TSTP Solution File: SET585+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n006.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 06:37:02 EDT 2022
% Result : Theorem 0.63s 0.86s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n006.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 13:58:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.63/0.86 (* PROOF-FOUND *)
% 0.63/0.86 % SZS status Theorem
% 0.63/0.86 (* BEGIN-PROOF *)
% 0.63/0.86 % SZS output start Proof
% 0.63/0.86 Theorem prove_intersection_subset_of_union : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (subset (intersection B C) (union B D))))).
% 0.63/0.86 Proof.
% 0.63/0.86 apply NNPP. intro zenon_G.
% 0.63/0.86 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (subset (intersection B C) (union B D))))) zenon_G); [ zenon_intro zenon_Hb; idtac ].
% 0.63/0.86 elim zenon_Hb. zenon_intro zenon_TB_m. zenon_intro zenon_Hd.
% 0.63/0.86 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (subset (intersection zenon_TB_m C) (union zenon_TB_m D)))) zenon_Hd); [ zenon_intro zenon_He; idtac ].
% 0.63/0.86 elim zenon_He. zenon_intro zenon_TC_p. zenon_intro zenon_H10.
% 0.63/0.86 apply (zenon_notallex_s (fun D : zenon_U => (subset (intersection zenon_TB_m zenon_TC_p) (union zenon_TB_m D))) zenon_H10); [ zenon_intro zenon_H11; idtac ].
% 0.63/0.86 elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13.
% 0.63/0.86 generalize (subset_defn (intersection zenon_TB_m zenon_TC_p)). zenon_intro zenon_H14.
% 0.63/0.86 generalize (zenon_H14 (union zenon_TB_m zenon_TD_s)). zenon_intro zenon_H15.
% 0.63/0.86 apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_H13; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ].
% 0.63/0.86 apply (zenon_notallex_s (fun D : zenon_U => ((member D (intersection zenon_TB_m zenon_TC_p))->(member D (union zenon_TB_m zenon_TD_s)))) zenon_H18); [ zenon_intro zenon_H19; idtac ].
% 0.63/0.86 elim zenon_H19. zenon_intro zenon_TD_ba. zenon_intro zenon_H1b.
% 0.63/0.86 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.63/0.86 generalize (union_defn zenon_TB_m). zenon_intro zenon_H1e.
% 0.63/0.86 generalize (intersection_is_subset zenon_TB_m). zenon_intro zenon_H1f.
% 0.63/0.86 generalize (zenon_H1e zenon_TD_s). zenon_intro zenon_H20.
% 0.63/0.86 generalize (zenon_H20 zenon_TD_ba). zenon_intro zenon_H21.
% 0.63/0.86 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H1c; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ].
% 0.63/0.86 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25.
% 0.63/0.86 generalize (zenon_H1f zenon_TC_p). zenon_intro zenon_H27.
% 0.63/0.86 generalize (subset_defn (intersection zenon_TB_m zenon_TC_p)). zenon_intro zenon_H14.
% 0.63/0.86 generalize (zenon_H14 zenon_TB_m). zenon_intro zenon_H28.
% 0.63/0.86 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H2b; zenon_intro zenon_H2a | zenon_intro zenon_H27; zenon_intro zenon_H29 ].
% 0.63/0.86 exact (zenon_H2b zenon_H27).
% 0.63/0.86 generalize (zenon_H29 zenon_TD_ba). zenon_intro zenon_H2c.
% 0.63/0.86 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.63/0.86 exact (zenon_H2e zenon_H1d).
% 0.63/0.86 exact (zenon_H26 zenon_H2d).
% 0.63/0.86 exact (zenon_H1c zenon_H23).
% 0.63/0.86 exact (zenon_H13 zenon_H17).
% 0.63/0.86 Qed.
% 0.63/0.86 % SZS output end Proof
% 0.63/0.86 (* END-PROOF *)
% 0.63/0.86 nodes searched: 12156
% 0.63/0.86 max branch formulas: 1638
% 0.63/0.86 proof nodes created: 681
% 0.63/0.86 formulas created: 31711
% 0.63/0.86
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