1 b40,b39,b38,b37) is not empty implies b24 is not empty) &
         (b25 is not empty implies AND4(b40,NOT1 b39,NOT1 b38,NOT1 b37) is not empty) &
         (AND4(b40,NOT1 b39,NOT1 b38,NOT1 b37) is not empty implies b25 is not empty) &
         (b26 is not empty implies AND4(b40,NOT1 b39,NOT1 b38,b37) is not empty) &
         (AND4(b40,NOT1 b39,NOT1 b38,b37) is not empty implies b26 is not empty) &
         (b27 is not empty implies AND4(b40,NOT1 b39,b38,NOT1 b37) is not empty) &
         (AND4(b40,NOT1 b39,b38,NOT1 b37) is not empty implies b27 is not empty) &
         (b28 is not empty implies AND4(b40,NOT1 b39,b38,b37) is not empty) &
         (AND4(b40,NOT1 b39,b38,b37) is not empty implies b28 is not empty) &
         (b29 is not empty implies AND4(b40,b39,NOT1 b38,NOT1 b37) is not empty) &
         (AND4(b40,b39,NOT1 b38,NOT1 b37) is not empty implies b29 is not empty) &
         (b30 is not empty implies AND4(b40,b39,NOT1 b38,b37) is not empty) &
         (AND4(b40,b39,NOT1 b38,b37) is not empty implies b30 is not empty) &
         (b31 is not empty implies AND4(b40,b39,b38,NOT1 b37) is not empty) &
         (AND4(b40,b39,b38,NOT1 b37) is not empty implies b31 is not empty) &
         (b32 is not empty implies AND4(b40,b39,b38,b37) is not empty) &
         (AND4(b40,b39,b38,b37) is not empty implies b32 is not empty) &
         (b37 is not empty implies NOT1 b36 is not empty) &
         (NOT1 b36 is not empty implies b37 is not empty) &
         (b38 is not empty implies b33 is not empty) &
         (b33 is not empty implies b38 is not empty) &
         (b39 is not empty implies b34 is not empty) &
         (b34 is not empty implies b39 is not empty) &
         (b40 is not empty implies b35 is not empty) &
         (b35 is not empty implies b40 is not empty)
   holds (b18 is not empty implies b1 is not empty) & (b1 is not empty implies b18 is not empty) & (b20 is not empty implies b2 is not empty) & (b2 is not empty implies b20 is not empty) & (b24 is not empty implies b4 is not empty) & (b4 is not empty implies b24 is not empty) & (b32 is not empty implies b8 is not empty) & (b8 is not empty implies b32 is not empty) & (b31 is not empty implies b16 is not empty) & (b16 is not empty implies b31 is not empty) & (b29 is not empty implies b15 is not empty) & (b15 is not empty implies b29 is not empty) & (b25 is not empty implies b13 is not empty) & (b13 is not empty implies b25 is not empty) & (b17 is not empty implies b9 is not empty) & (b9 is not empty implies b17 is not empty) & (b22 is not empty implies b3 is not empty) & (b3 is not empty implies b22 is not empty) & (b28 is not empty implies b6 is not empty) & (b6 is not empty implies b28 is not empty) & (b23 is not empty implies b12 is not empty) & (b12 is not empty implies b23 is not empty) & (b30 is not empty implies b7 is not empty) & (b7 is not empty implies b30 is not empty) & (b27 is not empty implies b14 is not empty) & (b14 is not empty implies b27 is not empty) & (b21 is not empty implies b11 is not empty) & (b11 is not empty implies b21 is not empty) & (b26 is not empty implies b5 is not empty) & (b5 is not empty implies b26 is not empty) & (b19 is not empty implies b10 is not empty) & (b10 is not empty implies b19 is not empty);

:: GATE_3:th 6
theorem
for b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35, b36, b37, b38, b39, b40, b41 being set
      st (b1 is not empty implies AND4(NOT1 b36,NOT1 b35,NOT1 b34,NOT1 b33) is not empty) &
         (AND4(NOT1 b36,NOT1 b35,NOT1 b34,NOT1 b33) is not empty implies b1 is not empty) &
         (b2 is not empty implies AND4(NOT1 b36,NOT1 b35,NOT1 b34,b33) is not empty) &
         (AND4(NOT1 b36,NOT1 b35,NOT1 b34,b33) is not empty implies b2 is not empty) &
         (b3 is not empty implies AND4(NOT1 b36,NOT1 b35,b34,NOT1 b33) is not empty) &
         (AND4(NOT1 b36,NOT1 b35,b34,NOT1 b33) is not empty implies b3 is not empty) &
         (b4 is not empty implies AND4(NOT1 b36,NOT1 b35,b34,b33) is not empty) &
         (AND4(NOT1 b36,NOT1 b35,b34,b33) is not empty implies b4 is not empty) &
         (b5 is not empty implies AND4(NOT1 b36,b35,NOT1 b34,NOT1 b33) is not empty) &
         (AND4(NOT1 b36,b35,NOT1 b34,NOT1 b33) is not empty implies b5 is not empty) &
         (b6 is not empty implies AND4(NOT1 b36,b35,NOT1 b34,b33) is not empty) &
         (AND4(NOT1 b36,b35,NOT1 b34,b33) is not empty implies b6 is not empty) &
         (b7 is not empty implies AND4(NOT1 b36,b35,b34,NOT1 b33) is not empty) &
         (AND4(NOT1 b36,b35,b34,NOT1 b33) is not empty implies b7 is not empty) &
         (b8 is not empty implies AND4(NOT1 b36,b35,b34,b33) is not empty) &
         (AND4(NOT1 b36,b35,b34,b33) is not empty implies b8 is not empty) &
         (b9 is not empty implies AND4(b36,NOT1 b35,NOT1 b34,NOT1 b33) is not empty) &
         (AND4(b36,NOT1 b35,NOT1 b34,NOT1 b33) is not empty implies b9 is not empty) &
         (b10 is not empty implies AND4(b36,NOT1 b35,NOT1 b34,b33) is not empty) &
         (AND4(b36,NOT1 b35,NOT1 b34,b33) is not empty implies b10 is not empty) &
         (b11 is not empty implies AND4(b36,NOT1 b35,b34,NOT1 b33) is not empty) &
         (AND4(b36,NOT1 b35,b34,NOT1 b33) is not empty implies b11 is not empty) &
         (b12 is not empty implies AND4(b36,NOT1 b35,b34,b33) is not empty) &
         (AND4(b36,NOT1 b35,b34,b33) is not empty implies b12 is not empty) &
         (b13 is not empty implies AND4(b36,b35,NOT1 b34,NOT1 b33) is not empty) &
         (AND4(b36,b35,NOT1 b34,NOT1 b33) is not empty implies b13 is not empty) &
         (b14 is not empty implies AND4(b36,b35,NOT1 b34,b33) is not empty) &
         (AND4(b36,b35,NOT1 b34,b33) is not empty implies b14 is not empty) &
         (b15 is not empty implies AND4(b36,b35,b34,NOT1 b33) is not empty) &
         (AND4(b36,b35,b34,NOT1 b33) is not empty implies b15 is not empty) &
         (b16 is not empty implies AND4(b36,b35,b34,b33) is not empty) &
         (AND4(b36,b35,b34,b33) is not empty implies b16 is not empty) &
         (b17 is not empty implies AND4(NOT1 b40,NOT1 b39,NOT1 b38,NOT1 b37) is not empty) &
         (AND4(NOT1 b40,NOT1 b39,NOT1 b38,NOT1 b37) is not empty implies b17 is not empty) &
         (b18 is not empty implies AND4(NOT1 b40,NOT1 b39,NOT1 b38,b37) is not empty) &
         (AND4(NOT1 b40,NOT1 b39,NOT1 b38,b37) is not empty implies b18 is not empty) &
         (b19 is not empty implies AND4(NOT1 b40,NOT1 b39,b38,NOT1 b37) is not empty) &
         (AND4(NOT1 b40,NOT1 b39,b38,NOT1 b37) is not empty implies b19 is not empty) &
         (b20 is not empty implies AND4(NOT1 b40,NOT1 b39,b38,b37) is not empty) &
         (AND4(NOT1 b40,NOT1 b39,b38,b37) is not empty implies b20 is not empty) &
         (b21 is not empty implies AND4(NOT1 b40,b39,NOT1 b38,NOT1 b37) is not empty) &
         (AND4(NOT1 b40,b39,NOT1 b38,NOT1 b37) is not empty implies b21 is not empty) &
         (b22 is not empty implies AND4(NOT1 b40,b39,NOT1 b38,b37) is not empty) &
         (AND4(NOT1 b40,b39,NOT1 b38,b37) is not empty implies b22 is not empty) &
         (b23 is not empty implies AND4(NOT1 b40,b39,b38,NOT1 b37) is not empty) &
         (AND4(NOT1 b40,b39,b38,NOT1 b37) is not empty implies b23 is not empty) &
         (b24 is not empty implies AND4(NOT1 b40,b39,b38,b37) is not empty) &
         (AND4(NOT1 b40,b39,b38,b37) is not empty implies b24 is not empty) &
         (b25 is not empty implies AND4(b40,NOT1 b39,NOT1 b38,NOT1 b37) is not empty) &
         (AND4(b40,NOT1 b39,NOT1 b38,NOT1 b37) is not empty implies b25 is not empty) &
         (b26 is not empty implies AND4(b40,NOT1 b39,NOT1 b38,b37) is not empty) &
         (AND4(b40,NOT1 b39,NOT1 b38,b37) is not empty implies b26 is not empty) &
         (b27 is not empty implies AND4(b40,NOT1 b39,b38,NOT1 b37) is not empty) &
         (AND4(b40,NOT1 b39,b38,NOT1 b37) is not empty implies b27 is not empty) &
         (b28 is not empty implies AND4(b40,NOT1 b39,b38,b37) is not empty) &
         (AND4(b40,NOT1 b39,b38,b37) is not empty implies b28 is not empty) &
         (b29 is not empty implies AND4(b40,b39,NOT1 b38,NOT1 b37) is not empty) &
         (AND4(b40,b39,NOT1 b38,NOT1 b37) is not empty implies b29 is not empty) &
         (b30 is not empty implies AND4(b40,b39,NOT1 b38,b37) is not empty) &
         (AND4(b40,b39,NOT1 b38,b37) is not empty implies b30 is not empty) &
         (b31 is not empty implies AND4(b40,b39,b38,NOT1 b37) is not empty) &
         (AND4(b40,b39,b38,NOT1 b37) is not empty implies b31 is not empty) &
         (b32 is not empty implies AND4(b40,b39,b38,b37) is not empty) &
         (AND4(b40,b39,b38,b37) is not empty implies b32 is not empty) &
         (b37 is not empty implies AND2(NOT1 b36,b41) is not empty) &
         (AND2(NOT1 b36,b41) is not empty implies b37 is not empty) &
         (b38 is not empty implies AND2(b33,b41) is not empty) &
         (AND2(b33,b41) is not empty implies b38 is not empty) &
         (b39 is not empty implies AND2(b34,b41) is not empty) &
         (AND2(b34,b41) is not empty implies b39 is not empty) &
         (b40 is not empty implies AND2(b35,b41) is not empty) &
         (AND2(b35,b41) is not empty implies b40 is not empty)
   holds (b18 is not empty implies AND2(b1,b41) is not empty) &
    (AND2(b1,b41) is not empty implies b18 is not empty) &
    (b20 is not empty implies AND2(b2,b41) is not empty) &
    (AND2(b2,b41) is not empty implies b20 is not empty) &
    (b24 is not empty implies AND2(b4,b41) is not empty) &
    (AND2(b4,b41) is not empty implies b24 is not empty) &
    (b32 is not empty implies AND2(b8,b41) is not empty) &
    (AND2(b8,b41) is not empty implies b32 is not empty) &
    (b31 is not empty implies AND2(b16,b41) is not empty) &
    (AND2(b16,b41) is not empty implies b31 is not empty) &
    (b29 is not empty implies AND2(b15,b41) is not empty) &
    (AND2(b15,b41) is not empty implies b29 is not empty) &
    (b25 is not empty implies AND2(b13,b41) is not empty) &
    (AND2(b13,b41) is not empty implies b25 is not empty) &
    (b17 is not empty implies OR2(AND2(b9,b41),NOT1 b41) is not empty) &
    (OR2(AND2(b9,b41),NOT1 b41) is not empty implies b17 is not empty) &
    (b22 is not empty implies AND2(b3,b41) is not empty) &
    (AND2(b3,b41) is not empty implies b22 is not empty) &
    (b28 is not empty implies AND2(b6,b41) is not empty) &
    (AND2(b6,b41) is not empty implies b28 is not empty) &
    (b23 is not empty implies AND2(b12,b41) is not empty) &
    (AND2(b12,b41) is not empty implies b23 is not empty) &
    (b30 is not empty implies AND2(b7,b41) is not empty) &
    (AND2(b7,b41) is not empty implies b30 is not empty) &
    (b27 is not empty implies AND2(b14,b41) is not empty) &
    (AND2(b14,b41) is not empty implies b27 is not empty) &
    (b21 is not empty implies AND2(b11,b41) is not empty) &
    (AND2(b11,b41) is not empty implies b21 is not empty) &
    (b26 is not empty implies AND2(b5,b41) is not empty) &
    (AND2(b5,b41) is not empty implies b26 is not empty) &
    (b19 is not empty implies AND2(b10,b41) is not empty) &
    (AND2(b10,b41) is not empty implies b19 is not empty);