TSTP Solution File: SEU147+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n016.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 15:59:42 EDT 2022
% Result : Theorem 72.62s 72.81s
% Output : Proof 72.62s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.04/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n016.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 Jun 18 22:34:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 72.62/72.81 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 72.62/72.81 (* PROOF-FOUND *)
% 72.62/72.81 % SZS status Theorem
% 72.62/72.81 (* BEGIN-PROOF *)
% 72.62/72.81 % SZS output start Proof
% 72.62/72.81 Theorem t1_zfmisc_1 : ((powerset (empty_set)) = (singleton (empty_set))).
% 72.62/72.81 Proof.
% 72.62/72.81 assert (zenon_L1_ : forall (zenon_TC_p : zenon_U), (forall x : zenon_U, (subset x x)) -> (~(subset zenon_TC_p (empty_set))) -> (forall C : zenon_U, ((in C (singleton (empty_set)))<->(C = (empty_set)))) -> (in zenon_TC_p (singleton (empty_set))) -> False).
% 72.62/72.81 do 1 intro. intros zenon_Hb zenon_Hc zenon_Hd zenon_He.
% 72.62/72.81 generalize (zenon_Hb zenon_TC_p). zenon_intro zenon_H10.
% 72.62/72.81 cut ((subset zenon_TC_p zenon_TC_p) = (subset zenon_TC_p (empty_set))).
% 72.62/72.81 intro zenon_D_pnotp.
% 72.62/72.81 apply zenon_Hc.
% 72.62/72.81 rewrite <- zenon_D_pnotp.
% 72.62/72.81 exact zenon_H10.
% 72.62/72.81 cut ((zenon_TC_p = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H11].
% 72.62/72.81 cut ((zenon_TC_p = zenon_TC_p)); [idtac | apply NNPP; zenon_intro zenon_H12].
% 72.62/72.81 congruence.
% 72.62/72.81 apply zenon_H12. apply refl_equal.
% 72.62/72.81 generalize (zenon_Hd zenon_TC_p). zenon_intro zenon_H13.
% 72.62/72.81 apply (zenon_equiv_s _ _ zenon_H13); [ zenon_intro zenon_H15; zenon_intro zenon_H11 | zenon_intro zenon_He; zenon_intro zenon_H14 ].
% 72.62/72.81 exact (zenon_H15 zenon_He).
% 72.62/72.81 exact (zenon_H11 zenon_H14).
% 72.62/72.81 (* end of lemma zenon_L1_ *)
% 72.62/72.81 apply NNPP. intro zenon_G.
% 72.62/72.81 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_Hb | zenon_intro zenon_H16 ].
% 72.62/72.81 generalize (d1_tarski (empty_set)). zenon_intro zenon_H17.
% 72.62/72.81 generalize (d1_zfmisc_1 (empty_set)). zenon_intro zenon_H18.
% 72.62/72.81 generalize (zenon_H17 (singleton (empty_set))). zenon_intro zenon_H19.
% 72.62/72.81 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H1a; zenon_intro zenon_Hd ].
% 72.62/72.81 apply zenon_H1c. apply refl_equal.
% 72.62/72.81 generalize (zenon_H18 (singleton (empty_set))). zenon_intro zenon_H1d.
% 72.62/72.81 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ].
% 72.62/72.81 apply (zenon_notallex_s (fun C : zenon_U => ((in C (singleton (empty_set)))<->(subset C (empty_set)))) zenon_H20); [ zenon_intro zenon_H22; idtac ].
% 72.62/72.81 elim zenon_H22. zenon_intro zenon_TC_p. zenon_intro zenon_H23.
% 72.62/72.81 apply (zenon_notequiv_s _ _ zenon_H23); [ zenon_intro zenon_H15; zenon_intro zenon_H24 | zenon_intro zenon_He; zenon_intro zenon_Hc ].
% 72.62/72.81 generalize (t3_xboole_1 zenon_TC_p). zenon_intro zenon_H25.
% 72.62/72.81 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_Hc | zenon_intro zenon_H14 ].
% 72.62/72.81 exact (zenon_Hc zenon_H24).
% 72.62/72.81 generalize (zenon_Hd zenon_TC_p). zenon_intro zenon_H13.
% 72.62/72.81 apply (zenon_equiv_s _ _ zenon_H13); [ zenon_intro zenon_H15; zenon_intro zenon_H11 | zenon_intro zenon_He; zenon_intro zenon_H14 ].
% 72.62/72.81 exact (zenon_H11 zenon_H14).
% 72.62/72.81 exact (zenon_H15 zenon_He).
% 72.62/72.81 apply (zenon_L1_ zenon_TC_p); trivial.
% 72.62/72.81 apply zenon_G. apply sym_equal. exact zenon_H1f.
% 72.62/72.81 apply zenon_H16. zenon_intro zenon_Tx_bm. apply NNPP. zenon_intro zenon_H27.
% 72.62/72.81 generalize (reflexivity_r1_tarski zenon_Tx_bm). zenon_intro zenon_H0.
% 72.62/72.81 generalize (zenon_H0 zenon_E). zenon_intro zenon_H28.
% 72.62/72.81 exact (zenon_H27 zenon_H28).
% 72.62/72.81 Qed.
% 72.62/72.81 % SZS output end Proof
% 72.62/72.81 (* END-PROOF *)
% 72.62/72.81 nodes searched: 1321505
% 72.62/72.81 max branch formulas: 13028
% 72.62/72.81 proof nodes created: 73236
% 72.62/72.81 formulas created: 6062416
% 72.62/72.81
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