TSTP Solution File: GEO214+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO214+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n014.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 07:00:55 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO214+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n014.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 : Fri Jun 17 18:19:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.52 (* PROOF-FOUND *)
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 (* BEGIN-PROOF *)
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 Theorem con : (forall L : zenon_U, (forall M : zenon_U, ((unorthogonal_lines L M)->(unorthogonal_lines M L)))).
% 0.19/0.52 Proof.
% 0.19/0.52 assert (zenon_L1_ : forall (zenon_TL_y : zenon_U) (zenon_TM_z : zenon_U), (forall M : zenon_U, ((convergent_lines zenon_TM_z M)\/(unorthogonal_lines zenon_TM_z M))) -> (~(convergent_lines zenon_TL_y zenon_TM_z)) -> (~(unorthogonal_lines zenon_TM_z zenon_TL_y)) -> False).
% 0.19/0.52 do 2 intro. intros zenon_H15 zenon_H16 zenon_H17.
% 0.19/0.52 generalize (zenon_H15 zenon_TL_y). zenon_intro zenon_H1a.
% 0.19/0.52 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.19/0.52 generalize (apart3 zenon_TM_z). zenon_intro zenon_H1d.
% 0.19/0.52 generalize (apart6 zenon_TM_z). zenon_intro zenon_H1e.
% 0.19/0.52 generalize (zenon_H1e zenon_TL_y). zenon_intro zenon_H1f.
% 0.19/0.52 generalize (zenon_H1f zenon_TM_z). zenon_intro zenon_H20.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ].
% 0.19/0.52 exact (zenon_H22 zenon_H1c).
% 0.19/0.52 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ].
% 0.19/0.52 exact (zenon_H1d zenon_H24).
% 0.19/0.52 exact (zenon_H16 zenon_H23).
% 0.19/0.52 exact (zenon_H17 zenon_H1b).
% 0.19/0.52 (* end of lemma zenon_L1_ *)
% 0.19/0.52 assert (zenon_L2_ : forall (zenon_TL_y : zenon_U), (convergent_lines zenon_TL_y zenon_TL_y) -> False).
% 0.19/0.52 do 1 intro. intros zenon_H25.
% 0.19/0.52 generalize (apart3 zenon_TL_y). zenon_intro zenon_H26.
% 0.19/0.52 exact (zenon_H26 zenon_H25).
% 0.19/0.52 (* end of lemma zenon_L2_ *)
% 0.19/0.52 apply NNPP. intro zenon_G.
% 0.19/0.52 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, ((unorthogonal_lines L M)->(unorthogonal_lines M L)))) zenon_G); [ zenon_intro zenon_H27; idtac ].
% 0.19/0.52 elim zenon_H27. zenon_intro zenon_TL_y. zenon_intro zenon_H28.
% 0.19/0.52 apply (zenon_notallex_s (fun M : zenon_U => ((unorthogonal_lines zenon_TL_y M)->(unorthogonal_lines M zenon_TL_y))) zenon_H28); [ zenon_intro zenon_H29; idtac ].
% 0.19/0.52 elim zenon_H29. zenon_intro zenon_TM_z. zenon_intro zenon_H2a.
% 0.19/0.52 apply (zenon_notimply_s _ _ zenon_H2a). zenon_intro zenon_H2b. zenon_intro zenon_H17.
% 0.19/0.52 generalize (oac1 zenon_TL_y). zenon_intro zenon_H2c.
% 0.19/0.52 generalize (zenon_H2c zenon_TM_z). zenon_intro zenon_H2d.
% 0.19/0.52 generalize (occu1 zenon_TM_z). zenon_intro zenon_H15.
% 0.19/0.52 generalize (zenon_H2d zenon_TL_y). zenon_intro zenon_H2e.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.19/0.52 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H16 | zenon_intro zenon_H31 ].
% 0.19/0.52 apply (zenon_L1_ zenon_TL_y zenon_TM_z); trivial.
% 0.19/0.52 exact (zenon_H31 zenon_H2b).
% 0.19/0.52 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 0.19/0.52 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H25. zenon_intro zenon_H34.
% 0.19/0.52 apply (zenon_L2_ zenon_TL_y); trivial.
% 0.19/0.52 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H1c. zenon_intro zenon_H1b.
% 0.19/0.52 exact (zenon_H17 zenon_H1b).
% 0.19/0.52 Qed.
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52 (* END-PROOF *)
% 0.19/0.52 nodes searched: 511
% 0.19/0.52 max branch formulas: 273
% 0.19/0.52 proof nodes created: 66
% 0.19/0.52 formulas created: 2231
% 0.19/0.52
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