TSTP Solution File: LCL640+1.005 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LCL640+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 : n025.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 14:52:10 EDT 2022
% Result : Theorem 5.15s 5.32s
% Output : Proof 5.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL640+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.32 % Computer : n025.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Tue Jul 5 00:02:41 EDT 2022
% 0.13/0.32 % CPUTime :
% 5.15/5.32 % SZS status Theorem
% 5.15/5.32 (* PROOF-FOUND *)
% 5.15/5.32 (* BEGIN-PROOF *)
% 5.15/5.32 % SZS output start Proof
% 5.15/5.32 1. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 5.15/5.32 2. (r1 T_1 T_2) (-. (r1 T_1 T_2)) ### Axiom
% 5.15/5.32 3. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 5.15/5.32 4. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 5.15/5.32 5. (r1 T_1 T_2) (-. (r1 T_1 T_2)) ### Axiom
% 5.15/5.32 6. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 5.15/5.32 7. (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (All X, ((-. (r1 T_3 X)) \/ (p1 X))) ### Axiom
% 5.15/5.32 8. (p1 T_3) (-. (p1 T_3)) ### Axiom
% 5.15/5.32 9. (r1 T_3 T_4) (-. (r1 T_3 T_4)) ### Axiom
% 5.15/5.32 10. (r1 T_3 T_4) (-. (r1 T_3 T_4)) ### Axiom
% 5.15/5.32 11. (r1 T_4 T_5) (-. (r1 T_4 T_5)) ### Axiom
% 5.15/5.32 12. (-. (All Y, ((-. (r1 T_5 Y)) \/ (p1 Y)))) (All Y, ((-. (r1 T_5 Y)) \/ (p1 Y))) ### Axiom
% 5.15/5.32 13. ((-. (r1 T_4 T_5)) \/ (All Y, ((-. (r1 T_5 Y)) \/ (p1 Y)))) (-. (All Y, ((-. (r1 T_5 Y)) \/ (p1 Y)))) (r1 T_4 T_5) ### Or 11 12
% 5.15/5.32 14. (All X, ((-. (r1 T_4 X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) (r1 T_4 T_5) (-. (All Y, ((-. (r1 T_5 Y)) \/ (p1 Y)))) ### All 13
% 5.15/5.32 15. (-. ((-. (r1 T_4 T_5)) \/ ((All Y, ((-. (r1 T_5 Y)) \/ (p1 Y))) \/ (-. (p1 T_5))))) (All X, ((-. (r1 T_4 X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) ### ConjTree 14
% 5.15/5.32 16. (-. (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))) (All X, ((-. (r1 T_4 X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) ### NotAllEx 15
% 5.15/5.32 17. ((-. (r1 T_3 T_4)) \/ (-. (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))) (All X, ((-. (r1 T_4 X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) (r1 T_3 T_4) ### Or 10 16
% 5.15/5.32 18. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) (r1 T_3 T_4) (All X, ((-. (r1 T_4 X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) ### All 17
% 5.15/5.32 19. (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (-. (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y)))) ### Axiom
% 5.15/5.32 20. ((-. (r1 T_3 T_4)) \/ ((All X, ((-. (r1 T_4 X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y)))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) (r1 T_3 T_4) ### DisjTree 9 18 19
% 5.15/5.32 21. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (r1 T_3 T_4) (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) ### All 20
% 5.15/5.32 22. (r1 T_6 T_7) (-. (r1 T_6 T_7)) ### Axiom
% 5.15/5.32 23. (r1 T_3 T_6) (-. (r1 T_3 T_6)) ### Axiom
% 5.15/5.32 24. (r1 T_6 T_7) (-. (r1 T_6 T_7)) ### Axiom
% 5.15/5.32 25. (-. (p1 T_7)) (p1 T_7) ### Axiom
% 5.15/5.32 26. (All X, ((-. (r1 T_7 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) (-. (All X, ((-. (r1 T_7 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))) ### Axiom
% 5.15/5.32 27. ((-. (r1 T_6 T_7)) \/ ((p1 T_7) \/ (-. (All X, ((-. (r1 T_7 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))) (All X, ((-. (r1 T_7 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) (-. (p1 T_7)) (r1 T_6 T_7) ### DisjTree 24 25 26
% 5.15/5.32 28. (All Y, ((-. (r1 T_6 Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))) (r1 T_6 T_7) (-. (p1 T_7)) (All X, ((-. (r1 T_7 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) ### All 27
% 5.15/5.32 29. ((-. (r1 T_3 T_6)) \/ (All Y, ((-. (r1 T_6 Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))))) (All X, ((-. (r1 T_7 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) (-. (p1 T_7)) (r1 T_6 T_7) (r1 T_3 T_6) ### Or 23 28
% 5.15/5.32 30. (All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) (r1 T_3 T_6) (r1 T_6 T_7) (-. (p1 T_7)) (All X, ((-. (r1 T_7 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) ### All 29
% 5.15/5.32 31. (-. (p1 T_7)) (p1 T_7) ### Axiom
% 5.15/5.32 32. (-. (-. (p1 T_7))) (-. (p1 T_7)) ### NotNot 31
% 5.15/5.32 33. (-. ((All X, ((-. (r1 T_7 X)) \/ (p1 X))) \/ (-. (p1 T_7)))) (-. (p1 T_7)) ### NotOr 32
% 5.15/5.32 34. ((-. (r1 T_6 T_7)) \/ ((All X, ((-. (r1 T_7 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 T_7 X)) \/ (p1 X))) \/ (-. (p1 T_7)))))) (-. (p1 T_7)) (r1 T_3 T_6) (All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) (r1 T_6 T_7) ### DisjTree 22 30 33
% 5.15/5.32 35. (All Y, ((-. (r1 T_6 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) (r1 T_6 T_7) (All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) (r1 T_3 T_6) (-. (p1 T_7)) ### All 34
% 5.15/5.32 36. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))) ### Axiom
% 5.15/5.32 37. ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (p1 T_7)) (r1 T_3 T_6) (r1 T_6 T_7) (All Y, ((-. (r1 T_6 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) ### Or 35 36
% 5.15/5.32 38. (-. (-. (r1 T_6 T_7))) (All Y, ((-. (r1 T_6 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) (r1 T_3 T_6) (-. (p1 T_7)) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) ### NotNot 37
% 5.15/5.32 39. (-. ((-. (r1 T_6 T_7)) \/ (p1 T_7))) ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (r1 T_3 T_6) (All Y, ((-. (r1 T_6 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) ### NotOr 38
% 5.15/5.32 40. (-. (All Y, ((-. (r1 T_6 Y)) \/ (p1 Y)))) (All Y, ((-. (r1 T_6 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) (r1 T_3 T_6) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) ### NotAllEx 39
% 5.15/5.32 41. (-. ((-. (r1 T_3 T_6)) \/ ((All Y, ((-. (r1 T_6 Y)) \/ (p1 Y))) \/ ((-. (p1 T_6)) \/ (-. (All Y, ((-. (r1 T_6 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ### ConjTree 40
% 5.15/5.32 42. (-. (All X, ((-. (r1 T_3 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) ### NotAllEx 41
% 5.15/5.32 43. ((All X, ((-. (r1 T_3 X)) \/ (p1 X))) \/ ((-. (p1 T_3)) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (r1 T_3 T_4) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (p1 T_3) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) ### DisjTree 7 8 21 42
% 5.15/5.32 44. (((All X, ((-. (r1 T_3 X)) \/ (p1 X))) \/ ((-. (p1 T_3)) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 T_3) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (p1 T_3) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (r1 T_3 T_4) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ### ConjTree 43
% 5.15/5.32 45. ((-. (r1 T_2 T_3)) \/ (((All X, ((-. (r1 T_3 X)) \/ (p1 X))) \/ ((-. (p1 T_3)) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 T_3) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (r1 T_3 T_4) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (p1 T_3) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (r1 T_2 T_3) ### Or 6 44
% 5.15/5.32 46. (All Y, ((-. (r1 T_2 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) (r1 T_2 T_3) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (p1 T_3) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (r1 T_3 T_4) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ### All 45
% 5.15/5.32 47. ((-. (r1 T_1 T_2)) \/ (All Y, ((-. (r1 T_2 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (r1 T_3 T_4) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (p1 T_3) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (r1 T_2 T_3) (r1 T_1 T_2) ### Or 5 46
% 5.15/5.33 48. (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))) (r1 T_1 T_2) (r1 T_2 T_3) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (p1 T_3) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (r1 T_3 T_4) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ### All 47
% 5.15/5.33 49. ((-. (r1 T_0 T_1)) \/ (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (r1 T_3 T_4) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (p1 T_3) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) ### Or 4 48
% 5.15/5.33 50. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (r1 T_2 T_3) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (p1 T_3) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (r1 T_3 T_4) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ### All 49
% 5.15/5.33 51. (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) ### Axiom
% 5.15/5.33 52. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))) ### Axiom
% 5.15/5.33 53. ((p1 T_3) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (r1 T_3 T_4) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) ### DisjTree 50 51 52
% 5.15/5.33 54. (((All X, ((-. (r1 T_3 X)) \/ (p1 X))) \/ ((-. (p1 T_3)) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 T_3) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (r1 T_2 T_3) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (r1 T_3 T_4) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) ### ConjTree 53
% 5.15/5.33 55. ((-. (r1 T_2 T_3)) \/ (((All X, ((-. (r1 T_3 X)) \/ (p1 X))) \/ ((-. (p1 T_3)) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 T_3) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ ((All X, ((-. (r1 T_3 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (r1 T_3 T_4) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_2 T_3) ### Or 3 54
% 5.15/5.33 56. (All Y, ((-. (r1 T_2 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_0 T_1) (r1 T_1 T_2) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (r1 T_3 T_4) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) ### All 55
% 5.15/5.33 57. ((-. (r1 T_1 T_2)) \/ (All Y, ((-. (r1 T_2 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (r1 T_3 T_4) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_2 T_3) (r1 T_1 T_2) ### Or 2 56
% 5.15/5.33 58. (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_0 T_1) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (r1 T_3 T_4) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) ### All 57
% 5.15/5.33 59. ((-. (r1 T_0 T_1)) \/ (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (r1 T_3 T_4) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) ### Or 1 58
% 5.15/5.33 60. (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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (r1 T_3 T_4) (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) ### All 59
% 5.15/5.33 61. (-. (-. (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (r1 T_3 T_4) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) ### NotNot 60
% 5.15/5.33 62. (-. (-. (r1 T_3 T_4))) (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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (-. (-. (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))))) ### NotNot 61
% 5.15/5.33 63. (-. ((-. (r1 T_3 T_4)) \/ (-. (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y)))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_0 T_1) ### NotOr 62
% 5.15/5.33 64. (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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (p1 X)))) (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) ### NotAllEx 63
% 5.15/5.33 65. (-. ((-. (r1 T_2 T_3)) \/ ((All X, ((-. (r1 T_3 X)) \/ (p1 X))) \/ ((All X, ((-. (r1 T_3 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_3 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_1 T_2) (r1 T_0 T_1) ### ConjTree 64
% 5.15/5.33 66. (-. (All Y, ((-. (r1 T_2 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) ### NotAllEx 65
% 5.15/5.34 67. (-. (-. (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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_0 T_1) (-. (All Y, ((-. (r1 T_2 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))) ### NotNot 66
% 5.15/5.34 68. (-. ((-. (r1 T_1 T_2)) \/ (All Y, ((-. (r1 T_2 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) ### NotOr 67
% 5.15/5.34 69. (-. (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (r1 T_0 T_1) ### NotAllEx 68
% 5.15/5.34 70. (-. (-. (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)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))) ### NotNot 69
% 5.15/5.34 71. (-. ((-. (r1 T_0 T_1)) \/ (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) ### NotOr 70
% 5.15/5.34 72. (-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))))) ### NotAllEx 71
% 5.15/5.34 73. (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (((p1 X) \/ ((All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))))))))))))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))))) \/ (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))) /\ ((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (((p1 X) \/ ((All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))))) /\ (All Y, ((-. (r1 T_0 Y)) \/ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))))))) ### ConjTree 72
% 5.15/5.34 74. (Ex X, (-. ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (((p1 X) \/ ((All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))))) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))) /\ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (((p1 X) \/ ((All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))))))))) ### Exists 73
% 5.15/5.34 75. (-. (-. (Ex X, (-. ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (((p1 X) \/ ((All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))))))))))))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))))) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))) /\ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (((p1 X) \/ ((All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))))))))))) ### NotNot 74
% 5.15/5.34 % SZS output end Proof
% 5.15/5.34 (* END-PROOF *)
%------------------------------------------------------------------------------