TSTP Solution File: SYO607+1 by SuperZenon---0.0.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SuperZenon---0.0.1
% Problem  : SYO607+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_super_zenon -p0 -itptp -om -max-time %d %s

% Computer : n027.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 : Thu Jul 21 20:05:13 EDT 2022

% Result   : Theorem 0.87s 1.02s
% Output   : Proof 0.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : SYO607+1 : TPTP v8.1.0. Released v7.0.0.
% 0.07/0.14  % Command  : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.15/0.36  % Computer : n027.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Fri Jul  8 20:11:16 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.87/1.02  % SZS status Theorem
% 0.87/1.02  (* PROOF-FOUND *)
% 0.87/1.02  (* BEGIN-PROOF *)
% 0.87/1.02  % SZS output start Proof
% 0.87/1.02  1. (-. (g_true (a) T_0)) (g_true (a) T_0)   ### Axiom
% 0.87/1.02  2. (g_true_only (a) T_0) (-. (g_true (a) T_0))   ### Extension/test/true_only_g 1
% 0.87/1.02  3. (-. (g_true (a) T_0)) (g_true (a) T_0)   ### Axiom
% 0.87/1.02  4. (g_both (a) T_0) (-. (g_true (a) T_0))   ### Extension/test/both_g 3
% 0.87/1.02  5. (g_false_only (a) T_0) (-. (g_false_only (a) T_0))   ### Axiom
% 0.87/1.02  6. (-. (g_true T_0 T_1)) (g_true T_0 T_1)   ### Axiom
% 0.87/1.02  7. (g_true_only T_0 T_1) (-. (g_true T_0 T_1))   ### Extension/test/true_only_g 6
% 0.87/1.02  8. (g_both T_0 T_1) (-. (g_both T_0 T_1))   ### Axiom
% 0.87/1.02  9. (-. (Ex B, (g_both T_0 B))) (g_both T_0 T_1)   ### NotExists 8
% 0.87/1.02  10. (g_false_only T_0 T_1) (-. (g_false_only T_0 T_1))   ### Axiom
% 0.87/1.02  11. (-. (Ex B, (g_false_only T_0 B))) (g_false_only T_0 T_1)   ### NotExists 10
% 0.87/1.02  12. ((g_true_only T_0 T_1) \/ ((g_both T_0 T_1) \/ (g_false_only T_0 T_1))) (-. (Ex B, (g_false_only T_0 B))) (-. (Ex B, (g_both T_0 B))) (-. (g_true T_0 T_1))   ### DisjTree 7 9 11
% 0.87/1.02  13. (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (-. (g_true T_0 T_1)) (-. (Ex B, (g_both T_0 B))) (-. (Ex B, (g_false_only T_0 B)))   ### All 12
% 0.87/1.02  14. (-. ((g_false_only (a) T_0) /\ (Ex B, (g_false_only T_0 B)))) (-. (Ex B, (g_both T_0 B))) (-. (g_true T_0 T_1)) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (g_false_only (a) T_0)   ### NotAnd 5 13
% 0.87/1.02  15. (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_0) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (-. (g_true T_0 T_1)) (-. (Ex B, (g_both T_0 B)))   ### NotExists 14
% 0.87/1.02  16. (g_false T_0 T_1) (-. (g_false T_0 T_1))   ### Axiom
% 0.87/1.02  17. (g_true_only T_0 T_1) (g_false T_0 T_1)   ### Extension/test/true_only_g 16
% 0.87/1.02  18. (g_false_only (a) T_0) (-. (g_false_only (a) T_0))   ### Axiom
% 0.87/1.02  19. (-. ((g_false_only (a) T_0) /\ (Ex B, (g_false_only T_0 B)))) (g_false_only T_0 T_1) (g_false_only (a) T_0)   ### NotAnd 18 11
% 0.87/1.02  20. (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_0) (g_false_only T_0 T_1)   ### NotExists 19
% 0.87/1.02  21. ((g_true_only T_0 T_1) \/ ((g_both T_0 T_1) \/ (g_false_only T_0 T_1))) (g_false_only (a) T_0) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex B, (g_both T_0 B))) (g_false T_0 T_1)   ### DisjTree 17 9 20
% 0.87/1.02  22. (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (g_false T_0 T_1) (-. (Ex B, (g_both T_0 B))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_0)   ### All 21
% 0.87/1.02  23. (-. (g_true_only T_0 T_1)) (-. (Ex B, (g_both T_0 B))) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (g_false_only (a) T_0) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))))   ### Extension/test/not_true_only_g 15 22
% 0.87/1.02  24. (-. (All B, (g_true_only T_0 B))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_0) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (-. (Ex B, (g_both T_0 B)))   ### NotAllEx 23
% 0.87/1.02  25. (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex B, (g_both T_0 B))) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (g_false_only (a) T_0) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))))   ### NotExists 24
% 0.87/1.02  26. ((g_true_only (a) T_0) \/ ((g_both (a) T_0) \/ (g_false_only (a) T_0))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (-. (Ex B, (g_both T_0 B))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (g_true (a) T_0))   ### DisjTree 2 4 25
% 0.87/1.02  27. (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (g_true (a) T_0)) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex B, (g_both T_0 B))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) ((g_true_only (a) T_0) \/ ((g_both (a) T_0) \/ (g_false_only (a) T_0)))   ### All 26
% 0.87/1.02  28. (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex B, (g_both T_0 B))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (g_true (a) T_0)) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1)))))   ### All 27
% 0.87/1.02  29. (g_false_only (a) T_0) (-. (g_false_only (a) T_0))   ### Axiom
% 0.87/1.02  30. (Ex B, (g_false_only T_0 B)) (-. (Ex B, (g_false_only T_0 B)))   ### Axiom
% 0.87/1.02  31. (-. ((g_false_only (a) T_0) /\ (Ex B, (g_false_only T_0 B)))) (Ex B, (g_false_only T_0 B)) (g_false_only (a) T_0)   ### NotAnd 29 30
% 0.87/1.02  32. (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_0) (Ex B, (g_false_only T_0 B))   ### NotExists 31
% 0.87/1.02  33. ((g_true_only (a) T_0) \/ ((g_both (a) T_0) \/ (g_false_only (a) T_0))) (Ex B, (g_false_only T_0 B)) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (g_true (a) T_0))   ### DisjTree 2 4 32
% 0.87/1.02  34. (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (g_true (a) T_0)) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (Ex B, (g_false_only T_0 B))   ### All 33
% 0.87/1.02  35. (-. (-. (Ex B, (g_false_only T_0 B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (g_true (a) T_0)) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1))))   ### NotNot 34
% 0.87/1.02  36. (-. ((Ex B, (g_both T_0 B)) /\ (-. (Ex B, (g_false_only T_0 B))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (g_true (a) T_0)) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1))))   ### NotAnd 28 35
% 0.87/1.02  37. (g_false (a) T_0) (-. (g_false (a) T_0))   ### Axiom
% 0.87/1.02  38. (-. (g_both (a) T_0)) (g_false (a) T_0) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. ((Ex B, (g_both T_0 B)) /\ (-. (Ex B, (g_false_only T_0 B)))))   ### Extension/test/not_both_g 36 37
% 0.87/1.02  39. (-. ((g_both (a) T_0) \/ ((Ex B, (g_both T_0 B)) /\ (-. (Ex B, (g_false_only T_0 B)))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (g_false (a) T_0)   ### NotOr 38
% 0.87/1.02  40. (g_false (a) T_0) (-. (g_false (a) T_0))   ### Axiom
% 0.87/1.02  41. (g_true_only (a) T_0) (g_false (a) T_0)   ### Extension/test/true_only_g 40
% 0.87/1.02  42. (All B, (g_true_only T_0 B)) (-. (All B, (g_true_only T_0 B)))   ### Axiom
% 0.87/1.02  43. (-. (Ex A, (All B, (g_true_only A B)))) (All B, (g_true_only T_0 B))   ### NotExists 42
% 0.87/1.02  44. (-. (((g_both (a) T_0) \/ ((Ex B, (g_both T_0 B)) /\ (-. (Ex B, (g_false_only T_0 B))))) /\ ((-. (g_true_only (a) T_0)) /\ (-. (All B, (g_true_only T_0 B)))))) (g_false (a) T_0) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1)))))   ### DisjTree 39 41 43
% 0.87/1.02  45. (-. (Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B))))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (g_false (a) T_0)   ### NotExists 44
% 0.87/1.02  46. (g_false_only (a) T_0) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B)))))))   ### Extension/test/false_only_g 45
% 0.87/1.03  47. ((g_true_only (a) T_0) \/ ((g_both (a) T_0) \/ (g_false_only (a) T_0))) (-. (Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B))))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (g_true (a) T_0))   ### DisjTree 2 4 46
% 0.87/1.03  48. (-. (g_true (a) T_0)) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B)))))))   ### All 47
% 0.87/1.03  49. (-. (g_true_only (a) T_0)) (-. (Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B))))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1))))   ### Extension/test/not_true_only_g 48 45
% 0.87/1.03  50. (-. (All B, (g_true_only (a) B))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B)))))))   ### NotAllEx 49
% 0.87/1.03  51. (-. (Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B))))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1))))   ### NotExists 50
% 0.87/1.03  52. (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B)))))))   ### All 51
% 0.87/1.03  53. (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))   ### Axiom
% 0.87/1.03  54. (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (g_true (a) T_0)) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex B, (g_both T_0 B))) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))))   ### All 26
% 0.87/1.03  55. (-. ((Ex B, (g_both T_0 B)) /\ (-. (Ex B, (g_false_only T_0 B))))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (g_true (a) T_0)) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1))))   ### NotAnd 54 35
% 0.87/1.03  56. (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B)))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (g_true (a) T_0)) (-. (Ex A, (All B, (g_true_only A B)))) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))))   ### NotExists 55
% 0.87/1.03  57. (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (g_true (a) T_0)) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))))   ### All 56
% 0.87/1.03  58. (g_false (a) T_0) (-. (g_false (a) T_0))   ### Axiom
% 0.87/1.03  59. (-. (g_both (a) T_0)) (g_false (a) T_0) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))))   ### Extension/test/not_both_g 56 58
% 0.87/1.03  60. (-. (Ex B, (g_both (a) B))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B)))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_1, ((g_true_only T_0 X_1) \/ ((g_both T_0 X_1) \/ (g_false_only T_0 X_1)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false (a) T_0)   ### NotExists 59
% 0.87/1.03  61. (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (g_false (a) T_0) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B)))))) (-. (Ex B, (g_both (a) B)))   ### All 60
% 0.87/1.03  62. (-. (g_true_only (a) T_0)) (-. (Ex B, (g_both (a) B))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B)))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1)))))   ### Extension/test/not_true_only_g 57 61
% 0.87/1.03  63. (-. (All B, (g_true_only (a) B))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B)))))) (-. (Ex B, (g_both (a) B)))   ### NotAllEx 62
% 0.87/1.03  64. (-. (Ex B, (g_both (a) B))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B)))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1)))))   ### NotExists 63
% 0.87/1.03  65. (g_false_only (a) T_2) (-. (g_false_only (a) T_2))   ### Axiom
% 0.87/1.03  66. (-. (g_true T_2 T_3)) (g_true T_2 T_3)   ### Axiom
% 0.87/1.03  67. (g_true_only T_2 T_3) (-. (g_true T_2 T_3))   ### Extension/test/true_only_g 66
% 0.87/1.03  68. (-. (g_true T_2 T_3)) (g_true T_2 T_3)   ### Axiom
% 0.87/1.03  69. (g_both T_2 T_3) (-. (g_true T_2 T_3))   ### Extension/test/both_g 68
% 0.87/1.03  70. (g_false T_2 T_3) (-. (g_false T_2 T_3))   ### Axiom
% 0.87/1.03  71. (-. (g_true T_2 T_3)) (g_true T_2 T_3)   ### Axiom
% 0.87/1.03  72. (-. (g_false_only T_2 T_3)) (-. (g_true T_2 T_3)) (g_false T_2 T_3)   ### Extension/test/not_false_only_g 70 71
% 0.87/1.03  73. (-. (Ex B, (g_false_only T_2 B))) (g_false T_2 T_3) (-. (g_true T_2 T_3))   ### NotExists 72
% 0.87/1.03  74. (g_false T_2 T_3) (-. (g_false T_2 T_3))   ### Axiom
% 0.87/1.03  75. (-. (g_both T_2 T_3)) (g_false T_2 T_3) (-. (Ex B, (g_false_only T_2 B)))   ### Extension/test/not_both_g 73 74
% 0.87/1.03  76. (-. (Ex B, (g_both T_2 B))) (-. (Ex B, (g_false_only T_2 B))) (g_false T_2 T_3)   ### NotExists 75
% 0.87/1.03  77. (g_false_only T_2 T_3) (-. (Ex B, (g_false_only T_2 B))) (-. (Ex B, (g_both T_2 B)))   ### Extension/test/false_only_g 76
% 0.87/1.03  78. ((g_true_only T_2 T_3) \/ ((g_both T_2 T_3) \/ (g_false_only T_2 T_3))) (-. (Ex B, (g_both T_2 B))) (-. (Ex B, (g_false_only T_2 B))) (-. (g_true T_2 T_3))   ### DisjTree 67 69 77
% 0.87/1.03  79. (All X_1, ((g_true_only T_2 X_1) \/ ((g_both T_2 X_1) \/ (g_false_only T_2 X_1)))) (-. (g_true T_2 T_3)) (-. (Ex B, (g_false_only T_2 B))) (-. (Ex B, (g_both T_2 B)))   ### All 78
% 0.87/1.03  80. (-. ((g_false_only (a) T_2) /\ (Ex B, (g_false_only T_2 B)))) (-. (Ex B, (g_both T_2 B))) (-. (g_true T_2 T_3)) (All X_1, ((g_true_only T_2 X_1) \/ ((g_both T_2 X_1) \/ (g_false_only T_2 X_1)))) (g_false_only (a) T_2)   ### NotAnd 65 79
% 0.87/1.03  81. (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_2) (All X_1, ((g_true_only T_2 X_1) \/ ((g_both T_2 X_1) \/ (g_false_only T_2 X_1)))) (-. (g_true T_2 T_3)) (-. (Ex B, (g_both T_2 B)))   ### NotExists 80
% 0.87/1.03  82. (g_false_only (a) T_2) (-. (g_false_only (a) T_2))   ### Axiom
% 0.87/1.03  83. (-. ((g_false_only (a) T_2) /\ (Ex B, (g_false_only T_2 B)))) (g_false T_2 T_3) (-. (Ex B, (g_both T_2 B))) (g_false_only (a) T_2)   ### NotAnd 82 76
% 0.87/1.03  84. (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_2) (-. (Ex B, (g_both T_2 B))) (g_false T_2 T_3)   ### NotExists 83
% 0.87/1.03  85. (-. (g_true_only T_2 T_3)) (-. (Ex B, (g_both T_2 B))) (All X_1, ((g_true_only T_2 X_1) \/ ((g_both T_2 X_1) \/ (g_false_only T_2 X_1)))) (g_false_only (a) T_2) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))))   ### Extension/test/not_true_only_g 81 84
% 0.87/1.03  86. (-. (All B, (g_true_only T_2 B))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_2) (All X_1, ((g_true_only T_2 X_1) \/ ((g_both T_2 X_1) \/ (g_false_only T_2 X_1)))) (-. (Ex B, (g_both T_2 B)))   ### NotAllEx 85
% 0.87/1.03  87. (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex B, (g_both T_2 B))) (All X_1, ((g_true_only T_2 X_1) \/ ((g_both T_2 X_1) \/ (g_false_only T_2 X_1)))) (g_false_only (a) T_2) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))))   ### NotExists 86
% 0.87/1.03  88. (g_false_only (a) T_2) (-. (g_false_only (a) T_2))   ### Axiom
% 0.87/1.03  89. (Ex B, (g_false_only T_2 B)) (-. (Ex B, (g_false_only T_2 B)))   ### Axiom
% 0.87/1.03  90. (-. ((g_false_only (a) T_2) /\ (Ex B, (g_false_only T_2 B)))) (Ex B, (g_false_only T_2 B)) (g_false_only (a) T_2)   ### NotAnd 88 89
% 0.87/1.03  91. (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_2) (Ex B, (g_false_only T_2 B))   ### NotExists 90
% 0.87/1.03  92. (-. (-. (Ex B, (g_false_only T_2 B)))) (g_false_only (a) T_2) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))))   ### NotNot 91
% 0.87/1.03  93. (-. ((Ex B, (g_both T_2 B)) /\ (-. (Ex B, (g_false_only T_2 B))))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_2) (All X_1, ((g_true_only T_2 X_1) \/ ((g_both T_2 X_1) \/ (g_false_only T_2 X_1)))) (-. (Ex A, (All B, (g_true_only A B))))   ### NotAnd 87 92
% 0.87/1.03  94. (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B)))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_1, ((g_true_only T_2 X_1) \/ ((g_both T_2 X_1) \/ (g_false_only T_2 X_1)))) (g_false_only (a) T_2) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))))   ### NotExists 93
% 0.87/1.03  95. (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (g_false_only (a) T_2) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))))   ### All 94
% 0.87/1.03  96. (Ex B, (g_false_only (a) B)) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B)))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1)))))   ### Exists 95
% 0.87/1.03  97. (-. (-. (Ex B, (g_false_only (a) B)))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))))   ### NotNot 96
% 0.87/1.03  98. (-. ((Ex B, (g_both (a) B)) /\ (-. (Ex B, (g_false_only (a) B))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))))   ### NotAnd 64 97
% 0.87/1.03  99. (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B)))))) (All X_1, ((g_true_only (a) X_1) \/ ((g_both (a) X_1) \/ (g_false_only (a) X_1)))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1)))))   ### NotExists 98
% 0.87/1.03  100. (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))))   ### All 99
% 0.87/1.03  101. (-. (Ex A, (All B, (g_true_only A B)))) (Ex A, (All B, (g_true_only A B)))   ### Axiom
% 0.87/1.03  102. (-. ((Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B)))))) /\ ((-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) /\ ((Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ (-. (Ex A, (All B, (g_true_only A B)))))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1))))) (-. (Ex A, (All B, (g_true_only A B)))) (-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))))   ### DisjTree 52 53 100 101
% 0.87/1.03  103. (-. ((Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B)))) \/ ((Ex A, (All B, (g_true_only A B))) \/ ((Ex A, (((g_both (a) A) \/ ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ ((-. (g_true_only (a) A)) /\ (-. (All B, (g_true_only A B)))))) /\ ((-. (Ex A, ((g_false_only (a) A) /\ (Ex B, (g_false_only A B))))) /\ ((Ex A, ((Ex B, (g_both A B)) /\ (-. (Ex B, (g_false_only A B))))) /\ (-. (Ex A, (All B, (g_true_only A B)))))))))) (All X_2, (All X_1, ((g_true_only X_2 X_1) \/ ((g_both X_2 X_1) \/ (g_false_only X_2 X_1)))))   ### ConjTree 102
% 0.87/1.03  % SZS output end Proof
% 0.87/1.03  (* END-PROOF *)
%------------------------------------------------------------------------------