TSTP Solution File: LCL660+1.001 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LCL660+1.001 : 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 : n009.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 14:52:37 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL660+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 18:50:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 (* PROOF-FOUND *)
% 0.19/0.48 (* BEGIN-PROOF *)
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 1. (-. (r1 T_0 T_0)) ### Extension/test/reflexivity
% 0.19/0.48 2. (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y)))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y))))) ### Axiom
% 0.19/0.48 3. ((-. (r1 T_0 T_0)) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y)))))) (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y)))) ### Or 1 2
% 0.19/0.48 4. (All Y, ((-. (r1 T_0 Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p3 X))))))) (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y)))) ### All 3
% 0.19/0.48 5. (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p3 X))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y)))) ### NotNot 4
% 0.19/0.48 6. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 0.19/0.48 7. (-. (p2 T_1)) (p2 T_1) ### Axiom
% 0.19/0.48 8. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 0.19/0.48 9. (-. (All Y, ((-. (r1 T_1 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (All Y, ((-. (r1 T_1 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) ### Axiom
% 0.19/0.48 10. ((-. (r1 T_0 T_1)) \/ (All Y, ((-. (r1 T_1 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (-. (All Y, ((-. (r1 T_1 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (r1 T_0 T_1) ### Or 8 9
% 0.19/0.48 11. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) (r1 T_0 T_1) (-. (All Y, ((-. (r1 T_1 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) ### All 10
% 0.19/0.48 12. ((-. (r1 T_0 T_1)) \/ ((p2 T_1) \/ (-. (All Y, ((-. (r1 T_1 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) (-. (p2 T_1)) (r1 T_0 T_1) ### DisjTree 6 7 11
% 0.19/0.48 13. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) (r1 T_0 T_1) (-. (p2 T_1)) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) ### All 12
% 0.19/0.48 14. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) ### Axiom
% 0.19/0.48 15. ((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) (-. (p2 T_1)) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) ### Or 13 14
% 0.19/0.48 16. (((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) (r1 T_0 T_1) (-. (p2 T_1)) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) ### And 15
% 0.19/0.48 17. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 0.19/0.48 18. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 0.19/0.48 19. (r1 T_3 T_4) (-. (r1 T_3 T_4)) ### Axiom
% 0.19/0.48 20. (-. (p2 T_4)) (p2 T_4) ### Axiom
% 0.19/0.48 21. (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))) ### Axiom
% 0.19/0.48 22. ((p2 T_4) \/ (-. (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (p2 T_4)) ### Or 20 21
% 0.19/0.48 23. (((All X, ((-. (r1 T_4 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 T_4 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 T_4) \/ (-. (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) (-. (p2 T_4)) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) ### And 22
% 0.19/0.48 24. ((-. (r1 T_3 T_4)) \/ (((All X, ((-. (r1 T_4 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 T_4 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 T_4) \/ (-. (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (p2 T_4)) (r1 T_3 T_4) ### Or 19 23
% 0.19/0.48 25. (All Y, ((-. (r1 T_3 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (r1 T_3 T_4) (-. (p2 T_4)) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) ### All 24
% 0.19/0.48 26. (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) ### Axiom
% 0.19/0.48 27. (-. (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) ### NotNot 26
% 0.19/0.48 28. (-. ((All Y, ((-. (r1 T_3 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) ### NotOr 27
% 0.19/0.48 29. (p2 T_3) (-. (p2 T_3)) ### Axiom
% 0.19/0.48 30. (-. ((p2 T_3) \/ (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) (p2 T_3) ### NotOr 29
% 0.19/0.48 31. ((-. (r1 T_2 T_3)) \/ ((All Y, ((-. (r1 T_3 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 T_3 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_3) \/ (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) (p2 T_3) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (p2 T_4)) (r1 T_3 T_4) (r1 T_2 T_3) ### DisjTree 18 25 28 30
% 0.19/0.48 32. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (r1 T_2 T_3) (r1 T_3 T_4) (-. (p2 T_4)) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (p2 T_3) ### All 31
% 0.19/0.48 33. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 0.19/0.48 34. (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))) (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))) ### Axiom
% 0.19/0.48 35. (-. (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))) ### NotNot 34
% 0.19/0.48 36. (-. ((p2 T_3) \/ (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))) ### NotOr 35
% 0.19/0.48 37. ((-. (r1 T_2 T_3)) \/ ((All Y, ((-. (r1 T_3 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 T_3 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_3) \/ (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (p2 T_4)) (r1 T_3 T_4) (r1 T_2 T_3) ### DisjTree 33 25 28 36
% 0.19/0.48 38. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (r1 T_2 T_3) (r1 T_3 T_4) (-. (p2 T_4)) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))) ### All 37
% 0.19/0.48 39. ((-. (r1 T_2 T_3)) \/ ((p2 T_3) \/ (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (p2 T_4)) (r1 T_3 T_4) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (r1 T_2 T_3) ### DisjTree 17 32 38
% 0.19/0.48 40. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))) (r1 T_2 T_3) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (r1 T_3 T_4) (-. (p2 T_4)) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) ### All 39
% 0.19/0.48 41. (-. (-. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (p2 T_4)) (r1 T_3 T_4) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (r1 T_2 T_3) ### NotNot 40
% 0.19/0.48 42. (-. ((-. (r1 T_3 T_4)) \/ ((p2 T_4) \/ (-. (All X, ((-. (r1 T_4 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) (r1 T_2 T_3) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (-. (-. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) ### ConjTree 41
% 0.19/0.48 43. (-. (-. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (r1 T_2 T_3) ### NotAllEx 42
% 0.19/0.48 44. (-. (-. (r1 T_2 T_3))) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (-. (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) (-. (-. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) ### NotNot 43
% 0.19/0.48 45. (-. ((-. (r1 T_2 T_3)) \/ (All Y, ((-. (r1 T_3 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) (-. (-. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) ### NotOr 44
% 0.19/0.48 46. (-. (All X, ((-. (r1 T_2 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (-. (-. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) ### NotAllEx 45
% 0.19/0.48 47. (-. ((All X, ((-. (r1 T_2 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) ### NotOr 46
% 0.19/0.48 48. (r1 T_0 T_2) (-. (r1 T_0 T_2)) ### Axiom
% 0.19/0.48 49. (-. (p2 T_2)) (p2 T_2) ### Axiom
% 0.19/0.48 50. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))) ### Axiom
% 0.19/0.48 51. ((-. (r1 T_0 T_2)) \/ ((p2 T_2) \/ (-. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) (-. (p2 T_2)) (r1 T_0 T_2) ### DisjTree 48 49 50
% 0.19/0.48 52. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) (r1 T_0 T_2) (-. (p2 T_2)) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))) ### All 51
% 0.19/0.48 53. (-. (-. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))) (-. (p2 T_2)) (r1 T_0 T_2) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) ### NotNot 52
% 0.19/0.49 54. (-. ((p2 T_2) \/ (-. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) (r1 T_0 T_2) ### NotOr 53
% 0.19/0.49 55. (-. (((All X, ((-. (r1 T_2 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 T_2) \/ (-. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) (r1 T_0 T_2) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))) ### NotAnd 47 54
% 0.19/0.49 56. (-. ((-. (r1 T_0 T_2)) \/ ((((All X, ((-. (r1 T_2 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 T_2 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 T_2) \/ (-. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) ### ConjTree 55
% 0.19/0.49 57. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) ### NotAllEx 56
% 0.19/0.49 58. ((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))) (-. (p2 T_1)) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) ### Or 16 57
% 0.19/0.49 59. (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) (r1 T_0 T_1) (-. (p2 T_1)) ((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) ### NotNot 58
% 0.19/0.49 60. (-. (-. (r1 T_0 T_1))) ((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) (-. (p2 T_1)) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) ### NotNot 59
% 0.19/0.49 61. (-. ((-. (r1 T_0 T_1)) \/ (p2 T_1))) (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) ((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) ### NotOr 60
% 0.19/0.49 62. (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) ((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) ### NotAllEx 61
% 0.19/0.49 63. (-. ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) ((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) ### NotOr 62
% 0.19/0.50 64. (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p3 X)))))))) /\ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))))) ((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y)))) ### NotAnd 5 63
% 0.19/0.50 65. (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y)))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) ((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p3 X)))))))) /\ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))))) ### NotNot 64
% 0.19/0.50 66. (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y))))) /\ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p3 X)))))))) /\ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))))) ((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))) ### NotAnd 65 63
% 0.19/0.50 67. (-. (((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (p3 Y))))) /\ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p4 Y))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ ((p4 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p4 Y))) \/ (-. (p4 X)))))))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p3 X)))))))) /\ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))))) \/ (-. (((((All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 T_0) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 T_0 Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) /\ (All Y, ((-. (r1 T_0 Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))))))) ### ConjTree 66
% 0.19/0.50 68. (Ex X, (-. (((-. (All Y, ((-. (r1 X Y)) \/ (-. (p3 Y))))) /\ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p4 Y))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ ((p4 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p4 Y))) \/ (-. (p4 X)))))))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p3 X)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (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)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))))))))))))) ### Exists 67
% 0.19/0.50 69. (-. (-. (Ex X, (-. (((-. (All Y, ((-. (r1 X Y)) \/ (-. (p3 Y))))) /\ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p4 Y))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ ((p4 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p4 Y))) \/ (-. (p4 X)))))))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p3 X)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (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)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) /\ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X)))))))))) \/ (-. (((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ (-. (p2 X))))))))))) /\ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))))))))))))))))))) ### NotNot 68
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50 (* END-PROOF *)
%------------------------------------------------------------------------------