TSTP Solution File: LCL658+1.001 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LCL658+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 : n004.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 14:52:34 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL658+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n004.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 : Sat Jul 2 15:56:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 (* PROOF-FOUND *)
% 0.20/0.55 (* BEGIN-PROOF *)
% 0.20/0.55 % SZS output start Proof
% 0.20/0.55 1. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 0.20/0.55 2. (-. (All X, ((-. (r1 T_1 X)) \/ (p1 X)))) (All X, ((-. (r1 T_1 X)) \/ (p1 X))) ### Axiom
% 0.20/0.55 3. (-. (p1 T_1)) (p1 T_1) ### Axiom
% 0.20/0.55 4. (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) ### Axiom
% 0.20/0.55 5. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))) ### Axiom
% 0.20/0.55 6. ((p1 T_1) \/ ((All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (-. (p1 T_1)) ### DisjTree 3 4 5
% 0.20/0.55 7. (r1 T_1 T_2) (-. (r1 T_1 T_2)) ### Axiom
% 0.20/0.55 8. (r1 T_1 T_2) (-. (r1 T_1 T_2)) ### Axiom
% 0.20/0.55 9. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 0.20/0.55 10. (-. (All Y, ((-. (r1 T_3 Y)) \/ (p1 Y)))) (All Y, ((-. (r1 T_3 Y)) \/ (p1 Y))) ### Axiom
% 0.20/0.55 11. ((-. (r1 T_2 T_3)) \/ (All Y, ((-. (r1 T_3 Y)) \/ (p1 Y)))) (-. (All Y, ((-. (r1 T_3 Y)) \/ (p1 Y)))) (r1 T_2 T_3) ### Or 9 10
% 0.20/0.55 12. (All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) (r1 T_2 T_3) (-. (All Y, ((-. (r1 T_3 Y)) \/ (p1 Y)))) ### All 11
% 0.20/0.55 13. (-. ((-. (r1 T_2 T_3)) \/ ((All Y, ((-. (r1 T_3 Y)) \/ (p1 Y))) \/ (-. (p1 T_3))))) (All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) ### ConjTree 12
% 0.20/0.55 14. (-. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))) (All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) ### NotAllEx 13
% 0.20/0.55 15. ((-. (r1 T_1 T_2)) \/ (-. (All X, ((-. (r1 T_2 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))) (All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) (r1 T_1 T_2) ### Or 8 14
% 0.20/0.55 16. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) (r1 T_1 T_2) (All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) ### All 15
% 0.20/0.55 17. (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))) (-. (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y)))) ### Axiom
% 0.20/0.55 18. ((-. (r1 T_1 T_2)) \/ ((All Y, ((-. (r1 T_2 Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y)))))) (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))) (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) (r1 T_1 T_2) ### DisjTree 7 16 17
% 0.20/0.55 19. (All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (r1 T_1 T_2) (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))) ### All 18
% 0.20/0.55 20. (r1 T_4 T_5) (-. (r1 T_4 T_5)) ### Axiom
% 0.20/0.55 21. (r1 T_1 T_4) (-. (r1 T_1 T_4)) ### Axiom
% 0.20/0.55 22. (r1 T_4 T_5) (-. (r1 T_4 T_5)) ### Axiom
% 0.20/0.55 23. (-. (p1 T_5)) (p1 T_5) ### Axiom
% 0.20/0.55 24. (All X, ((-. (r1 T_5 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) (-. (All X, ((-. (r1 T_5 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))) ### Axiom
% 0.20/0.55 25. ((-. (r1 T_4 T_5)) \/ ((p1 T_5) \/ (-. (All X, ((-. (r1 T_5 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))) (All X, ((-. (r1 T_5 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) (-. (p1 T_5)) (r1 T_4 T_5) ### DisjTree 22 23 24
% 0.20/0.55 26. (All Y, ((-. (r1 T_4 Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))) (r1 T_4 T_5) (-. (p1 T_5)) (All X, ((-. (r1 T_5 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) ### All 25
% 0.20/0.55 27. ((-. (r1 T_1 T_4)) \/ (All Y, ((-. (r1 T_4 Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X)))))))))) (All X, ((-. (r1 T_5 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) (-. (p1 T_5)) (r1 T_4 T_5) (r1 T_1 T_4) ### Or 21 26
% 0.20/0.55 28. (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) (r1 T_1 T_4) (r1 T_4 T_5) (-. (p1 T_5)) (All X, ((-. (r1 T_5 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) ### All 27
% 0.20/0.55 29. (-. (p1 T_5)) (p1 T_5) ### Axiom
% 0.20/0.55 30. (-. (-. (p1 T_5))) (-. (p1 T_5)) ### NotNot 29
% 0.20/0.55 31. (-. ((All X, ((-. (r1 T_5 X)) \/ (p1 X))) \/ (-. (p1 T_5)))) (-. (p1 T_5)) ### NotOr 30
% 0.20/0.55 32. ((-. (r1 T_4 T_5)) \/ ((All X, ((-. (r1 T_5 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 T_5 X)) \/ (p1 X))) \/ (-. (p1 T_5)))))) (-. (p1 T_5)) (r1 T_1 T_4) (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) (r1 T_4 T_5) ### DisjTree 20 28 31
% 0.20/0.55 33. (All Y, ((-. (r1 T_4 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) (r1 T_4 T_5) (All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) (r1 T_1 T_4) (-. (p1 T_5)) ### All 32
% 0.20/0.55 34. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))) ### Axiom
% 0.20/0.55 35. ((All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (p1 T_5)) (r1 T_1 T_4) (r1 T_4 T_5) (All Y, ((-. (r1 T_4 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) ### Or 33 34
% 0.20/0.55 36. (-. (-. (r1 T_4 T_5))) (All Y, ((-. (r1 T_4 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) (r1 T_1 T_4) (-. (p1 T_5)) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ((All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) ### NotNot 35
% 0.20/0.55 37. (-. ((-. (r1 T_4 T_5)) \/ (p1 T_5))) ((All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (r1 T_1 T_4) (All Y, ((-. (r1 T_4 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) ### NotOr 36
% 0.20/0.55 38. (-. (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y)))) (All Y, ((-. (r1 T_4 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))) (r1 T_1 T_4) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ((All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) ### NotAllEx 37
% 0.20/0.56 39. (-. ((-. (r1 T_1 T_4)) \/ ((All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))) \/ ((-. (p1 T_4)) \/ (-. (All Y, ((-. (r1 T_4 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) ((All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ### ConjTree 38
% 0.20/0.56 40. (-. (All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ((All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) ### NotAllEx 39
% 0.20/0.56 41. ((All X, ((-. (r1 T_1 X)) \/ (p1 X))) \/ ((-. (p1 T_1)) \/ ((All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) ((All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))) (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))) (r1 T_1 T_2) (All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) ((p1 T_1) \/ ((All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (p1 X)))) ### DisjTree 2 6 19 40
% 0.20/0.56 42. (((All X, ((-. (r1 T_1 X)) \/ (p1 X))) \/ ((-. (p1 T_1)) \/ ((All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 T_1) \/ ((All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (p1 X)))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (r1 T_1 T_2) (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))) ### ConjTree 41
% 0.20/0.56 43. ((-. (r1 T_0 T_1)) \/ (((All X, ((-. (r1 T_1 X)) \/ (p1 X))) \/ ((-. (p1 T_1)) \/ ((All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 T_1) \/ ((All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 T_1 X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))) (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))) (r1 T_1 T_2) (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (p1 X)))) (r1 T_0 T_1) ### Or 1 42
% 0.20/0.56 44. (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) (r1 T_0 T_1) (-. (All X, ((-. (r1 T_1 X)) \/ (p1 X)))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (r1 T_1 T_2) (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))) ### All 43
% 0.20/0.56 45. (-. (-. (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))))) (r1 T_1 T_2) (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (p1 X)))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) ### NotNot 44
% 0.20/0.56 46. (-. (-. (r1 T_1 T_2))) (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) (r1 T_0 T_1) (-. (All X, ((-. (r1 T_1 X)) \/ (p1 X)))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (-. (-. (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))))) ### NotNot 45
% 0.20/0.56 47. (-. ((-. (r1 T_1 T_2)) \/ (-. (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y)))))) (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (p1 X)))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) ### NotOr 46
% 0.20/0.56 48. (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) (r1 T_0 T_1) (-. (All X, ((-. (r1 T_1 X)) \/ (p1 X)))) (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))) (-. (All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) ### NotAllEx 47
% 0.20/0.56 49. (-. ((-. (r1 T_0 T_1)) \/ ((All X, ((-. (r1 T_1 X)) \/ (p1 X))) \/ ((All X, ((-. (r1 T_1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 T_1 X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) ### ConjTree 48
% 0.20/0.56 50. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) ### NotAllEx 49
% 0.20/0.56 51. (-. (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))) (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) ### NotNot 50
% 0.20/0.56 52. (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))) (-. (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))) ### NotNot 51
% 0.20/0.56 53. (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))) \/ (-. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))))) ### NotOr 52
% 0.20/0.56 54. (Ex X, (-. ((-. (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))) \/ (-. (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))) ### Exists 53
% 0.20/0.56 55. (-. (-. (Ex X, (-. ((-. (All Y, ((-. (r1 X Y)) \/ (((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((-. (p1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ ((-. (p1 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))))))) /\ (((p1 Y) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y)))))))))))) /\ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ ((All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ ((p1 Y) \/ (-. (All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (-. (p1 X))))))))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))) \/ (-. (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (-. (All X, ((-. (r1 Y X)) \/ ((p1 X) \/ (-. (All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p1 X))) \/ (-. (p1 Y))))))))))))))))))))) ### NotNot 54
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56 (* END-PROOF *)
%------------------------------------------------------------------------------