TSTP Solution File: GEO112+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n026.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 06:59:59 EDT 2022
% Result : Theorem 0.42s 0.59s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n026.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 17 23:43:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/0.59 (* PROOF-FOUND *)
% 0.42/0.59 % SZS status Theorem
% 0.42/0.59 (* BEGIN-PROOF *)
% 0.42/0.59 % SZS output start Proof
% 0.42/0.59 Theorem theorem_3_8_2 : (forall C : zenon_U, (forall P : zenon_U, (forall Q : zenon_U, (forall R : zenon_U, ((between_c C P Q R)->(between_c C R Q P)))))).
% 0.42/0.59 Proof.
% 0.42/0.59 apply NNPP. intro zenon_G.
% 0.42/0.59 apply (zenon_notallex_s (fun C : zenon_U => (forall P : zenon_U, (forall Q : zenon_U, (forall R : zenon_U, ((between_c C P Q R)->(between_c C R Q P)))))) zenon_G); [ zenon_intro zenon_H12; idtac ].
% 0.42/0.59 elim zenon_H12. zenon_intro zenon_TC_t. zenon_intro zenon_H14.
% 0.42/0.59 apply (zenon_notallex_s (fun P : zenon_U => (forall Q : zenon_U, (forall R : zenon_U, ((between_c zenon_TC_t P Q R)->(between_c zenon_TC_t R Q P))))) zenon_H14); [ zenon_intro zenon_H15; idtac ].
% 0.42/0.59 elim zenon_H15. zenon_intro zenon_TP_w. zenon_intro zenon_H17.
% 0.42/0.59 apply (zenon_notallex_s (fun Q : zenon_U => (forall R : zenon_U, ((between_c zenon_TC_t zenon_TP_w Q R)->(between_c zenon_TC_t R Q zenon_TP_w)))) zenon_H17); [ zenon_intro zenon_H18; idtac ].
% 0.42/0.59 elim zenon_H18. zenon_intro zenon_TQ_z. zenon_intro zenon_H1a.
% 0.42/0.59 apply (zenon_notallex_s (fun R : zenon_U => ((between_c zenon_TC_t zenon_TP_w zenon_TQ_z R)->(between_c zenon_TC_t R zenon_TQ_z zenon_TP_w))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ].
% 0.42/0.59 elim zenon_H1b. zenon_intro zenon_TR_bc. zenon_intro zenon_H1d.
% 0.42/0.59 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 0.42/0.59 generalize (between_c_defn zenon_TC_t). zenon_intro zenon_H20.
% 0.42/0.59 generalize (zenon_H20 zenon_TP_w). zenon_intro zenon_H21.
% 0.42/0.59 generalize (zenon_H21 zenon_TQ_z). zenon_intro zenon_H22.
% 0.42/0.59 generalize (zenon_H22 zenon_TR_bc). zenon_intro zenon_H23.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H26; zenon_intro zenon_H25 | zenon_intro zenon_H1f; zenon_intro zenon_H24 ].
% 0.42/0.59 exact (zenon_H26 zenon_H1f).
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H28. zenon_intro zenon_H27.
% 0.42/0.59 elim zenon_H27. zenon_intro zenon_TCpp_bp. zenon_intro zenon_H2a.
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2c. zenon_intro zenon_H2b.
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H30. zenon_intro zenon_H2f.
% 0.42/0.59 generalize (part_of_defn zenon_TC_t). zenon_intro zenon_H31.
% 0.42/0.59 generalize (zenon_H31 zenon_TCpp_bp). zenon_intro zenon_H32.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H35; zenon_intro zenon_H34 | zenon_intro zenon_H2c; zenon_intro zenon_H33 ].
% 0.42/0.59 exact (zenon_H35 zenon_H2c).
% 0.42/0.59 generalize (end_point_defn zenon_TP_w). zenon_intro zenon_H36.
% 0.42/0.59 generalize (zenon_H36 zenon_TCpp_bp). zenon_intro zenon_H37.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3a; zenon_intro zenon_H39 | zenon_intro zenon_H2e; zenon_intro zenon_H38 ].
% 0.42/0.59 exact (zenon_H3a zenon_H2e).
% 0.42/0.59 generalize (end_point_defn zenon_TR_bc). zenon_intro zenon_H3b.
% 0.42/0.59 generalize (zenon_H3b zenon_TCpp_bp). zenon_intro zenon_H3c.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3f; zenon_intro zenon_H3e | zenon_intro zenon_H30; zenon_intro zenon_H3d ].
% 0.42/0.59 exact (zenon_H3f zenon_H30).
% 0.42/0.59 generalize (inner_point_defn zenon_TQ_z). zenon_intro zenon_H40.
% 0.42/0.59 generalize (zenon_H40 zenon_TCpp_bp). zenon_intro zenon_H41.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H2f; zenon_intro zenon_H42 ].
% 0.42/0.59 exact (zenon_H44 zenon_H2f).
% 0.42/0.59 generalize (between_c_defn zenon_TC_t). zenon_intro zenon_H20.
% 0.42/0.59 generalize (zenon_H20 zenon_TR_bc). zenon_intro zenon_H45.
% 0.42/0.59 generalize (zenon_H45 zenon_TQ_z). zenon_intro zenon_H46.
% 0.42/0.59 generalize (zenon_H46 zenon_TP_w). zenon_intro zenon_H47.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H47); [ zenon_intro zenon_H1e; zenon_intro zenon_H4a | zenon_intro zenon_H49; zenon_intro zenon_H48 ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 0.42/0.59 apply zenon_H4c. zenon_intro zenon_H4d.
% 0.42/0.59 apply zenon_H28. apply sym_equal. exact zenon_H4d.
% 0.42/0.59 apply zenon_H4b. exists zenon_TCpp_bp. apply NNPP. zenon_intro zenon_H4e.
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H35 | zenon_intro zenon_H4f ].
% 0.42/0.59 generalize (part_of_defn zenon_TC_t). zenon_intro zenon_H31.
% 0.42/0.59 generalize (zenon_H31 zenon_TCpp_bp). zenon_intro zenon_H32.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H35; zenon_intro zenon_H34 | zenon_intro zenon_H2c; zenon_intro zenon_H33 ].
% 0.42/0.59 exact (zenon_H34 zenon_H33).
% 0.42/0.59 exact (zenon_H35 zenon_H2c).
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H3f | zenon_intro zenon_H50 ].
% 0.42/0.59 generalize (end_point_defn zenon_TR_bc). zenon_intro zenon_H3b.
% 0.42/0.59 generalize (zenon_H3b zenon_TCpp_bp). zenon_intro zenon_H3c.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3f; zenon_intro zenon_H3e | zenon_intro zenon_H30; zenon_intro zenon_H3d ].
% 0.42/0.59 exact (zenon_H3e zenon_H3d).
% 0.42/0.59 exact (zenon_H3f zenon_H30).
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H3a | zenon_intro zenon_H44 ].
% 0.42/0.59 generalize (end_point_defn zenon_TP_w). zenon_intro zenon_H36.
% 0.42/0.59 generalize (zenon_H36 zenon_TCpp_bp). zenon_intro zenon_H37.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3a; zenon_intro zenon_H39 | zenon_intro zenon_H2e; zenon_intro zenon_H38 ].
% 0.42/0.59 exact (zenon_H39 zenon_H38).
% 0.42/0.59 exact (zenon_H3a zenon_H2e).
% 0.42/0.59 generalize (inner_point_defn zenon_TQ_z). zenon_intro zenon_H40.
% 0.42/0.59 generalize (zenon_H40 zenon_TCpp_bp). zenon_intro zenon_H41.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H2f; zenon_intro zenon_H42 ].
% 0.42/0.59 exact (zenon_H43 zenon_H42).
% 0.42/0.59 exact (zenon_H44 zenon_H2f).
% 0.42/0.59 exact (zenon_H1e zenon_H49).
% 0.42/0.59 Qed.
% 0.42/0.59 % SZS output end Proof
% 0.42/0.59 (* END-PROOF *)
% 0.42/0.59 nodes searched: 2740
% 0.42/0.59 max branch formulas: 1491
% 0.42/0.59 proof nodes created: 117
% 0.42/0.59 formulas created: 23110
% 0.42/0.59
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