TSTP Solution File: SET162+4 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET162+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n018.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 06:34:32 EDT 2022
% Result : Theorem 6.75s 6.98s
% Output : Proof 6.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET162+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n018.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 : Mon Jul 11 10:21:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 6.75/6.98 (* PROOF-FOUND *)
% 6.75/6.98 % SZS status Theorem
% 6.75/6.98 (* BEGIN-PROOF *)
% 6.75/6.98 % SZS output start Proof
% 6.75/6.98 Theorem thI18 : (forall A : zenon_U, (equal_set (union A (empty_set)) A)).
% 6.75/6.98 Proof.
% 6.75/6.98 assert (zenon_L1_ : forall (zenon_TA_q : zenon_U) (zenon_TX_r : zenon_U), (forall A : zenon_U, (forall B : zenon_U, ((member zenon_TX_r (union A B))<->((member zenon_TX_r A)\/(member zenon_TX_r B))))) -> (~(member zenon_TX_r zenon_TA_q)) -> (~(member zenon_TX_r (empty_set))) -> (member zenon_TX_r (union zenon_TA_q (empty_set))) -> False).
% 6.75/6.98 do 2 intro. intros zenon_Hc zenon_Hd zenon_He zenon_Hf.
% 6.75/6.98 generalize (zenon_Hc zenon_TA_q). zenon_intro zenon_H12.
% 6.75/6.98 generalize (zenon_H12 (empty_set)). zenon_intro zenon_H13.
% 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H13); [ zenon_intro zenon_H16; zenon_intro zenon_H15 | zenon_intro zenon_Hf; zenon_intro zenon_H14 ].
% 6.75/6.98 exact (zenon_H16 zenon_Hf).
% 6.75/6.98 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 6.75/6.98 exact (zenon_Hd zenon_H18).
% 6.75/6.98 exact (zenon_He zenon_H17).
% 6.75/6.98 (* end of lemma zenon_L1_ *)
% 6.75/6.98 assert (zenon_L2_ : forall (zenon_TX_r : zenon_U), (member zenon_TX_r (empty_set)) -> False).
% 6.75/6.98 do 1 intro. intros zenon_H17.
% 6.75/6.98 generalize (empty_set zenon_TX_r). zenon_intro zenon_He.
% 6.75/6.98 exact (zenon_He zenon_H17).
% 6.75/6.98 (* end of lemma zenon_L2_ *)
% 6.75/6.98 apply NNPP. intro zenon_G.
% 6.75/6.98 apply (zenon_notallex_s (fun A : zenon_U => (equal_set (union A (empty_set)) A)) zenon_G); [ zenon_intro zenon_H19; idtac ].
% 6.75/6.98 elim zenon_H19. zenon_intro zenon_TA_q. zenon_intro zenon_H1a.
% 6.75/6.98 generalize (equal_set (union zenon_TA_q (empty_set))). zenon_intro zenon_H1b.
% 6.75/6.98 generalize (zenon_H1b zenon_TA_q). zenon_intro zenon_H1c.
% 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1a; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ].
% 6.75/6.98 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 6.75/6.98 generalize (subset (union zenon_TA_q (empty_set))). zenon_intro zenon_H22.
% 6.75/6.98 generalize (zenon_H22 zenon_TA_q). zenon_intro zenon_H23.
% 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H21; zenon_intro zenon_H26 | zenon_intro zenon_H25; zenon_intro zenon_H24 ].
% 6.75/6.98 apply (zenon_notallex_s (fun X : zenon_U => ((member X (union zenon_TA_q (empty_set)))->(member X zenon_TA_q))) zenon_H26); [ zenon_intro zenon_H27; idtac ].
% 6.75/6.98 elim zenon_H27. zenon_intro zenon_TX_r. zenon_intro zenon_H28.
% 6.75/6.98 apply (zenon_notimply_s _ _ zenon_H28). zenon_intro zenon_Hf. zenon_intro zenon_Hd.
% 6.75/6.98 generalize (difference zenon_TX_r). zenon_intro zenon_H29.
% 6.75/6.98 generalize (union zenon_TX_r). zenon_intro zenon_Hc.
% 6.75/6.98 generalize (zenon_H29 zenon_TA_q). zenon_intro zenon_H2a.
% 6.75/6.98 generalize (zenon_H2a (empty_set)). zenon_intro zenon_H2b.
% 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H2d; zenon_intro zenon_H2c ].
% 6.75/6.98 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_He | zenon_intro zenon_H30 ].
% 6.75/6.98 apply (zenon_L1_ zenon_TA_q zenon_TX_r); trivial.
% 6.75/6.98 exact (zenon_H30 zenon_Hd).
% 6.75/6.98 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H17. zenon_intro zenon_Hd.
% 6.75/6.98 apply (zenon_L2_ zenon_TX_r); trivial.
% 6.75/6.98 exact (zenon_H21 zenon_H25).
% 6.75/6.98 generalize (subset zenon_TA_q). zenon_intro zenon_H31.
% 6.75/6.98 generalize (zenon_H31 (union zenon_TA_q (empty_set))). zenon_intro zenon_H32.
% 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H20; zenon_intro zenon_H35 | zenon_intro zenon_H34; zenon_intro zenon_H33 ].
% 6.75/6.98 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_q)->(member X (union zenon_TA_q (empty_set))))) zenon_H35); [ zenon_intro zenon_H36; idtac ].
% 6.75/6.98 elim zenon_H36. zenon_intro zenon_TX_cd. zenon_intro zenon_H38.
% 6.75/6.98 apply (zenon_notimply_s _ _ zenon_H38). zenon_intro zenon_H3a. zenon_intro zenon_H39.
% 6.75/6.98 generalize (union zenon_TX_cd). zenon_intro zenon_H3b.
% 6.75/6.98 generalize (zenon_H3b zenon_TA_q). zenon_intro zenon_H3c.
% 6.75/6.98 generalize (zenon_H3c (empty_set)). zenon_intro zenon_H3d.
% 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H3d); [ zenon_intro zenon_H39; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3e ].
% 6.75/6.98 apply (zenon_notor_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41.
% 6.75/6.98 exact (zenon_H42 zenon_H3a).
% 6.75/6.98 exact (zenon_H39 zenon_H3f).
% 6.75/6.98 exact (zenon_H20 zenon_H34).
% 6.82/6.98 exact (zenon_H1a zenon_H1e).
% 6.82/6.98 Qed.
% 6.82/6.98 % SZS output end Proof
% 6.82/6.98 (* END-PROOF *)
% 6.82/6.98 nodes searched: 305162
% 6.82/6.98 max branch formulas: 34613
% 6.82/6.98 proof nodes created: 7041
% 6.82/6.98 formulas created: 1404913
% 6.82/6.98
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