TSTP Solution File: LCL664+1.005 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LCL664+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n029.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 : Sun Jul 17 14:52:43 EDT 2022
% Result : Theorem 1.61s 1.77s
% Output : Proof 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL664+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n029.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 : Mon Jul 4 18:18:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.61/1.77 % SZS status Theorem
% 1.61/1.77 (* PROOF-FOUND *)
% 1.61/1.77 (* BEGIN-PROOF *)
% 1.61/1.77 % SZS output start Proof
% 1.61/1.77 1. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 1.61/1.77 2. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 1.61/1.77 3. (r1 T_1 T_2) (-. (r1 T_1 T_2)) ### Axiom
% 1.61/1.77 4. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 1.61/1.77 5. (r1 T_1 T_2) (-. (r1 T_1 T_2)) ### Axiom
% 1.61/1.77 6. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 1.61/1.77 7. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 1.61/1.77 8. (r1 T_1 T_2) (-. (r1 T_1 T_2)) ### Axiom
% 1.61/1.77 9. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 1.61/1.77 10. (r1 T_3 T_4) (-. (r1 T_3 T_4)) ### Axiom
% 1.61/1.77 11. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 1.61/1.77 12. (r1 T_1 T_2) (-. (r1 T_1 T_2)) ### Axiom
% 1.61/1.77 13. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 1.61/1.77 14. (r1 T_3 T_4) (-. (r1 T_3 T_4)) ### Axiom
% 1.61/1.77 15. (-. (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y))) ### Axiom
% 1.61/1.77 16. ((-. (r1 T_3 T_4)) \/ (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) (-. (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) (r1 T_3 T_4) ### Or 14 15
% 1.61/1.77 17. (All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))) (r1 T_3 T_4) (-. (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) ### All 16
% 1.61/1.77 18. ((-. (r1 T_2 T_3)) \/ (All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y)))))) (-. (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) (r1 T_3 T_4) (r1 T_2 T_3) ### Or 13 17
% 1.61/1.77 19. (All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))) (r1 T_2 T_3) (r1 T_3 T_4) (-. (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) ### All 18
% 1.61/1.77 20. ((-. (r1 T_1 T_2)) \/ (All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y)))))))) (-. (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) (r1 T_3 T_4) (r1 T_2 T_3) (r1 T_1 T_2) ### Or 12 19
% 1.61/1.77 21. (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))) (r1 T_1 T_2) (r1 T_2 T_3) (r1 T_3 T_4) (-. (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) ### All 20
% 1.61/1.77 22. ((-. (r1 T_0 T_1)) \/ (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y)))))))))) (-. (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) (r1 T_3 T_4) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) ### Or 11 21
% 1.61/1.77 23. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (r1 T_2 T_3) (r1 T_3 T_4) (-. (All Y, ((-. (r1 T_4 Y)) \/ (p54 Y)))) ### All 22
% 1.61/1.77 24. (-. (p41 T_4)) (p41 T_4) ### Axiom
% 1.61/1.77 25. ((-. (r1 T_3 T_4)) \/ (-. ((All Y, ((-. (r1 T_4 Y)) \/ (p54 Y))) /\ (-. (p41 T_4))))) (-. (p41 T_4)) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_3 T_4) ### DisjTree 10 23 24
% 1.61/1.77 26. (All X, ((-. (r1 T_3 X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))) (r1 T_3 T_4) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (r1 T_2 T_3) (-. (p41 T_4)) ### All 25
% 1.61/1.77 27. ((-. (r1 T_2 T_3)) \/ (All X, ((-. (r1 T_3 X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X))))))) (-. (p41 T_4)) (r1 T_1 T_2) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_3 T_4) (r1 T_2 T_3) ### Or 9 26
% 1.61/1.77 28. (All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))) (r1 T_2 T_3) (r1 T_3 T_4) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (-. (p41 T_4)) ### All 27
% 1.61/1.77 29. ((-. (r1 T_1 T_2)) \/ (All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X))))))))) (-. (p41 T_4)) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_3 T_4) (r1 T_2 T_3) (r1 T_1 T_2) ### Or 8 28
% 1.61/1.77 30. (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))) (r1 T_1 T_2) (r1 T_2 T_3) (r1 T_3 T_4) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_0 T_1) (-. (p41 T_4)) ### All 29
% 1.61/1.77 31. ((-. (r1 T_0 T_1)) \/ (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X))))))))))) (-. (p41 T_4)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_3 T_4) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) ### Or 7 30
% 1.61/1.77 32. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (r1 T_2 T_3) (r1 T_3 T_4) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (-. (p41 T_4)) ### All 31
% 1.61/1.77 33. (-. (-. (r1 T_3 T_4))) (-. (p41 T_4)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) ### NotNot 32
% 1.61/1.77 34. (-. ((-. (r1 T_3 T_4)) \/ (p41 T_4))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (r1 T_2 T_3) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) ### NotOr 33
% 1.61/1.77 35. (-. (All X, ((-. (r1 T_3 X)) \/ (p41 X)))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) ### NotAllEx 34
% 1.61/1.77 36. (-. (p34 T_3)) (p34 T_3) ### Axiom
% 1.61/1.77 37. ((-. (r1 T_2 T_3)) \/ (-. ((All X, ((-. (r1 T_3 X)) \/ (p41 X))) /\ (-. (p34 T_3))))) (-. (p34 T_3)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_2 T_3) ### DisjTree 6 35 36
% 1.61/1.77 38. (All Y, ((-. (r1 T_2 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))) (r1 T_2 T_3) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_1 T_2) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (-. (p34 T_3)) ### All 37
% 1.61/1.77 39. ((-. (r1 T_1 T_2)) \/ (All Y, ((-. (r1 T_2 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y))))))) (-. (p34 T_3)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_2 T_3) (r1 T_1 T_2) ### Or 5 38
% 1.61/1.77 40. (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))) (r1 T_1 T_2) (r1 T_2 T_3) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (-. (p34 T_3)) ### All 39
% 1.65/1.84 41. ((-. (r1 T_0 T_1)) \/ (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y))))))))) (-. (p34 T_3)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) ### Or 4 40
% 1.65/1.84 42. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (r1 T_2 T_3) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (-. (p34 T_3)) ### All 41
% 1.65/1.84 43. (-. (-. (r1 T_2 T_3))) (-. (p34 T_3)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_1 T_2) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) ### NotNot 42
% 1.65/1.84 44. (-. ((-. (r1 T_2 T_3)) \/ (p34 T_3))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) ### NotOr 43
% 1.65/1.84 45. (-. (All Y, ((-. (r1 T_2 Y)) \/ (p34 Y)))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_1 T_2) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) ### NotAllEx 44
% 1.65/1.84 46. (-. (p21 T_2)) (p21 T_2) ### Axiom
% 1.65/1.84 47. ((-. (r1 T_1 T_2)) \/ (-. ((All Y, ((-. (r1 T_2 Y)) \/ (p34 Y))) /\ (-. (p21 T_2))))) (-. (p21 T_2)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (r1 T_1 T_2) ### DisjTree 3 45 46
% 1.65/1.84 48. (All X, ((-. (r1 T_1 X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))) (r1 T_1 T_2) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (-. (p21 T_2)) ### All 47
% 1.65/1.84 49. ((-. (r1 T_0 T_1)) \/ (All X, ((-. (r1 T_1 X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X))))))) (-. (p21 T_2)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (r1 T_1 T_2) (r1 T_0 T_1) ### Or 2 48
% 1.65/1.84 50. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))))) (r1 T_0 T_1) (r1 T_1 T_2) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (-. (p21 T_2)) ### All 49
% 1.65/1.84 51. (-. (-. (r1 T_1 T_2))) (-. (p21 T_2)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))))) ### NotNot 50
% 1.65/1.84 52. (-. ((-. (r1 T_1 T_2)) \/ (p21 T_2))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) ### NotOr 51
% 1.65/1.84 53. (-. (All X, ((-. (r1 T_1 X)) \/ (p21 X)))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))))) ### NotAllEx 52
% 1.65/1.84 54. (-. (p12 T_1)) (p12 T_1) ### Axiom
% 1.65/1.84 55. ((-. (r1 T_0 T_1)) \/ (-. ((All X, ((-. (r1 T_1 X)) \/ (p21 X))) /\ (-. (p12 T_1))))) (-. (p12 T_1)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (r1 T_0 T_1) ### DisjTree 1 53 54
% 1.65/1.84 56. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p21 X))) /\ (-. (p12 Y)))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))))) (-. (p12 T_1)) ### All 55
% 1.65/1.84 57. (-. (-. (r1 T_0 T_1))) (-. (p12 T_1)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p21 X))) /\ (-. (p12 Y)))))) ### NotNot 56
% 1.65/1.84 58. (-. ((-. (r1 T_0 T_1)) \/ (p12 T_1))) (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p21 X))) /\ (-. (p12 Y)))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))))) ### NotOr 57
% 1.65/1.84 59. (-. (All Y, ((-. (r1 T_0 Y)) \/ (p12 Y)))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X)))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y)))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p21 X))) /\ (-. (p12 Y)))))) ### NotAllEx 58
% 1.65/1.84 60. (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p56 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p52 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p56 Y))) /\ (-. (p46 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p56 Y))) /\ (-. (p44 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p56 Y))) /\ (-. (p42 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p46 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p44 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p42 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p52 Y))) /\ (-. (p46 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p52 Y))) /\ (-. (p44 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p52 Y))) /\ (-. (p42 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p46 X))) /\ (-. (p36 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p46 X))) /\ (-. (p32 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p55 Y))) /\ (-. (p45 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p53 Y))) /\ (-. (p45 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p51 Y))) /\ (-. (p45 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p44 X))) /\ (-. (p36 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p44 X))) /\ (-. (p32 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p55 Y))) /\ (-. (p43 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p53 Y))) /\ (-. (p43 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p51 Y))) /\ (-. (p43 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p42 X))) /\ (-. (p36 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p42 X))) /\ (-. (p32 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p55 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p53 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p51 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p36 Y))) /\ (-. (p26 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p36 Y))) /\ (-. (p24 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p36 Y))) /\ (-. (p22 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p45 X))) /\ (-. (p35 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p43 X))) /\ (-. (p35 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p26 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p24 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p22 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p45 X))) /\ (-. (p33 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p43 X))) /\ (-. (p33 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p32 Y))) /\ (-. (p26 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p32 Y))) /\ (-. (p24 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p32 Y))) /\ (-. (p22 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p45 X))) /\ (-. (p31 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p43 X))) /\ (-. (p31 Y))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p26 X))) /\ (-. (p16 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p26 X))) /\ (-. (p14 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p35 Y))) /\ (-. (p25 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p33 Y))) /\ (-. (p25 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p31 Y))) /\ (-. (p25 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p24 X))) /\ (-. (p16 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p24 X))) /\ (-. (p14 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p35 Y))) /\ (-. (p23 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p33 Y))) /\ (-. (p23 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p31 Y))) /\ (-. (p23 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p22 X))) /\ (-. (p16 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p22 X))) /\ (-. (p14 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p35 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p33 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p31 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p25 X))) /\ (-. (p15 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p23 X))) /\ (-. (p15 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p25 X))) /\ (-. (p13 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p23 X))) /\ (-. (p13 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p21 X))) /\ (-. (p12 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p25 X))) /\ (-. (p11 Y))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p23 X))) /\ (-. (p11 Y))))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p15 Y))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p13 Y))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p12 Y))) \/ (All Y, ((-. (r1 T_0 Y)) \/ (p11 Y))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ### ConjTree 59
% 1.65/1.84 61. (Ex X, (-. ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p56 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p52 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p56 Y))) /\ (-. (p46 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p56 Y))) /\ (-. (p44 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p56 Y))) /\ (-. (p42 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p46 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p44 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p42 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p52 Y))) /\ (-. (p46 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p52 Y))) /\ (-. (p44 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p52 Y))) /\ (-. (p42 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p46 X))) /\ (-. (p36 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p46 X))) /\ (-. (p32 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p55 Y))) /\ (-. (p45 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p53 Y))) /\ (-. (p45 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p51 Y))) /\ (-. (p45 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p44 X))) /\ (-. (p36 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p44 X))) /\ (-. (p32 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p55 Y))) /\ (-. (p43 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p53 Y))) /\ (-. (p43 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p51 Y))) /\ (-. (p43 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p42 X))) /\ (-. (p36 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p42 X))) /\ (-. (p32 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p55 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p53 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p51 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p36 Y))) /\ (-. (p26 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p36 Y))) /\ (-. (p24 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p36 Y))) /\ (-. (p22 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p45 X))) /\ (-. (p35 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p43 X))) /\ (-. (p35 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p26 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p24 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p22 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p45 X))) /\ (-. (p33 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p43 X))) /\ (-. (p33 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p32 Y))) /\ (-. (p26 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p32 Y))) /\ (-. (p24 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p32 Y))) /\ (-. (p22 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p45 X))) /\ (-. (p31 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p43 X))) /\ (-. (p31 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p26 X))) /\ (-. (p16 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p26 X))) /\ (-. (p14 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p35 Y))) /\ (-. (p25 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p33 Y))) /\ (-. (p25 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p31 Y))) /\ (-. (p25 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p24 X))) /\ (-. (p16 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p24 X))) /\ (-. (p14 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p35 Y))) /\ (-. (p23 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p33 Y))) /\ (-. (p23 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p31 Y))) /\ (-. (p23 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p22 X))) /\ (-. (p16 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p22 X))) /\ (-. (p14 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p35 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p33 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p31 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p25 X))) /\ (-. (p15 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p23 X))) /\ (-. (p15 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p25 X))) /\ (-. (p13 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p23 X))) /\ (-. (p13 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p21 X))) /\ (-. (p12 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p25 X))) /\ (-. (p11 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p23 X))) /\ (-. (p11 Y))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p15 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ (p13 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ (p12 Y))) \/ (All Y, ((-. (r1 X Y)) \/ (p11 Y)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ### Exists 60
% 1.65/1.84 62. (-. (-. (Ex X, (-. ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p56 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p54 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p52 Y)))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p56 Y))) /\ (-. (p46 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p56 Y))) /\ (-. (p44 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p56 Y))) /\ (-. (p42 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p46 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p44 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p42 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p52 Y))) /\ (-. (p46 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p52 Y))) /\ (-. (p44 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p52 Y))) /\ (-. (p42 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p46 X))) /\ (-. (p36 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p46 X))) /\ (-. (p32 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p55 Y))) /\ (-. (p45 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p53 Y))) /\ (-. (p45 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p51 Y))) /\ (-. (p45 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p44 X))) /\ (-. (p36 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p44 X))) /\ (-. (p32 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p55 Y))) /\ (-. (p43 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p53 Y))) /\ (-. (p43 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p51 Y))) /\ (-. (p43 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p42 X))) /\ (-. (p36 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p42 X))) /\ (-. (p32 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p55 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p54 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p53 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p51 Y))) /\ (-. (p41 X))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p36 Y))) /\ (-. (p26 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p36 Y))) /\ (-. (p24 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p36 Y))) /\ (-. (p22 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p45 X))) /\ (-. (p35 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p43 X))) /\ (-. (p35 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p26 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p24 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p22 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p41 X))) /\ (-. (p34 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p45 X))) /\ (-. (p33 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p43 X))) /\ (-. (p33 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p32 Y))) /\ (-. (p26 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p32 Y))) /\ (-. (p24 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p32 Y))) /\ (-. (p22 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p45 X))) /\ (-. (p31 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p43 X))) /\ (-. (p31 Y))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p26 X))) /\ (-. (p16 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p26 X))) /\ (-. (p14 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p35 Y))) /\ (-. (p25 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p33 Y))) /\ (-. (p25 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p31 Y))) /\ (-. (p25 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p24 X))) /\ (-. (p16 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p24 X))) /\ (-. (p14 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p35 Y))) /\ (-. (p23 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p33 Y))) /\ (-. (p23 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p31 Y))) /\ (-. (p23 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p22 X))) /\ (-. (p16 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p22 X))) /\ (-. (p14 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p35 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p34 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p33 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((All Y, ((-. (r1 X Y)) \/ (p31 Y))) /\ (-. (p21 X))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p25 X))) /\ (-. (p15 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p23 X))) /\ (-. (p15 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p25 X))) /\ (-. (p13 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p23 X))) /\ (-. (p13 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p21 X))) /\ (-. (p12 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p25 X))) /\ (-. (p11 Y))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p23 X))) /\ (-. (p11 Y))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p15 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ (p13 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ (p12 Y))) \/ (All Y, ((-. (r1 X Y)) \/ (p11 Y)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ### NotNot 61
% 1.65/1.84 % SZS output end Proof
% 1.65/1.84 (* END-PROOF *)
%------------------------------------------------------------------------------