TSTP Solution File: SET592+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n024.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 06:37:06 EDT 2022
% Result : Theorem 32.19s 32.46s
% Output : Proof 32.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n024.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 09:53:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 32.19/32.46 (* PROOF-FOUND *)
% 32.19/32.46 % SZS status Theorem
% 32.19/32.46 (* BEGIN-PROOF *)
% 32.19/32.46 % SZS output start Proof
% 32.19/32.46 Theorem prove_th51 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\((subset B D)/\((intersection C D) = (empty_set))))->(B = (empty_set)))))).
% 32.19/32.46 Proof.
% 32.19/32.46 assert (zenon_L1_ : forall (zenon_TC_n : zenon_U) (zenon_TB_o : zenon_U), (forall D : zenon_U, ((member D zenon_TB_o)->(member D zenon_TC_n))) -> (~(subset zenon_TB_o zenon_TC_n)) -> False).
% 32.19/32.46 do 2 intro. intros zenon_Hb zenon_Hc.
% 32.19/32.46 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf.
% 32.19/32.46 generalize (zenon_Hf zenon_TC_n). zenon_intro zenon_H10.
% 32.19/32.46 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hc; zenon_intro zenon_H12 | zenon_intro zenon_H11; zenon_intro zenon_Hb ].
% 32.19/32.46 exact (zenon_H12 zenon_Hb).
% 32.19/32.46 exact (zenon_Hc zenon_H11).
% 32.19/32.46 (* end of lemma zenon_L1_ *)
% 32.19/32.46 assert (zenon_L2_ : forall (zenon_TD_v : zenon_U) (zenon_TB_o : zenon_U), (forall D : zenon_U, ((member D zenon_TB_o)->(member D zenon_TD_v))) -> (~(subset zenon_TB_o zenon_TD_v)) -> False).
% 32.19/32.46 do 2 intro. intros zenon_H13 zenon_H14.
% 32.19/32.47 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf.
% 32.19/32.47 generalize (zenon_Hf zenon_TD_v). zenon_intro zenon_H16.
% 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H14; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H13 ].
% 32.19/32.47 exact (zenon_H18 zenon_H13).
% 32.19/32.47 exact (zenon_H14 zenon_H17).
% 32.19/32.47 (* end of lemma zenon_L2_ *)
% 32.19/32.47 assert (zenon_L3_ : forall (zenon_TD_bc : zenon_U) (zenon_TD_v : zenon_U) (zenon_TC_n : zenon_U) (zenon_TB_o : zenon_U), (forall D : zenon_U, ((member D zenon_TB_o)->(member D (intersection zenon_TC_n zenon_TD_v)))) -> (member zenon_TD_bc zenon_TB_o) -> (~(member zenon_TD_bc (intersection zenon_TC_n zenon_TD_v))) -> False).
% 32.19/32.47 do 4 intro. intros zenon_H19 zenon_H1a zenon_H1b.
% 32.19/32.47 generalize (zenon_H19 zenon_TD_bc). zenon_intro zenon_H1d.
% 32.19/32.47 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 32.19/32.47 exact (zenon_H1f zenon_H1a).
% 32.19/32.47 exact (zenon_H1b zenon_H1e).
% 32.19/32.47 (* end of lemma zenon_L3_ *)
% 32.19/32.47 assert (zenon_L4_ : forall (zenon_TD_bc : zenon_U) (zenon_TD_v : zenon_U) (zenon_TB_o : zenon_U), (forall D : zenon_U, ((member D zenon_TB_o)->(member D zenon_TD_v))) -> (member zenon_TD_bc zenon_TB_o) -> (~(member zenon_TD_bc zenon_TD_v)) -> False).
% 32.19/32.47 do 3 intro. intros zenon_H13 zenon_H1a zenon_H20.
% 32.19/32.47 generalize (zenon_H13 zenon_TD_bc). zenon_intro zenon_H21.
% 32.19/32.47 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H1f | zenon_intro zenon_H22 ].
% 32.19/32.47 exact (zenon_H1f zenon_H1a).
% 32.19/32.47 exact (zenon_H20 zenon_H22).
% 32.19/32.47 (* end of lemma zenon_L4_ *)
% 32.19/32.47 assert (zenon_L5_ : forall (zenon_TD_v : zenon_U) (zenon_TC_n : zenon_U), (~((intersection (intersection zenon_TC_n zenon_TD_v) zenon_TD_v) = (intersection (empty_set) zenon_TD_v))) -> ((intersection zenon_TC_n zenon_TD_v) = (empty_set)) -> False).
% 32.19/32.47 do 2 intro. intros zenon_H23 zenon_H24.
% 32.19/32.47 cut ((zenon_TD_v = zenon_TD_v)); [idtac | apply NNPP; zenon_intro zenon_H25].
% 32.19/32.47 cut (((intersection zenon_TC_n zenon_TD_v) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H26].
% 32.19/32.47 congruence.
% 32.19/32.47 exact (zenon_H26 zenon_H24).
% 32.19/32.47 apply zenon_H25. apply refl_equal.
% 32.19/32.47 (* end of lemma zenon_L5_ *)
% 32.19/32.47 assert (zenon_L6_ : forall (zenon_TD_v : zenon_U) (zenon_TD_bc : zenon_U), ((member zenon_TD_bc (empty_set))/\(member zenon_TD_bc zenon_TD_v)) -> (~(member zenon_TD_bc (empty_set))) -> False).
% 32.19/32.47 do 2 intro. intros zenon_H27 zenon_H28.
% 32.19/32.47 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H22.
% 32.19/32.47 exact (zenon_H28 zenon_H29).
% 32.19/32.47 (* end of lemma zenon_L6_ *)
% 32.19/32.47 assert (zenon_L7_ : forall (zenon_TD_bc : zenon_U), (member zenon_TD_bc (empty_set)) -> False).
% 32.19/32.47 do 1 intro. intros zenon_H29.
% 32.19/32.47 generalize (empty_set_defn zenon_TD_bc). zenon_intro zenon_H28.
% 32.19/32.47 exact (zenon_H28 zenon_H29).
% 32.19/32.47 (* end of lemma zenon_L7_ *)
% 32.19/32.47 apply NNPP. intro zenon_G.
% 32.19/32.47 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\((subset B D)/\((intersection C D) = (empty_set))))->(B = (empty_set)))))) zenon_G); [ zenon_intro zenon_H2a; idtac ].
% 32.19/32.47 elim zenon_H2a. zenon_intro zenon_TB_o. zenon_intro zenon_H2b.
% 32.19/32.47 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TB_o C)/\((subset zenon_TB_o D)/\((intersection C D) = (empty_set))))->(zenon_TB_o = (empty_set))))) zenon_H2b); [ zenon_intro zenon_H2c; idtac ].
% 32.19/32.47 elim zenon_H2c. zenon_intro zenon_TC_n. zenon_intro zenon_H2d.
% 32.19/32.47 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TB_o zenon_TC_n)/\((subset zenon_TB_o D)/\((intersection zenon_TC_n D) = (empty_set))))->(zenon_TB_o = (empty_set)))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ].
% 32.19/32.47 elim zenon_H2e. zenon_intro zenon_TD_v. zenon_intro zenon_H2f.
% 32.19/32.47 apply (zenon_notimply_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30.
% 32.19/32.47 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H11. zenon_intro zenon_H32.
% 32.19/32.47 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H17. zenon_intro zenon_H24.
% 32.19/32.47 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf.
% 32.19/32.47 generalize (zenon_Hf zenon_TC_n). zenon_intro zenon_H10.
% 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hc; zenon_intro zenon_H12 | zenon_intro zenon_H11; zenon_intro zenon_Hb ].
% 32.19/32.47 exact (zenon_Hc zenon_H11).
% 32.19/32.47 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf.
% 32.19/32.47 generalize (zenon_Hf zenon_TD_v). zenon_intro zenon_H16.
% 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H14; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H13 ].
% 32.19/32.47 exact (zenon_H14 zenon_H17).
% 32.19/32.47 generalize (equal_member_defn (empty_set)). zenon_intro zenon_H33.
% 32.19/32.47 generalize (zenon_H33 zenon_TB_o). zenon_intro zenon_H34.
% 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H38; zenon_intro zenon_H37 | zenon_intro zenon_H36; zenon_intro zenon_H35 ].
% 32.19/32.47 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))<->(member D zenon_TB_o))) zenon_H37); [ zenon_intro zenon_H39; idtac ].
% 32.19/32.47 elim zenon_H39. zenon_intro zenon_TD_bc. zenon_intro zenon_H3a.
% 32.19/32.47 apply (zenon_notequiv_s _ _ zenon_H3a); [ zenon_intro zenon_H28; zenon_intro zenon_H1a | zenon_intro zenon_H29; zenon_intro zenon_H1f ].
% 32.19/32.47 generalize (intersection_of_subsets zenon_TB_o). zenon_intro zenon_H3b.
% 32.19/32.47 generalize (intersection_defn (empty_set)). zenon_intro zenon_H3c.
% 32.19/32.47 generalize (zenon_H3b zenon_TC_n). zenon_intro zenon_H3d.
% 32.19/32.47 generalize (zenon_H3c zenon_TD_v). zenon_intro zenon_H3e.
% 32.19/32.47 generalize (zenon_H3e zenon_TD_bc). zenon_intro zenon_H3f.
% 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H42; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H27 ].
% 32.19/32.47 generalize (zenon_H3d zenon_TD_v). zenon_intro zenon_H43.
% 32.19/32.47 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 32.19/32.47 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_Hc | zenon_intro zenon_H14 ].
% 32.19/32.47 apply (zenon_L1_ zenon_TC_n zenon_TB_o); trivial.
% 32.19/32.47 apply (zenon_L2_ zenon_TD_v zenon_TB_o); trivial.
% 32.19/32.47 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf.
% 32.19/32.47 generalize (zenon_Hf (intersection zenon_TC_n zenon_TD_v)). zenon_intro zenon_H46.
% 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H48; zenon_intro zenon_H47 | zenon_intro zenon_H44; zenon_intro zenon_H19 ].
% 32.19/32.47 exact (zenon_H48 zenon_H44).
% 32.19/32.47 generalize (intersection_defn (intersection zenon_TC_n zenon_TD_v)). zenon_intro zenon_H49.
% 32.19/32.47 generalize (zenon_H49 zenon_TD_v). zenon_intro zenon_H4a.
% 32.19/32.47 generalize (zenon_H4a zenon_TD_bc). zenon_intro zenon_H4b.
% 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_H4c ].
% 32.19/32.47 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H1b | zenon_intro zenon_H20 ].
% 32.19/32.47 apply (zenon_L3_ zenon_TD_bc zenon_TD_v zenon_TC_n zenon_TB_o); trivial.
% 32.19/32.47 apply (zenon_L4_ zenon_TD_bc zenon_TD_v zenon_TB_o); trivial.
% 32.19/32.47 cut ((member zenon_TD_bc (intersection (intersection zenon_TC_n zenon_TD_v) zenon_TD_v)) = (member zenon_TD_bc (intersection (empty_set) zenon_TD_v))).
% 32.19/32.47 intro zenon_D_pnotp.
% 32.19/32.47 apply zenon_H42.
% 32.19/32.47 rewrite <- zenon_D_pnotp.
% 32.19/32.47 exact zenon_H4d.
% 32.19/32.47 cut (((intersection (intersection zenon_TC_n zenon_TD_v) zenon_TD_v) = (intersection (empty_set) zenon_TD_v))); [idtac | apply NNPP; zenon_intro zenon_H23].
% 32.19/32.47 cut ((zenon_TD_bc = zenon_TD_bc)); [idtac | apply NNPP; zenon_intro zenon_H50].
% 32.19/32.47 congruence.
% 32.19/32.47 apply zenon_H50. apply refl_equal.
% 32.29/32.48 apply (zenon_L5_ zenon_TD_v zenon_TC_n); trivial.
% 32.29/32.48 apply (zenon_L6_ zenon_TD_v zenon_TD_bc); trivial.
% 32.29/32.48 apply (zenon_L7_ zenon_TD_bc); trivial.
% 32.29/32.48 apply zenon_H30. apply sym_equal. exact zenon_H36.
% 32.29/32.48 Qed.
% 32.29/32.48 % SZS output end Proof
% 32.29/32.48 (* END-PROOF *)
% 32.29/32.48 nodes searched: 1165023
% 32.29/32.48 max branch formulas: 21838
% 32.29/32.48 proof nodes created: 30538
% 32.29/32.48 formulas created: 2167699
% 32.29/32.48
%------------------------------------------------------------------------------