Suggested Problems for Proof Designer

1. Hypotheses: AB, AC
   Conclusion: ABC
2. Hypotheses: AB
   Conclusion: C \ BC \ A
3. Hypotheses: A \ BC
   Conclusion: A \ CB
4. Hypotheses: none
   Conclusion: A \ (B \ C)(A \ B)C
5. Hypotheses: none
   Conclusion: A \ (BC) = (A \ B)(A \ C)
6. Hypotheses: none
   Conclusion: A(BC)(AB)C
7. Hypotheses: none
   Conclusion: (AB) \ CA(B \ C)
8. Hypotheses: A(B \ C) =
   Conclusion: ABC
9. Hypotheses: AB, AC
   Conclusion: BC
10. Hypotheses: AB, AC =
    Conclusion: AB \ C
11. Hypotheses: AB \ C, A ≠
    Conclusion: BC
12. Hypotheses: A \ B C, AC
    Conclusion: AB ≠
13. Hypotheses: AB \ C
    Conclusion: AC =
14. Hypotheses: none
    Conclusion: A \ C(A \ B)(B \ C)
15. Hypotheses: ACBC, ACBC
    Conclusion: AB
16. Hypotheses: none
    Conclusion: !AB(AB = B)
17. Hypotheses: none
    Conclusion: AB(A)(B)
18. Hypotheses: none
    Conclusion: (AB) = (A)(B)
19. Hypotheses: none
    Conclusion: (A)(B)(AB)
20. Hypotheses: (A)(B) = (AB)
    Conclusion: ABBA
21. Hypotheses: x(xAxA)
    Conclusion: x(x(A)x(A))
22. Hypotheses: AF
    Conclusion: AF
23. Hypotheses: AF
    Conclusion: UFA
24. Hypotheses: FG
    Conclusion: FG
25. Hypotheses: FG
    Conclusion: UGUF
26. Hypotheses: none
    Conclusion: (FG) = (F)(G)
27. Hypotheses: none
    Conclusion: (FG)(F)(G)
28. Hypotheses: none
    Conclusion: U(FG) = (UF)(UG)
29. Hypotheses: none
    Conclusion: A(F) = {AX | XF}
30. Hypotheses: AU
    Conclusion: A(UF) = U{AX | XF}
31. Hypotheses: none
    Conclusion: U \ F = U{U \ X | XF}
32. Hypotheses: AU
    Conclusion: A \ (UF) = {A \ X | XF}
33. Hypotheses: none
    Conclusion: F \ G(F \ G)
34. Hypotheses: none
    Conclusion: (F \ G)F \ GFG(FG)
35. Hypotheses: AFBG(ABH)
    Conclusion: (F)GH
36. Hypotheses: none
    Conclusion: F(F)
37. Hypotheses: none
    Conclusion: A = (A)
38. Hypotheses: none
    Conclusion: UF(U){(X) | XF}
39. Hypotheses: none
    Conclusion: {X \ A | XF}{XF | XA}
40. Hypotheses: none
    Conclusion: (F)(G) = AFBG(AB = )
41. Hypotheses: none
    Conclusion: {(X) | XF}(F)
42. Hypotheses: none
    Conclusion: (U){(X) | XF} = (UF)
43. Hypotheses: {(X) | XF} = (F)
    Conclusion: AFBF(BA)
44. Hypotheses: F(F = AAF)
    Conclusion: x(A = {x})
45. Hypotheses: none
    Conclusion: (A \ B) \ ((A) \ (B)) = {}
46. Hypotheses: none
    Conclusion: A(BC) = (AB)(AC)
47. Hypotheses: none
    Conclusion: A(BC) = (AB)(AC)
48. Hypotheses: none
    Conclusion: (AB)C = (AC)(BC)
49. Hypotheses: ABB
    Conclusion: AB
50. Hypotheses: none
    Conclusion: AB(AC)(BC)
51. Hypotheses: none
    Conclusion: A(AB) = A \ B
52. Hypotheses: none
    Conclusion: A(AB) = B \ A
53. Hypotheses: none
    Conclusion: (AB)C = A(BC)
54. Hypotheses: none
    Conclusion: AA =
55. Hypotheses: AC = BC
    Conclusion: A = B
56. Hypotheses: none
    Conclusion: !AB(AB = B)
57. Hypotheses: none
    Conclusion: AB!C(AC = B)
58. Hypotheses: none
    Conclusion: UA(AU)
59. Hypotheses: none
    Conclusion: (RS)^-1 = S^-1R^-1
60. Hypotheses: none
    Conclusion: (RS)T = R(ST)
61. Hypotheses: ST
    Conclusion: RSRT
62. Hypotheses: none
    Conclusion: (ST)R(SR)(TR)
63. Hypotheses: none
    Conclusion: (ST)R = (SR)(TR)
64. Hypotheses: none
    Conclusion: (SR) \ (TR)(S \ T)R