TSTP Solution File: SET063+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n019.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 06:33:21 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% 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 : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n019.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 21:48:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.49 (* PROOF-FOUND *)
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 (* BEGIN-PROOF *)
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Theorem prove_subset_of_empty_set_is_empty_set : (forall B : zenon_U, ((subset B (empty_set))->(B = (empty_set)))).
% 0.19/0.49 Proof.
% 0.19/0.49 apply NNPP. intro zenon_G.
% 0.19/0.49 apply (zenon_notallex_s (fun B : zenon_U => ((subset B (empty_set))->(B = (empty_set)))) zenon_G); [ zenon_intro zenon_H7; idtac ].
% 0.19/0.49 elim zenon_H7. zenon_intro zenon_TB_i. zenon_intro zenon_H9.
% 0.19/0.49 apply (zenon_notimply_s _ _ zenon_H9). zenon_intro zenon_Hb. zenon_intro zenon_Ha.
% 0.19/0.49 generalize (subset_defn zenon_TB_i). zenon_intro zenon_Hc.
% 0.19/0.49 generalize (zenon_Hc (empty_set)). zenon_intro zenon_Hd.
% 0.19/0.49 apply (zenon_equiv_s _ _ zenon_Hd); [ zenon_intro zenon_H10; zenon_intro zenon_Hf | zenon_intro zenon_Hb; zenon_intro zenon_He ].
% 0.19/0.49 exact (zenon_H10 zenon_Hb).
% 0.19/0.49 generalize (equal_defn (empty_set)). zenon_intro zenon_H11.
% 0.19/0.49 generalize (zenon_H11 zenon_TB_i). zenon_intro zenon_H12.
% 0.19/0.49 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_H16; zenon_intro zenon_H15 | zenon_intro zenon_H14; zenon_intro zenon_H13 ].
% 0.19/0.49 apply (zenon_notand_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H10 ].
% 0.19/0.49 generalize (subset_defn (empty_set)). zenon_intro zenon_H18.
% 0.19/0.49 generalize (zenon_H18 zenon_TB_i). zenon_intro zenon_H19.
% 0.19/0.49 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H17; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1a ].
% 0.19/0.49 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))->(member D zenon_TB_i))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ].
% 0.19/0.49 elim zenon_H1d. zenon_intro zenon_TD_be. zenon_intro zenon_H1f.
% 0.19/0.49 apply (zenon_notimply_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 0.19/0.49 generalize (empty_set_defn zenon_TD_be). zenon_intro zenon_H22.
% 0.19/0.49 exact (zenon_H22 zenon_H21).
% 0.19/0.49 exact (zenon_H17 zenon_H1b).
% 0.19/0.49 generalize (subset_defn zenon_TB_i). zenon_intro zenon_Hc.
% 0.19/0.49 generalize (zenon_Hc (empty_set)). zenon_intro zenon_Hd.
% 0.19/0.49 apply (zenon_equiv_s _ _ zenon_Hd); [ zenon_intro zenon_H10; zenon_intro zenon_Hf | zenon_intro zenon_Hb; zenon_intro zenon_He ].
% 0.19/0.49 exact (zenon_Hf zenon_He).
% 0.19/0.49 exact (zenon_H10 zenon_Hb).
% 0.19/0.49 apply zenon_Ha. apply sym_equal. exact zenon_H14.
% 0.19/0.49 Qed.
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49 (* END-PROOF *)
% 0.19/0.49 nodes searched: 67
% 0.19/0.49 max branch formulas: 60
% 0.19/0.49 proof nodes created: 17
% 0.19/0.49 formulas created: 462
% 0.19/0.49
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