TSTP Solution File: GEO224+3 by Zenon---0.7.1
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% File : Zenon---0.7.1
% Problem : GEO224+3 : TPTP v8.1.0. Released v4.0.0.
% 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 07:01:04 EDT 2022
% Result : Theorem 8.10s 8.30s
% Output : Proof 8.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO224+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 15:28:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 8.10/8.30 (* PROOF-FOUND *)
% 8.10/8.30 % SZS status Theorem
% 8.10/8.30 (* BEGIN-PROOF *)
% 8.10/8.30 % SZS output start Proof
% 8.10/8.30 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (((point X)/\(line Y))->(exists Z : zenon_U, ((point Z)/\(incident_point_and_line Z Y)))))).
% 8.10/8.30 Proof.
% 8.10/8.30 assert (zenon_L1_ : forall (zenon_TY_bm : zenon_U) (zenon_TX_bn : zenon_U), (forall Y : zenon_U, (~(apart_point_and_line zenon_TX_bn (parallel_through_point Y zenon_TX_bn)))) -> (apart_point_and_line zenon_TX_bn (parallel_through_point zenon_TY_bm zenon_TX_bn)) -> False).
% 8.10/8.30 do 2 intro. intros zenon_H24 zenon_H25.
% 8.10/8.30 generalize (zenon_H24 zenon_TY_bm). zenon_intro zenon_H28.
% 8.10/8.30 exact (zenon_H28 zenon_H25).
% 8.10/8.30 (* end of lemma zenon_L1_ *)
% 8.10/8.30 apply NNPP. intro zenon_G.
% 8.10/8.30 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (((point X)/\(line Y))->(exists Z : zenon_U, ((point Z)/\(incident_point_and_line Z Y)))))) zenon_G); [ zenon_intro zenon_H29; idtac ].
% 8.10/8.30 elim zenon_H29. zenon_intro zenon_TX_bn. zenon_intro zenon_H2a.
% 8.10/8.30 apply (zenon_notallex_s (fun Y : zenon_U => (((point zenon_TX_bn)/\(line Y))->(exists Z : zenon_U, ((point Z)/\(incident_point_and_line Z Y))))) zenon_H2a); [ zenon_intro zenon_H2b; idtac ].
% 8.10/8.30 elim zenon_H2b. zenon_intro zenon_TY_bm. zenon_intro zenon_H2c.
% 8.10/8.30 apply (zenon_notimply_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 8.10/8.30 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f.
% 8.10/8.30 generalize (ceq2 zenon_TX_bn). zenon_intro zenon_H31.
% 8.10/8.30 generalize (zenon_H31 zenon_TY_bm). zenon_intro zenon_H32.
% 8.10/8.30 generalize (zenon_H32 zenon_TY_bm). zenon_intro zenon_H33.
% 8.10/8.30 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 8.10/8.30 apply zenon_H2d. exists zenon_TX_bn. apply NNPP. zenon_intro zenon_H36.
% 8.10/8.30 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ].
% 8.10/8.30 exact (zenon_H38 zenon_H30).
% 8.10/8.30 generalize (a4 zenon_TX_bn). zenon_intro zenon_H39.
% 8.10/8.30 generalize (zenon_H39 zenon_TY_bm). zenon_intro zenon_H3a.
% 8.10/8.30 apply (zenon_equiv_s _ _ zenon_H3a); [ zenon_intro zenon_H37; zenon_intro zenon_H3c | zenon_intro zenon_H3b; zenon_intro zenon_H35 ].
% 8.10/8.30 exact (zenon_H3c zenon_H35).
% 8.10/8.30 exact (zenon_H37 zenon_H3b).
% 8.10/8.30 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ].
% 8.10/8.30 generalize (apart2 zenon_TY_bm). zenon_intro zenon_H3f.
% 8.10/8.30 exact (zenon_H3f zenon_H3e).
% 8.10/8.30 generalize (apart2 zenon_TY_bm). zenon_intro zenon_H3f.
% 8.10/8.30 generalize (apart5 zenon_TY_bm). zenon_intro zenon_H40.
% 8.10/8.30 generalize (cp2 zenon_TX_bn). zenon_intro zenon_H24.
% 8.10/8.30 generalize (cp1 zenon_TX_bn). zenon_intro zenon_H41.
% 8.10/8.30 generalize (zenon_H41 zenon_TY_bm). zenon_intro zenon_H42.
% 8.10/8.30 generalize (p1 (parallel_through_point zenon_TY_bm zenon_TX_bn)). zenon_intro zenon_H43.
% 8.10/8.30 generalize (zenon_H43 zenon_TY_bm). zenon_intro zenon_H44.
% 8.10/8.30 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 8.10/8.30 generalize (zenon_H32 (parallel_through_point zenon_TY_bm zenon_TX_bn)). zenon_intro zenon_H47.
% 8.10/8.30 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H35 | zenon_intro zenon_H48 ].
% 8.10/8.30 exact (zenon_H35 zenon_H3d).
% 8.10/8.30 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H49 | zenon_intro zenon_H25 ].
% 8.10/8.30 generalize (zenon_H40 (parallel_through_point zenon_TY_bm zenon_TX_bn)). zenon_intro zenon_H4a.
% 8.10/8.30 generalize (zenon_H4a zenon_TY_bm). zenon_intro zenon_H4b.
% 8.10/8.30 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 8.10/8.30 exact (zenon_H4d zenon_H49).
% 8.10/8.30 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H3e | zenon_intro zenon_H4e ].
% 8.10/8.30 exact (zenon_H3f zenon_H3e).
% 8.10/8.30 exact (zenon_H46 zenon_H4e).
% 8.10/8.30 apply (zenon_L1_ zenon_TY_bm zenon_TX_bn); trivial.
% 8.10/8.30 exact (zenon_H42 zenon_H45).
% 8.10/8.30 Qed.
% 8.10/8.30 % SZS output end Proof
% 8.10/8.30 (* END-PROOF *)
% 8.10/8.30 nodes searched: 1307080
% 8.10/8.30 max branch formulas: 34432
% 8.10/8.30 proof nodes created: 10260
% 8.10/8.30 formulas created: 1675651
% 8.10/8.30
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