TSTP Solution File: SET583+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET583+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n008.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 06:37:00 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET583+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n008.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 : Sat Jul 9 16:37:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.52 (* PROOF-FOUND *)
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 (* BEGIN-PROOF *)
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 Theorem prove_extensionality : (forall B : zenon_U, (forall C : zenon_U, (((subset B C)/\(subset C B))->(B = C)))).
% 0.20/0.52 Proof.
% 0.20/0.52 apply NNPP. intro zenon_G.
% 0.20/0.52 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((subset B C)/\(subset C B))->(B = C)))) zenon_G); [ zenon_intro zenon_H4; idtac ].
% 0.20/0.52 elim zenon_H4. zenon_intro zenon_TB_f. zenon_intro zenon_H6.
% 0.20/0.52 apply (zenon_notallex_s (fun C : zenon_U => (((subset zenon_TB_f C)/\(subset C zenon_TB_f))->(zenon_TB_f = C))) zenon_H6); [ zenon_intro zenon_H7; idtac ].
% 0.20/0.52 elim zenon_H7. zenon_intro zenon_TC_i. zenon_intro zenon_H9.
% 0.20/0.52 apply (zenon_notimply_s _ _ zenon_H9). zenon_intro zenon_Hb. zenon_intro zenon_Ha.
% 0.20/0.52 apply (zenon_and_s _ _ zenon_Hb). zenon_intro zenon_Hd. zenon_intro zenon_Hc.
% 0.20/0.52 generalize (subset_defn zenon_TB_f). zenon_intro zenon_He.
% 0.20/0.52 generalize (zenon_He zenon_TC_i). zenon_intro zenon_Hf.
% 0.20/0.52 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H12; zenon_intro zenon_H11 | zenon_intro zenon_Hd; zenon_intro zenon_H10 ].
% 0.20/0.52 exact (zenon_H12 zenon_Hd).
% 0.20/0.52 generalize (subset_defn zenon_TC_i). zenon_intro zenon_H13.
% 0.20/0.52 generalize (zenon_H13 zenon_TB_f). zenon_intro zenon_H14.
% 0.20/0.52 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H17; zenon_intro zenon_H16 | zenon_intro zenon_Hc; zenon_intro zenon_H15 ].
% 0.20/0.52 exact (zenon_H17 zenon_Hc).
% 0.20/0.52 generalize (equal_defn zenon_TB_f). zenon_intro zenon_H18.
% 0.20/0.52 generalize (zenon_H18 zenon_TC_i). zenon_intro zenon_H19.
% 0.20/0.52 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_Ha; zenon_intro zenon_H1b | zenon_intro zenon_H1a; zenon_intro zenon_Hb ].
% 0.20/0.52 apply (zenon_notand_s _ _ zenon_H1b); [ zenon_intro zenon_H12 | zenon_intro zenon_H17 ].
% 0.20/0.52 generalize (subset_defn zenon_TB_f). zenon_intro zenon_He.
% 0.20/0.52 generalize (zenon_He zenon_TC_i). zenon_intro zenon_Hf.
% 0.20/0.52 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H12; zenon_intro zenon_H11 | zenon_intro zenon_Hd; zenon_intro zenon_H10 ].
% 0.20/0.52 exact (zenon_H11 zenon_H10).
% 0.20/0.52 exact (zenon_H12 zenon_Hd).
% 0.20/0.52 generalize (subset_defn zenon_TC_i). zenon_intro zenon_H13.
% 0.20/0.52 generalize (zenon_H13 zenon_TB_f). zenon_intro zenon_H14.
% 0.20/0.52 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H17; zenon_intro zenon_H16 | zenon_intro zenon_Hc; zenon_intro zenon_H15 ].
% 0.20/0.52 exact (zenon_H16 zenon_H15).
% 0.20/0.52 exact (zenon_H17 zenon_Hc).
% 0.20/0.52 exact (zenon_Ha zenon_H1a).
% 0.20/0.52 Qed.
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52 (* END-PROOF *)
% 0.20/0.52 nodes searched: 68
% 0.20/0.52 max branch formulas: 64
% 0.20/0.52 proof nodes created: 14
% 0.20/0.52 formulas created: 445
% 0.20/0.52
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