TSTP Solution File: SWV204+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV204+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% 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 : Wed Jul 20 23:03:18 EDT 2022
% Result : Theorem 9.84s 10.07s
% Output : Proof 9.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV204+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 04:31:36 EDT 2022
% 0.14/0.36 % CPUTime :
% 9.84/10.07 (* PROOF-FOUND *)
% 9.84/10.07 % SZS status Theorem
% 9.84/10.07 (* BEGIN-PROOF *)
% 9.84/10.07 % SZS output start Proof
% 9.84/10.07 Theorem quaternion_ds1_inuse_0015 : ((((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))/\((forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (n2))/\(leq B (n998)))))->((a_select3 (u_defuse) A B) = (use)))))/\(forall C : zenon_U, (forall D : zenon_U, (((leq (n0) C)/\((leq (n0) D)/\((leq C (n2))/\(leq D (n998)))))->((a_select3 (z_defuse) C D) = (use)))))))))))))))))))))))))))))))))->(forall E : zenon_U, (((leq (n0) E)/\(leq E (n2)))->((a_select2 (rho_defuse) E) = (use))))).
% 9.84/10.07 Proof.
% 9.84/10.07 assert (zenon_L1_ : (~((rho_defuse) = (rho_defuse))) -> False).
% 9.84/10.07 do 0 intro. intros zenon_H5c.
% 9.84/10.07 apply zenon_H5c. apply refl_equal.
% 9.84/10.07 (* end of lemma zenon_L1_ *)
% 9.84/10.07 assert (zenon_L2_ : forall (zenon_TE_dr : zenon_U), (gt (succ zenon_TE_dr) (n0)) -> (~(leq (n0) zenon_TE_dr)) -> False).
% 9.84/10.07 do 1 intro. intros zenon_H5d zenon_H5e.
% 9.84/10.07 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H60.
% 9.84/10.07 generalize (zenon_H60 zenon_TE_dr). zenon_intro zenon_H61.
% 9.84/10.07 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H5e; zenon_intro zenon_H63 | zenon_intro zenon_H62; zenon_intro zenon_H5d ].
% 9.84/10.07 exact (zenon_H63 zenon_H5d).
% 9.84/10.07 exact (zenon_H5e zenon_H62).
% 9.84/10.07 (* end of lemma zenon_L2_ *)
% 9.84/10.07 assert (zenon_L3_ : forall (zenon_TE_dr : zenon_U), (gt (succ (n2)) zenon_TE_dr) -> (~(leq zenon_TE_dr (n2))) -> False).
% 9.84/10.07 do 1 intro. intros zenon_H64 zenon_H65.
% 9.84/10.07 generalize (leq_succ_gt_equiv zenon_TE_dr). zenon_intro zenon_H66.
% 9.84/10.07 generalize (zenon_H66 (n2)). zenon_intro zenon_H67.
% 9.84/10.07 apply (zenon_equiv_s _ _ zenon_H67); [ zenon_intro zenon_H65; zenon_intro zenon_H69 | zenon_intro zenon_H68; zenon_intro zenon_H64 ].
% 9.84/10.07 exact (zenon_H69 zenon_H64).
% 9.84/10.07 exact (zenon_H65 zenon_H68).
% 9.84/10.07 (* end of lemma zenon_L3_ *)
% 9.84/10.07 assert (zenon_L4_ : (~((use) = (use))) -> False).
% 9.84/10.07 do 0 intro. intros zenon_H6a.
% 9.84/10.07 apply zenon_H6a. apply refl_equal.
% 9.84/10.07 (* end of lemma zenon_L4_ *)
% 9.84/10.07 apply NNPP. intro zenon_G.
% 9.84/10.07 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H6c. zenon_intro zenon_H6b.
% 9.84/10.07 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 9.84/10.07 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 9.84/10.07 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71.
% 9.84/10.07 apply (zenon_notallex_s (fun E : zenon_U => (((leq (n0) E)/\(leq E (n2)))->((a_select2 (rho_defuse) E) = (use)))) zenon_H6b); [ zenon_intro zenon_H73; idtac ].
% 9.84/10.07 elim zenon_H73. zenon_intro zenon_TE_dr. zenon_intro zenon_H74.
% 9.84/10.07 apply (zenon_notimply_s _ _ zenon_H74). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 9.84/10.07 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H62. zenon_intro zenon_H68.
% 9.84/10.07 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H60.
% 9.84/10.07 generalize (zenon_H60 zenon_TE_dr). zenon_intro zenon_H61.
% 9.84/10.07 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H5e; zenon_intro zenon_H63 | zenon_intro zenon_H62; zenon_intro zenon_H5d ].
% 9.84/10.07 exact (zenon_H5e zenon_H62).
% 9.84/10.07 generalize (leq_succ_gt_equiv zenon_TE_dr). zenon_intro zenon_H66.
% 9.84/10.07 generalize (zenon_H66 (n2)). zenon_intro zenon_H67.
% 9.84/10.07 apply (zenon_equiv_s _ _ zenon_H67); [ zenon_intro zenon_H65; zenon_intro zenon_H69 | zenon_intro zenon_H68; zenon_intro zenon_H64 ].
% 9.84/10.07 exact (zenon_H65 zenon_H68).
% 9.84/10.07 cut (((a_select2 (rho_defuse) (n0)) = (use)) = ((a_select2 (rho_defuse) zenon_TE_dr) = (use))).
% 9.84/10.07 intro zenon_D_pnotp.
% 9.84/10.07 apply zenon_H75.
% 9.84/10.07 rewrite <- zenon_D_pnotp.
% 9.84/10.07 exact zenon_H6e.
% 9.84/10.07 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 9.84/10.07 cut (((a_select2 (rho_defuse) (n0)) = (a_select2 (rho_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_H77].
% 9.84/10.07 congruence.
% 9.84/10.07 elim (classic ((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) zenon_TE_dr))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ].
% 9.84/10.07 cut (((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) zenon_TE_dr)) = ((a_select2 (rho_defuse) (n0)) = (a_select2 (rho_defuse) zenon_TE_dr))).
% 9.84/10.07 intro zenon_D_pnotp.
% 9.84/10.07 apply zenon_H77.
% 9.84/10.07 rewrite <- zenon_D_pnotp.
% 9.84/10.07 exact zenon_H78.
% 9.84/10.07 cut (((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_H79].
% 9.84/10.07 cut (((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) (n0)))); [idtac | apply NNPP; zenon_intro zenon_H7a].
% 9.84/10.07 congruence.
% 9.84/10.07 cut ((zenon_TE_dr = (n0))); [idtac | apply NNPP; zenon_intro zenon_H7b].
% 9.84/10.07 cut (((rho_defuse) = (rho_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 9.84/10.07 congruence.
% 9.84/10.07 apply zenon_H5c. apply refl_equal.
% 9.84/10.07 cut (((a_select2 (rho_defuse) (n1)) = (use)) = ((a_select2 (rho_defuse) zenon_TE_dr) = (use))).
% 9.84/10.07 intro zenon_D_pnotp.
% 9.84/10.07 apply zenon_H75.
% 9.84/10.07 rewrite <- zenon_D_pnotp.
% 9.84/10.07 exact zenon_H70.
% 9.84/10.07 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 9.84/10.07 cut (((a_select2 (rho_defuse) (n1)) = (a_select2 (rho_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 9.84/10.07 congruence.
% 9.84/10.07 elim (classic ((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) zenon_TE_dr))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ].
% 9.84/10.07 cut (((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) zenon_TE_dr)) = ((a_select2 (rho_defuse) (n1)) = (a_select2 (rho_defuse) zenon_TE_dr))).
% 9.84/10.07 intro zenon_D_pnotp.
% 9.84/10.07 apply zenon_H7c.
% 9.84/10.07 rewrite <- zenon_D_pnotp.
% 9.84/10.07 exact zenon_H78.
% 9.84/10.07 cut (((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_H79].
% 9.84/10.07 cut (((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) (n1)))); [idtac | apply NNPP; zenon_intro zenon_H7d].
% 9.84/10.07 congruence.
% 9.84/10.07 cut ((zenon_TE_dr = (n1))); [idtac | apply NNPP; zenon_intro zenon_H7e].
% 9.84/10.07 cut (((rho_defuse) = (rho_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 9.84/10.07 congruence.
% 9.84/10.07 apply zenon_H5c. apply refl_equal.
% 9.84/10.07 cut (((a_select2 (rho_defuse) (n2)) = (use)) = ((a_select2 (rho_defuse) zenon_TE_dr) = (use))).
% 9.84/10.07 intro zenon_D_pnotp.
% 9.84/10.07 apply zenon_H75.
% 9.84/10.07 rewrite <- zenon_D_pnotp.
% 9.84/10.07 exact zenon_H72.
% 9.84/10.07 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 9.84/10.07 cut (((a_select2 (rho_defuse) (n2)) = (a_select2 (rho_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 9.84/10.07 congruence.
% 9.84/10.07 elim (classic ((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) zenon_TE_dr))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ].
% 9.84/10.07 cut (((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) zenon_TE_dr)) = ((a_select2 (rho_defuse) (n2)) = (a_select2 (rho_defuse) zenon_TE_dr))).
% 9.84/10.07 intro zenon_D_pnotp.
% 9.84/10.07 apply zenon_H7f.
% 9.84/10.07 rewrite <- zenon_D_pnotp.
% 9.84/10.07 exact zenon_H78.
% 9.84/10.07 cut (((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_H79].
% 9.84/10.07 cut (((a_select2 (rho_defuse) zenon_TE_dr) = (a_select2 (rho_defuse) (n2)))); [idtac | apply NNPP; zenon_intro zenon_H80].
% 9.84/10.07 congruence.
% 9.84/10.07 cut ((zenon_TE_dr = (n2))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 9.84/10.07 cut (((rho_defuse) = (rho_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 9.84/10.07 congruence.
% 9.84/10.07 apply zenon_H5c. apply refl_equal.
% 9.84/10.07 generalize (finite_domain_2 zenon_TE_dr). zenon_intro zenon_H82.
% 9.84/10.07 apply (zenon_imply_s _ _ zenon_H82); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ].
% 9.84/10.07 apply (zenon_notand_s _ _ zenon_H84); [ zenon_intro zenon_H5e | zenon_intro zenon_H65 ].
% 9.84/10.07 apply (zenon_L2_ zenon_TE_dr); trivial.
% 9.84/10.07 apply (zenon_L3_ zenon_TE_dr); trivial.
% 9.84/10.07 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ].
% 9.84/10.07 exact (zenon_H7b zenon_H86).
% 9.84/10.07 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ].
% 9.84/10.07 exact (zenon_H7e zenon_H88).
% 9.84/10.07 exact (zenon_H81 zenon_H87).
% 9.84/10.07 apply zenon_H79. apply refl_equal.
% 9.84/10.07 apply zenon_H79. apply refl_equal.
% 9.84/10.07 apply zenon_H6a. apply refl_equal.
% 9.84/10.07 apply zenon_H79. apply refl_equal.
% 9.84/10.07 apply zenon_H79. apply refl_equal.
% 9.84/10.07 apply zenon_H6a. apply refl_equal.
% 9.84/10.07 apply zenon_H79. apply refl_equal.
% 9.84/10.07 apply zenon_H79. apply refl_equal.
% 9.84/10.07 apply zenon_H6a. apply refl_equal.
% 9.84/10.07 Qed.
% 9.84/10.07 % SZS output end Proof
% 9.84/10.07 (* END-PROOF *)
% 9.84/10.07 nodes searched: 558628
% 9.84/10.07 max branch formulas: 3139
% 9.84/10.07 proof nodes created: 1122
% 9.84/10.07 formulas created: 319329
% 9.84/10.07
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