TSTP Solution File: MGT060+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT060+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n023.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 22:31:14 EDT 2022
% Result : Theorem 0.52s 0.73s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT060+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n023.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 08:21:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.52/0.73 (* PROOF-FOUND *)
% 0.52/0.73 % SZS status Theorem
% 0.52/0.73 (* BEGIN-PROOF *)
% 0.52/0.73 % SZS output start Proof
% 0.52/0.73 Theorem assumption_3 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((has_immunity X T0)/\(~(has_immunity X T))))->(greater (hazard_of_mortality X T) (hazard_of_mortality X T0)))))).
% 0.52/0.73 Proof.
% 0.52/0.73 assert (zenon_L1_ : forall (zenon_TT_r : zenon_U) (zenon_TX_s : zenon_U), (((~(is_aligned zenon_TX_s zenon_TT_r))/\(~(positional_advantage zenon_TX_s zenon_TT_r)))->((hazard_of_mortality zenon_TX_s zenon_TT_r) = (high))) -> (~(positional_advantage zenon_TX_s zenon_TT_r)) -> (~(is_aligned zenon_TX_s zenon_TT_r)) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (high))) -> False).
% 0.52/0.73 do 2 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_Hd); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ].
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ].
% 0.52/0.73 exact (zenon_H16 zenon_Hf).
% 0.52/0.73 exact (zenon_H15 zenon_He).
% 0.52/0.73 exact (zenon_H10 zenon_H13).
% 0.52/0.73 (* end of lemma zenon_L1_ *)
% 0.52/0.73 assert (zenon_L2_ : forall (zenon_TT_r : zenon_U) (zenon_TX_s : zenon_U), (forall T : zenon_U, ((organization zenon_TX_s)->(((has_immunity zenon_TX_s T)->((hazard_of_mortality zenon_TX_s T) = (very_low)))/\((~(has_immunity zenon_TX_s T))->((((is_aligned zenon_TX_s T)/\(positional_advantage zenon_TX_s T))->((hazard_of_mortality zenon_TX_s T) = (low)))/\((((~(is_aligned zenon_TX_s T))/\(positional_advantage zenon_TX_s T))->((hazard_of_mortality zenon_TX_s T) = (mod1)))/\((((is_aligned zenon_TX_s T)/\(~(positional_advantage zenon_TX_s T)))->((hazard_of_mortality zenon_TX_s T) = (mod2)))/\(((~(is_aligned zenon_TX_s T))/\(~(positional_advantage zenon_TX_s T)))->((hazard_of_mortality zenon_TX_s T) = (high)))))))))) -> (organization zenon_TX_s) -> (~(has_immunity zenon_TX_s zenon_TT_r)) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod1))) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (high))) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod2))) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (low))) -> False).
% 0.52/0.73 do 2 intro. intros zenon_H17 zenon_H18 zenon_H19 zenon_H1a zenon_H10 zenon_H1b zenon_H1c.
% 0.52/0.73 generalize (zenon_H17 zenon_TT_r). zenon_intro zenon_H1d.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.52/0.73 exact (zenon_H1f zenon_H18).
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ].
% 0.52/0.73 exact (zenon_H23 zenon_H19).
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H28. zenon_intro zenon_Hd.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_Hf | zenon_intro zenon_He ].
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ].
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H2c); [ zenon_intro zenon_H16 | zenon_intro zenon_He ].
% 0.52/0.73 exact (zenon_H16 zenon_Hf).
% 0.52/0.73 apply (zenon_L1_ zenon_TT_r zenon_TX_s); trivial.
% 0.52/0.73 exact (zenon_H1a zenon_H2b).
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_Hf | zenon_intro zenon_H15 ].
% 0.52/0.73 apply (zenon_L1_ zenon_TT_r zenon_TX_s); trivial.
% 0.52/0.73 exact (zenon_H15 zenon_He).
% 0.52/0.73 exact (zenon_H1b zenon_H2d).
% 0.52/0.73 exact (zenon_H1c zenon_H29).
% 0.52/0.73 (* end of lemma zenon_L2_ *)
% 0.52/0.73 assert (zenon_L3_ : forall (zenon_TT_r : zenon_U) (zenon_TX_s : zenon_U), (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (low))) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod2))) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (high))) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod1))) -> (~(has_immunity zenon_TX_s zenon_TT_r)) -> (organization zenon_TX_s) -> False).
% 0.52/0.73 do 2 intro. intros zenon_H1c zenon_H1b zenon_H10 zenon_H1a zenon_H19 zenon_H18.
% 0.52/0.73 generalize (assumption_17 zenon_TX_s). zenon_intro zenon_H17.
% 0.52/0.73 apply (zenon_L2_ zenon_TT_r zenon_TX_s); trivial.
% 0.52/0.73 (* end of lemma zenon_L3_ *)
% 0.52/0.73 assert (zenon_L4_ : (~((low) = (low))) -> False).
% 0.52/0.73 do 0 intro. intros zenon_H2f.
% 0.52/0.73 apply zenon_H2f. apply refl_equal.
% 0.52/0.73 (* end of lemma zenon_L4_ *)
% 0.52/0.73 assert (zenon_L5_ : forall (zenon_TT_r : zenon_U) (zenon_TX_s : zenon_U), (organization zenon_TX_s) -> (~(has_immunity zenon_TX_s zenon_TT_r)) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (high))) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod2))) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (low))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (low))) -> False).
% 0.52/0.73 do 2 intro. intros zenon_H18 zenon_H19 zenon_H10 zenon_H1b zenon_H1c zenon_H30 zenon_H31.
% 0.52/0.73 elim (classic ((~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod1)))/\(~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (mod1))))); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ].
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H1a. zenon_intro zenon_H34.
% 0.52/0.73 apply (zenon_L3_ zenon_TT_r zenon_TX_s); trivial.
% 0.52/0.73 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (low))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H31.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact assumption_18b.
% 0.52/0.73 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H2f].
% 0.52/0.73 cut (((mod1) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H35].
% 0.52/0.73 congruence.
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.52/0.73 apply zenon_H37. zenon_intro zenon_H2b.
% 0.52/0.73 elim (classic ((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [ zenon_intro zenon_H38 | zenon_intro zenon_H39 ].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r)) = ((mod1) = (hazard_of_mortality zenon_TX_s zenon_TT_r))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H35.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact zenon_H38.
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 0.52/0.73 congruence.
% 0.52/0.73 exact (zenon_H1a zenon_H2b).
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H36. zenon_intro zenon_H3a.
% 0.52/0.73 generalize (zenon_H30 (hazard_of_mortality zenon_TX_s zenon_TT_r)). zenon_intro zenon_H3b.
% 0.52/0.73 generalize (zenon_H3b (mod1)). zenon_intro zenon_H3c.
% 0.52/0.73 generalize (zenon_H3c (low)). zenon_intro zenon_H3d.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H34 | zenon_intro zenon_H3e ].
% 0.52/0.73 exact (zenon_H34 zenon_H3a).
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ].
% 0.52/0.73 exact (zenon_H40 assumption_18b).
% 0.52/0.73 exact (zenon_H31 zenon_H3f).
% 0.52/0.73 apply zenon_H2f. apply refl_equal.
% 0.52/0.73 (* end of lemma zenon_L5_ *)
% 0.52/0.73 assert (zenon_L6_ : forall (zenon_TT_r : zenon_U) (zenon_TX_s : zenon_U), (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (low))) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (high))) -> (~(has_immunity zenon_TX_s zenon_TT_r)) -> (organization zenon_TX_s) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (low))) -> False).
% 0.52/0.73 do 2 intro. intros zenon_H1c zenon_H10 zenon_H19 zenon_H18 zenon_H30 zenon_H31.
% 0.52/0.73 elim (classic ((~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (mod2))))); [ zenon_intro zenon_H41 | zenon_intro zenon_H42 ].
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H1b. zenon_intro zenon_H43.
% 0.52/0.73 apply (zenon_L5_ zenon_TT_r zenon_TX_s); trivial.
% 0.52/0.73 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (low))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H31.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact assumption_18e.
% 0.52/0.73 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H2f].
% 0.52/0.73 cut (((mod2) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H44].
% 0.52/0.73 congruence.
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H42); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 0.52/0.73 apply zenon_H46. zenon_intro zenon_H2d.
% 0.52/0.73 elim (classic ((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [ zenon_intro zenon_H38 | zenon_intro zenon_H39 ].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r)) = ((mod2) = (hazard_of_mortality zenon_TX_s zenon_TT_r))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H44.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact zenon_H38.
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1b].
% 0.52/0.73 congruence.
% 0.52/0.73 exact (zenon_H1b zenon_H2d).
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H45. zenon_intro zenon_H47.
% 0.52/0.73 generalize (zenon_H30 (hazard_of_mortality zenon_TX_s zenon_TT_r)). zenon_intro zenon_H3b.
% 0.52/0.73 generalize (zenon_H3b (mod2)). zenon_intro zenon_H48.
% 0.52/0.73 generalize (zenon_H48 (low)). zenon_intro zenon_H49.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H43 | zenon_intro zenon_H4a ].
% 0.52/0.73 exact (zenon_H43 zenon_H47).
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H4b | zenon_intro zenon_H3f ].
% 0.52/0.73 exact (zenon_H4b assumption_18e).
% 0.52/0.73 exact (zenon_H31 zenon_H3f).
% 0.52/0.73 apply zenon_H2f. apply refl_equal.
% 0.52/0.73 (* end of lemma zenon_L6_ *)
% 0.52/0.73 assert (zenon_L7_ : (~((mod2) = (mod2))) -> False).
% 0.52/0.73 do 0 intro. intros zenon_H4c.
% 0.52/0.73 apply zenon_H4c. apply refl_equal.
% 0.52/0.73 (* end of lemma zenon_L7_ *)
% 0.52/0.73 assert (zenon_L8_ : forall (zenon_TT_r : zenon_U) (zenon_TX_s : zenon_U), (~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (low))) -> (organization zenon_TX_s) -> (~(has_immunity zenon_TX_s zenon_TT_r)) -> (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (low))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (mod2))) -> False).
% 0.52/0.73 do 2 intro. intros zenon_H31 zenon_H18 zenon_H19 zenon_H1c zenon_H30 zenon_H43.
% 0.52/0.73 elim (classic ((~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (high))))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ].
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H10. zenon_intro zenon_H4f.
% 0.52/0.73 apply (zenon_L6_ zenon_TT_r zenon_TX_s); trivial.
% 0.52/0.73 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (mod2))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H43.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact assumption_18d.
% 0.52/0.73 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 0.52/0.73 cut (((high) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 0.52/0.73 congruence.
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ].
% 0.52/0.73 apply zenon_H52. zenon_intro zenon_H13.
% 0.52/0.73 elim (classic ((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [ zenon_intro zenon_H38 | zenon_intro zenon_H39 ].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r)) = ((high) = (hazard_of_mortality zenon_TX_s zenon_TT_r))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H50.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact zenon_H38.
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (high))); [idtac | apply NNPP; zenon_intro zenon_H10].
% 0.52/0.73 congruence.
% 0.52/0.73 exact (zenon_H10 zenon_H13).
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H51. zenon_intro zenon_H53.
% 0.52/0.73 generalize (zenon_H30 (hazard_of_mortality zenon_TX_s zenon_TT_r)). zenon_intro zenon_H3b.
% 0.52/0.73 generalize (zenon_H3b (high)). zenon_intro zenon_H54.
% 0.52/0.73 generalize (zenon_H54 (mod2)). zenon_intro zenon_H55.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H4f | zenon_intro zenon_H56 ].
% 0.52/0.73 exact (zenon_H4f zenon_H53).
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H57 | zenon_intro zenon_H47 ].
% 0.52/0.73 exact (zenon_H57 assumption_18d).
% 0.52/0.73 exact (zenon_H43 zenon_H47).
% 0.52/0.73 apply zenon_H4c. apply refl_equal.
% 0.52/0.73 (* end of lemma zenon_L8_ *)
% 0.52/0.73 assert (zenon_L9_ : forall (zenon_TT_r : zenon_U) (zenon_TX_s : zenon_U), (~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (low))) -> (~(has_immunity zenon_TX_s zenon_TT_r)) -> (organization zenon_TX_s) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (low))) -> False).
% 0.52/0.73 do 2 intro. intros zenon_H1c zenon_H19 zenon_H18 zenon_H30 zenon_H31.
% 0.52/0.73 elim (classic ((~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (mod2))))); [ zenon_intro zenon_H41 | zenon_intro zenon_H42 ].
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H1b. zenon_intro zenon_H43.
% 0.52/0.73 apply (zenon_L8_ zenon_TT_r zenon_TX_s); trivial.
% 0.52/0.73 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (low))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H31.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact assumption_18e.
% 0.52/0.73 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H2f].
% 0.52/0.73 cut (((mod2) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H44].
% 0.52/0.73 congruence.
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H42); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 0.52/0.73 apply zenon_H46. zenon_intro zenon_H2d.
% 0.52/0.73 elim (classic ((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [ zenon_intro zenon_H38 | zenon_intro zenon_H39 ].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r)) = ((mod2) = (hazard_of_mortality zenon_TX_s zenon_TT_r))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H44.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact zenon_H38.
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1b].
% 0.52/0.73 congruence.
% 0.52/0.73 exact (zenon_H1b zenon_H2d).
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H45. zenon_intro zenon_H47.
% 0.52/0.73 generalize (zenon_H30 (hazard_of_mortality zenon_TX_s zenon_TT_r)). zenon_intro zenon_H3b.
% 0.52/0.73 generalize (zenon_H3b (mod2)). zenon_intro zenon_H48.
% 0.52/0.73 generalize (zenon_H48 (low)). zenon_intro zenon_H49.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H43 | zenon_intro zenon_H4a ].
% 0.52/0.73 exact (zenon_H43 zenon_H47).
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H4b | zenon_intro zenon_H3f ].
% 0.52/0.73 exact (zenon_H4b assumption_18e).
% 0.52/0.73 exact (zenon_H31 zenon_H3f).
% 0.52/0.73 apply zenon_H2f. apply refl_equal.
% 0.52/0.73 (* end of lemma zenon_L9_ *)
% 0.52/0.73 assert (zenon_L10_ : (~((very_low) = (very_low))) -> False).
% 0.52/0.73 do 0 intro. intros zenon_H58.
% 0.52/0.73 apply zenon_H58. apply refl_equal.
% 0.52/0.73 (* end of lemma zenon_L10_ *)
% 0.52/0.73 assert (zenon_L11_ : forall (zenon_TT_r : zenon_U) (zenon_TX_s : zenon_U), (organization zenon_TX_s) -> (~(has_immunity zenon_TX_s zenon_TT_r)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (very_low))) -> False).
% 0.52/0.73 do 2 intro. intros zenon_H18 zenon_H19 zenon_H30 zenon_H59.
% 0.52/0.73 elim (classic ((~((hazard_of_mortality zenon_TX_s zenon_TT_r) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (low))))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ].
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H1c. zenon_intro zenon_H31.
% 0.52/0.73 apply (zenon_L9_ zenon_TT_r zenon_TX_s); trivial.
% 0.52/0.73 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (very_low))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H59.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact assumption_18c.
% 0.52/0.73 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 0.52/0.73 cut (((low) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 0.52/0.73 congruence.
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H5b); [ zenon_intro zenon_H5e | zenon_intro zenon_H5d ].
% 0.52/0.73 apply zenon_H5e. zenon_intro zenon_H29.
% 0.52/0.73 elim (classic ((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [ zenon_intro zenon_H38 | zenon_intro zenon_H39 ].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r)) = ((low) = (hazard_of_mortality zenon_TX_s zenon_TT_r))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H5c.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact zenon_H38.
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 0.52/0.73 congruence.
% 0.52/0.73 exact (zenon_H1c zenon_H29).
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 apply zenon_H5d. zenon_intro zenon_H3f.
% 0.52/0.73 generalize (zenon_H30 (hazard_of_mortality zenon_TX_s zenon_TT_r)). zenon_intro zenon_H3b.
% 0.52/0.73 generalize (zenon_H3b (low)). zenon_intro zenon_H5f.
% 0.52/0.73 generalize (zenon_H5f (very_low)). zenon_intro zenon_H60.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H31 | zenon_intro zenon_H61 ].
% 0.52/0.73 exact (zenon_H31 zenon_H3f).
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ].
% 0.52/0.73 exact (zenon_H63 assumption_18c).
% 0.52/0.73 exact (zenon_H59 zenon_H62).
% 0.52/0.73 apply zenon_H58. apply refl_equal.
% 0.52/0.73 (* end of lemma zenon_L11_ *)
% 0.52/0.73 apply NNPP. intro zenon_G.
% 0.52/0.73 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z))))))); [ zenon_intro zenon_H30 | zenon_intro zenon_H64 ].
% 0.52/0.73 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((has_immunity X T0)/\(~(has_immunity X T))))->(greater (hazard_of_mortality X T) (hazard_of_mortality X T0)))))) zenon_G); [ zenon_intro zenon_H65; idtac ].
% 0.52/0.73 elim zenon_H65. zenon_intro zenon_TX_s. zenon_intro zenon_H66.
% 0.52/0.73 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T : zenon_U, (((organization zenon_TX_s)/\((has_immunity zenon_TX_s T0)/\(~(has_immunity zenon_TX_s T))))->(greater (hazard_of_mortality zenon_TX_s T) (hazard_of_mortality zenon_TX_s T0))))) zenon_H66); [ zenon_intro zenon_H67; idtac ].
% 0.52/0.73 elim zenon_H67. zenon_intro zenon_TT0_ea. zenon_intro zenon_H69.
% 0.52/0.73 apply (zenon_notallex_s (fun T : zenon_U => (((organization zenon_TX_s)/\((has_immunity zenon_TX_s zenon_TT0_ea)/\(~(has_immunity zenon_TX_s T))))->(greater (hazard_of_mortality zenon_TX_s T) (hazard_of_mortality zenon_TX_s zenon_TT0_ea)))) zenon_H69); [ zenon_intro zenon_H6a; idtac ].
% 0.52/0.73 elim zenon_H6a. zenon_intro zenon_TT_r. zenon_intro zenon_H6b.
% 0.52/0.73 apply (zenon_notimply_s _ _ zenon_H6b). zenon_intro zenon_H6d. zenon_intro zenon_H6c.
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H18. zenon_intro zenon_H6e.
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H6f. zenon_intro zenon_H19.
% 0.52/0.73 generalize (assumption_17 zenon_TX_s). zenon_intro zenon_H17.
% 0.52/0.73 generalize (zenon_H17 zenon_TT0_ea). zenon_intro zenon_H70.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H1f | zenon_intro zenon_H71 ].
% 0.52/0.73 exact (zenon_H1f zenon_H18).
% 0.52/0.73 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H73. zenon_intro zenon_H72.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ].
% 0.52/0.73 exact (zenon_H75 zenon_H6f).
% 0.52/0.73 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_s zenon_TT0_ea))); [ zenon_intro zenon_H76 | zenon_intro zenon_H77 ].
% 0.52/0.73 elim (classic (greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (very_low))); [ zenon_intro zenon_H62 | zenon_intro zenon_H59 ].
% 0.52/0.73 cut ((greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (very_low)) = (greater (hazard_of_mortality zenon_TX_s zenon_TT_r) (hazard_of_mortality zenon_TX_s zenon_TT0_ea))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H6c.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact zenon_H62.
% 0.52/0.73 cut (((very_low) = (hazard_of_mortality zenon_TX_s zenon_TT0_ea))); [idtac | apply NNPP; zenon_intro zenon_H77].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT_r) = (hazard_of_mortality zenon_TX_s zenon_TT_r))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 0.52/0.73 congruence.
% 0.52/0.73 apply zenon_H39. apply refl_equal.
% 0.52/0.73 exact (zenon_H77 zenon_H76).
% 0.52/0.73 apply (zenon_L11_ zenon_TT_r zenon_TX_s); trivial.
% 0.52/0.73 elim (classic ((hazard_of_mortality zenon_TX_s zenon_TT0_ea) = (hazard_of_mortality zenon_TX_s zenon_TT0_ea))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT0_ea) = (hazard_of_mortality zenon_TX_s zenon_TT0_ea)) = ((very_low) = (hazard_of_mortality zenon_TX_s zenon_TT0_ea))).
% 0.52/0.73 intro zenon_D_pnotp.
% 0.52/0.73 apply zenon_H77.
% 0.52/0.73 rewrite <- zenon_D_pnotp.
% 0.52/0.73 exact zenon_H78.
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT0_ea) = (hazard_of_mortality zenon_TX_s zenon_TT0_ea))); [idtac | apply NNPP; zenon_intro zenon_H79].
% 0.52/0.73 cut (((hazard_of_mortality zenon_TX_s zenon_TT0_ea) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H7a].
% 0.52/0.73 congruence.
% 0.52/0.73 exact (zenon_H7a zenon_H74).
% 0.52/0.73 apply zenon_H79. apply refl_equal.
% 0.52/0.73 apply zenon_H79. apply refl_equal.
% 0.52/0.73 apply zenon_H64. zenon_intro zenon_Tx_et. apply NNPP. zenon_intro zenon_H7c.
% 0.52/0.73 apply zenon_H7c. zenon_intro zenon_Ty_ev. apply NNPP. zenon_intro zenon_H7e.
% 0.52/0.73 apply zenon_H7e. zenon_intro zenon_Tz_ex. apply NNPP. zenon_intro zenon_H80.
% 0.52/0.73 apply (zenon_notimply_s _ _ zenon_H80). zenon_intro zenon_H82. zenon_intro zenon_H81.
% 0.52/0.73 apply (zenon_notimply_s _ _ zenon_H81). zenon_intro zenon_H84. zenon_intro zenon_H83.
% 0.52/0.73 generalize (meaning_postulate_greater_transitive zenon_Tx_et). zenon_intro zenon_H85.
% 0.52/0.73 generalize (zenon_H85 zenon_Ty_ev). zenon_intro zenon_H86.
% 0.52/0.73 generalize (zenon_H86 zenon_Tz_ex). zenon_intro zenon_H87.
% 0.52/0.73 apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H89 | zenon_intro zenon_H88 ].
% 0.52/0.73 apply (zenon_notand_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ].
% 0.52/0.73 exact (zenon_H8b zenon_H82).
% 0.52/0.73 exact (zenon_H8a zenon_H84).
% 0.52/0.73 exact (zenon_H83 zenon_H88).
% 0.52/0.73 Qed.
% 0.52/0.73 % SZS output end Proof
% 0.52/0.73 (* END-PROOF *)
% 0.52/0.73 nodes searched: 6304
% 0.52/0.73 max branch formulas: 213
% 0.52/0.73 proof nodes created: 609
% 0.52/0.73 formulas created: 4412
% 0.52/0.73
%------------------------------------------------------------------------------