TSTP Solution File: SET653+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET653+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n006.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 06:37:46 EDT 2022
% Result : Theorem 2.98s 3.19s
% Output : Proof 2.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET653+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n006.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 : Sun Jul 10 23:04:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.98/3.19 (* PROOF-FOUND *)
% 2.98/3.19 % SZS status Theorem
% 2.98/3.19 (* BEGIN-PROOF *)
% 2.98/3.19 % SZS output start Proof
% 2.98/3.19 Theorem prove_relset_1_15 : (forall B : zenon_U, ((ilf_type B (set_type))->(forall C : zenon_U, ((ilf_type C (set_type))->(forall D : zenon_U, ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type B D))->((subset B C)->(ilf_type E (relation_type C D))))))))))).
% 2.98/3.19 Proof.
% 2.98/3.19 assert (zenon_L1_ : forall (zenon_TE_ba : zenon_U) (zenon_TD_bb : zenon_U) (zenon_TB_bc : zenon_U), (forall D : zenon_U, ((ilf_type D (relation_type zenon_TB_bc zenon_TD_bb))->((subset (domain_of D) zenon_TB_bc)/\(subset (range_of D) zenon_TD_bb)))) -> (ilf_type zenon_TE_ba (relation_type zenon_TB_bc zenon_TD_bb)) -> (~(subset (domain_of zenon_TE_ba) zenon_TB_bc)) -> False).
% 2.98/3.19 do 3 intro. intros zenon_H17 zenon_H18 zenon_H19.
% 2.98/3.19 generalize (zenon_H17 zenon_TE_ba). zenon_intro zenon_H1d.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 2.98/3.19 exact (zenon_H1f zenon_H18).
% 2.98/3.19 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 2.98/3.19 exact (zenon_H19 zenon_H21).
% 2.98/3.19 (* end of lemma zenon_L1_ *)
% 2.98/3.19 assert (zenon_L2_ : forall (zenon_TE_ba : zenon_U) (zenon_TD_bn : zenon_U) (zenon_TC_bo : zenon_U) (zenon_TB_bc : zenon_U), (forall D : zenon_U, ((ilf_type D (set_type))->((member D zenon_TB_bc)->(member D zenon_TC_bo)))) -> (ilf_type zenon_TD_bn (set_type)) -> (forall D : zenon_U, ((ilf_type D (set_type))->((member D (domain_of zenon_TE_ba))->(member D zenon_TB_bc)))) -> (member zenon_TD_bn (domain_of zenon_TE_ba)) -> (~(member zenon_TD_bn zenon_TC_bo)) -> False).
% 2.98/3.19 do 4 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25 zenon_H26.
% 2.98/3.19 generalize (zenon_H22 zenon_TD_bn). zenon_intro zenon_H29.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 2.98/3.19 exact (zenon_H2b zenon_H23).
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 2.98/3.19 generalize (zenon_H24 zenon_TD_bn). zenon_intro zenon_H2e.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H2b | zenon_intro zenon_H2f ].
% 2.98/3.19 exact (zenon_H2b zenon_H23).
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ].
% 2.98/3.19 exact (zenon_H31 zenon_H25).
% 2.98/3.19 exact (zenon_H2d zenon_H30).
% 2.98/3.19 exact (zenon_H26 zenon_H2c).
% 2.98/3.19 (* end of lemma zenon_L2_ *)
% 2.98/3.19 apply NNPP. intro zenon_G.
% 2.98/3.19 apply (zenon_notallex_s (fun B : zenon_U => ((ilf_type B (set_type))->(forall C : zenon_U, ((ilf_type C (set_type))->(forall D : zenon_U, ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type B D))->((subset B C)->(ilf_type E (relation_type C D))))))))))) zenon_G); [ zenon_intro zenon_H32; idtac ].
% 2.98/3.19 elim zenon_H32. zenon_intro zenon_TB_bc. zenon_intro zenon_H33.
% 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34.
% 2.98/3.19 apply (zenon_notallex_s (fun C : zenon_U => ((ilf_type C (set_type))->(forall D : zenon_U, ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type zenon_TB_bc D))->((subset zenon_TB_bc C)->(ilf_type E (relation_type C D))))))))) zenon_H34); [ zenon_intro zenon_H36; idtac ].
% 2.98/3.19 elim zenon_H36. zenon_intro zenon_TC_bo. zenon_intro zenon_H37.
% 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 2.98/3.19 apply (zenon_notallex_s (fun D : zenon_U => ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type zenon_TB_bc D))->((subset zenon_TB_bc zenon_TC_bo)->(ilf_type E (relation_type zenon_TC_bo D))))))) zenon_H38); [ zenon_intro zenon_H3a; idtac ].
% 2.98/3.19 elim zenon_H3a. zenon_intro zenon_TD_bb. zenon_intro zenon_H3b.
% 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c.
% 2.98/3.19 apply (zenon_notallex_s (fun E : zenon_U => ((ilf_type E (relation_type zenon_TB_bc zenon_TD_bb))->((subset zenon_TB_bc zenon_TC_bo)->(ilf_type E (relation_type zenon_TC_bo zenon_TD_bb))))) zenon_H3c); [ zenon_intro zenon_H3e; idtac ].
% 2.98/3.19 elim zenon_H3e. zenon_intro zenon_TE_ba. zenon_intro zenon_H3f.
% 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H3f). zenon_intro zenon_H18. zenon_intro zenon_H40.
% 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41.
% 2.98/3.19 generalize (p3 zenon_TB_bc). zenon_intro zenon_H43.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 2.98/3.19 exact (zenon_H45 zenon_H35).
% 2.98/3.19 generalize (zenon_H44 zenon_TC_bo). zenon_intro zenon_H46.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ].
% 2.98/3.19 exact (zenon_H48 zenon_H39).
% 2.98/3.19 generalize (zenon_H47 zenon_TD_bb). zenon_intro zenon_H49.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 2.98/3.19 exact (zenon_H4b zenon_H3d).
% 2.98/3.19 generalize (zenon_H4a zenon_TE_ba). zenon_intro zenon_H4c.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H1f | zenon_intro zenon_H4d ].
% 2.98/3.19 exact (zenon_H1f zenon_H18).
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ].
% 2.98/3.19 generalize (p6 (domain_of zenon_TE_ba)). zenon_intro zenon_H50.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ].
% 2.98/3.19 generalize (p22 (domain_of zenon_TE_ba)). zenon_intro zenon_H53.
% 2.98/3.19 exact (zenon_H52 zenon_H53).
% 2.98/3.19 generalize (zenon_H51 zenon_TC_bo). zenon_intro zenon_H54.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H48 | zenon_intro zenon_H55 ].
% 2.98/3.19 exact (zenon_H48 zenon_H39).
% 2.98/3.19 apply (zenon_equiv_s _ _ zenon_H55); [ zenon_intro zenon_H4f; zenon_intro zenon_H58 | zenon_intro zenon_H57; zenon_intro zenon_H56 ].
% 2.98/3.19 apply (zenon_notallex_s (fun D : zenon_U => ((ilf_type D (set_type))->((member D (domain_of zenon_TE_ba))->(member D zenon_TC_bo)))) zenon_H58); [ zenon_intro zenon_H59; idtac ].
% 2.98/3.19 elim zenon_H59. zenon_intro zenon_TD_bn. zenon_intro zenon_H5a.
% 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H5a). zenon_intro zenon_H23. zenon_intro zenon_H5b.
% 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H5b). zenon_intro zenon_H25. zenon_intro zenon_H26.
% 2.98/3.19 generalize (p2 zenon_TB_bc). zenon_intro zenon_H5c.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H45 | zenon_intro zenon_H5d ].
% 2.98/3.19 exact (zenon_H45 zenon_H35).
% 2.98/3.19 generalize (p6 zenon_TB_bc). zenon_intro zenon_H5e.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H45 | zenon_intro zenon_H5f ].
% 2.98/3.19 exact (zenon_H45 zenon_H35).
% 2.98/3.19 generalize (zenon_H5f zenon_TC_bo). zenon_intro zenon_H60.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H48 | zenon_intro zenon_H61 ].
% 2.98/3.19 exact (zenon_H48 zenon_H39).
% 2.98/3.19 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H63; zenon_intro zenon_H62 | zenon_intro zenon_H42; zenon_intro zenon_H22 ].
% 2.98/3.19 exact (zenon_H63 zenon_H42).
% 2.98/3.19 generalize (zenon_H51 zenon_TB_bc). zenon_intro zenon_H64.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H45 | zenon_intro zenon_H65 ].
% 2.98/3.19 exact (zenon_H45 zenon_H35).
% 2.98/3.19 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H19; zenon_intro zenon_H66 | zenon_intro zenon_H21; zenon_intro zenon_H24 ].
% 2.98/3.19 generalize (zenon_H5d zenon_TD_bb). zenon_intro zenon_H67.
% 2.98/3.19 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H4b | zenon_intro zenon_H17 ].
% 2.98/3.19 exact (zenon_H4b zenon_H3d).
% 2.98/3.19 apply (zenon_L1_ zenon_TE_ba zenon_TD_bb zenon_TB_bc); trivial.
% 2.98/3.19 apply (zenon_L2_ zenon_TE_ba zenon_TD_bn zenon_TC_bo zenon_TB_bc); trivial.
% 2.98/3.19 exact (zenon_H4f zenon_H57).
% 2.98/3.19 exact (zenon_H41 zenon_H4e).
% 2.98/3.19 Qed.
% 2.98/3.19 % SZS output end Proof
% 2.98/3.19 (* END-PROOF *)
% 2.98/3.19 nodes searched: 194358
% 2.98/3.19 max branch formulas: 13139
% 2.98/3.19 proof nodes created: 10968
% 2.98/3.19 formulas created: 517498
% 2.98/3.19
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