TSTP Solution File: SET626+3 by Zenon---0.7.1
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% File : Zenon---0.7.1
% Problem : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n027.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 06:37:31 EDT 2022
% Result : Theorem 19.53s 19.71s
% Output : Proof 19.53s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 09:05:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 19.53/19.71 (* PROOF-FOUND *)
% 19.53/19.71 % SZS status Theorem
% 19.53/19.71 (* BEGIN-PROOF *)
% 19.53/19.71 % SZS output start Proof
% 19.53/19.71 Theorem prove_th102 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((intersect B (intersection C D))->(intersect B C))))).
% 19.53/19.71 Proof.
% 19.53/19.71 assert (zenon_L1_ : forall (zenon_TD_j : zenon_U) (zenon_TC_k : zenon_U) (zenon_TB_l : zenon_U), (~(exists D : zenon_U, ((member D zenon_TB_l)/\(member D zenon_TC_k)))) -> (member zenon_TD_j zenon_TB_l) -> (member zenon_TD_j zenon_TC_k) -> False).
% 19.53/19.71 do 3 intro. intros zenon_H6 zenon_H7 zenon_H8.
% 19.53/19.71 apply zenon_H6. exists zenon_TD_j. apply NNPP. zenon_intro zenon_Hc.
% 19.53/19.71 apply (zenon_notand_s _ _ zenon_Hc); [ zenon_intro zenon_He | zenon_intro zenon_Hd ].
% 19.53/19.71 exact (zenon_He zenon_H7).
% 19.53/19.71 exact (zenon_Hd zenon_H8).
% 19.53/19.71 (* end of lemma zenon_L1_ *)
% 19.53/19.71 apply NNPP. intro zenon_G.
% 19.53/19.71 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((intersect B (intersection C D))->(intersect B C))))) zenon_G); [ zenon_intro zenon_Hf; idtac ].
% 19.53/19.71 elim zenon_Hf. zenon_intro zenon_TB_l. zenon_intro zenon_H10.
% 19.53/19.71 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((intersect zenon_TB_l (intersection C D))->(intersect zenon_TB_l C)))) zenon_H10); [ zenon_intro zenon_H11; idtac ].
% 19.53/19.71 elim zenon_H11. zenon_intro zenon_TC_k. zenon_intro zenon_H12.
% 19.53/19.71 apply (zenon_notallex_s (fun D : zenon_U => ((intersect zenon_TB_l (intersection zenon_TC_k D))->(intersect zenon_TB_l zenon_TC_k))) zenon_H12); [ zenon_intro zenon_H13; idtac ].
% 19.53/19.71 elim zenon_H13. zenon_intro zenon_TD_u. zenon_intro zenon_H15.
% 19.53/19.71 apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 19.53/19.71 generalize (intersect_defn zenon_TB_l). zenon_intro zenon_H18.
% 19.53/19.71 generalize (zenon_H18 (intersection zenon_TC_k zenon_TD_u)). zenon_intro zenon_H19.
% 19.53/19.71 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H17; zenon_intro zenon_H1a ].
% 19.53/19.71 exact (zenon_H1c zenon_H17).
% 19.53/19.71 elim zenon_H1a. zenon_intro zenon_TD_j. zenon_intro zenon_H1d.
% 19.53/19.71 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H7. zenon_intro zenon_H1e.
% 19.53/19.71 generalize (intersect_defn zenon_TB_l). zenon_intro zenon_H18.
% 19.53/19.71 generalize (zenon_H18 zenon_TC_k). zenon_intro zenon_H1f.
% 19.53/19.71 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H16; zenon_intro zenon_H6 | zenon_intro zenon_H21; zenon_intro zenon_H20 ].
% 19.53/19.71 generalize (intersection_defn zenon_TC_k). zenon_intro zenon_H22.
% 19.53/19.71 generalize (zenon_H22 zenon_TB_l). zenon_intro zenon_H23.
% 19.53/19.71 generalize (zenon_H23 zenon_TD_j). zenon_intro zenon_H24.
% 19.53/19.71 apply (zenon_equiv_s _ _ zenon_H24); [ zenon_intro zenon_H28; zenon_intro zenon_H27 | zenon_intro zenon_H26; zenon_intro zenon_H25 ].
% 19.53/19.71 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_Hd | zenon_intro zenon_He ].
% 19.53/19.71 generalize (zenon_H22 zenon_TD_u). zenon_intro zenon_H29.
% 19.53/19.71 generalize (zenon_H29 zenon_TD_j). zenon_intro zenon_H2a.
% 19.53/19.71 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H2d; zenon_intro zenon_H2c | zenon_intro zenon_H1e; zenon_intro zenon_H2b ].
% 19.53/19.71 exact (zenon_H2d zenon_H1e).
% 19.53/19.71 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H8. zenon_intro zenon_H2e.
% 19.53/19.71 exact (zenon_Hd zenon_H8).
% 19.53/19.71 exact (zenon_He zenon_H7).
% 19.53/19.71 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H8. zenon_intro zenon_H7.
% 19.53/19.71 apply (zenon_L1_ zenon_TD_j zenon_TC_k zenon_TB_l); trivial.
% 19.53/19.71 exact (zenon_H16 zenon_H21).
% 19.53/19.71 Qed.
% 19.53/19.71 % SZS output end Proof
% 19.53/19.71 (* END-PROOF *)
% 19.53/19.71 nodes searched: 620721
% 19.53/19.71 max branch formulas: 13462
% 19.53/19.71 proof nodes created: 20174
% 19.53/19.71 formulas created: 780137
% 19.53/19.71
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