TSTP Solution File: GEO192+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n022.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 07:00:37 EDT 2022
% Result : Theorem 0.89s 1.06s
% Output : Proof 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n022.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 : Fri Jun 17 16:02:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.89/1.06 (* PROOF-FOUND *)
% 0.89/1.06 % SZS status Theorem
% 0.89/1.06 (* BEGIN-PROOF *)
% 0.89/1.06 % SZS output start Proof
% 0.89/1.06 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines X Y)->((apart_point_and_line (intersection_point X Y) Z)->((distinct_lines X Z)/\(distinct_lines Y Z))))))).
% 0.89/1.06 Proof.
% 0.89/1.06 assert (zenon_L1_ : forall (zenon_TZ_o : zenon_U), (distinct_lines zenon_TZ_o zenon_TZ_o) -> False).
% 0.89/1.06 do 1 intro. intros zenon_Hd.
% 0.89/1.06 generalize (apart2 zenon_TZ_o). zenon_intro zenon_Hf.
% 0.89/1.06 exact (zenon_Hf zenon_Hd).
% 0.89/1.06 (* end of lemma zenon_L1_ *)
% 0.89/1.06 assert (zenon_L2_ : forall (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U), (apart_point_and_line (intersection_point zenon_TX_t zenon_TY_s) zenon_TY_s) -> (convergent_lines zenon_TX_t zenon_TY_s) -> False).
% 0.89/1.06 do 2 intro. intros zenon_H10 zenon_H11.
% 0.89/1.06 generalize (con2 zenon_TX_t). zenon_intro zenon_H14.
% 0.89/1.06 generalize (zenon_H14 zenon_TY_s). zenon_intro zenon_H15.
% 0.89/1.06 generalize (apart1 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H16.
% 0.89/1.06 generalize (zenon_H15 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H17.
% 0.89/1.06 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 0.89/1.06 exact (zenon_H19 zenon_H11).
% 0.89/1.06 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ].
% 0.89/1.06 apply (zenon_notor_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.89/1.06 exact (zenon_H1c zenon_H10).
% 0.89/1.06 exact (zenon_H16 zenon_H1a).
% 0.89/1.06 (* end of lemma zenon_L2_ *)
% 0.89/1.06 apply NNPP. intro zenon_G.
% 0.89/1.06 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines X Y)->((apart_point_and_line (intersection_point X Y) Z)->((distinct_lines X Z)/\(distinct_lines Y Z))))))) zenon_G); [ zenon_intro zenon_H1e; idtac ].
% 0.89/1.06 elim zenon_H1e. zenon_intro zenon_TX_t. zenon_intro zenon_H1f.
% 0.89/1.06 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((convergent_lines zenon_TX_t Y)->((apart_point_and_line (intersection_point zenon_TX_t Y) Z)->((distinct_lines zenon_TX_t Z)/\(distinct_lines Y Z)))))) zenon_H1f); [ zenon_intro zenon_H20; idtac ].
% 0.89/1.06 elim zenon_H20. zenon_intro zenon_TY_s. zenon_intro zenon_H21.
% 0.89/1.06 apply (zenon_notallex_s (fun Z : zenon_U => ((convergent_lines zenon_TX_t zenon_TY_s)->((apart_point_and_line (intersection_point zenon_TX_t zenon_TY_s) Z)->((distinct_lines zenon_TX_t Z)/\(distinct_lines zenon_TY_s Z))))) zenon_H21); [ zenon_intro zenon_H22; idtac ].
% 0.89/1.06 elim zenon_H22. zenon_intro zenon_TZ_o. zenon_intro zenon_H23.
% 0.89/1.06 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H11. zenon_intro zenon_H24.
% 0.89/1.06 apply (zenon_notimply_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25.
% 0.89/1.06 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 0.89/1.06 generalize (ceq2 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H29.
% 0.89/1.06 generalize (zenon_H29 zenon_TZ_o). zenon_intro zenon_H2a.
% 0.89/1.06 generalize (apart5 zenon_TZ_o). zenon_intro zenon_H2b.
% 0.89/1.06 generalize (zenon_H2a zenon_TX_t). zenon_intro zenon_H2c.
% 0.89/1.06 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.89/1.06 exact (zenon_H2e zenon_H26).
% 0.89/1.06 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.89/1.06 generalize (zenon_H2b zenon_TX_t). zenon_intro zenon_H31.
% 0.89/1.06 generalize (zenon_H31 zenon_TZ_o). zenon_intro zenon_H32.
% 0.89/1.06 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.89/1.06 exact (zenon_H34 zenon_H30).
% 0.89/1.06 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_Hd | zenon_intro zenon_H35 ].
% 0.89/1.06 apply (zenon_L1_ zenon_TZ_o); trivial.
% 0.89/1.06 exact (zenon_H28 zenon_H35).
% 0.89/1.06 generalize (con2 zenon_TX_t). zenon_intro zenon_H14.
% 0.89/1.06 generalize (zenon_H14 zenon_TY_s). zenon_intro zenon_H15.
% 0.89/1.06 generalize (apart1 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H16.
% 0.89/1.06 generalize (zenon_H15 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H17.
% 0.89/1.06 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 0.89/1.06 exact (zenon_H19 zenon_H11).
% 0.89/1.06 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ].
% 0.89/1.06 apply (zenon_notor_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.89/1.06 exact (zenon_H1d zenon_H2f).
% 0.89/1.06 exact (zenon_H16 zenon_H1a).
% 0.89/1.06 generalize (ceq2 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H29.
% 0.89/1.06 generalize (zenon_H29 zenon_TZ_o). zenon_intro zenon_H2a.
% 0.89/1.06 generalize (zenon_H2a zenon_TY_s). zenon_intro zenon_H36.
% 0.89/1.06 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H2e | zenon_intro zenon_H37 ].
% 0.89/1.06 exact (zenon_H2e zenon_H26).
% 0.89/1.06 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H38 | zenon_intro zenon_H10 ].
% 0.89/1.06 generalize (apart5 zenon_TZ_o). zenon_intro zenon_H2b.
% 0.89/1.06 generalize (zenon_H2b zenon_TY_s). zenon_intro zenon_H39.
% 0.89/1.06 generalize (zenon_H39 zenon_TZ_o). zenon_intro zenon_H3a.
% 0.89/1.06 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 0.89/1.06 exact (zenon_H3c zenon_H38).
% 0.89/1.06 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_Hd | zenon_intro zenon_H3d ].
% 0.89/1.06 apply (zenon_L1_ zenon_TZ_o); trivial.
% 0.89/1.06 exact (zenon_H27 zenon_H3d).
% 0.89/1.06 apply (zenon_L2_ zenon_TY_s zenon_TX_t); trivial.
% 0.89/1.06 Qed.
% 0.89/1.06 % SZS output end Proof
% 0.89/1.06 (* END-PROOF *)
% 0.89/1.06 nodes searched: 76102
% 0.89/1.06 max branch formulas: 3644
% 0.89/1.06 proof nodes created: 1200
% 0.89/1.06 formulas created: 89240
% 0.89/1.06
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