TSTP Solution File: LCL642+1.001 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LCL642+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 : n013.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 14:52:12 EDT 2022
% Result : Theorem 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL642+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 2 16:49:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.54 % SZS status Theorem
% 0.20/0.54 (* PROOF-FOUND *)
% 0.20/0.54 (* BEGIN-PROOF *)
% 0.20/0.54 % SZS output start Proof
% 0.20/0.54 1. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 0.20/0.54 2. (-. (p2 T_1)) (p2 T_1) ### Axiom
% 0.20/0.54 3. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 0.20/0.54 4. (-. (All X, ((-. (r1 T_1 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))) (All X, ((-. (r1 T_1 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y))))))))) ### Axiom
% 0.20/0.54 5. ((-. (r1 T_0 T_1)) \/ (All X, ((-. (r1 T_1 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))) (r1 T_0 T_1) ### Or 3 4
% 0.20/0.54 6. (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 X, ((-. (r1 T_1 X)) \/ ((p2 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))))) ### All 5
% 0.20/0.54 7. ((-. (r1 T_0 T_1)) \/ ((p2 T_1) \/ (-. (All X, ((-. (r1 T_1 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))))))))))) (-. (p2 T_1)) (r1 T_0 T_1) ### DisjTree 1 2 6
% 0.20/0.54 8. (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 7
% 0.20/0.54 9. (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
% 0.20/0.54 10. ((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 8 9
% 0.20/0.54 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))))))))))) \/ (-. (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 10
% 0.20/0.54 12. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 0.20/0.54 13. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 0.20/0.54 14. (r1 T_3 T_4) (-. (r1 T_3 T_4)) ### Axiom
% 0.20/0.54 15. (-. (p2 T_4)) (p2 T_4) ### Axiom
% 0.20/0.54 16. (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
% 0.20/0.54 17. ((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 15 16
% 0.20/0.54 18. (((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 17
% 0.20/0.54 19. ((-. (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 14 18
% 0.20/0.54 20. (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 19
% 0.20/0.54 21. (-. (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
% 0.20/0.54 22. (-. (-. (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 21
% 0.20/0.54 23. (-. ((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 22
% 0.20/0.54 24. (p2 T_3) (-. (p2 T_3)) ### Axiom
% 0.20/0.54 25. (-. ((p2 T_3) \/ (-. (All Y, ((-. (r1 T_3 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ (-. (p2 Y)))))))) (p2 T_3) ### NotOr 24
% 0.20/0.54 26. ((-. (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 13 20 23 25
% 0.20/0.54 27. (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 26
% 0.20/0.54 28. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 0.20/0.54 29. (-. (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
% 0.20/0.54 30. (-. (-. (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 29
% 0.20/0.54 31. (-. ((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 30
% 0.20/0.54 32. ((-. (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 28 20 23 31
% 0.20/0.54 33. (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 32
% 0.20/0.54 34. ((-. (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 12 27 33
% 0.20/0.54 35. (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 34
% 0.20/0.54 36. (-. (-. (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 35
% 0.20/0.54 37. (-. ((-. (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 36
% 0.20/0.54 38. (-. (-. (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 37
% 0.20/0.54 39. (-. (-. (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 38
% 0.20/0.54 40. (-. ((-. (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 39
% 0.20/0.54 41. (-. (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 40
% 0.20/0.54 42. (-. ((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 41
% 0.20/0.54 43. (r1 T_0 T_2) (-. (r1 T_0 T_2)) ### Axiom
% 0.20/0.54 44. (-. (p2 T_2)) (p2 T_2) ### Axiom
% 0.20/0.54 45. (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
% 0.20/0.54 46. ((-. (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 43 44 45
% 0.20/0.54 47. (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 46
% 0.20/0.54 48. (-. (-. (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 47
% 0.20/0.54 49. (-. ((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 48
% 0.20/0.54 50. (-. (((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 42 49
% 0.20/0.55 51. (-. ((-. (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 50
% 0.20/0.55 52. (-. (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 51
% 0.20/0.55 53. ((((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 11 52
% 0.20/0.55 54. (-. (-. (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))))))))))))) (-. (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)) \/ (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 53
% 0.20/0.55 55. (-. ((-. (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)))))))))))))))))) (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))))))))))))) ### NotOr 54
% 0.20/0.55 56. (-. (All Y, ((-. (r1 T_0 Y)) \/ (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))))))))) ((((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)))))))))))))))))) ### NotAllEx 55
% 0.20/0.55 57. (-. ((All Y, ((-. (r1 T_0 Y)) \/ (p3 Y))) \/ ((-. (All Y, ((-. (r1 T_0 Y)) \/ ((p3 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p3 Y))) \/ (-. (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 56
% 0.20/0.55 58. (Ex X, (-. ((All Y, ((-. (r1 X Y)) \/ (p3 Y))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ ((p3 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p3 Y))) \/ (-. (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 57
% 0.20/0.55 59. (-. (-. (Ex X, (-. ((All Y, ((-. (r1 X Y)) \/ (p3 Y))) \/ ((-. (All Y, ((-. (r1 X Y)) \/ ((p3 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p3 Y))) \/ (-. (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 58
% 0.20/0.55 % SZS output end Proof
% 0.20/0.55 (* END-PROOF *)
%------------------------------------------------------------------------------