TSTP Solution File: SET639+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n026.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 06:37:39 EDT 2022
% Result : Theorem 22.38s 22.57s
% Output : Proof 22.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n026.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 : Sat Jul 9 21:19:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 22.38/22.57 (* PROOF-FOUND *)
% 22.38/22.57 % SZS status Theorem
% 22.38/22.57 (* BEGIN-PROOF *)
% 22.38/22.57 % SZS output start Proof
% 22.38/22.57 Theorem prove_th121 : (forall B : zenon_U, (forall C : zenon_U, (((subset B C)/\((intersection C B) = (empty_set)))->(B = (empty_set))))).
% 22.38/22.57 Proof.
% 22.38/22.57 assert (zenon_L1_ : forall (zenon_TB_m : zenon_U) (zenon_TC_n : zenon_U), (~((intersection (intersection zenon_TC_n zenon_TB_m) zenon_TB_m) = (intersection (empty_set) zenon_TB_m))) -> ((intersection zenon_TC_n zenon_TB_m) = (empty_set)) -> False).
% 22.38/22.57 do 2 intro. intros zenon_Ha zenon_Hb.
% 22.38/22.57 cut ((zenon_TB_m = zenon_TB_m)); [idtac | apply NNPP; zenon_intro zenon_He].
% 22.38/22.57 cut (((intersection zenon_TC_n zenon_TB_m) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_Hf].
% 22.38/22.57 congruence.
% 22.38/22.57 exact (zenon_Hf zenon_Hb).
% 22.38/22.57 apply zenon_He. apply refl_equal.
% 22.38/22.57 (* end of lemma zenon_L1_ *)
% 22.38/22.57 assert (zenon_L2_ : forall (zenon_TB_m : zenon_U) (zenon_TD_s : zenon_U), ((member zenon_TD_s (empty_set))/\(member zenon_TD_s zenon_TB_m)) -> (~(member zenon_TD_s (empty_set))) -> False).
% 22.38/22.57 do 2 intro. intros zenon_H10 zenon_H11.
% 22.38/22.57 apply (zenon_and_s _ _ zenon_H10). zenon_intro zenon_H14. zenon_intro zenon_H13.
% 22.38/22.57 exact (zenon_H11 zenon_H14).
% 22.38/22.57 (* end of lemma zenon_L2_ *)
% 22.38/22.57 assert (zenon_L3_ : forall (zenon_TB_m : zenon_U), (~(subset (empty_set) zenon_TB_m)) -> False).
% 22.38/22.57 do 1 intro. intros zenon_H15.
% 22.38/22.57 generalize (subset_defn (empty_set)). zenon_intro zenon_H16.
% 22.38/22.57 generalize (zenon_H16 zenon_TB_m). zenon_intro zenon_H17.
% 22.38/22.57 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ].
% 22.38/22.57 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))->(member D zenon_TB_m))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ].
% 22.38/22.57 elim zenon_H1b. zenon_intro zenon_TD_bc. zenon_intro zenon_H1d.
% 22.38/22.57 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 22.38/22.57 generalize (empty_set_defn zenon_TD_bc). zenon_intro zenon_H20.
% 22.38/22.57 exact (zenon_H20 zenon_H1f).
% 22.38/22.57 exact (zenon_H15 zenon_H19).
% 22.38/22.57 (* end of lemma zenon_L3_ *)
% 22.38/22.57 apply NNPP. intro zenon_G.
% 22.38/22.57 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((subset B C)/\((intersection C B) = (empty_set)))->(B = (empty_set))))) zenon_G); [ zenon_intro zenon_H21; idtac ].
% 22.38/22.57 elim zenon_H21. zenon_intro zenon_TB_m. zenon_intro zenon_H22.
% 22.38/22.57 apply (zenon_notallex_s (fun C : zenon_U => (((subset zenon_TB_m C)/\((intersection C zenon_TB_m) = (empty_set)))->(zenon_TB_m = (empty_set)))) zenon_H22); [ zenon_intro zenon_H23; idtac ].
% 22.38/22.57 elim zenon_H23. zenon_intro zenon_TC_n. zenon_intro zenon_H24.
% 22.38/22.57 apply (zenon_notimply_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25.
% 22.38/22.57 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H27. zenon_intro zenon_Hb.
% 22.38/22.57 generalize (subset_defn zenon_TB_m). zenon_intro zenon_H28.
% 22.38/22.57 generalize (zenon_H28 zenon_TC_n). zenon_intro zenon_H29.
% 22.38/22.57 apply (zenon_equiv_s _ _ zenon_H29); [ zenon_intro zenon_H2c; zenon_intro zenon_H2b | zenon_intro zenon_H27; zenon_intro zenon_H2a ].
% 22.38/22.57 exact (zenon_H2c zenon_H27).
% 22.38/22.57 generalize (commutativity_of_intersection zenon_TB_m). zenon_intro zenon_H2d.
% 22.38/22.57 generalize (intersection_defn (intersection zenon_TC_n zenon_TB_m)). zenon_intro zenon_H2e.
% 22.38/22.57 generalize (intersection_defn (empty_set)). zenon_intro zenon_H2f.
% 22.38/22.57 generalize (intersection_defn zenon_TB_m). zenon_intro zenon_H30.
% 22.38/22.57 generalize (zenon_H2d zenon_TC_n). zenon_intro zenon_H31.
% 22.38/22.57 generalize (zenon_H2f zenon_TB_m). zenon_intro zenon_H32.
% 22.38/22.57 generalize (zenon_H2e zenon_TB_m). zenon_intro zenon_H33.
% 22.38/22.57 generalize (equal_defn zenon_TB_m). zenon_intro zenon_H34.
% 22.38/22.57 generalize (zenon_H30 zenon_TC_n). zenon_intro zenon_H35.
% 22.38/22.57 generalize (zenon_H34 (empty_set)). zenon_intro zenon_H36.
% 22.38/22.57 apply (zenon_equiv_s _ _ zenon_H36); [ zenon_intro zenon_H25; zenon_intro zenon_H39 | zenon_intro zenon_H38; zenon_intro zenon_H37 ].
% 22.38/22.57 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3a | zenon_intro zenon_H15 ].
% 22.38/22.57 generalize (subset_defn zenon_TB_m). zenon_intro zenon_H28.
% 22.38/22.57 generalize (zenon_H28 (empty_set)). zenon_intro zenon_H3b.
% 22.38/22.57 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3a; zenon_intro zenon_H3e | zenon_intro zenon_H3d; zenon_intro zenon_H3c ].
% 22.38/22.57 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_m)->(member D (empty_set)))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ].
% 22.38/22.58 elim zenon_H3f. zenon_intro zenon_TD_s. zenon_intro zenon_H40.
% 22.38/22.58 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H13. zenon_intro zenon_H11.
% 22.38/22.58 generalize (zenon_H32 zenon_TD_s). zenon_intro zenon_H41.
% 22.38/22.58 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H42; zenon_intro zenon_H10 ].
% 22.38/22.58 generalize (zenon_H33 zenon_TD_s). zenon_intro zenon_H45.
% 22.38/22.58 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H49; zenon_intro zenon_H48 | zenon_intro zenon_H47; zenon_intro zenon_H46 ].
% 22.38/22.58 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 22.38/22.58 generalize (zenon_H35 zenon_TD_s). zenon_intro zenon_H4c.
% 22.38/22.58 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H50; zenon_intro zenon_H4f | zenon_intro zenon_H4e; zenon_intro zenon_H4d ].
% 22.38/22.58 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H4a | zenon_intro zenon_H51 ].
% 22.38/22.58 exact (zenon_H4a zenon_H13).
% 22.38/22.58 generalize (zenon_H2a zenon_TD_s). zenon_intro zenon_H52.
% 22.38/22.58 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H4a | zenon_intro zenon_H53 ].
% 22.38/22.58 exact (zenon_H4a zenon_H13).
% 22.38/22.58 exact (zenon_H51 zenon_H53).
% 22.38/22.58 cut ((member zenon_TD_s (intersection zenon_TB_m zenon_TC_n)) = (member zenon_TD_s (intersection zenon_TC_n zenon_TB_m))).
% 22.38/22.58 intro zenon_D_pnotp.
% 22.38/22.58 apply zenon_H4b.
% 22.38/22.58 rewrite <- zenon_D_pnotp.
% 22.38/22.58 exact zenon_H4e.
% 22.38/22.58 cut (((intersection zenon_TB_m zenon_TC_n) = (intersection zenon_TC_n zenon_TB_m))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 22.38/22.58 cut ((zenon_TD_s = zenon_TD_s)); [idtac | apply NNPP; zenon_intro zenon_H55].
% 22.38/22.58 congruence.
% 22.38/22.58 apply zenon_H55. apply refl_equal.
% 22.38/22.58 exact (zenon_H54 zenon_H31).
% 22.38/22.58 exact (zenon_H4a zenon_H13).
% 22.38/22.58 cut ((member zenon_TD_s (intersection (intersection zenon_TC_n zenon_TB_m) zenon_TB_m)) = (member zenon_TD_s (intersection (empty_set) zenon_TB_m))).
% 22.38/22.58 intro zenon_D_pnotp.
% 22.38/22.58 apply zenon_H44.
% 22.38/22.58 rewrite <- zenon_D_pnotp.
% 22.38/22.58 exact zenon_H47.
% 22.38/22.58 cut (((intersection (intersection zenon_TC_n zenon_TB_m) zenon_TB_m) = (intersection (empty_set) zenon_TB_m))); [idtac | apply NNPP; zenon_intro zenon_Ha].
% 22.38/22.58 cut ((zenon_TD_s = zenon_TD_s)); [idtac | apply NNPP; zenon_intro zenon_H55].
% 22.38/22.58 congruence.
% 22.38/22.58 apply zenon_H55. apply refl_equal.
% 22.38/22.58 apply (zenon_L1_ zenon_TB_m zenon_TC_n); trivial.
% 22.38/22.58 apply (zenon_L2_ zenon_TB_m zenon_TD_s); trivial.
% 22.38/22.58 exact (zenon_H3a zenon_H3d).
% 22.38/22.58 apply (zenon_L3_ zenon_TB_m); trivial.
% 22.38/22.58 exact (zenon_H25 zenon_H38).
% 22.38/22.58 Qed.
% 22.38/22.58 % SZS output end Proof
% 22.38/22.58 (* END-PROOF *)
% 22.38/22.58 nodes searched: 841821
% 22.38/22.58 max branch formulas: 17798
% 22.38/22.58 proof nodes created: 42917
% 22.38/22.58 formulas created: 1538224
% 22.38/22.58
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