TSTP Solution File: GEO213+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO213+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n018.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 : Sat Jul 16 07:00:54 EDT 2022
% Result : Theorem 0.37s 0.55s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO213+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 00:21:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.37/0.55 (* PROOF-FOUND *)
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 (* BEGIN-PROOF *)
% 0.37/0.55 % SZS output start Proof
% 0.37/0.55 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((distinct_lines L N)\/(unorthogonal_lines M N)))))).
% 0.37/0.55 Proof.
% 0.37/0.55 assert (zenon_L1_ : forall (zenon_TL_ba : zenon_U) (zenon_TN_bb : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_lines zenon_TN_bb Y)->((distinct_lines zenon_TN_bb Z)\/(distinct_lines Y Z))))) -> (~(distinct_lines zenon_TL_ba zenon_TN_bb)) -> (distinct_lines zenon_TN_bb zenon_TL_ba) -> False).
% 0.37/0.55 do 2 intro. intros zenon_H17 zenon_H18 zenon_H19.
% 0.37/0.55 generalize (zenon_H17 zenon_TL_ba). zenon_intro zenon_H1c.
% 0.37/0.55 generalize (zenon_H1c zenon_TN_bb). zenon_intro zenon_H1d.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.37/0.55 exact (zenon_H1f zenon_H19).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H1e); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 0.37/0.55 generalize (apart2 zenon_TN_bb). zenon_intro zenon_H22.
% 0.37/0.55 exact (zenon_H22 zenon_H21).
% 0.37/0.55 exact (zenon_H18 zenon_H20).
% 0.37/0.55 (* end of lemma zenon_L1_ *)
% 0.37/0.55 assert (zenon_L2_ : forall (zenon_TL_ba : zenon_U) (zenon_TN_bb : zenon_U) (zenon_TM_bm : zenon_U), (~(unorthogonal_lines zenon_TM_bm zenon_TN_bb)) -> (~(convergent_lines zenon_TL_ba zenon_TM_bm)) -> (~(distinct_lines zenon_TL_ba zenon_TN_bb)) -> (forall M : zenon_U, ((convergent_lines zenon_TM_bm M)\/(unorthogonal_lines zenon_TM_bm M))) -> False).
% 0.37/0.55 do 3 intro. intros zenon_H23 zenon_H24 zenon_H18 zenon_H25.
% 0.37/0.55 generalize (apart3 zenon_TM_bm). zenon_intro zenon_H27.
% 0.37/0.55 generalize (zenon_H25 zenon_TN_bb). zenon_intro zenon_H28.
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 0.37/0.55 generalize (ceq3 zenon_TM_bm). zenon_intro zenon_H2b.
% 0.37/0.55 generalize (zenon_H2b zenon_TN_bb). zenon_intro zenon_H2c.
% 0.37/0.55 generalize (ax6 zenon_TM_bm). zenon_intro zenon_H2d.
% 0.37/0.55 generalize (apart5 zenon_TN_bb). zenon_intro zenon_H17.
% 0.37/0.55 generalize (zenon_H2c zenon_TL_ba). zenon_intro zenon_H2e.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.37/0.55 exact (zenon_H30 zenon_H2a).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H19 | zenon_intro zenon_H31 ].
% 0.37/0.55 apply (zenon_L1_ zenon_TL_ba zenon_TN_bb); trivial.
% 0.37/0.55 generalize (zenon_H2d zenon_TL_ba). zenon_intro zenon_H32.
% 0.37/0.55 generalize (zenon_H32 zenon_TM_bm). zenon_intro zenon_H33.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.37/0.55 exact (zenon_H35 zenon_H31).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.37/0.55 exact (zenon_H27 zenon_H37).
% 0.37/0.55 exact (zenon_H24 zenon_H36).
% 0.37/0.55 exact (zenon_H23 zenon_H29).
% 0.37/0.55 (* end of lemma zenon_L2_ *)
% 0.37/0.55 assert (zenon_L3_ : forall (zenon_TM_bm : zenon_U) (zenon_TN_bb : zenon_U) (zenon_TL_ba : zenon_U), (~(distinct_lines zenon_TL_ba zenon_TN_bb)) -> (~(convergent_lines zenon_TL_ba zenon_TM_bm)) -> (~(unorthogonal_lines zenon_TM_bm zenon_TN_bb)) -> False).
% 0.37/0.55 do 3 intro. intros zenon_H18 zenon_H24 zenon_H23.
% 0.37/0.55 generalize (occu1 zenon_TM_bm). zenon_intro zenon_H25.
% 0.37/0.55 apply (zenon_L2_ zenon_TL_ba zenon_TN_bb zenon_TM_bm); trivial.
% 0.37/0.55 (* end of lemma zenon_L3_ *)
% 0.37/0.55 apply NNPP. intro zenon_G.
% 0.37/0.55 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((distinct_lines L N)\/(unorthogonal_lines M N)))))) zenon_G); [ zenon_intro zenon_H38; idtac ].
% 0.37/0.55 elim zenon_H38. zenon_intro zenon_TL_ba. zenon_intro zenon_H39.
% 0.37/0.55 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, ((unorthogonal_lines zenon_TL_ba M)->((distinct_lines zenon_TL_ba N)\/(unorthogonal_lines M N))))) zenon_H39); [ zenon_intro zenon_H3a; idtac ].
% 0.37/0.55 elim zenon_H3a. zenon_intro zenon_TM_bm. zenon_intro zenon_H3b.
% 0.37/0.55 apply (zenon_notallex_s (fun N : zenon_U => ((unorthogonal_lines zenon_TL_ba zenon_TM_bm)->((distinct_lines zenon_TL_ba N)\/(unorthogonal_lines zenon_TM_bm N)))) zenon_H3b); [ zenon_intro zenon_H3c; idtac ].
% 0.37/0.55 elim zenon_H3c. zenon_intro zenon_TN_bb. zenon_intro zenon_H3d.
% 0.37/0.55 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e.
% 0.37/0.55 apply (zenon_notor_s _ _ zenon_H3e). zenon_intro zenon_H18. zenon_intro zenon_H23.
% 0.37/0.55 generalize (oac1 zenon_TL_ba). zenon_intro zenon_H40.
% 0.37/0.55 generalize (zenon_H40 zenon_TM_bm). zenon_intro zenon_H41.
% 0.37/0.55 generalize (zenon_H41 zenon_TN_bb). zenon_intro zenon_H42.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.37/0.55 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H24 | zenon_intro zenon_H45 ].
% 0.37/0.55 apply (zenon_L3_ zenon_TM_bm zenon_TN_bb zenon_TL_ba); trivial.
% 0.37/0.55 exact (zenon_H45 zenon_H3f).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.37/0.55 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.37/0.55 generalize (ceq3 zenon_TL_ba). zenon_intro zenon_H4a.
% 0.37/0.55 generalize (zenon_H4a zenon_TN_bb). zenon_intro zenon_H4b.
% 0.37/0.55 generalize (apart5 zenon_TN_bb). zenon_intro zenon_H17.
% 0.37/0.55 generalize (zenon_H4b zenon_TL_ba). zenon_intro zenon_H4c.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ].
% 0.37/0.55 exact (zenon_H4e zenon_H49).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H19 | zenon_intro zenon_H4f ].
% 0.37/0.55 apply (zenon_L1_ zenon_TL_ba zenon_TN_bb); trivial.
% 0.37/0.55 generalize (apart3 zenon_TL_ba). zenon_intro zenon_H50.
% 0.37/0.55 exact (zenon_H50 zenon_H4f).
% 0.37/0.55 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H2a. zenon_intro zenon_H29.
% 0.37/0.55 exact (zenon_H23 zenon_H29).
% 0.37/0.55 Qed.
% 0.37/0.55 % SZS output end Proof
% 0.37/0.55 (* END-PROOF *)
% 0.37/0.55 nodes searched: 2630
% 0.37/0.55 max branch formulas: 856
% 0.37/0.55 proof nodes created: 247
% 0.37/0.55 formulas created: 10724
% 0.37/0.55
%------------------------------------------------------------------------------