TSTP Solution File: SET199+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET199+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n025.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 06:34:50 EDT 2022
% Result : Theorem 0.55s 0.71s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET199+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n025.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 02:09:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.71 (* PROOF-FOUND *)
% 0.55/0.71 % SZS status Theorem
% 0.55/0.71 (* BEGIN-PROOF *)
% 0.55/0.71 % SZS output start Proof
% 0.55/0.71 Theorem prove_intersection_of_subsets : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset B D))->(subset B (intersection C D)))))).
% 0.55/0.71 Proof.
% 0.55/0.71 assert (zenon_L1_ : forall (zenon_TD_j : zenon_U) (zenon_TC_k : zenon_U) (zenon_TD_l : zenon_U), (~(member zenon_TD_l (intersection zenon_TC_k zenon_TD_j))) -> (member zenon_TD_l (intersection zenon_TD_j zenon_TC_k)) -> ((intersection zenon_TD_j zenon_TC_k) = (intersection zenon_TC_k zenon_TD_j)) -> False).
% 0.55/0.71 do 3 intro. intros zenon_H6 zenon_H7 zenon_H8.
% 0.55/0.71 cut ((member zenon_TD_l (intersection zenon_TD_j zenon_TC_k)) = (member zenon_TD_l (intersection zenon_TC_k zenon_TD_j))).
% 0.55/0.71 intro zenon_D_pnotp.
% 0.55/0.71 apply zenon_H6.
% 0.55/0.71 rewrite <- zenon_D_pnotp.
% 0.55/0.71 exact zenon_H7.
% 0.55/0.71 cut (((intersection zenon_TD_j zenon_TC_k) = (intersection zenon_TC_k zenon_TD_j))); [idtac | apply NNPP; zenon_intro zenon_Hc].
% 0.55/0.71 cut ((zenon_TD_l = zenon_TD_l)); [idtac | apply NNPP; zenon_intro zenon_Hd].
% 0.55/0.71 congruence.
% 0.55/0.71 apply zenon_Hd. apply refl_equal.
% 0.55/0.71 exact (zenon_Hc zenon_H8).
% 0.55/0.71 (* end of lemma zenon_L1_ *)
% 0.55/0.71 apply NNPP. intro zenon_G.
% 0.55/0.71 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset B D))->(subset B (intersection C D)))))) zenon_G); [ zenon_intro zenon_He; idtac ].
% 0.55/0.71 elim zenon_He. zenon_intro zenon_TB_p. zenon_intro zenon_H10.
% 0.55/0.71 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TB_p C)/\(subset zenon_TB_p D))->(subset zenon_TB_p (intersection C D))))) zenon_H10); [ zenon_intro zenon_H11; idtac ].
% 0.55/0.71 elim zenon_H11. zenon_intro zenon_TC_k. zenon_intro zenon_H12.
% 0.55/0.71 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TB_p zenon_TC_k)/\(subset zenon_TB_p D))->(subset zenon_TB_p (intersection zenon_TC_k D)))) zenon_H12); [ zenon_intro zenon_H13; idtac ].
% 0.55/0.71 elim zenon_H13. zenon_intro zenon_TD_j. zenon_intro zenon_H14.
% 0.55/0.71 apply (zenon_notimply_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15.
% 0.55/0.71 apply (zenon_and_s _ _ zenon_H16). zenon_intro zenon_H18. zenon_intro zenon_H17.
% 0.55/0.71 generalize (subset_defn zenon_TB_p). zenon_intro zenon_H19.
% 0.55/0.71 generalize (zenon_H19 zenon_TC_k). zenon_intro zenon_H1a.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H1d; zenon_intro zenon_H1c | zenon_intro zenon_H18; zenon_intro zenon_H1b ].
% 0.55/0.71 exact (zenon_H1d zenon_H18).
% 0.55/0.71 generalize (subset_defn zenon_TB_p). zenon_intro zenon_H19.
% 0.55/0.71 generalize (zenon_H19 zenon_TD_j). zenon_intro zenon_H1e.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H17; zenon_intro zenon_H1f ].
% 0.55/0.71 exact (zenon_H21 zenon_H17).
% 0.55/0.71 generalize (subset_defn zenon_TB_p). zenon_intro zenon_H19.
% 0.55/0.71 generalize (zenon_H19 (intersection zenon_TC_k zenon_TD_j)). zenon_intro zenon_H22.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H22); [ zenon_intro zenon_H15; zenon_intro zenon_H25 | zenon_intro zenon_H24; zenon_intro zenon_H23 ].
% 0.55/0.71 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_p)->(member D (intersection zenon_TC_k zenon_TD_j)))) zenon_H25); [ zenon_intro zenon_H26; idtac ].
% 0.55/0.71 elim zenon_H26. zenon_intro zenon_TD_l. zenon_intro zenon_H27.
% 0.55/0.71 apply (zenon_notimply_s _ _ zenon_H27). zenon_intro zenon_H28. zenon_intro zenon_H6.
% 0.55/0.71 generalize (commutativity_of_intersection zenon_TD_j). zenon_intro zenon_H29.
% 0.55/0.71 generalize (zenon_H29 zenon_TC_k). zenon_intro zenon_H8.
% 0.55/0.71 generalize (intersection_defn zenon_TD_j). zenon_intro zenon_H2a.
% 0.55/0.71 generalize (zenon_H2a zenon_TC_k). zenon_intro zenon_H2b.
% 0.55/0.71 generalize (zenon_H2b zenon_TD_l). zenon_intro zenon_H2c.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H7; zenon_intro zenon_H2d ].
% 0.55/0.71 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ].
% 0.55/0.71 generalize (zenon_H1f zenon_TD_l). zenon_intro zenon_H32.
% 0.55/0.71 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.55/0.71 exact (zenon_H34 zenon_H28).
% 0.55/0.71 exact (zenon_H31 zenon_H33).
% 0.55/0.71 generalize (zenon_H1b zenon_TD_l). zenon_intro zenon_H35.
% 0.55/0.71 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H34 | zenon_intro zenon_H36 ].
% 0.55/0.71 exact (zenon_H34 zenon_H28).
% 0.55/0.71 exact (zenon_H30 zenon_H36).
% 0.55/0.71 apply (zenon_L1_ zenon_TD_j zenon_TC_k zenon_TD_l); trivial.
% 0.55/0.71 exact (zenon_H15 zenon_H24).
% 0.55/0.71 Qed.
% 0.55/0.71 % SZS output end Proof
% 0.55/0.71 (* END-PROOF *)
% 0.55/0.71 nodes searched: 7493
% 0.55/0.71 max branch formulas: 1010
% 0.55/0.71 proof nodes created: 508
% 0.55/0.71 formulas created: 13798
% 0.55/0.71
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