TSTP Solution File: SET603+4 by Zenon---0.7.1
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% File : Zenon---0.7.1
% Problem : SET603+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n009.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 06:37:14 EDT 2022
% Result : Theorem 0.40s 0.57s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET603+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n009.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 20:28:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.40/0.57 (* PROOF-FOUND *)
% 0.40/0.57 % SZS status Theorem
% 0.40/0.57 (* BEGIN-PROOF *)
% 0.40/0.57 % SZS output start Proof
% 0.40/0.57 Theorem thI30 : (forall E : zenon_U, (equal_set (difference E (empty_set)) E)).
% 0.40/0.57 Proof.
% 0.40/0.57 assert (zenon_L1_ : forall (zenon_TX_n : zenon_U), (member zenon_TX_n (empty_set)) -> False).
% 0.40/0.57 do 1 intro. intros zenon_Hc.
% 0.40/0.57 generalize (empty_set zenon_TX_n). zenon_intro zenon_He.
% 0.40/0.57 exact (zenon_He zenon_Hc).
% 0.40/0.57 (* end of lemma zenon_L1_ *)
% 0.40/0.57 assert (zenon_L2_ : forall (zenon_TX_n : zenon_U), (~(~(member zenon_TX_n (empty_set)))) -> False).
% 0.40/0.57 do 1 intro. intros zenon_Hf.
% 0.40/0.57 apply zenon_Hf. zenon_intro zenon_Hc.
% 0.40/0.57 apply (zenon_L1_ zenon_TX_n); trivial.
% 0.40/0.57 (* end of lemma zenon_L2_ *)
% 0.40/0.57 apply NNPP. intro zenon_G.
% 0.40/0.57 apply (zenon_notallex_s (fun E : zenon_U => (equal_set (difference E (empty_set)) E)) zenon_G); [ zenon_intro zenon_H10; idtac ].
% 0.40/0.57 elim zenon_H10. zenon_intro zenon_TE_r. zenon_intro zenon_H12.
% 0.40/0.57 generalize (equal_set (difference zenon_TE_r (empty_set))). zenon_intro zenon_H13.
% 0.40/0.57 generalize (zenon_H13 zenon_TE_r). zenon_intro zenon_H14.
% 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H12; zenon_intro zenon_H17 | zenon_intro zenon_H16; zenon_intro zenon_H15 ].
% 0.40/0.57 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 0.40/0.57 generalize (subset (difference zenon_TE_r (empty_set))). zenon_intro zenon_H1a.
% 0.40/0.57 generalize (zenon_H1a zenon_TE_r). zenon_intro zenon_H1b.
% 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H19; zenon_intro zenon_H1e | zenon_intro zenon_H1d; zenon_intro zenon_H1c ].
% 0.40/0.57 apply (zenon_notallex_s (fun X : zenon_U => ((member X (difference zenon_TE_r (empty_set)))->(member X zenon_TE_r))) zenon_H1e); [ zenon_intro zenon_H1f; idtac ].
% 0.40/0.57 elim zenon_H1f. zenon_intro zenon_TX_bg. zenon_intro zenon_H21.
% 0.40/0.57 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 0.40/0.57 generalize (difference zenon_TX_bg). zenon_intro zenon_H24.
% 0.40/0.57 generalize (zenon_H24 (empty_set)). zenon_intro zenon_H25.
% 0.40/0.57 generalize (zenon_H25 zenon_TE_r). zenon_intro zenon_H26.
% 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H29; zenon_intro zenon_H28 | zenon_intro zenon_H23; zenon_intro zenon_H27 ].
% 0.40/0.57 exact (zenon_H29 zenon_H23).
% 0.40/0.57 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2b. zenon_intro zenon_H2a.
% 0.40/0.57 exact (zenon_H22 zenon_H2b).
% 0.40/0.57 exact (zenon_H19 zenon_H1d).
% 0.40/0.57 generalize (subset zenon_TE_r). zenon_intro zenon_H2c.
% 0.40/0.57 generalize (zenon_H2c (difference zenon_TE_r (empty_set))). zenon_intro zenon_H2d.
% 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H18; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ].
% 0.40/0.57 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TE_r)->(member X (difference zenon_TE_r (empty_set))))) zenon_H30); [ zenon_intro zenon_H31; idtac ].
% 0.40/0.57 elim zenon_H31. zenon_intro zenon_TX_n. zenon_intro zenon_H32.
% 0.40/0.57 apply (zenon_notimply_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 0.40/0.57 generalize (difference zenon_TX_n). zenon_intro zenon_H35.
% 0.40/0.57 generalize (zenon_H35 (empty_set)). zenon_intro zenon_H36.
% 0.40/0.57 generalize (zenon_H36 zenon_TE_r). zenon_intro zenon_H37.
% 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H33; zenon_intro zenon_H3a | zenon_intro zenon_H39; zenon_intro zenon_H38 ].
% 0.40/0.57 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3b | zenon_intro zenon_Hf ].
% 0.40/0.57 exact (zenon_H3b zenon_H34).
% 0.40/0.57 apply (zenon_L2_ zenon_TX_n); trivial.
% 0.40/0.57 exact (zenon_H33 zenon_H39).
% 0.40/0.57 exact (zenon_H18 zenon_H2f).
% 0.40/0.57 exact (zenon_H12 zenon_H16).
% 0.40/0.57 Qed.
% 0.40/0.57 % SZS output end Proof
% 0.40/0.57 (* END-PROOF *)
% 0.40/0.57 nodes searched: 2166
% 0.40/0.57 max branch formulas: 698
% 0.40/0.57 proof nodes created: 118
% 0.40/0.57 formulas created: 12436
% 0.40/0.57
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