TSTP Solution File: SET002+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET002+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n010.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 06:32:10 EDT 2022
% Result : Theorem 0.18s 0.53s
% 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
% 0.07/0.12 % Problem : SET002+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n010.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 : Sat Jul 9 19:29:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.53 (* PROOF-FOUND *)
% 0.18/0.53 % SZS status Theorem
% 0.18/0.53 (* BEGIN-PROOF *)
% 0.18/0.53 % SZS output start Proof
% 0.18/0.53 Theorem prove_idempotency_of_union : (forall B : zenon_U, ((union B B) = B)).
% 0.18/0.53 Proof.
% 0.18/0.53 apply NNPP. intro zenon_G.
% 0.18/0.53 apply (zenon_notallex_s (fun B : zenon_U => ((union B B) = B)) zenon_G); [ zenon_intro zenon_H8; idtac ].
% 0.18/0.53 elim zenon_H8. zenon_intro zenon_TB_j. zenon_intro zenon_Ha.
% 0.18/0.53 generalize (equal_member_defn zenon_TB_j). zenon_intro zenon_Hb.
% 0.18/0.53 generalize (zenon_Hb (union zenon_TB_j zenon_TB_j)). zenon_intro zenon_Hc.
% 0.18/0.53 apply (zenon_equiv_s _ _ zenon_Hc); [ zenon_intro zenon_H10; zenon_intro zenon_Hf | zenon_intro zenon_He; zenon_intro zenon_Hd ].
% 0.18/0.53 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_j)<->(member D (union zenon_TB_j zenon_TB_j)))) zenon_Hf); [ zenon_intro zenon_H11; idtac ].
% 0.18/0.53 elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13.
% 0.18/0.53 apply (zenon_notequiv_s _ _ zenon_H13); [ zenon_intro zenon_H17; zenon_intro zenon_H16 | zenon_intro zenon_H15; zenon_intro zenon_H14 ].
% 0.18/0.53 generalize (union_defn zenon_TB_j). zenon_intro zenon_H18.
% 0.18/0.54 generalize (zenon_H18 zenon_TB_j). zenon_intro zenon_H19.
% 0.18/0.54 generalize (zenon_H19 zenon_TD_s). zenon_intro zenon_H1a.
% 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H14; zenon_intro zenon_H1c | zenon_intro zenon_H16; zenon_intro zenon_H1b ].
% 0.18/0.54 exact (zenon_H14 zenon_H16).
% 0.18/0.54 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H15 | zenon_intro zenon_H15 ].
% 0.18/0.54 exact (zenon_H17 zenon_H15).
% 0.18/0.54 exact (zenon_H17 zenon_H15).
% 0.18/0.54 generalize (union_defn zenon_TB_j). zenon_intro zenon_H18.
% 0.18/0.54 generalize (zenon_H18 zenon_TB_j). zenon_intro zenon_H19.
% 0.18/0.54 generalize (zenon_H19 zenon_TD_s). zenon_intro zenon_H1a.
% 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H14; zenon_intro zenon_H1c | zenon_intro zenon_H16; zenon_intro zenon_H1b ].
% 0.18/0.54 apply (zenon_notor_s _ _ zenon_H1c). zenon_intro zenon_H17. zenon_intro zenon_H17.
% 0.18/0.54 exact (zenon_H17 zenon_H15).
% 0.18/0.54 exact (zenon_H14 zenon_H16).
% 0.18/0.54 apply zenon_Ha. apply sym_equal. exact zenon_He.
% 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: 886
% 0.18/0.54 max branch formulas: 324
% 0.18/0.54 proof nodes created: 105
% 0.18/0.54 formulas created: 3479
% 0.18/0.54
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