TSTP Solution File: GEO176+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO176+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n019.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 07:00:24 EDT 2022
% Result : Theorem 1.60s 1.77s
% Output : Proof 1.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO176+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n019.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 : Sat Jun 18 11:02:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.60/1.77 (* PROOF-FOUND *)
% 1.60/1.77 % SZS status Theorem
% 1.60/1.77 (* BEGIN-PROOF *)
% 1.60/1.77 % SZS output start Proof
% 1.60/1.77 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\((apart_point_and_line X U)\/(apart_point_and_line X V))))->(distinct_points X (intersection_point U V))))))).
% 1.60/1.77 Proof.
% 1.60/1.77 assert (zenon_L1_ : forall (zenon_TV_s : zenon_U) (zenon_TU_t : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TU_t Y)->(~(apart_point_and_line (intersection_point zenon_TU_t Y) zenon_TU_t)))) -> (convergent_lines zenon_TU_t zenon_TV_s) -> (apart_point_and_line (intersection_point zenon_TU_t zenon_TV_s) zenon_TU_t) -> False).
% 1.60/1.77 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11.
% 1.60/1.77 generalize (zenon_Hf zenon_TV_s). zenon_intro zenon_H14.
% 1.60/1.77 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ].
% 1.60/1.77 exact (zenon_H16 zenon_H10).
% 1.60/1.77 exact (zenon_H15 zenon_H11).
% 1.60/1.77 (* end of lemma zenon_L1_ *)
% 1.60/1.77 assert (zenon_L2_ : forall (zenon_TV_s : zenon_U) (zenon_TU_t : zenon_U) (zenon_TX_bb : zenon_U), (forall Z : zenon_U, ((apart_point_and_line zenon_TX_bb zenon_TU_t)->((distinct_points zenon_TX_bb Z)\/(apart_point_and_line Z zenon_TU_t)))) -> (apart_point_and_line zenon_TX_bb zenon_TU_t) -> (~(distinct_points zenon_TX_bb (intersection_point zenon_TU_t zenon_TV_s))) -> (~(distinct_lines zenon_TU_t zenon_TU_t)) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_t Y)->(~(apart_point_and_line (intersection_point zenon_TU_t Y) zenon_TU_t)))) -> (convergent_lines zenon_TU_t zenon_TV_s) -> False).
% 1.60/1.77 do 3 intro. intros zenon_H17 zenon_H18 zenon_H19 zenon_H1a zenon_Hf zenon_H10.
% 1.60/1.77 generalize (ceq2 (intersection_point zenon_TU_t zenon_TV_s)). zenon_intro zenon_H1c.
% 1.60/1.77 generalize (zenon_H1c zenon_TU_t). zenon_intro zenon_H1d.
% 1.60/1.77 generalize (zenon_H1d zenon_TU_t). zenon_intro zenon_H1e.
% 1.60/1.77 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H15 | zenon_intro zenon_H1f ].
% 1.60/1.77 generalize (zenon_H17 (intersection_point zenon_TU_t zenon_TV_s)). zenon_intro zenon_H20.
% 1.60/1.77 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ].
% 1.60/1.77 exact (zenon_H22 zenon_H18).
% 1.60/1.77 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H11 ].
% 1.60/1.77 exact (zenon_H19 zenon_H23).
% 1.60/1.77 exact (zenon_H15 zenon_H11).
% 1.60/1.77 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H11 ].
% 1.60/1.77 exact (zenon_H1a zenon_H24).
% 1.60/1.77 apply (zenon_L1_ zenon_TV_s zenon_TU_t); trivial.
% 1.60/1.77 (* end of lemma zenon_L2_ *)
% 1.60/1.77 assert (zenon_L3_ : forall (zenon_TV_s : zenon_U) (zenon_TU_t : zenon_U), (apart_point_and_line (intersection_point zenon_TU_t zenon_TV_s) zenon_TV_s) -> (convergent_lines zenon_TU_t zenon_TV_s) -> False).
% 1.60/1.77 do 2 intro. intros zenon_H25 zenon_H10.
% 1.60/1.77 generalize (ci4 zenon_TU_t). zenon_intro zenon_H26.
% 1.60/1.77 generalize (zenon_H26 zenon_TV_s). zenon_intro zenon_H27.
% 1.60/1.77 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H16 | zenon_intro zenon_H28 ].
% 1.60/1.77 exact (zenon_H16 zenon_H10).
% 1.60/1.77 exact (zenon_H28 zenon_H25).
% 1.60/1.77 (* end of lemma zenon_L3_ *)
% 1.60/1.77 apply NNPP. intro zenon_G.
% 1.60/1.77 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\((apart_point_and_line X U)\/(apart_point_and_line X V))))->(distinct_points X (intersection_point U V))))))) zenon_G); [ zenon_intro zenon_H29; idtac ].
% 1.60/1.77 elim zenon_H29. zenon_intro zenon_TX_bb. zenon_intro zenon_H2a.
% 1.60/1.77 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bb Y)/\((convergent_lines U V)/\((apart_point_and_line zenon_TX_bb U)\/(apart_point_and_line zenon_TX_bb V))))->(distinct_points zenon_TX_bb (intersection_point U V)))))) zenon_H2a); [ zenon_intro zenon_H2b; idtac ].
% 1.60/1.77 elim zenon_H2b. zenon_intro zenon_TY_bs. zenon_intro zenon_H2d.
% 1.60/1.77 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bb zenon_TY_bs)/\((convergent_lines U V)/\((apart_point_and_line zenon_TX_bb U)\/(apart_point_and_line zenon_TX_bb V))))->(distinct_points zenon_TX_bb (intersection_point U V))))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ].
% 1.60/1.77 elim zenon_H2e. zenon_intro zenon_TU_t. zenon_intro zenon_H2f.
% 1.60/1.77 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bb zenon_TY_bs)/\((convergent_lines zenon_TU_t V)/\((apart_point_and_line zenon_TX_bb zenon_TU_t)\/(apart_point_and_line zenon_TX_bb V))))->(distinct_points zenon_TX_bb (intersection_point zenon_TU_t V)))) zenon_H2f); [ zenon_intro zenon_H30; idtac ].
% 1.60/1.77 elim zenon_H30. zenon_intro zenon_TV_s. zenon_intro zenon_H31.
% 1.60/1.77 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H32. zenon_intro zenon_H19.
% 1.60/1.77 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 1.60/1.77 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H10. zenon_intro zenon_H35.
% 1.60/1.77 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H18 | zenon_intro zenon_H36 ].
% 1.60/1.77 generalize (ci3 zenon_TU_t). zenon_intro zenon_Hf.
% 1.60/1.77 generalize (apart2 zenon_TU_t). zenon_intro zenon_H1a.
% 1.60/1.77 generalize (ceq1 zenon_TX_bb). zenon_intro zenon_H37.
% 1.60/1.77 generalize (zenon_H37 zenon_TU_t). zenon_intro zenon_H17.
% 1.60/1.77 apply (zenon_L2_ zenon_TV_s zenon_TU_t zenon_TX_bb); trivial.
% 1.60/1.77 generalize (ceq1 zenon_TX_bb). zenon_intro zenon_H37.
% 1.60/1.77 generalize (zenon_H37 zenon_TV_s). zenon_intro zenon_H38.
% 1.60/1.77 generalize (apart2 zenon_TV_s). zenon_intro zenon_H39.
% 1.60/1.77 generalize (ceq2 (intersection_point zenon_TU_t zenon_TV_s)). zenon_intro zenon_H1c.
% 1.60/1.77 generalize (zenon_H1c zenon_TV_s). zenon_intro zenon_H3a.
% 1.60/1.77 generalize (zenon_H3a zenon_TV_s). zenon_intro zenon_H3b.
% 1.60/1.77 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H28 | zenon_intro zenon_H3c ].
% 1.60/1.77 generalize (zenon_H38 (intersection_point zenon_TU_t zenon_TV_s)). zenon_intro zenon_H3d.
% 1.60/1.77 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ].
% 1.60/1.77 exact (zenon_H3f zenon_H36).
% 1.60/1.77 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H23 | zenon_intro zenon_H25 ].
% 1.60/1.77 exact (zenon_H19 zenon_H23).
% 1.60/1.77 exact (zenon_H28 zenon_H25).
% 1.60/1.77 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H40 | zenon_intro zenon_H25 ].
% 1.60/1.77 exact (zenon_H39 zenon_H40).
% 1.60/1.77 apply (zenon_L3_ zenon_TV_s zenon_TU_t); trivial.
% 1.60/1.77 Qed.
% 1.60/1.77 % SZS output end Proof
% 1.60/1.77 (* END-PROOF *)
% 1.60/1.77 nodes searched: 118289
% 1.60/1.77 max branch formulas: 5693
% 1.60/1.77 proof nodes created: 3013
% 1.60/1.77 formulas created: 253236
% 1.60/1.77
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