TSTP Solution File: SET775+4 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET775+4 : TPTP v8.1.0. Released v2.2.0.
% 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 : Tue Jul 19 06:38:29 EDT 2022
% Result : Theorem 0.62s 0.80s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET775+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 02:14:27 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.62/0.80 (* PROOF-FOUND *)
% 0.62/0.80 % SZS status Theorem
% 0.62/0.80 (* BEGIN-PROOF *)
% 0.62/0.80 % SZS output start Proof
% 0.62/0.80 Theorem thIII11 : (forall E : zenon_U, (forall P : zenon_U, (forall R : zenon_U, (((pre_order P E)/\(forall A : zenon_U, (forall B : zenon_U, (((member A E)/\(member B E))->((apply R A B)<->((apply P A B)/\(apply P B A)))))))->(equivalence R E))))).
% 0.62/0.80 Proof.
% 0.62/0.80 apply NNPP. intro zenon_G.
% 0.62/0.80 apply (zenon_notallex_s (fun E : zenon_U => (forall P : zenon_U, (forall R : zenon_U, (((pre_order P E)/\(forall A : zenon_U, (forall B : zenon_U, (((member A E)/\(member B E))->((apply R A B)<->((apply P A B)/\(apply P B A)))))))->(equivalence R E))))) zenon_G); [ zenon_intro zenon_H11; idtac ].
% 0.62/0.80 elim zenon_H11. zenon_intro zenon_TE_s. zenon_intro zenon_H13.
% 0.62/0.80 apply (zenon_notallex_s (fun P : zenon_U => (forall R : zenon_U, (((pre_order P zenon_TE_s)/\(forall A : zenon_U, (forall B : zenon_U, (((member A zenon_TE_s)/\(member B zenon_TE_s))->((apply R A B)<->((apply P A B)/\(apply P B A)))))))->(equivalence R zenon_TE_s)))) zenon_H13); [ zenon_intro zenon_H14; idtac ].
% 0.62/0.80 elim zenon_H14. zenon_intro zenon_TP_v. zenon_intro zenon_H16.
% 0.62/0.80 apply (zenon_notallex_s (fun R : zenon_U => (((pre_order zenon_TP_v zenon_TE_s)/\(forall A : zenon_U, (forall B : zenon_U, (((member A zenon_TE_s)/\(member B zenon_TE_s))->((apply R A B)<->((apply zenon_TP_v A B)/\(apply zenon_TP_v B A)))))))->(equivalence R zenon_TE_s))) zenon_H16); [ zenon_intro zenon_H17; idtac ].
% 0.62/0.80 elim zenon_H17. zenon_intro zenon_TR_y. zenon_intro zenon_H19.
% 0.62/0.80 apply (zenon_notimply_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a.
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.62/0.80 generalize (pre_order zenon_TP_v). zenon_intro zenon_H1e.
% 0.62/0.80 generalize (zenon_H1e zenon_TE_s). zenon_intro zenon_H1f.
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H1d; zenon_intro zenon_H20 ].
% 0.62/0.80 exact (zenon_H22 zenon_H1d).
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 0.62/0.80 generalize (equivalence zenon_TE_s). zenon_intro zenon_H25.
% 0.62/0.80 generalize (zenon_H25 zenon_TR_y). zenon_intro zenon_H26.
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H1a; zenon_intro zenon_H29 | zenon_intro zenon_H28; zenon_intro zenon_H27 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.62/0.80 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TE_s)->(apply zenon_TR_y X X))) zenon_H2b); [ zenon_intro zenon_H2c; idtac ].
% 0.62/0.80 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e.
% 0.62/0.80 apply (zenon_notimply_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f.
% 0.62/0.80 generalize (zenon_H1c zenon_TX_bt). zenon_intro zenon_H31.
% 0.62/0.80 generalize (zenon_H24 zenon_TX_bt). zenon_intro zenon_H32.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.62/0.80 exact (zenon_H34 zenon_H30).
% 0.62/0.80 generalize (zenon_H31 zenon_TX_bt). zenon_intro zenon_H35.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H34 | zenon_intro zenon_H34 ].
% 0.62/0.80 exact (zenon_H34 zenon_H30).
% 0.62/0.80 exact (zenon_H34 zenon_H30).
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H36); [ zenon_intro zenon_H2f; zenon_intro zenon_H3a | zenon_intro zenon_H39; zenon_intro zenon_H38 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3b | zenon_intro zenon_H3b ].
% 0.62/0.80 exact (zenon_H3b zenon_H33).
% 0.62/0.80 exact (zenon_H3b zenon_H33).
% 0.62/0.80 exact (zenon_H2f zenon_H39).
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 0.62/0.80 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (((member X zenon_TE_s)/\(member Y zenon_TE_s))->((apply zenon_TR_y X Y)->(apply zenon_TR_y Y X))))) zenon_H3d); [ zenon_intro zenon_H3e; idtac ].
% 0.62/0.80 elim zenon_H3e. zenon_intro zenon_TX_cl. zenon_intro zenon_H40.
% 0.62/0.80 apply (zenon_notallex_s (fun Y : zenon_U => (((member zenon_TX_cl zenon_TE_s)/\(member Y zenon_TE_s))->((apply zenon_TR_y zenon_TX_cl Y)->(apply zenon_TR_y Y zenon_TX_cl)))) zenon_H40); [ zenon_intro zenon_H41; idtac ].
% 0.62/0.80 elim zenon_H41. zenon_intro zenon_TY_co. zenon_intro zenon_H43.
% 0.62/0.80 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44.
% 0.62/0.80 apply (zenon_notimply_s _ _ zenon_H44). zenon_intro zenon_H47. zenon_intro zenon_H46.
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.62/0.80 generalize (zenon_H1c zenon_TY_co). zenon_intro zenon_H4a.
% 0.62/0.80 generalize (zenon_H4a zenon_TX_cl). zenon_intro zenon_H4b.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ].
% 0.62/0.80 exact (zenon_H4f zenon_H48).
% 0.62/0.80 exact (zenon_H4e zenon_H49).
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H46; zenon_intro zenon_H52 | zenon_intro zenon_H51; zenon_intro zenon_H50 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ].
% 0.62/0.80 generalize (zenon_H1c zenon_TX_cl). zenon_intro zenon_H55.
% 0.62/0.80 generalize (zenon_H55 zenon_TY_co). zenon_intro zenon_H56.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H58); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ].
% 0.62/0.80 exact (zenon_H4e zenon_H49).
% 0.62/0.80 exact (zenon_H4f zenon_H48).
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H57); [ zenon_intro zenon_H5b; zenon_intro zenon_H5a | zenon_intro zenon_H47; zenon_intro zenon_H59 ].
% 0.62/0.80 exact (zenon_H5b zenon_H47).
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 0.62/0.80 exact (zenon_H54 zenon_H5c).
% 0.62/0.80 generalize (zenon_H1c zenon_TX_cl). zenon_intro zenon_H55.
% 0.62/0.80 generalize (zenon_H55 zenon_TY_co). zenon_intro zenon_H56.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H58); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ].
% 0.62/0.80 exact (zenon_H4e zenon_H49).
% 0.62/0.80 exact (zenon_H4f zenon_H48).
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H57); [ zenon_intro zenon_H5b; zenon_intro zenon_H5a | zenon_intro zenon_H47; zenon_intro zenon_H59 ].
% 0.62/0.80 exact (zenon_H5b zenon_H47).
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 0.62/0.80 exact (zenon_H53 zenon_H5d).
% 0.62/0.80 exact (zenon_H46 zenon_H51).
% 0.62/0.80 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((member X zenon_TE_s)/\((member Y zenon_TE_s)/\(member Z zenon_TE_s)))->(((apply zenon_TR_y X Y)/\(apply zenon_TR_y Y Z))->(apply zenon_TR_y X Z)))))) zenon_H3c); [ zenon_intro zenon_H5e; idtac ].
% 0.62/0.80 elim zenon_H5e. zenon_intro zenon_TX_dr. zenon_intro zenon_H60.
% 0.62/0.80 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((member zenon_TX_dr zenon_TE_s)/\((member Y zenon_TE_s)/\(member Z zenon_TE_s)))->(((apply zenon_TR_y zenon_TX_dr Y)/\(apply zenon_TR_y Y Z))->(apply zenon_TR_y zenon_TX_dr Z))))) zenon_H60); [ zenon_intro zenon_H61; idtac ].
% 0.62/0.80 elim zenon_H61. zenon_intro zenon_TY_du. zenon_intro zenon_H63.
% 0.62/0.80 apply (zenon_notallex_s (fun Z : zenon_U => (((member zenon_TX_dr zenon_TE_s)/\((member zenon_TY_du zenon_TE_s)/\(member Z zenon_TE_s)))->(((apply zenon_TR_y zenon_TX_dr zenon_TY_du)/\(apply zenon_TR_y zenon_TY_du Z))->(apply zenon_TR_y zenon_TX_dr Z)))) zenon_H63); [ zenon_intro zenon_H64; idtac ].
% 0.62/0.80 elim zenon_H64. zenon_intro zenon_TZ_dx. zenon_intro zenon_H66.
% 0.62/0.80 apply (zenon_notimply_s _ _ zenon_H66). zenon_intro zenon_H68. zenon_intro zenon_H67.
% 0.62/0.80 apply (zenon_notimply_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69.
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6c. zenon_intro zenon_H6b.
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 0.62/0.80 generalize (zenon_H1c zenon_TX_dr). zenon_intro zenon_H71.
% 0.62/0.80 generalize (zenon_H71 zenon_TZ_dx). zenon_intro zenon_H72.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H74 | zenon_intro zenon_H73 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H74); [ zenon_intro zenon_H76 | zenon_intro zenon_H75 ].
% 0.62/0.80 exact (zenon_H76 zenon_H6e).
% 0.62/0.80 exact (zenon_H75 zenon_H6f).
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H73); [ zenon_intro zenon_H69; zenon_intro zenon_H79 | zenon_intro zenon_H78; zenon_intro zenon_H77 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H79); [ zenon_intro zenon_H7b | zenon_intro zenon_H7a ].
% 0.62/0.80 generalize (zenon_H23 zenon_TX_dr). zenon_intro zenon_H7c.
% 0.62/0.80 generalize (zenon_H7c zenon_TY_du). zenon_intro zenon_H7d.
% 0.62/0.80 generalize (zenon_H7d zenon_TZ_dx). zenon_intro zenon_H7e.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H7e); [ zenon_intro zenon_H80 | zenon_intro zenon_H7f ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H80); [ zenon_intro zenon_H76 | zenon_intro zenon_H81 ].
% 0.62/0.80 exact (zenon_H76 zenon_H6e).
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H82 | zenon_intro zenon_H75 ].
% 0.62/0.80 exact (zenon_H82 zenon_H70).
% 0.62/0.80 exact (zenon_H75 zenon_H6f).
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H84); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ].
% 0.62/0.80 generalize (zenon_H71 zenon_TY_du). zenon_intro zenon_H87.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H89 | zenon_intro zenon_H88 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H89); [ zenon_intro zenon_H76 | zenon_intro zenon_H82 ].
% 0.62/0.80 exact (zenon_H76 zenon_H6e).
% 0.62/0.80 exact (zenon_H82 zenon_H70).
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H88); [ zenon_intro zenon_H8c; zenon_intro zenon_H8b | zenon_intro zenon_H6c; zenon_intro zenon_H8a ].
% 0.62/0.80 exact (zenon_H8c zenon_H6c).
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 0.62/0.80 exact (zenon_H86 zenon_H8e).
% 0.62/0.80 generalize (zenon_H1c zenon_TY_du). zenon_intro zenon_H8f.
% 0.62/0.80 generalize (zenon_H8f zenon_TZ_dx). zenon_intro zenon_H90.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H81 | zenon_intro zenon_H91 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H82 | zenon_intro zenon_H75 ].
% 0.62/0.80 exact (zenon_H82 zenon_H70).
% 0.62/0.80 exact (zenon_H75 zenon_H6f).
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H91); [ zenon_intro zenon_H94; zenon_intro zenon_H93 | zenon_intro zenon_H6b; zenon_intro zenon_H92 ].
% 0.62/0.80 exact (zenon_H94 zenon_H6b).
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H96. zenon_intro zenon_H95.
% 0.62/0.80 exact (zenon_H85 zenon_H96).
% 0.62/0.80 exact (zenon_H7b zenon_H83).
% 0.62/0.80 generalize (zenon_H23 zenon_TZ_dx). zenon_intro zenon_H97.
% 0.62/0.80 generalize (zenon_H97 zenon_TY_du). zenon_intro zenon_H98.
% 0.62/0.80 generalize (zenon_H98 zenon_TX_dr). zenon_intro zenon_H99.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H9b | zenon_intro zenon_H9a ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H9b); [ zenon_intro zenon_H75 | zenon_intro zenon_H9c ].
% 0.62/0.80 exact (zenon_H75 zenon_H6f).
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H9c); [ zenon_intro zenon_H82 | zenon_intro zenon_H76 ].
% 0.62/0.80 exact (zenon_H82 zenon_H70).
% 0.62/0.80 exact (zenon_H76 zenon_H6e).
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9e | zenon_intro zenon_H9d ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H9e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9f ].
% 0.62/0.80 generalize (zenon_H1c zenon_TY_du). zenon_intro zenon_H8f.
% 0.62/0.80 generalize (zenon_H8f zenon_TZ_dx). zenon_intro zenon_H90.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H81 | zenon_intro zenon_H91 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H82 | zenon_intro zenon_H75 ].
% 0.62/0.80 exact (zenon_H82 zenon_H70).
% 0.62/0.80 exact (zenon_H75 zenon_H6f).
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H91); [ zenon_intro zenon_H94; zenon_intro zenon_H93 | zenon_intro zenon_H6b; zenon_intro zenon_H92 ].
% 0.62/0.80 exact (zenon_H94 zenon_H6b).
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H96. zenon_intro zenon_H95.
% 0.62/0.80 exact (zenon_Ha0 zenon_H95).
% 0.62/0.80 generalize (zenon_H71 zenon_TY_du). zenon_intro zenon_H87.
% 0.62/0.80 apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H89 | zenon_intro zenon_H88 ].
% 0.62/0.80 apply (zenon_notand_s _ _ zenon_H89); [ zenon_intro zenon_H76 | zenon_intro zenon_H82 ].
% 0.62/0.80 exact (zenon_H76 zenon_H6e).
% 0.62/0.80 exact (zenon_H82 zenon_H70).
% 0.62/0.80 apply (zenon_equiv_s _ _ zenon_H88); [ zenon_intro zenon_H8c; zenon_intro zenon_H8b | zenon_intro zenon_H6c; zenon_intro zenon_H8a ].
% 0.62/0.80 exact (zenon_H8c zenon_H6c).
% 0.62/0.80 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 0.62/0.80 exact (zenon_H9f zenon_H8d).
% 0.62/0.80 exact (zenon_H7a zenon_H9d).
% 0.62/0.80 exact (zenon_H69 zenon_H78).
% 0.62/0.80 exact (zenon_H1a zenon_H28).
% 0.62/0.80 Qed.
% 0.62/0.80 % SZS output end Proof
% 0.62/0.80 (* END-PROOF *)
% 0.62/0.80 nodes searched: 11121
% 0.62/0.80 max branch formulas: 1800
% 0.62/0.80 proof nodes created: 641
% 0.62/0.80 formulas created: 50015
% 0.62/0.80
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