TSTP Solution File: GEO179+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO179+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n029.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 07:00:26 EDT 2022
% Result : Theorem 0.41s 0.61s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEO179+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n029.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 15:42:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.41/0.61 (* PROOF-FOUND *)
% 0.41/0.61 % SZS status Theorem
% 0.41/0.61 (* BEGIN-PROOF *)
% 0.41/0.61 % SZS output start Proof
% 0.41/0.61 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\(apart_point_and_line Z (line_connecting X Y)))->((distinct_lines (line_connecting X Y) (line_connecting Z X))/\(distinct_lines (line_connecting X Y) (line_connecting Z Y))))))).
% 0.41/0.61 Proof.
% 0.41/0.61 apply NNPP. intro zenon_G.
% 0.41/0.61 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\(apart_point_and_line Z (line_connecting X Y)))->((distinct_lines (line_connecting X Y) (line_connecting Z X))/\(distinct_lines (line_connecting X Y) (line_connecting Z Y))))))) zenon_G); [ zenon_intro zenon_Hf; idtac ].
% 0.41/0.61 elim zenon_Hf. zenon_intro zenon_TX_q. zenon_intro zenon_H11.
% 0.41/0.61 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_q Y)/\(apart_point_and_line Z (line_connecting zenon_TX_q Y)))->((distinct_lines (line_connecting zenon_TX_q Y) (line_connecting Z zenon_TX_q))/\(distinct_lines (line_connecting zenon_TX_q Y) (line_connecting Z Y)))))) zenon_H11); [ zenon_intro zenon_H12; idtac ].
% 0.41/0.61 elim zenon_H12. zenon_intro zenon_TY_t. zenon_intro zenon_H14.
% 0.41/0.61 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_q zenon_TY_t)/\(apart_point_and_line Z (line_connecting zenon_TX_q zenon_TY_t)))->((distinct_lines (line_connecting zenon_TX_q zenon_TY_t) (line_connecting Z zenon_TX_q))/\(distinct_lines (line_connecting zenon_TX_q zenon_TY_t) (line_connecting Z zenon_TY_t))))) zenon_H14); [ zenon_intro zenon_H15; idtac ].
% 0.41/0.61 elim zenon_H15. zenon_intro zenon_TZ_w. zenon_intro zenon_H17.
% 0.41/0.61 apply (zenon_notimply_s _ _ zenon_H17). zenon_intro zenon_H19. zenon_intro zenon_H18.
% 0.41/0.61 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a.
% 0.41/0.61 apply (zenon_notand_s _ _ zenon_H18); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ].
% 0.41/0.61 generalize (ci1 zenon_TX_q). zenon_intro zenon_H1e.
% 0.41/0.61 generalize (ceq2 zenon_TZ_w). zenon_intro zenon_H1f.
% 0.41/0.61 generalize (zenon_H1e zenon_TY_t). zenon_intro zenon_H20.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ].
% 0.41/0.61 exact (zenon_H22 zenon_H1b).
% 0.41/0.61 generalize (apart1 zenon_TX_q). zenon_intro zenon_H23.
% 0.41/0.61 generalize (zenon_H1f (line_connecting zenon_TX_q zenon_TY_t)). zenon_intro zenon_H24.
% 0.41/0.61 generalize (apart4 zenon_TZ_w). zenon_intro zenon_H25.
% 0.41/0.61 generalize (zenon_H25 zenon_TX_q). zenon_intro zenon_H26.
% 0.41/0.61 generalize (zenon_H26 zenon_TX_q). zenon_intro zenon_H27.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.41/0.61 generalize (ceq1 zenon_TZ_w). zenon_intro zenon_H2a.
% 0.41/0.61 generalize (zenon_H2a (line_connecting zenon_TX_q zenon_TY_t)). zenon_intro zenon_H2b.
% 0.41/0.61 generalize (zenon_H2b zenon_TX_q). zenon_intro zenon_H2c.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.41/0.61 exact (zenon_H2e zenon_H1a).
% 0.41/0.61 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.41/0.61 exact (zenon_H29 zenon_H30).
% 0.41/0.61 exact (zenon_H21 zenon_H2f).
% 0.41/0.61 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H30 | zenon_intro zenon_H31 ].
% 0.41/0.61 generalize (ci1 zenon_TZ_w). zenon_intro zenon_H32.
% 0.41/0.61 generalize (zenon_H32 zenon_TX_q). zenon_intro zenon_H33.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H29 | zenon_intro zenon_H34 ].
% 0.41/0.61 exact (zenon_H29 zenon_H30).
% 0.41/0.61 generalize (zenon_H24 (line_connecting zenon_TZ_w zenon_TX_q)). zenon_intro zenon_H35.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H2e | zenon_intro zenon_H36 ].
% 0.41/0.61 exact (zenon_H2e zenon_H1a).
% 0.41/0.61 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ].
% 0.41/0.61 exact (zenon_H1d zenon_H38).
% 0.41/0.61 exact (zenon_H34 zenon_H37).
% 0.41/0.61 exact (zenon_H23 zenon_H31).
% 0.41/0.61 generalize (apart1 zenon_TY_t). zenon_intro zenon_H39.
% 0.41/0.61 generalize (ceq2 zenon_TZ_w). zenon_intro zenon_H1f.
% 0.41/0.61 generalize (ci2 zenon_TX_q). zenon_intro zenon_H3a.
% 0.41/0.61 generalize (zenon_H3a zenon_TY_t). zenon_intro zenon_H3b.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H22 | zenon_intro zenon_H3c ].
% 0.41/0.61 exact (zenon_H22 zenon_H1b).
% 0.41/0.61 generalize (zenon_H1f (line_connecting zenon_TX_q zenon_TY_t)). zenon_intro zenon_H24.
% 0.41/0.61 generalize (apart4 zenon_TZ_w). zenon_intro zenon_H25.
% 0.41/0.61 generalize (zenon_H25 zenon_TY_t). zenon_intro zenon_H3d.
% 0.41/0.61 generalize (zenon_H3d zenon_TY_t). zenon_intro zenon_H3e.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ].
% 0.41/0.61 generalize (ceq1 zenon_TZ_w). zenon_intro zenon_H2a.
% 0.41/0.61 generalize (zenon_H2a (line_connecting zenon_TX_q zenon_TY_t)). zenon_intro zenon_H2b.
% 0.41/0.61 generalize (zenon_H2b zenon_TY_t). zenon_intro zenon_H41.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H2e | zenon_intro zenon_H42 ].
% 0.41/0.61 exact (zenon_H2e zenon_H1a).
% 0.41/0.61 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.41/0.61 exact (zenon_H40 zenon_H44).
% 0.41/0.61 exact (zenon_H3c zenon_H43).
% 0.41/0.61 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ].
% 0.41/0.61 generalize (ci1 zenon_TZ_w). zenon_intro zenon_H32.
% 0.41/0.61 generalize (zenon_H32 zenon_TY_t). zenon_intro zenon_H46.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H40 | zenon_intro zenon_H47 ].
% 0.41/0.61 exact (zenon_H40 zenon_H44).
% 0.41/0.61 generalize (zenon_H24 (line_connecting zenon_TZ_w zenon_TY_t)). zenon_intro zenon_H48.
% 0.41/0.61 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H2e | zenon_intro zenon_H49 ].
% 0.41/0.61 exact (zenon_H2e zenon_H1a).
% 0.41/0.61 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 0.41/0.61 exact (zenon_H1c zenon_H4b).
% 0.41/0.61 exact (zenon_H47 zenon_H4a).
% 0.41/0.61 exact (zenon_H39 zenon_H45).
% 0.41/0.61 Qed.
% 0.41/0.61 % SZS output end Proof
% 0.41/0.61 (* END-PROOF *)
% 0.41/0.61 nodes searched: 6896
% 0.41/0.61 max branch formulas: 1209
% 0.41/0.61 proof nodes created: 471
% 0.41/0.61 formulas created: 17826
% 0.41/0.61
%------------------------------------------------------------------------------