TSTP Solution File: LCL672+1.005 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LCL672+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n011.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 14:52:55 EDT 2022
% Result : Theorem 0.80s 1.00s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : LCL672+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 3 06:48:50 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.80/1.00 % SZS status Theorem
% 0.80/1.00 (* PROOF-FOUND *)
% 0.80/1.00 (* BEGIN-PROOF *)
% 0.80/1.00 % SZS output start Proof
% 0.80/1.00 1. (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) ### Axiom
% 0.80/1.00 2. (r1 T_1 T_2) (-. (r1 T_1 T_2)) ### Axiom
% 0.80/1.00 3. (r1 T_2 T_3) (-. (r1 T_2 T_3)) ### Axiom
% 0.80/1.00 4. (-. (r1 T_1 T_3)) (r1 T_1 T_3) ### Axiom
% 0.80/1.00 5. (((r1 T_1 T_2) /\ (r1 T_2 T_3)) => (r1 T_1 T_3)) (-. (r1 T_1 T_3)) (r1 T_2 T_3) (r1 T_1 T_2) ### DisjTree 2 3 4
% 0.80/1.00 6. (All Z, (((r1 T_1 T_2) /\ (r1 T_2 Z)) => (r1 T_1 Z))) (r1 T_1 T_2) (r1 T_2 T_3) (-. (r1 T_1 T_3)) ### All 5
% 0.80/1.00 7. (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) (-. (r1 T_1 T_3)) (r1 T_2 T_3) (r1 T_1 T_2) ### All 6
% 0.80/1.00 8. (r1 T_3 T_4) (-. (r1 T_3 T_4)) ### Axiom
% 0.80/1.00 9. (-. (r1 T_1 T_4)) (r1 T_1 T_4) ### Axiom
% 0.80/1.00 10. (((r1 T_1 T_3) /\ (r1 T_3 T_4)) => (r1 T_1 T_4)) (-. (r1 T_1 T_4)) (r1 T_3 T_4) (r1 T_1 T_2) (r1 T_2 T_3) (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) ### DisjTree 7 8 9
% 0.80/1.00 11. (All Z, (((r1 T_1 T_3) /\ (r1 T_3 Z)) => (r1 T_1 Z))) (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_3 T_4) (-. (r1 T_1 T_4)) ### All 10
% 0.80/1.00 12. (-. (r1 T_1 T_4)) (r1 T_3 T_4) (r1 T_1 T_2) (r1 T_2 T_3) (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) ### All 11
% 0.80/1.00 13. (-. (r1 T_4 T_4)) ### Extension/test/reflexivity
% 0.80/1.00 14. (r1 T_1 T_4) (-. (r1 T_1 T_4)) ### Axiom
% 0.80/1.00 15. (r1 T_4 T_5) (-. (r1 T_4 T_5)) ### Axiom
% 0.80/1.00 16. (-. (r1 T_1 T_5)) (r1 T_1 T_5) ### Axiom
% 0.80/1.00 17. (((r1 T_1 T_4) /\ (r1 T_4 T_5)) => (r1 T_1 T_5)) (-. (r1 T_1 T_5)) (r1 T_4 T_5) (r1 T_1 T_4) ### DisjTree 14 15 16
% 0.80/1.00 18. (All Z, (((r1 T_1 T_4) /\ (r1 T_4 Z)) => (r1 T_1 Z))) (r1 T_1 T_4) (r1 T_4 T_5) (-. (r1 T_1 T_5)) ### All 17
% 0.80/1.00 19. (((r1 T_1 T_4) /\ (r1 T_4 T_4)) => (r1 T_1 T_4)) (-. (r1 T_1 T_5)) (r1 T_4 T_5) (All Z, (((r1 T_1 T_4) /\ (r1 T_4 Z)) => (r1 T_1 Z))) (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_3 T_4) ### DisjTree 12 13 18
% 0.80/1.00 20. (r1 T_3 T_4) (r1 T_1 T_2) (r1 T_2 T_3) (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) (All Z, (((r1 T_1 T_4) /\ (r1 T_4 Z)) => (r1 T_1 Z))) (r1 T_4 T_5) (-. (r1 T_1 T_5)) ### All 19
% 0.80/1.00 21. (-. (r1 T_5 T_5)) ### Extension/test/reflexivity
% 0.80/1.00 22. (r1 T_0 T_1) (-. (r1 T_0 T_1)) ### Axiom
% 0.80/1.00 23. (r1 T_1 T_5) (-. (r1 T_1 T_5)) ### Axiom
% 0.80/1.00 24. (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) ### Axiom
% 0.80/1.00 25. (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) (All X, ((-. (r1 T_5 X)) \/ (p1 X))) ### Axiom
% 0.80/1.00 26. ((-. (r1 T_1 T_5)) \/ (-. ((-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X))))))) (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (r1 T_1 T_5) ### DisjTree 23 24 25
% 0.80/1.00 27. (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_5) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) ### All 26
% 0.80/1.00 28. ((-. (r1 T_0 T_1)) \/ (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_5 X)) \/ (p1 X)))) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (r1 T_1 T_5) (r1 T_0 T_1) ### Or 22 27
% 0.80/1.00 29. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) (r1 T_0 T_1) (r1 T_1 T_5) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) ### All 28
% 0.80/1.00 30. (((r1 T_1 T_5) /\ (r1 T_5 T_5)) => (r1 T_1 T_5)) (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) (r1 T_4 T_5) (All Z, (((r1 T_1 T_4) /\ (r1 T_4 Z)) => (r1 T_1 Z))) (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_3 T_4) ### DisjTree 20 21 29
% 0.80/1.00 31. (All Z, (((r1 T_1 T_5) /\ (r1 T_5 Z)) => (r1 T_1 Z))) (r1 T_3 T_4) (r1 T_1 T_2) (r1 T_2 T_3) (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) (All Z, (((r1 T_1 T_4) /\ (r1 T_4 Z)) => (r1 T_1 Z))) (r1 T_4 T_5) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) (r1 T_0 T_1) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) ### All 30
% 0.80/1.00 32. (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) (r1 T_4 T_5) (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_3 T_4) (All Z, (((r1 T_1 T_5) /\ (r1 T_5 Z)) => (r1 T_1 Z))) ### All 31
% 0.80/1.00 33. (r1 T_3 T_4) (r1 T_1 T_2) (r1 T_2 T_3) (All Y, (All Z, (((r1 T_1 Y) /\ (r1 Y Z)) => (r1 T_1 Z)))) (r1 T_4 T_5) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) (r1 T_0 T_1) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) ### All 32
% 0.80/1.00 34. (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (r1 T_0 T_1) (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) (r1 T_4 T_5) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_3 T_4) ### All 33
% 0.80/1.00 35. (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))) ### Axiom
% 0.80/1.00 36. (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (r1 T_3 T_4) (r1 T_1 T_2) (r1 T_2 T_3) (r1 T_4 T_5) (r1 T_0 T_1) (-. (All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) (-. (All X, ((-. (r1 T_5 X)) \/ (p1 X)))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) ### DisjTree 1 34 35
% 0.80/1.00 37. (-. ((-. (r1 T_4 T_5)) \/ ((All X, ((-. (r1 T_5 X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 T_5 X)) \/ (p1 X)))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (r1 T_0 T_1) (r1 T_2 T_3) (r1 T_1 T_2) (r1 T_3 T_4) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) ### ConjTree 36
% 0.80/1.00 38. (-. (All Y, ((-. (r1 T_4 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (r1 T_3 T_4) (r1 T_1 T_2) (r1 T_2 T_3) (r1 T_0 T_1) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) ### NotAllEx 37
% 0.85/1.01 39. (-. ((-. (r1 T_3 T_4)) \/ ((All Y, ((-. (r1 T_4 Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 T_4 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 T_4 Y)) \/ (p1 Y))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (r1 T_0 T_1) (r1 T_2 T_3) (r1 T_1 T_2) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) ### ConjTree 38
% 0.85/1.01 40. (-. (All X, ((-. (r1 T_3 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (r1 T_1 T_2) (r1 T_2 T_3) (r1 T_0 T_1) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) ### NotAllEx 39
% 0.85/1.01 41. (-. ((-. (r1 T_2 T_3)) \/ ((All X, ((-. (r1 T_3 X)) \/ (p2 X))) \/ ((All X, ((-. (r1 T_3 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 T_3 X)) \/ (p1 X))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (r1 T_0 T_1) (r1 T_1 T_2) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) ### ConjTree 40
% 0.85/1.01 42. (-. (All Y, ((-. (r1 T_2 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (r1 T_1 T_2) (r1 T_0 T_1) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) ### NotAllEx 41
% 0.85/1.01 43. (-. ((-. (r1 T_1 T_2)) \/ ((All Y, ((-. (r1 T_2 Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 T_2 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 T_2 Y)) \/ (p1 Y))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (r1 T_0 T_1) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) ### ConjTree 42
% 0.85/1.01 44. (-. (All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (r1 T_0 T_1) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) ### NotAllEx 43
% 0.85/1.01 45. (-. ((-. (r1 T_0 T_1)) \/ ((All X, ((-. (r1 T_1 X)) \/ (p2 X))) \/ ((All X, ((-. (r1 T_1 X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 T_1 X)) \/ (p1 X))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) ### ConjTree 44
% 0.85/1.01 46. (-. (All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))))) (-. ((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) (-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) ### NotAllEx 45
% 0.85/1.01 47. (-. (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (p1 Y)))))))) /\ (p1 Y)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ False)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p1 X)))))))) /\ (p1 X)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ False)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (p1 Y)))))))) /\ (p1 Y)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ False)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p1 X)))))))) /\ (p1 X)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ False)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (p1 Y)))))))) /\ (p1 Y)))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 T_0 Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 T_0 Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ False)))))) /\ (-. (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 T_0 Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 T_0 Y)) \/ (p1 Y)))))))))))))))))))))))))))))))))))))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) ### ConjTree 46
% 0.85/1.01 48. (Ex X, (-. (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (p1 Y)))))))) /\ (p1 Y)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ False)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p1 X)))))))) /\ (p1 X)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ False)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (p1 Y)))))))) /\ (p1 Y)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ False)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p1 X)))))))) /\ (p1 X)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ False)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (p1 Y)))))))) /\ (p1 Y)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ False)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))))))))))))))))))))))))))))))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) ### Exists 47
% 0.85/1.01 49. (-. (-. (Ex X, (-. (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (p1 Y)))))))) /\ (p1 Y)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ False)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p1 X)))))))) /\ (p1 X)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ False)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (p1 Y)))))))) /\ (p1 Y)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ False)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (p1 X)))))))) /\ (p1 X)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (p2 X)))) /\ ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ False)))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (p1 Y)))))))) /\ (p1 Y)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (All X, ((-. (r1 Y X)) \/ (-. ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. ((-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ (p1 X)))))))))) /\ (-. (All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))))))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (((-. (All Y, ((-. (r1 X Y)) \/ (p2 Y)))) /\ ((-. (All Y, ((-. (r1 X Y)) \/ (-. (All X, ((-. (r1 Y X)) \/ False)))))) /\ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (p2 X))) \/ ((All X, ((-. (r1 Y X)) \/ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) \/ ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ (-. (All Y, ((-. (r1 X Y)) \/ (p1 Y)))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X)))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))) \/ (All X, ((-. (r1 Y X)) \/ (p1 X))))))) \/ (All Y, ((-. (r1 X Y)) \/ (p1 Y))))))))))))))))))))))))))))))))))))))))) (All X, (All Y, (All Z, (((r1 X Y) /\ (r1 Y Z)) => (r1 X Z))))) ### NotNot 48
% 0.85/1.01 % SZS output end Proof
% 0.85/1.01 (* END-PROOF *)
%------------------------------------------------------------------------------