TSTP Solution File: SET593+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET593+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n011.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 06:37:07 EDT 2022
% Result : Theorem 2.15s 2.31s
% Output : Proof 2.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET593+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 11:36:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.15/2.31 (* PROOF-FOUND *)
% 2.15/2.31 % SZS status Theorem
% 2.15/2.31 (* BEGIN-PROOF *)
% 2.15/2.31 % SZS output start Proof
% 2.15/2.31 Theorem prove_th52 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((subset B (union C D))->((subset (difference B C) D)/\(subset (difference B D) C)))))).
% 2.15/2.31 Proof.
% 2.15/2.31 assert (zenon_L1_ : forall (zenon_TC_k : zenon_U) (zenon_TD_l : zenon_U) (zenon_TD_m : zenon_U), (~(member zenon_TD_m (union zenon_TD_l zenon_TC_k))) -> (member zenon_TD_m (union zenon_TC_k zenon_TD_l)) -> ((union zenon_TD_l zenon_TC_k) = (union zenon_TC_k zenon_TD_l)) -> False).
% 2.15/2.31 do 3 intro. intros zenon_H7 zenon_H8 zenon_H9.
% 2.15/2.31 cut ((member zenon_TD_m (union zenon_TC_k zenon_TD_l)) = (member zenon_TD_m (union zenon_TD_l zenon_TC_k))).
% 2.15/2.31 intro zenon_D_pnotp.
% 2.15/2.31 apply zenon_H7.
% 2.15/2.31 rewrite <- zenon_D_pnotp.
% 2.15/2.31 exact zenon_H8.
% 2.15/2.31 cut (((union zenon_TC_k zenon_TD_l) = (union zenon_TD_l zenon_TC_k))); [idtac | apply NNPP; zenon_intro zenon_Hd].
% 2.15/2.31 cut ((zenon_TD_m = zenon_TD_m)); [idtac | apply NNPP; zenon_intro zenon_He].
% 2.15/2.31 congruence.
% 2.15/2.31 apply zenon_He. apply refl_equal.
% 2.15/2.31 apply zenon_Hd. apply sym_equal. exact zenon_H9.
% 2.15/2.31 (* end of lemma zenon_L1_ *)
% 2.15/2.31 apply NNPP. intro zenon_G.
% 2.15/2.31 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((subset B (union C D))->((subset (difference B C) D)/\(subset (difference B D) C)))))) zenon_G); [ zenon_intro zenon_Hf; idtac ].
% 2.15/2.31 elim zenon_Hf. zenon_intro zenon_TB_q. zenon_intro zenon_H11.
% 2.15/2.31 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((subset zenon_TB_q (union C D))->((subset (difference zenon_TB_q C) D)/\(subset (difference zenon_TB_q D) C))))) zenon_H11); [ zenon_intro zenon_H12; idtac ].
% 2.15/2.31 elim zenon_H12. zenon_intro zenon_TC_k. zenon_intro zenon_H13.
% 2.15/2.31 apply (zenon_notallex_s (fun D : zenon_U => ((subset zenon_TB_q (union zenon_TC_k D))->((subset (difference zenon_TB_q zenon_TC_k) D)/\(subset (difference zenon_TB_q D) zenon_TC_k)))) zenon_H13); [ zenon_intro zenon_H14; idtac ].
% 2.15/2.31 elim zenon_H14. zenon_intro zenon_TD_l. zenon_intro zenon_H15.
% 2.15/2.31 apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 2.15/2.31 generalize (subset_defn zenon_TB_q). zenon_intro zenon_H18.
% 2.15/2.31 generalize (zenon_H18 (union zenon_TC_k zenon_TD_l)). zenon_intro zenon_H19.
% 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H17; zenon_intro zenon_H1a ].
% 2.15/2.31 exact (zenon_H1c zenon_H17).
% 2.15/2.31 apply (zenon_notand_s _ _ zenon_H16); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 2.15/2.31 generalize (subset_defn (difference zenon_TB_q zenon_TC_k)). zenon_intro zenon_H1f.
% 2.15/2.31 generalize (zenon_H1f zenon_TD_l). zenon_intro zenon_H20.
% 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H1e; zenon_intro zenon_H23 | zenon_intro zenon_H22; zenon_intro zenon_H21 ].
% 2.15/2.31 apply (zenon_notallex_s (fun D : zenon_U => ((member D (difference zenon_TB_q zenon_TC_k))->(member D zenon_TD_l))) zenon_H23); [ zenon_intro zenon_H24; idtac ].
% 2.15/2.31 elim zenon_H24. zenon_intro zenon_TD_bl. zenon_intro zenon_H26.
% 2.15/2.31 apply (zenon_notimply_s _ _ zenon_H26). zenon_intro zenon_H28. zenon_intro zenon_H27.
% 2.15/2.31 generalize (union_defn zenon_TC_k). zenon_intro zenon_H29.
% 2.15/2.31 generalize (zenon_H29 zenon_TD_l). zenon_intro zenon_H2a.
% 2.15/2.31 generalize (zenon_H2a zenon_TD_bl). zenon_intro zenon_H2b.
% 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H2d; zenon_intro zenon_H2c ].
% 2.15/2.31 generalize (zenon_H1a zenon_TD_bl). zenon_intro zenon_H30.
% 2.15/2.31 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H31 | zenon_intro zenon_H2d ].
% 2.15/2.31 generalize (difference_defn zenon_TB_q). zenon_intro zenon_H32.
% 2.15/2.31 generalize (zenon_H32 zenon_TC_k). zenon_intro zenon_H33.
% 2.15/2.31 generalize (zenon_H33 zenon_TD_bl). zenon_intro zenon_H34.
% 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H28; zenon_intro zenon_H35 ].
% 2.15/2.31 exact (zenon_H37 zenon_H28).
% 2.15/2.31 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 2.15/2.31 exact (zenon_H31 zenon_H39).
% 2.15/2.31 exact (zenon_H2f zenon_H2d).
% 2.15/2.31 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 2.15/2.31 generalize (difference_defn zenon_TB_q). zenon_intro zenon_H32.
% 2.15/2.31 generalize (zenon_H32 zenon_TC_k). zenon_intro zenon_H33.
% 2.15/2.31 generalize (zenon_H33 zenon_TD_bl). zenon_intro zenon_H34.
% 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H28; zenon_intro zenon_H35 ].
% 2.15/2.31 exact (zenon_H37 zenon_H28).
% 2.15/2.31 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 2.15/2.31 exact (zenon_H38 zenon_H3b).
% 2.15/2.31 exact (zenon_H27 zenon_H3a).
% 2.15/2.31 exact (zenon_H1e zenon_H22).
% 2.15/2.31 generalize (subset_defn (difference zenon_TB_q zenon_TD_l)). zenon_intro zenon_H3c.
% 2.15/2.31 generalize (zenon_H3c zenon_TC_k). zenon_intro zenon_H3d.
% 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H3d); [ zenon_intro zenon_H1d; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3e ].
% 2.15/2.31 apply (zenon_notallex_s (fun D : zenon_U => ((member D (difference zenon_TB_q zenon_TD_l))->(member D zenon_TC_k))) zenon_H40); [ zenon_intro zenon_H41; idtac ].
% 2.15/2.31 elim zenon_H41. zenon_intro zenon_TD_m. zenon_intro zenon_H42.
% 2.15/2.31 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43.
% 2.15/2.31 generalize (commutativity_of_union zenon_TD_l). zenon_intro zenon_H45.
% 2.15/2.31 generalize (zenon_H45 zenon_TC_k). zenon_intro zenon_H9.
% 2.15/2.31 generalize (union_defn zenon_TD_l). zenon_intro zenon_H46.
% 2.15/2.31 generalize (zenon_H46 zenon_TC_k). zenon_intro zenon_H47.
% 2.15/2.31 generalize (zenon_H47 zenon_TD_m). zenon_intro zenon_H48.
% 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H48); [ zenon_intro zenon_H7; zenon_intro zenon_H4b | zenon_intro zenon_H4a; zenon_intro zenon_H49 ].
% 2.15/2.31 generalize (difference_defn zenon_TB_q). zenon_intro zenon_H32.
% 2.15/2.31 generalize (zenon_H1a zenon_TD_m). zenon_intro zenon_H4c.
% 2.15/2.31 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4d | zenon_intro zenon_H8 ].
% 2.15/2.31 generalize (zenon_H32 zenon_TD_l). zenon_intro zenon_H4e.
% 2.15/2.31 generalize (zenon_H4e zenon_TD_m). zenon_intro zenon_H4f.
% 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H52; zenon_intro zenon_H51 | zenon_intro zenon_H44; zenon_intro zenon_H50 ].
% 2.15/2.31 exact (zenon_H52 zenon_H44).
% 2.15/2.31 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 2.15/2.31 exact (zenon_H4d zenon_H54).
% 2.15/2.31 apply (zenon_L1_ zenon_TC_k zenon_TD_l zenon_TD_m); trivial.
% 2.15/2.31 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ].
% 2.15/2.31 generalize (difference_defn zenon_TB_q). zenon_intro zenon_H32.
% 2.15/2.31 generalize (zenon_H32 zenon_TD_l). zenon_intro zenon_H4e.
% 2.15/2.31 generalize (zenon_H4e zenon_TD_m). zenon_intro zenon_H4f.
% 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H52; zenon_intro zenon_H51 | zenon_intro zenon_H44; zenon_intro zenon_H50 ].
% 2.15/2.31 exact (zenon_H52 zenon_H44).
% 2.15/2.31 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 2.15/2.31 exact (zenon_H53 zenon_H56).
% 2.15/2.31 exact (zenon_H43 zenon_H55).
% 2.15/2.31 exact (zenon_H1d zenon_H3f).
% 2.15/2.31 Qed.
% 2.15/2.31 % SZS output end Proof
% 2.15/2.31 (* END-PROOF *)
% 2.15/2.31 nodes searched: 79628
% 2.15/2.31 max branch formulas: 3580
% 2.15/2.31 proof nodes created: 3881
% 2.15/2.31 formulas created: 142906
% 2.15/2.31
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