TSTP Solution File: SET631+3 by Zenon---0.7.1
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% File : Zenon---0.7.1
% Problem : SET631+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 06:37:35 EDT 2022
% Result : Theorem 3.99s 4.22s
% Output : Proof 3.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.08 % Problem : SET631+3 : TPTP v8.1.0. Released v2.2.0.
% 0.01/0.09 % Command : run_zenon %s %d
% 0.08/0.28 % Computer : n011.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Sat Jul 9 23:52:11 EDT 2022
% 0.08/0.28 % CPUTime :
% 3.99/4.22 (* PROOF-FOUND *)
% 3.99/4.22 % SZS status Theorem
% 3.99/4.22 (* BEGIN-PROOF *)
% 3.99/4.22 % SZS output start Proof
% 3.99/4.22 Theorem prove_th113 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((intersect B (difference C D))->(intersect B C))))).
% 3.99/4.22 Proof.
% 3.99/4.22 assert (zenon_L1_ : forall (zenon_TD_h : zenon_U) (zenon_TC_i : zenon_U) (zenon_TB_j : zenon_U), (~(exists D : zenon_U, ((member D zenon_TB_j)/\(member D zenon_TC_i)))) -> (member zenon_TD_h zenon_TB_j) -> (member zenon_TD_h zenon_TC_i) -> False).
% 3.99/4.22 do 3 intro. intros zenon_H4 zenon_H5 zenon_H6.
% 3.99/4.22 apply zenon_H4. exists zenon_TD_h. apply NNPP. zenon_intro zenon_Ha.
% 3.99/4.22 apply (zenon_notand_s _ _ zenon_Ha); [ zenon_intro zenon_Hc | zenon_intro zenon_Hb ].
% 3.99/4.22 exact (zenon_Hc zenon_H5).
% 3.99/4.22 exact (zenon_Hb zenon_H6).
% 3.99/4.22 (* end of lemma zenon_L1_ *)
% 3.99/4.22 apply NNPP. intro zenon_G.
% 3.99/4.22 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((intersect B (difference C D))->(intersect B C))))) zenon_G); [ zenon_intro zenon_Hd; idtac ].
% 3.99/4.22 elim zenon_Hd. zenon_intro zenon_TB_j. zenon_intro zenon_He.
% 3.99/4.22 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((intersect zenon_TB_j (difference C D))->(intersect zenon_TB_j C)))) zenon_He); [ zenon_intro zenon_Hf; idtac ].
% 3.99/4.22 elim zenon_Hf. zenon_intro zenon_TC_i. zenon_intro zenon_H10.
% 3.99/4.22 apply (zenon_notallex_s (fun D : zenon_U => ((intersect zenon_TB_j (difference zenon_TC_i D))->(intersect zenon_TB_j zenon_TC_i))) zenon_H10); [ zenon_intro zenon_H11; idtac ].
% 3.99/4.22 elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13.
% 3.99/4.22 apply (zenon_notimply_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14.
% 3.99/4.22 generalize (intersect_defn zenon_TB_j). zenon_intro zenon_H16.
% 3.99/4.22 generalize (zenon_H16 (difference zenon_TC_i zenon_TD_s)). zenon_intro zenon_H17.
% 3.99/4.22 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H1a; zenon_intro zenon_H19 | zenon_intro zenon_H15; zenon_intro zenon_H18 ].
% 3.99/4.22 exact (zenon_H1a zenon_H15).
% 3.99/4.22 elim zenon_H18. zenon_intro zenon_TD_h. zenon_intro zenon_H1b.
% 3.99/4.22 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H5. zenon_intro zenon_H1c.
% 3.99/4.22 generalize (intersect_defn zenon_TB_j). zenon_intro zenon_H16.
% 3.99/4.22 generalize (zenon_H16 zenon_TC_i). zenon_intro zenon_H1d.
% 3.99/4.22 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H14; zenon_intro zenon_H4 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ].
% 3.99/4.22 generalize (difference_defn zenon_TC_i). zenon_intro zenon_H20.
% 3.99/4.22 generalize (zenon_H20 zenon_TC_i). zenon_intro zenon_H21.
% 3.99/4.22 generalize (zenon_H20 zenon_TD_s). zenon_intro zenon_H22.
% 3.99/4.22 generalize (zenon_H21 zenon_TD_h). zenon_intro zenon_H23.
% 3.99/4.22 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H27; zenon_intro zenon_H26 | zenon_intro zenon_H25; zenon_intro zenon_H24 ].
% 3.99/4.22 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_Hb | zenon_intro zenon_H28 ].
% 3.99/4.22 generalize (zenon_H22 zenon_TD_h). zenon_intro zenon_H29.
% 3.99/4.22 apply (zenon_equiv_s _ _ zenon_H29); [ zenon_intro zenon_H2c; zenon_intro zenon_H2b | zenon_intro zenon_H1c; zenon_intro zenon_H2a ].
% 3.99/4.22 exact (zenon_H2c zenon_H1c).
% 3.99/4.22 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H6. zenon_intro zenon_H2d.
% 3.99/4.22 exact (zenon_Hb zenon_H6).
% 3.99/4.22 apply zenon_H28. zenon_intro zenon_H6.
% 3.99/4.22 apply (zenon_L1_ zenon_TD_h zenon_TC_i zenon_TB_j); trivial.
% 3.99/4.22 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6. zenon_intro zenon_Hb.
% 3.99/4.22 exact (zenon_Hb zenon_H6).
% 3.99/4.22 exact (zenon_H14 zenon_H1f).
% 3.99/4.22 Qed.
% 3.99/4.22 % SZS output end Proof
% 3.99/4.22 (* END-PROOF *)
% 3.99/4.22 nodes searched: 240547
% 3.99/4.22 max branch formulas: 40541
% 3.99/4.22 proof nodes created: 4198
% 3.99/4.22 formulas created: 527260
% 3.99/4.22
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