TSTP Solution File: SET183+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n005.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 06:34:43 EDT 2022
% Result : Theorem 0.92s 1.08s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 21:58:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.92/1.08 (* PROOF-FOUND *)
% 0.92/1.08 % SZS status Theorem
% 0.92/1.08 (* BEGIN-PROOF *)
% 0.92/1.08 % SZS output start Proof
% 0.92/1.08 Theorem prove_subset_intersection : (forall B : zenon_U, (forall C : zenon_U, ((subset B C)->((intersection B C) = B)))).
% 0.92/1.08 Proof.
% 0.92/1.08 apply NNPP. intro zenon_G.
% 0.92/1.08 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((subset B C)->((intersection B C) = B)))) zenon_G); [ zenon_intro zenon_H8; idtac ].
% 0.92/1.08 elim zenon_H8. zenon_intro zenon_TB_j. zenon_intro zenon_Ha.
% 0.92/1.08 apply (zenon_notallex_s (fun C : zenon_U => ((subset zenon_TB_j C)->((intersection zenon_TB_j C) = zenon_TB_j))) zenon_Ha); [ zenon_intro zenon_Hb; idtac ].
% 0.92/1.08 elim zenon_Hb. zenon_intro zenon_TC_m. zenon_intro zenon_Hd.
% 0.92/1.08 apply (zenon_notimply_s _ _ zenon_Hd). zenon_intro zenon_Hf. zenon_intro zenon_He.
% 0.92/1.08 generalize (subset_defn zenon_TB_j). zenon_intro zenon_H10.
% 0.92/1.08 generalize (zenon_H10 zenon_TC_m). zenon_intro zenon_H11.
% 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H11); [ zenon_intro zenon_H14; zenon_intro zenon_H13 | zenon_intro zenon_Hf; zenon_intro zenon_H12 ].
% 0.92/1.08 exact (zenon_H14 zenon_Hf).
% 0.92/1.08 generalize (commutativity_of_intersection zenon_TC_m). zenon_intro zenon_H15.
% 0.92/1.08 generalize (intersection_defn zenon_TC_m). zenon_intro zenon_H16.
% 0.92/1.08 generalize (equal_defn zenon_TB_j). zenon_intro zenon_H17.
% 0.92/1.08 generalize (zenon_H15 zenon_TB_j). zenon_intro zenon_H18.
% 0.92/1.08 generalize (zenon_H16 zenon_TB_j). zenon_intro zenon_H19.
% 0.92/1.08 elim (classic (zenon_TB_j = zenon_TB_j)); [ zenon_intro zenon_H1a | zenon_intro zenon_H1b ].
% 0.92/1.08 cut ((zenon_TB_j = zenon_TB_j) = ((intersection zenon_TB_j zenon_TC_m) = zenon_TB_j)).
% 0.92/1.08 intro zenon_D_pnotp.
% 0.92/1.08 apply zenon_He.
% 0.92/1.08 rewrite <- zenon_D_pnotp.
% 0.92/1.08 exact zenon_H1a.
% 0.92/1.08 cut ((zenon_TB_j = zenon_TB_j)); [idtac | apply NNPP; zenon_intro zenon_H1b].
% 0.92/1.08 cut ((zenon_TB_j = (intersection zenon_TB_j zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 0.92/1.08 congruence.
% 0.92/1.08 cut (((intersection zenon_TC_m zenon_TB_j) = (intersection zenon_TB_j zenon_TC_m)) = (zenon_TB_j = (intersection zenon_TB_j zenon_TC_m))).
% 0.92/1.08 intro zenon_D_pnotp.
% 0.92/1.08 apply zenon_H1c.
% 0.92/1.08 rewrite <- zenon_D_pnotp.
% 0.92/1.08 exact zenon_H18.
% 0.92/1.08 cut (((intersection zenon_TB_j zenon_TC_m) = (intersection zenon_TB_j zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_H1d].
% 0.92/1.08 cut (((intersection zenon_TC_m zenon_TB_j) = zenon_TB_j)); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 0.92/1.08 congruence.
% 0.92/1.08 elim (classic (zenon_TB_j = zenon_TB_j)); [ zenon_intro zenon_H1a | zenon_intro zenon_H1b ].
% 0.92/1.08 cut ((zenon_TB_j = zenon_TB_j) = ((intersection zenon_TC_m zenon_TB_j) = zenon_TB_j)).
% 0.92/1.08 intro zenon_D_pnotp.
% 0.92/1.08 apply zenon_H1e.
% 0.92/1.08 rewrite <- zenon_D_pnotp.
% 0.92/1.08 exact zenon_H1a.
% 0.92/1.08 cut ((zenon_TB_j = zenon_TB_j)); [idtac | apply NNPP; zenon_intro zenon_H1b].
% 0.92/1.08 cut ((zenon_TB_j = (intersection zenon_TC_m zenon_TB_j))); [idtac | apply NNPP; zenon_intro zenon_H1f].
% 0.92/1.08 congruence.
% 0.92/1.08 generalize (zenon_H17 (intersection zenon_TC_m zenon_TB_j)). zenon_intro zenon_H20.
% 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H1f; zenon_intro zenon_H23 | zenon_intro zenon_H22; zenon_intro zenon_H21 ].
% 0.92/1.08 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ].
% 0.92/1.08 generalize (subset_defn zenon_TB_j). zenon_intro zenon_H10.
% 0.92/1.08 generalize (zenon_H10 (intersection zenon_TC_m zenon_TB_j)). zenon_intro zenon_H26.
% 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H25; zenon_intro zenon_H29 | zenon_intro zenon_H28; zenon_intro zenon_H27 ].
% 0.92/1.08 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_j)->(member D (intersection zenon_TC_m zenon_TB_j)))) zenon_H29); [ zenon_intro zenon_H2a; idtac ].
% 0.92/1.08 elim zenon_H2a. zenon_intro zenon_TD_br. zenon_intro zenon_H2c.
% 0.92/1.08 apply (zenon_notimply_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 0.92/1.08 generalize (zenon_H19 zenon_TD_br). zenon_intro zenon_H2f.
% 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H2d; zenon_intro zenon_H32 | zenon_intro zenon_H31; zenon_intro zenon_H30 ].
% 0.92/1.08 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.92/1.08 generalize (zenon_H12 zenon_TD_br). zenon_intro zenon_H35.
% 0.92/1.08 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H33 | zenon_intro zenon_H36 ].
% 0.92/1.08 exact (zenon_H33 zenon_H2e).
% 0.92/1.08 exact (zenon_H34 zenon_H36).
% 0.92/1.08 exact (zenon_H33 zenon_H2e).
% 0.92/1.08 exact (zenon_H2d zenon_H31).
% 0.92/1.08 exact (zenon_H25 zenon_H28).
% 0.92/1.08 generalize (subset_defn (intersection zenon_TC_m zenon_TB_j)). zenon_intro zenon_H37.
% 0.92/1.08 generalize (zenon_H37 zenon_TB_j). zenon_intro zenon_H38.
% 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H38); [ zenon_intro zenon_H24; zenon_intro zenon_H3b | zenon_intro zenon_H3a; zenon_intro zenon_H39 ].
% 0.92/1.08 apply (zenon_notallex_s (fun D : zenon_U => ((member D (intersection zenon_TC_m zenon_TB_j))->(member D zenon_TB_j))) zenon_H3b); [ zenon_intro zenon_H3c; idtac ].
% 0.92/1.08 elim zenon_H3c. zenon_intro zenon_TD_cj. zenon_intro zenon_H3e.
% 0.92/1.08 apply (zenon_notimply_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f.
% 0.92/1.08 generalize (zenon_H19 zenon_TD_cj). zenon_intro zenon_H41.
% 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H40; zenon_intro zenon_H42 ].
% 0.92/1.08 exact (zenon_H44 zenon_H40).
% 0.92/1.08 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H46. zenon_intro zenon_H45.
% 0.92/1.08 exact (zenon_H3f zenon_H45).
% 0.92/1.08 exact (zenon_H24 zenon_H3a).
% 0.92/1.08 exact (zenon_H1f zenon_H22).
% 0.92/1.08 apply zenon_H1b. apply refl_equal.
% 0.92/1.08 apply zenon_H1b. apply refl_equal.
% 0.92/1.08 apply zenon_H1d. apply refl_equal.
% 0.92/1.08 apply zenon_H1b. apply refl_equal.
% 0.92/1.08 apply zenon_H1b. apply refl_equal.
% 0.92/1.08 Qed.
% 0.92/1.08 % SZS output end Proof
% 0.92/1.08 (* END-PROOF *)
% 0.92/1.08 nodes searched: 18882
% 0.92/1.08 max branch formulas: 1946
% 0.92/1.08 proof nodes created: 1009
% 0.92/1.08 formulas created: 38648
% 0.92/1.08
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