TSTP Solution File: SET810+4 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n012.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 06:38:43 EDT 2022
% Result : Theorem 2.66s 2.90s
% Output : Proof 2.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n012.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 07:12:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.66/2.90 (* PROOF-FOUND *)
% 2.66/2.90 % SZS status Theorem
% 2.66/2.90 (* BEGIN-PROOF *)
% 2.66/2.90 % SZS output start Proof
% 2.66/2.90 Theorem thV3 : (forall A : zenon_U, (forall B : zenon_U, (((member A (on))/\(member B (on)))->(~((member A B)/\(member B A)))))).
% 2.66/2.90 Proof.
% 2.66/2.90 assert (zenon_L1_ : forall (zenon_TA_y : zenon_U) (zenon_TB_z : zenon_U), (~(~(member zenon_TB_z zenon_TB_z))) -> (member zenon_TB_z zenon_TA_y) -> (member zenon_TA_y zenon_TB_z) -> (forall X : zenon_U, (forall Y : zenon_U, (((member X zenon_TB_z)/\(member Y zenon_TB_z))->(~((apply (member_predicate) X Y)/\(apply (member_predicate) Y X)))))) -> False).
% 2.66/2.90 do 2 intro. intros zenon_H14 zenon_H15 zenon_H16 zenon_H17.
% 2.66/2.90 apply zenon_H14. zenon_intro zenon_H1a.
% 2.66/2.90 generalize (zenon_H17 zenon_TA_y). zenon_intro zenon_H1b.
% 2.66/2.90 generalize (rel_member zenon_TB_z). zenon_intro zenon_H1c.
% 2.66/2.90 generalize (rel_member zenon_TA_y). zenon_intro zenon_H1d.
% 2.66/2.90 generalize (zenon_H1c zenon_TA_y). zenon_intro zenon_H1e.
% 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H15 ].
% 2.66/2.90 exact (zenon_H20 zenon_H15).
% 2.66/2.90 generalize (zenon_H1d zenon_TB_z). zenon_intro zenon_H22.
% 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H22); [ zenon_intro zenon_H25; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H16 ].
% 2.66/2.90 exact (zenon_H24 zenon_H16).
% 2.66/2.90 generalize (zenon_H1b zenon_TB_z). zenon_intro zenon_H26.
% 2.66/2.90 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 2.66/2.90 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H24 | zenon_intro zenon_H29 ].
% 2.66/2.90 exact (zenon_H24 zenon_H16).
% 2.66/2.90 exact (zenon_H29 zenon_H1a).
% 2.66/2.90 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H25 | zenon_intro zenon_H21 ].
% 2.66/2.90 exact (zenon_H25 zenon_H23).
% 2.66/2.90 exact (zenon_H21 zenon_H1f).
% 2.66/2.90 (* end of lemma zenon_L1_ *)
% 2.66/2.90 assert (zenon_L2_ : forall (zenon_TA_y : zenon_U) (zenon_TB_z : zenon_U), (~((member zenon_TB_z (on))/\(~(member zenon_TB_z zenon_TB_z)))) -> (forall X : zenon_U, (forall Y : zenon_U, (((member X zenon_TB_z)/\(member Y zenon_TB_z))->(~((apply (member_predicate) X Y)/\(apply (member_predicate) Y X)))))) -> (member zenon_TA_y zenon_TB_z) -> (member zenon_TB_z zenon_TA_y) -> (member zenon_TB_z (on)) -> False).
% 2.66/2.90 do 2 intro. intros zenon_H2a zenon_H17 zenon_H16 zenon_H15 zenon_H2b.
% 2.66/2.90 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H14 ].
% 2.66/2.90 exact (zenon_H2c zenon_H2b).
% 2.66/2.90 apply (zenon_L1_ zenon_TA_y zenon_TB_z); trivial.
% 2.66/2.90 (* end of lemma zenon_L2_ *)
% 2.66/2.90 assert (zenon_L3_ : forall (zenon_TB_z : zenon_U) (zenon_TA_y : zenon_U), (forall X : zenon_U, ((member X zenon_TA_y)->(member X zenon_TB_z))) -> (member zenon_TB_z zenon_TA_y) -> (~(member zenon_TB_z zenon_TB_z)) -> False).
% 2.66/2.90 do 2 intro. intros zenon_H2d zenon_H15 zenon_H29.
% 2.66/2.90 generalize (zenon_H2d zenon_TB_z). zenon_intro zenon_H2e.
% 2.66/2.90 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1a ].
% 2.66/2.90 exact (zenon_H20 zenon_H15).
% 2.66/2.90 exact (zenon_H29 zenon_H1a).
% 2.66/2.90 (* end of lemma zenon_L3_ *)
% 2.66/2.90 assert (zenon_L4_ : forall (zenon_TB_z : zenon_U) (zenon_TA_y : zenon_U), (subset zenon_TA_y zenon_TB_z) -> (member zenon_TB_z zenon_TA_y) -> (~(member zenon_TB_z zenon_TB_z)) -> False).
% 2.66/2.90 do 2 intro. intros zenon_H2f zenon_H15 zenon_H29.
% 2.66/2.90 generalize (subset zenon_TA_y). zenon_intro zenon_H30.
% 2.66/2.90 generalize (zenon_H30 zenon_TB_z). zenon_intro zenon_H31.
% 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H31); [ zenon_intro zenon_H33; zenon_intro zenon_H32 | zenon_intro zenon_H2f; zenon_intro zenon_H2d ].
% 2.66/2.90 exact (zenon_H33 zenon_H2f).
% 2.66/2.90 apply (zenon_L3_ zenon_TB_z zenon_TA_y); trivial.
% 2.66/2.90 (* end of lemma zenon_L4_ *)
% 2.66/2.90 assert (zenon_L5_ : forall (zenon_TA_y : zenon_U) (zenon_TB_z : zenon_U), (forall X : zenon_U, ((member X zenon_TB_z)->(subset X zenon_TB_z))) -> (member zenon_TA_y zenon_TB_z) -> (~(member zenon_TB_z zenon_TB_z)) -> (member zenon_TB_z zenon_TA_y) -> False).
% 2.66/2.90 do 2 intro. intros zenon_H34 zenon_H16 zenon_H29 zenon_H15.
% 2.66/2.90 generalize (zenon_H34 zenon_TA_y). zenon_intro zenon_H35.
% 2.66/2.90 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H24 | zenon_intro zenon_H2f ].
% 2.66/2.90 exact (zenon_H24 zenon_H16).
% 2.66/2.90 apply (zenon_L4_ zenon_TB_z zenon_TA_y); trivial.
% 2.66/2.90 (* end of lemma zenon_L5_ *)
% 2.66/2.90 apply NNPP. intro zenon_G.
% 2.66/2.90 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (((member A (on))/\(member B (on)))->(~((member A B)/\(member B A)))))) zenon_G); [ zenon_intro zenon_H36; idtac ].
% 2.66/2.90 elim zenon_H36. zenon_intro zenon_TA_y. zenon_intro zenon_H37.
% 2.66/2.90 apply (zenon_notallex_s (fun B : zenon_U => (((member zenon_TA_y (on))/\(member B (on)))->(~((member zenon_TA_y B)/\(member B zenon_TA_y))))) zenon_H37); [ zenon_intro zenon_H38; idtac ].
% 2.66/2.90 elim zenon_H38. zenon_intro zenon_TB_z. zenon_intro zenon_H39.
% 2.66/2.90 apply (zenon_notimply_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 2.66/2.90 apply zenon_H3a. zenon_intro zenon_H3c.
% 2.66/2.90 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H16. zenon_intro zenon_H15.
% 2.66/2.90 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H2b.
% 2.66/2.90 generalize (ordinal_number zenon_TB_z). zenon_intro zenon_H3e.
% 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H2c; zenon_intro zenon_H40 | zenon_intro zenon_H2b; zenon_intro zenon_H3f ].
% 2.66/2.90 exact (zenon_H2c zenon_H2b).
% 2.66/2.90 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41.
% 2.66/2.90 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H34.
% 2.66/2.90 generalize (strict_well_order (member_predicate)). zenon_intro zenon_H44.
% 2.66/2.90 generalize (zenon_H44 zenon_TB_z). zenon_intro zenon_H45.
% 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H48; zenon_intro zenon_H47 | zenon_intro zenon_H43; zenon_intro zenon_H46 ].
% 2.66/2.90 exact (zenon_H48 zenon_H43).
% 2.66/2.90 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 2.66/2.90 generalize (strict_order (member_predicate)). zenon_intro zenon_H4b.
% 2.66/2.90 generalize (zenon_H4b zenon_TB_z). zenon_intro zenon_H4c.
% 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H4a; zenon_intro zenon_H4d ].
% 2.66/2.90 exact (zenon_H4f zenon_H4a).
% 2.66/2.90 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H17. zenon_intro zenon_H50.
% 2.66/2.90 generalize (difference zenon_TB_z). zenon_intro zenon_H51.
% 2.66/2.90 generalize (zenon_H51 zenon_TB_z). zenon_intro zenon_H52.
% 2.66/2.90 generalize (zenon_H52 (on)). zenon_intro zenon_H53.
% 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H53); [ zenon_intro zenon_H56; zenon_intro zenon_H2a | zenon_intro zenon_H55; zenon_intro zenon_H54 ].
% 2.66/2.90 apply (zenon_L2_ zenon_TA_y zenon_TB_z); trivial.
% 2.66/2.90 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H2b. zenon_intro zenon_H29.
% 2.66/2.90 apply (zenon_L5_ zenon_TA_y zenon_TB_z); trivial.
% 2.66/2.90 Qed.
% 2.66/2.90 % SZS output end Proof
% 2.66/2.90 (* END-PROOF *)
% 2.66/2.90 nodes searched: 128172
% 2.66/2.90 max branch formulas: 8317
% 2.66/2.90 proof nodes created: 3642
% 2.66/2.90 formulas created: 527410
% 2.66/2.90
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