TSTP Solution File: SWV094+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV094+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n016.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 : Wed Jul 20 23:02:56 EDT 2022
% Result : Theorem 0.18s 0.52s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV094+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 15 16:46:17 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.52 (* PROOF-FOUND *)
% 0.18/0.52 % SZS status Theorem
% 0.18/0.52 (* BEGIN-PROOF *)
% 0.18/0.52 % SZS output start Proof
% 0.18/0.52 Theorem quaternion_ds1_inuse_0006 : ((((a_select2 (rho_defuse) (n0)) = (use))/\(((a_select2 (rho_defuse) (n1)) = (use))/\(((a_select2 (rho_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n0)) = (use))/\(((a_select2 (sigma_defuse) (n1)) = (use))/\(((a_select2 (sigma_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n3)) = (use))/\(((a_select2 (sigma_defuse) (n4)) = (use))/\(((a_select2 (sigma_defuse) (n5)) = (use))/\(((a_select3 (u_defuse) (n0) (n0)) = (use))/\(((a_select3 (u_defuse) (n1) (n0)) = (use))/\(((a_select3 (u_defuse) (n2) (n0)) = (use))/\(((a_select2 (xinit_defuse) (n3)) = (use))/\(((a_select2 (xinit_defuse) (n4)) = (use))/\(((a_select2 (xinit_defuse) (n5)) = (use))/\(((a_select2 (xinit_mean_defuse) (n0)) = (use))/\(((a_select2 (xinit_mean_defuse) (n1)) = (use))/\(((a_select2 (xinit_mean_defuse) (n2)) = (use))/\(((a_select2 (xinit_mean_defuse) (n3)) = (use))/\(((a_select2 (xinit_mean_defuse) (n4)) = (use))/\(((a_select2 (xinit_mean_defuse) (n5)) = (use))/\(((a_select2 (xinit_noise_defuse) (n0)) = (use))/\(((a_select2 (xinit_noise_defuse) (n1)) = (use))/\(((a_select2 (xinit_noise_defuse) (n2)) = (use))/\(((a_select2 (xinit_noise_defuse) (n3)) = (use))/\(((a_select2 (xinit_noise_defuse) (n4)) = (use))/\(((a_select2 (xinit_noise_defuse) (n5)) = (use))/\((leq (n0) (pv5))/\((leq (n0) (pv51))/\((leq (n0) (pv52))/\((leq (pv5) (minus (n999) (n1)))/\((leq (pv51) (minus (n6) (n1)))/\((leq (pv52) (minus (n6) (n1)))/\(forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (n2))/\(leq B (minus (pv5) (n1))))))->(((a_select3 (u_defuse) A B) = (use))/\((a_select3 (z_defuse) A B) = (use)))))))))))))))))))))))))))))))))))))))->(((~((pv51) = (pv52)))->(((a_select2 (rho_defuse) (n0)) = (use))/\(((a_select2 (rho_defuse) (n1)) = (use))/\(((a_select2 (rho_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n0)) = (use))/\(((a_select2 (sigma_defuse) (n1)) = (use))/\(((a_select2 (sigma_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n3)) = (use))/\(((a_select2 (sigma_defuse) (n4)) = (use))/\(((a_select2 (sigma_defuse) (n5)) = (use))/\(((a_select3 (u_defuse) (n0) (n0)) = (use))/\(((a_select3 (u_defuse) (n1) (n0)) = (use))/\(((a_select3 (u_defuse) (n2) (n0)) = (use))/\(((a_select2 (xinit_defuse) (n3)) = (use))/\(((a_select2 (xinit_defuse) (n4)) = (use))/\(((a_select2 (xinit_defuse) (n5)) = (use))/\(((a_select2 (xinit_mean_defuse) (n0)) = (use))/\(((a_select2 (xinit_mean_defuse) (n1)) = (use))/\(((a_select2 (xinit_mean_defuse) (n2)) = (use))/\(((a_select2 (xinit_mean_defuse) (n3)) = (use))/\(((a_select2 (xinit_mean_defuse) (n4)) = (use))/\(((a_select2 (xinit_mean_defuse) (n5)) = (use))/\(((a_select2 (xinit_noise_defuse) (n0)) = (use))/\(((a_select2 (xinit_noise_defuse) (n1)) = (use))/\(((a_select2 (xinit_noise_defuse) (n2)) = (use))/\(((a_select2 (xinit_noise_defuse) (n3)) = (use))/\(((a_select2 (xinit_noise_defuse) (n4)) = (use))/\(((a_select2 (xinit_noise_defuse) (n5)) = (use))/\((leq (n0) (pv5))/\((leq (n0) (pv51))/\((leq (pv5) (minus (n999) (n1)))/\((leq (pv51) (minus (n6) (n1)))/\(forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (n2))/\(leq B (minus (pv5) (n1))))))->(((a_select3 (u_defuse) A B) = (use))/\((a_select3 (z_defuse) A B) = (use))))))))))))))))))))))))))))))))))))))/\(((pv51) = (pv52))->(((a_select2 (rho_defuse) (n0)) = (use))/\(((a_select2 (rho_defuse) (n1)) = (use))/\(((a_select2 (rho_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n0)) = (use))/\(((a_select2 (sigma_defuse) (n1)) = (use))/\(((a_select2 (sigma_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n3)) = (use))/\(((a_select2 (sigma_defuse) (n4)) = (use))/\(((a_select2 (sigma_defuse) (n5)) = (use))/\(((a_select3 (u_defuse) (n0) (n0)) = (use))/\(((a_select3 (u_defuse) (n1) (n0)) = (use))/\(((a_select3 (u_defuse) (n2) (n0)) = (use))/\(((a_select2 (xinit_defuse) (n3)) = (use))/\(((a_select2 (xinit_defuse) (n4)) = (use))/\(((a_select2 (xinit_defuse) (n5)) = (use))/\(((a_select2 (xinit_mean_defuse) (n0)) = (use))/\(((a_select2 (xinit_mean_defuse) (n1)) = (use))/\(((a_select2 (xinit_mean_defuse) (n2)) = (use))/\(((a_select2 (xinit_mean_defuse) (n3)) = (use))/\(((a_select2 (xinit_mean_defuse) (n4)) = (use))/\(((a_select2 (xinit_mean_defuse) (n5)) = (use))/\(((a_select2 (xinit_noise_defuse) (n0)) = (use))/\(((a_select2 (xinit_noise_defuse) (n1)) = (use))/\(((a_select2 (xinit_noise_defuse) (n2)) = (use))/\(((a_select2 (xinit_noise_defuse) (n3)) = (use))/\(((a_select2 (xinit_noise_defuse) (n4)) = (use))/\(((a_select2 (xinit_noise_defuse) (n5)) = (use))/\((leq (n0) (pv5))/\((leq (n0) (pv51))/\((leq (pv5) (minus (n999) (n1)))/\((leq (pv51) (minus (n6) (n1)))/\(forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (n2))/\(leq B (minus (pv5) (n1))))))->(((a_select3 (u_defuse) A B) = (use))/\((a_select3 (z_defuse) A B) = (use)))))))))))))))))))))))))))))))))))))))).
% 0.18/0.52 Proof.
% 0.18/0.52 assert (zenon_L1_ : (~(((a_select2 (rho_defuse) (n0)) = (use))/\(((a_select2 (rho_defuse) (n1)) = (use))/\(((a_select2 (rho_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n0)) = (use))/\(((a_select2 (sigma_defuse) (n1)) = (use))/\(((a_select2 (sigma_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n3)) = (use))/\(((a_select2 (sigma_defuse) (n4)) = (use))/\(((a_select2 (sigma_defuse) (n5)) = (use))/\(((a_select3 (u_defuse) (n0) (n0)) = (use))/\(((a_select3 (u_defuse) (n1) (n0)) = (use))/\(((a_select3 (u_defuse) (n2) (n0)) = (use))/\(((a_select2 (xinit_defuse) (n3)) = (use))/\(((a_select2 (xinit_defuse) (n4)) = (use))/\(((a_select2 (xinit_defuse) (n5)) = (use))/\(((a_select2 (xinit_mean_defuse) (n0)) = (use))/\(((a_select2 (xinit_mean_defuse) (n1)) = (use))/\(((a_select2 (xinit_mean_defuse) (n2)) = (use))/\(((a_select2 (xinit_mean_defuse) (n3)) = (use))/\(((a_select2 (xinit_mean_defuse) (n4)) = (use))/\(((a_select2 (xinit_mean_defuse) (n5)) = (use))/\(((a_select2 (xinit_noise_defuse) (n0)) = (use))/\(((a_select2 (xinit_noise_defuse) (n1)) = (use))/\(((a_select2 (xinit_noise_defuse) (n2)) = (use))/\(((a_select2 (xinit_noise_defuse) (n3)) = (use))/\(((a_select2 (xinit_noise_defuse) (n4)) = (use))/\(((a_select2 (xinit_noise_defuse) (n5)) = (use))/\((leq (n0) (pv5))/\((leq (n0) (pv51))/\((leq (pv5) (minus (n999) (n1)))/\((leq (pv51) (minus (n6) (n1)))/\(forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (n2))/\(leq B (minus (pv5) (n1))))))->(((a_select3 (u_defuse) A B) = (use))/\((a_select3 (z_defuse) A B) = (use)))))))))))))))))))))))))))))))))))))) -> ((a_select2 (rho_defuse) (n0)) = (use)) -> ((a_select2 (rho_defuse) (n1)) = (use)) -> ((a_select2 (rho_defuse) (n2)) = (use)) -> ((a_select2 (sigma_defuse) (n0)) = (use)) -> ((a_select2 (sigma_defuse) (n1)) = (use)) -> ((a_select2 (sigma_defuse) (n2)) = (use)) -> ((a_select2 (sigma_defuse) (n3)) = (use)) -> ((a_select2 (sigma_defuse) (n4)) = (use)) -> ((a_select2 (sigma_defuse) (n5)) = (use)) -> ((a_select3 (u_defuse) (n0) (n0)) = (use)) -> ((a_select3 (u_defuse) (n1) (n0)) = (use)) -> ((a_select3 (u_defuse) (n2) (n0)) = (use)) -> ((a_select2 (xinit_defuse) (n3)) = (use)) -> ((a_select2 (xinit_defuse) (n4)) = (use)) -> ((a_select2 (xinit_defuse) (n5)) = (use)) -> ((a_select2 (xinit_mean_defuse) (n0)) = (use)) -> ((a_select2 (xinit_mean_defuse) (n1)) = (use)) -> ((a_select2 (xinit_mean_defuse) (n2)) = (use)) -> ((a_select2 (xinit_mean_defuse) (n3)) = (use)) -> ((a_select2 (xinit_mean_defuse) (n4)) = (use)) -> ((a_select2 (xinit_mean_defuse) (n5)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n0)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n4)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n5)) = (use)) -> (gt (succ (pv5)) (n0)) -> (gt (succ (pv51)) (n0)) -> (gt (succ (minus (n999) (n1))) (pv5)) -> (gt (succ (minus (n6) (n1))) (pv51)) -> (forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (n2))/\(leq B (minus (pv5) (n1))))))->(((a_select3 (u_defuse) A B) = (use))/\((a_select3 (z_defuse) A B) = (use)))))) -> False).
% 0.18/0.52 do 0 intro. intros zenon_H66 zenon_H67 zenon_H68 zenon_H69 zenon_H6a zenon_H6b zenon_H6c zenon_H6d zenon_H6e zenon_H6f zenon_H70 zenon_H71 zenon_H72 zenon_H73 zenon_H74 zenon_H75 zenon_H76 zenon_H77 zenon_H78 zenon_H79 zenon_H7a zenon_H7b zenon_H7c zenon_H7d zenon_H7e zenon_H7f zenon_H80 zenon_H81 zenon_H82 zenon_H83 zenon_H84 zenon_H85 zenon_H86.
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ].
% 0.18/0.52 exact (zenon_H88 zenon_H67).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H87); [ zenon_intro zenon_H8a | zenon_intro zenon_H89 ].
% 0.18/0.52 exact (zenon_H8a zenon_H68).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H89); [ zenon_intro zenon_H8c | zenon_intro zenon_H8b ].
% 0.18/0.52 exact (zenon_H8c zenon_H69).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H8b); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ].
% 0.18/0.52 exact (zenon_H8e zenon_H6a).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H8d); [ zenon_intro zenon_H90 | zenon_intro zenon_H8f ].
% 0.18/0.52 exact (zenon_H90 zenon_H6b).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H8f); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ].
% 0.18/0.52 exact (zenon_H92 zenon_H6c).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H94 | zenon_intro zenon_H93 ].
% 0.18/0.52 exact (zenon_H94 zenon_H6d).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ].
% 0.18/0.52 exact (zenon_H96 zenon_H6e).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H95); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ].
% 0.18/0.52 exact (zenon_H98 zenon_H6f).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ].
% 0.18/0.52 exact (zenon_H9a zenon_H70).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H99); [ zenon_intro zenon_H9c | zenon_intro zenon_H9b ].
% 0.18/0.52 exact (zenon_H9c zenon_H71).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H9b); [ zenon_intro zenon_H9e | zenon_intro zenon_H9d ].
% 0.18/0.52 exact (zenon_H9e zenon_H72).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H9d); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9f ].
% 0.18/0.52 exact (zenon_Ha0 zenon_H73).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha1 ].
% 0.18/0.52 exact (zenon_Ha2 zenon_H74).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Ha1); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ].
% 0.18/0.52 exact (zenon_Ha4 zenon_H75).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Ha3); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha5 ].
% 0.18/0.52 exact (zenon_Ha6 zenon_H76).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Ha5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ].
% 0.18/0.52 exact (zenon_Ha8 zenon_H77).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Ha7); [ zenon_intro zenon_Haa | zenon_intro zenon_Ha9 ].
% 0.18/0.52 exact (zenon_Haa zenon_H78).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Ha9); [ zenon_intro zenon_Hac | zenon_intro zenon_Hab ].
% 0.18/0.52 exact (zenon_Hac zenon_H79).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hab); [ zenon_intro zenon_Hae | zenon_intro zenon_Had ].
% 0.18/0.52 exact (zenon_Hae zenon_H7a).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Had); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Haf ].
% 0.18/0.52 exact (zenon_Hb0 zenon_H7b).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Haf); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb1 ].
% 0.18/0.52 exact (zenon_Hb2 zenon_H7c).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hb1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ].
% 0.18/0.52 exact (zenon_Hb4 zenon_H7d).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ].
% 0.18/0.52 exact (zenon_Hb6 zenon_H7e).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hb7 ].
% 0.18/0.52 exact (zenon_Hb8 zenon_H7f).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ].
% 0.18/0.52 exact (zenon_Hba zenon_H80).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbb ].
% 0.18/0.52 exact (zenon_Hbc zenon_H81).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hbd ].
% 0.18/0.52 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_Hbf.
% 0.18/0.52 generalize (zenon_Hbf (pv5)). zenon_intro zenon_Hc0.
% 0.18/0.52 apply (zenon_equiv_s _ _ zenon_Hc0); [ zenon_intro zenon_Hbe; zenon_intro zenon_Hc2 | zenon_intro zenon_Hc1; zenon_intro zenon_H82 ].
% 0.18/0.52 exact (zenon_Hc2 zenon_H82).
% 0.18/0.52 exact (zenon_Hbe zenon_Hc1).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hbd); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ].
% 0.18/0.52 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_Hbf.
% 0.18/0.52 generalize (zenon_Hbf (pv51)). zenon_intro zenon_Hc5.
% 0.18/0.52 apply (zenon_equiv_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc4; zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6; zenon_intro zenon_H83 ].
% 0.18/0.52 exact (zenon_Hc7 zenon_H83).
% 0.18/0.52 exact (zenon_Hc4 zenon_Hc6).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hc3); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hc8 ].
% 0.18/0.52 generalize (leq_succ_gt_equiv (pv5)). zenon_intro zenon_Hca.
% 0.18/0.52 generalize (zenon_Hca (minus (n999) (n1))). zenon_intro zenon_Hcb.
% 0.18/0.52 apply (zenon_equiv_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc9; zenon_intro zenon_Hcd | zenon_intro zenon_Hcc; zenon_intro zenon_H84 ].
% 0.18/0.52 exact (zenon_Hcd zenon_H84).
% 0.18/0.52 exact (zenon_Hc9 zenon_Hcc).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hce ].
% 0.18/0.52 generalize (leq_succ_gt_equiv (pv51)). zenon_intro zenon_Hd0.
% 0.18/0.52 generalize (zenon_Hd0 (minus (n6) (n1))). zenon_intro zenon_Hd1.
% 0.18/0.52 apply (zenon_equiv_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcf; zenon_intro zenon_Hd3 | zenon_intro zenon_Hd2; zenon_intro zenon_H85 ].
% 0.18/0.52 exact (zenon_Hd3 zenon_H85).
% 0.18/0.52 exact (zenon_Hcf zenon_Hd2).
% 0.18/0.52 exact (zenon_Hce zenon_H86).
% 0.18/0.52 (* end of lemma zenon_L1_ *)
% 0.18/0.52 apply NNPP. intro zenon_G.
% 0.18/0.52 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H67. zenon_intro zenon_Hd6.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_H68. zenon_intro zenon_Hd7.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H69. zenon_intro zenon_Hd8.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_H6a. zenon_intro zenon_Hd9.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hd9). zenon_intro zenon_H6b. zenon_intro zenon_Hda.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hda). zenon_intro zenon_H6c. zenon_intro zenon_Hdb.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hdb). zenon_intro zenon_H6d. zenon_intro zenon_Hdc.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hdc). zenon_intro zenon_H6e. zenon_intro zenon_Hdd.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hdd). zenon_intro zenon_H6f. zenon_intro zenon_Hde.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hde). zenon_intro zenon_H70. zenon_intro zenon_Hdf.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hdf). zenon_intro zenon_H71. zenon_intro zenon_He0.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He0). zenon_intro zenon_H72. zenon_intro zenon_He1.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He1). zenon_intro zenon_H73. zenon_intro zenon_He2.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He2). zenon_intro zenon_H74. zenon_intro zenon_He3.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He3). zenon_intro zenon_H75. zenon_intro zenon_He4.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He4). zenon_intro zenon_H76. zenon_intro zenon_He5.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He5). zenon_intro zenon_H77. zenon_intro zenon_He6.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He6). zenon_intro zenon_H78. zenon_intro zenon_He7.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He7). zenon_intro zenon_H79. zenon_intro zenon_He8.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He8). zenon_intro zenon_H7a. zenon_intro zenon_He9.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H7b. zenon_intro zenon_Hea.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_H7c. zenon_intro zenon_Heb.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Heb). zenon_intro zenon_H7d. zenon_intro zenon_Hec.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hec). zenon_intro zenon_H7e. zenon_intro zenon_Hed.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_H7f. zenon_intro zenon_Hee.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_H80. zenon_intro zenon_Hef.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hef). zenon_intro zenon_H81. zenon_intro zenon_Hf0.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hf0). zenon_intro zenon_Hc1. zenon_intro zenon_Hf1.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hf1). zenon_intro zenon_Hc6. zenon_intro zenon_Hf2.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Hf4. zenon_intro zenon_Hf3.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hf3). zenon_intro zenon_Hcc. zenon_intro zenon_Hf5.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hf5). zenon_intro zenon_Hd2. zenon_intro zenon_Hf6.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_Hf6). zenon_intro zenon_Hf7. zenon_intro zenon_H86.
% 0.18/0.52 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_Hbf.
% 0.18/0.52 generalize (zenon_Hbf (pv5)). zenon_intro zenon_Hc0.
% 0.18/0.52 apply (zenon_equiv_s _ _ zenon_Hc0); [ zenon_intro zenon_Hbe; zenon_intro zenon_Hc2 | zenon_intro zenon_Hc1; zenon_intro zenon_H82 ].
% 0.18/0.52 exact (zenon_Hbe zenon_Hc1).
% 0.18/0.52 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_Hbf.
% 0.18/0.52 generalize (zenon_Hbf (pv51)). zenon_intro zenon_Hc5.
% 0.18/0.52 apply (zenon_equiv_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc4; zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6; zenon_intro zenon_H83 ].
% 0.18/0.52 exact (zenon_Hc4 zenon_Hc6).
% 0.18/0.52 generalize (leq_succ_gt_equiv (pv5)). zenon_intro zenon_Hca.
% 0.18/0.52 generalize (zenon_Hca (minus (n999) (n1))). zenon_intro zenon_Hcb.
% 0.18/0.52 apply (zenon_equiv_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc9; zenon_intro zenon_Hcd | zenon_intro zenon_Hcc; zenon_intro zenon_H84 ].
% 0.18/0.52 exact (zenon_Hc9 zenon_Hcc).
% 0.18/0.52 generalize (leq_succ_gt_equiv (pv51)). zenon_intro zenon_Hd0.
% 0.18/0.52 generalize (zenon_Hd0 (minus (n6) (n1))). zenon_intro zenon_Hd1.
% 0.18/0.52 apply (zenon_equiv_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcf; zenon_intro zenon_Hd3 | zenon_intro zenon_Hd2; zenon_intro zenon_H85 ].
% 0.18/0.52 exact (zenon_Hcf zenon_Hd2).
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_Hd4); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hf8 ].
% 0.18/0.52 apply (zenon_notimply_s _ _ zenon_Hf9). zenon_intro zenon_Hfa. zenon_intro zenon_H66.
% 0.18/0.52 apply (zenon_L1_); trivial.
% 0.18/0.52 apply (zenon_notimply_s _ _ zenon_Hf8). zenon_intro zenon_Hfb. zenon_intro zenon_H66.
% 0.18/0.52 apply (zenon_L1_); trivial.
% 0.18/0.52 Qed.
% 0.18/0.52 % SZS output end Proof
% 0.18/0.52 (* END-PROOF *)
% 0.18/0.52 nodes searched: 56
% 0.18/0.52 max branch formulas: 154
% 0.18/0.52 proof nodes created: 45
% 0.18/0.52 formulas created: 3624
% 0.18/0.52
%------------------------------------------------------------------------------