TSTP Solution File: GEO206+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n008.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 07:00:49 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 02:13:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.53 (* PROOF-FOUND *)
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 (* BEGIN-PROOF *)
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((~(apart_point_and_line X Y))/\(~(convergent_lines Y Z)))->(~(distinct_lines Y (parallel_through_point Z X))))))).
% 0.20/0.53 Proof.
% 0.20/0.53 apply NNPP. intro zenon_G.
% 0.20/0.53 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((~(apart_point_and_line X Y))/\(~(convergent_lines Y Z)))->(~(distinct_lines Y (parallel_through_point Z X))))))) zenon_G); [ zenon_intro zenon_H12; idtac ].
% 0.20/0.53 elim zenon_H12. zenon_intro zenon_TX_t. zenon_intro zenon_H14.
% 0.20/0.53 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((~(apart_point_and_line zenon_TX_t Y))/\(~(convergent_lines Y Z)))->(~(distinct_lines Y (parallel_through_point Z zenon_TX_t)))))) zenon_H14); [ zenon_intro zenon_H15; idtac ].
% 0.20/0.53 elim zenon_H15. zenon_intro zenon_TY_w. zenon_intro zenon_H17.
% 0.20/0.53 apply (zenon_notallex_s (fun Z : zenon_U => (((~(apart_point_and_line zenon_TX_t zenon_TY_w))/\(~(convergent_lines zenon_TY_w Z)))->(~(distinct_lines zenon_TY_w (parallel_through_point Z zenon_TX_t))))) zenon_H17); [ zenon_intro zenon_H18; idtac ].
% 0.20/0.53 elim zenon_H18. zenon_intro zenon_TZ_z. zenon_intro zenon_H1a.
% 0.20/0.53 apply (zenon_notimply_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b.
% 0.20/0.53 apply zenon_H1b. zenon_intro zenon_H1d.
% 0.20/0.53 apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 0.20/0.53 generalize (cup1 zenon_TX_t). zenon_intro zenon_H20.
% 0.20/0.53 generalize (apart5 zenon_TY_w). zenon_intro zenon_H21.
% 0.20/0.53 generalize (zenon_H21 (parallel_through_point zenon_TZ_z zenon_TX_t)). zenon_intro zenon_H22.
% 0.20/0.53 generalize (cp2 zenon_TX_t). zenon_intro zenon_H23.
% 0.20/0.53 generalize (zenon_H23 zenon_TZ_z). zenon_intro zenon_H24.
% 0.20/0.53 generalize (zenon_H20 (parallel_through_point zenon_TZ_z zenon_TX_t)). zenon_intro zenon_H25.
% 0.20/0.53 generalize (apart2 zenon_TY_w). zenon_intro zenon_H26.
% 0.20/0.53 generalize (zenon_H22 zenon_TY_w). zenon_intro zenon_H27.
% 0.20/0.53 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.20/0.53 exact (zenon_H29 zenon_H1d).
% 0.20/0.53 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.20/0.53 exact (zenon_H26 zenon_H2b).
% 0.20/0.53 generalize (zenon_H25 zenon_TY_w). zenon_intro zenon_H2c.
% 0.20/0.53 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.20/0.53 exact (zenon_H2e zenon_H2a).
% 0.20/0.53 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.20/0.53 exact (zenon_H24 zenon_H30).
% 0.20/0.53 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 0.20/0.53 exact (zenon_H1f zenon_H32).
% 0.20/0.53 generalize (cp1 zenon_TX_t). zenon_intro zenon_H33.
% 0.20/0.53 generalize (zenon_H33 zenon_TZ_z). zenon_intro zenon_H34.
% 0.20/0.53 generalize (ax6 (parallel_through_point zenon_TZ_z zenon_TX_t)). zenon_intro zenon_H35.
% 0.20/0.53 generalize (zenon_H35 zenon_TY_w). zenon_intro zenon_H36.
% 0.20/0.53 generalize (zenon_H36 zenon_TZ_z). zenon_intro zenon_H37.
% 0.20/0.53 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ].
% 0.20/0.53 exact (zenon_H39 zenon_H31).
% 0.20/0.53 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 0.20/0.53 exact (zenon_H34 zenon_H3b).
% 0.20/0.53 exact (zenon_H1e zenon_H3a).
% 0.20/0.53 Qed.
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53 (* END-PROOF *)
% 0.20/0.53 nodes searched: 691
% 0.20/0.53 max branch formulas: 430
% 0.20/0.53 proof nodes created: 89
% 0.20/0.53 formulas created: 3186
% 0.20/0.53
%------------------------------------------------------------------------------