TSTP Solution File: SET586+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n008.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 0.76s 0.98s
% Output : Proof 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n008.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 : Mon Jul 11 07:27:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.76/0.98 (* PROOF-FOUND *)
% 0.76/0.98 % SZS status Theorem
% 0.76/0.98 (* BEGIN-PROOF *)
% 0.76/0.98 % SZS output start Proof
% 0.76/0.98 Theorem prove_intersection_of_subset : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((subset B C)->(subset (intersection B D) (intersection C D)))))).
% 0.76/0.98 Proof.
% 0.76/0.98 apply NNPP. intro zenon_G.
% 0.76/0.98 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((subset B C)->(subset (intersection B D) (intersection C D)))))) zenon_G); [ zenon_intro zenon_H6; idtac ].
% 0.76/0.98 elim zenon_H6. zenon_intro zenon_TB_h. zenon_intro zenon_H8.
% 0.76/0.98 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((subset zenon_TB_h C)->(subset (intersection zenon_TB_h D) (intersection C D))))) zenon_H8); [ zenon_intro zenon_H9; idtac ].
% 0.76/0.98 elim zenon_H9. zenon_intro zenon_TC_k. zenon_intro zenon_Hb.
% 0.76/0.98 apply (zenon_notallex_s (fun D : zenon_U => ((subset zenon_TB_h zenon_TC_k)->(subset (intersection zenon_TB_h D) (intersection zenon_TC_k D)))) zenon_Hb); [ zenon_intro zenon_Hc; idtac ].
% 0.76/0.98 elim zenon_Hc. zenon_intro zenon_TD_n. zenon_intro zenon_He.
% 0.76/0.98 apply (zenon_notimply_s _ _ zenon_He). zenon_intro zenon_H10. zenon_intro zenon_Hf.
% 0.76/0.98 generalize (subset_defn zenon_TB_h). zenon_intro zenon_H11.
% 0.76/0.98 generalize (zenon_H11 zenon_TC_k). zenon_intro zenon_H12.
% 0.76/0.98 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_H15; zenon_intro zenon_H14 | zenon_intro zenon_H10; zenon_intro zenon_H13 ].
% 0.76/0.98 exact (zenon_H15 zenon_H10).
% 0.76/0.98 generalize (subset_defn (intersection zenon_TB_h zenon_TD_n)). zenon_intro zenon_H16.
% 0.76/0.98 generalize (zenon_H16 (intersection zenon_TC_k zenon_TD_n)). zenon_intro zenon_H17.
% 0.76/0.98 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_Hf; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ].
% 0.76/0.98 apply (zenon_notallex_s (fun D : zenon_U => ((member D (intersection zenon_TB_h zenon_TD_n))->(member D (intersection zenon_TC_k zenon_TD_n)))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ].
% 0.76/0.98 elim zenon_H1b. zenon_intro zenon_TD_bc. zenon_intro zenon_H1d.
% 0.76/0.98 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 0.76/0.98 generalize (commutativity_of_intersection zenon_TD_n). zenon_intro zenon_H20.
% 0.76/0.98 generalize (intersection_defn zenon_TC_k). zenon_intro zenon_H21.
% 0.76/0.98 generalize (zenon_H21 zenon_TD_n). zenon_intro zenon_H22.
% 0.76/0.98 generalize (intersection_defn zenon_TD_n). zenon_intro zenon_H23.
% 0.76/0.98 generalize (intersection_defn zenon_TB_h). zenon_intro zenon_H24.
% 0.76/0.98 generalize (zenon_H20 zenon_TB_h). zenon_intro zenon_H25.
% 0.76/0.98 generalize (zenon_H23 zenon_TB_h). zenon_intro zenon_H26.
% 0.76/0.98 generalize (zenon_H22 zenon_TD_bc). zenon_intro zenon_H27.
% 0.76/0.98 apply (zenon_equiv_s _ _ zenon_H27); [ zenon_intro zenon_H1e; zenon_intro zenon_H2a | zenon_intro zenon_H29; zenon_intro zenon_H28 ].
% 0.76/0.98 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ].
% 0.76/0.98 generalize (zenon_H24 zenon_TD_n). zenon_intro zenon_H2d.
% 0.76/0.98 generalize (zenon_H13 zenon_TD_bc). zenon_intro zenon_H2e.
% 0.76/0.98 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.76/0.98 generalize (zenon_H2d zenon_TD_bc). zenon_intro zenon_H31.
% 0.76/0.98 apply (zenon_equiv_s _ _ zenon_H31); [ zenon_intro zenon_H34; zenon_intro zenon_H33 | zenon_intro zenon_H1f; zenon_intro zenon_H32 ].
% 0.76/0.98 exact (zenon_H34 zenon_H1f).
% 0.76/0.98 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H36. zenon_intro zenon_H35.
% 0.76/0.98 exact (zenon_H30 zenon_H36).
% 0.76/0.98 exact (zenon_H2c zenon_H2f).
% 0.76/0.98 generalize (zenon_H26 zenon_TD_bc). zenon_intro zenon_H37.
% 0.76/0.98 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3b; zenon_intro zenon_H3a | zenon_intro zenon_H39; zenon_intro zenon_H38 ].
% 0.76/0.98 cut ((member zenon_TD_bc (intersection zenon_TB_h zenon_TD_n)) = (member zenon_TD_bc (intersection zenon_TD_n zenon_TB_h))).
% 0.76/0.98 intro zenon_D_pnotp.
% 0.76/0.98 apply zenon_H3b.
% 0.76/0.98 rewrite <- zenon_D_pnotp.
% 0.76/0.98 exact zenon_H1f.
% 0.76/0.98 cut (((intersection zenon_TB_h zenon_TD_n) = (intersection zenon_TD_n zenon_TB_h))); [idtac | apply NNPP; zenon_intro zenon_H3c].
% 0.76/0.98 cut ((zenon_TD_bc = zenon_TD_bc)); [idtac | apply NNPP; zenon_intro zenon_H3d].
% 0.76/0.98 congruence.
% 0.76/0.98 apply zenon_H3d. apply refl_equal.
% 0.76/0.98 apply zenon_H3c. apply sym_equal. exact zenon_H25.
% 0.76/0.98 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H35. zenon_intro zenon_H36.
% 0.76/0.98 exact (zenon_H2b zenon_H35).
% 0.76/0.98 exact (zenon_H1e zenon_H29).
% 0.76/0.98 exact (zenon_Hf zenon_H19).
% 0.76/0.98 Qed.
% 0.76/0.98 % SZS output end Proof
% 0.76/0.98 (* END-PROOF *)
% 0.76/0.98 nodes searched: 18570
% 0.76/0.98 max branch formulas: 1155
% 0.76/0.98 proof nodes created: 1157
% 0.76/0.98 formulas created: 31657
% 0.76/0.98
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