TSTP Solution File: SET591+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n014.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 0.18s 0.54s
% Output : Proof 0.18s
% 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 : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n014.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 : Sun Jul 10 12:43:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.54 (* PROOF-FOUND *)
% 0.18/0.54 % SZS status Theorem
% 0.18/0.54 (* BEGIN-PROOF *)
% 0.18/0.54 % SZS output start Proof
% 0.18/0.54 Theorem prove_th50 : (forall B : zenon_U, (forall C : zenon_U, ((subset B (difference C B))->(B = (empty_set))))).
% 0.18/0.54 Proof.
% 0.18/0.54 apply NNPP. intro zenon_G.
% 0.18/0.54 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((subset B (difference C B))->(B = (empty_set))))) zenon_G); [ zenon_intro zenon_H7; idtac ].
% 0.18/0.54 elim zenon_H7. zenon_intro zenon_TB_i. zenon_intro zenon_H9.
% 0.18/0.54 apply (zenon_notallex_s (fun C : zenon_U => ((subset zenon_TB_i (difference C zenon_TB_i))->(zenon_TB_i = (empty_set)))) zenon_H9); [ zenon_intro zenon_Ha; idtac ].
% 0.18/0.54 elim zenon_Ha. zenon_intro zenon_TC_l. zenon_intro zenon_Hc.
% 0.18/0.54 apply (zenon_notimply_s _ _ zenon_Hc). zenon_intro zenon_He. zenon_intro zenon_Hd.
% 0.18/0.54 generalize (subset_defn zenon_TB_i). zenon_intro zenon_Hf.
% 0.18/0.54 generalize (zenon_Hf (difference zenon_TC_l zenon_TB_i)). zenon_intro zenon_H10.
% 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_H13; zenon_intro zenon_H12 | zenon_intro zenon_He; zenon_intro zenon_H11 ].
% 0.18/0.54 exact (zenon_H13 zenon_He).
% 0.18/0.54 generalize (difference_defn zenon_TC_l). zenon_intro zenon_H14.
% 0.18/0.54 generalize (equal_defn zenon_TB_i). zenon_intro zenon_H15.
% 0.18/0.54 generalize (zenon_H14 zenon_TB_i). zenon_intro zenon_H16.
% 0.18/0.54 generalize (zenon_H15 (empty_set)). zenon_intro zenon_H17.
% 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_Hd; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ].
% 0.18/0.54 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.18/0.54 generalize (subset_defn zenon_TB_i). zenon_intro zenon_Hf.
% 0.18/0.54 generalize (zenon_Hf (empty_set)). zenon_intro zenon_H1d.
% 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H1c; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ].
% 0.18/0.54 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_i)->(member D (empty_set)))) zenon_H20); [ zenon_intro zenon_H21; idtac ].
% 0.18/0.54 elim zenon_H21. zenon_intro zenon_TD_bi. zenon_intro zenon_H23.
% 0.18/0.54 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 0.18/0.54 generalize (zenon_H16 zenon_TD_bi). zenon_intro zenon_H26.
% 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H2a; zenon_intro zenon_H29 | zenon_intro zenon_H28; zenon_intro zenon_H27 ].
% 0.18/0.54 generalize (zenon_H11 zenon_TD_bi). zenon_intro zenon_H2b.
% 0.18/0.54 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2c | zenon_intro zenon_H28 ].
% 0.18/0.54 exact (zenon_H2c zenon_H25).
% 0.18/0.54 exact (zenon_H2a zenon_H28).
% 0.18/0.54 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 0.18/0.54 exact (zenon_H2c zenon_H25).
% 0.18/0.54 exact (zenon_H1c zenon_H1f).
% 0.18/0.54 generalize (subset_defn (empty_set)). zenon_intro zenon_H2e.
% 0.18/0.54 generalize (zenon_H2e zenon_TB_i). zenon_intro zenon_H2f.
% 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H1b; zenon_intro zenon_H32 | zenon_intro zenon_H31; zenon_intro zenon_H30 ].
% 0.18/0.54 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))->(member D zenon_TB_i))) zenon_H32); [ zenon_intro zenon_H33; idtac ].
% 0.18/0.54 elim zenon_H33. zenon_intro zenon_TD_ca. zenon_intro zenon_H35.
% 0.18/0.54 apply (zenon_notimply_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36.
% 0.18/0.54 generalize (empty_set_defn zenon_TD_ca). zenon_intro zenon_H38.
% 0.18/0.54 exact (zenon_H38 zenon_H37).
% 0.18/0.54 exact (zenon_H1b zenon_H31).
% 0.18/0.54 exact (zenon_Hd zenon_H19).
% 0.18/0.54 Qed.
% 0.18/0.54 % SZS output end Proof
% 0.18/0.54 (* END-PROOF *)
% 0.18/0.54 nodes searched: 2096
% 0.18/0.54 max branch formulas: 537
% 0.18/0.54 proof nodes created: 194
% 0.18/0.54 formulas created: 6455
% 0.18/0.54
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