TSTP Solution File: SET929+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n023.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 06:39:44 EDT 2022
% Result : Theorem 0.18s 0.56s
% 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 : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n023.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 22:08:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.56 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.18/0.56 (* PROOF-FOUND *)
% 0.18/0.56 % SZS status Theorem
% 0.18/0.56 (* BEGIN-PROOF *)
% 0.18/0.56 % SZS output start Proof
% 0.18/0.56 Theorem t73_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((set_difference (unordered_pair A B) C) = (empty_set))<->((in A C)/\(in B C)))))).
% 0.18/0.56 Proof.
% 0.18/0.56 assert (zenon_L1_ : forall (zenon_TC_l : zenon_U) (zenon_TB_m : zenon_U) (zenon_TA_n : zenon_U), ((set_difference (unordered_pair zenon_TA_n zenon_TB_m) zenon_TC_l) = (empty_set)) -> (~(subset (unordered_pair zenon_TA_n zenon_TB_m) zenon_TC_l)) -> False).
% 0.18/0.56 do 3 intro. intros zenon_H9 zenon_Ha.
% 0.18/0.56 generalize (t37_xboole_1 (unordered_pair zenon_TA_n zenon_TB_m)). zenon_intro zenon_He.
% 0.18/0.56 generalize (zenon_He zenon_TC_l). zenon_intro zenon_Hf.
% 0.18/0.56 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H11; zenon_intro zenon_Ha | zenon_intro zenon_H9; zenon_intro zenon_H10 ].
% 0.18/0.56 exact (zenon_H11 zenon_H9).
% 0.18/0.56 exact (zenon_Ha zenon_H10).
% 0.18/0.56 (* end of lemma zenon_L1_ *)
% 0.18/0.56 apply NNPP. intro zenon_G.
% 0.18/0.56 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((set_difference (unordered_pair A B) C) = (empty_set))<->((in A C)/\(in B C)))))) zenon_G); [ zenon_intro zenon_H12; idtac ].
% 0.18/0.56 elim zenon_H12. zenon_intro zenon_TA_n. zenon_intro zenon_H13.
% 0.18/0.56 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((set_difference (unordered_pair zenon_TA_n B) C) = (empty_set))<->((in zenon_TA_n C)/\(in B C))))) zenon_H13); [ zenon_intro zenon_H14; idtac ].
% 0.18/0.56 elim zenon_H14. zenon_intro zenon_TB_m. zenon_intro zenon_H15.
% 0.18/0.56 apply (zenon_notallex_s (fun C : zenon_U => (((set_difference (unordered_pair zenon_TA_n zenon_TB_m) C) = (empty_set))<->((in zenon_TA_n C)/\(in zenon_TB_m C)))) zenon_H15); [ zenon_intro zenon_H16; idtac ].
% 0.18/0.56 elim zenon_H16. zenon_intro zenon_TC_l. zenon_intro zenon_H17.
% 0.18/0.56 apply (zenon_notequiv_s _ _ zenon_H17); [ zenon_intro zenon_H11; zenon_intro zenon_H19 | zenon_intro zenon_H9; zenon_intro zenon_H18 ].
% 0.18/0.56 generalize (t38_zfmisc_1 zenon_TA_n). zenon_intro zenon_H1a.
% 0.18/0.56 generalize (zenon_H1a zenon_TB_m). zenon_intro zenon_H1b.
% 0.18/0.56 generalize (zenon_H1b zenon_TC_l). zenon_intro zenon_H1c.
% 0.18/0.56 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_Ha; zenon_intro zenon_H18 | zenon_intro zenon_H10; zenon_intro zenon_H19 ].
% 0.18/0.56 exact (zenon_H18 zenon_H19).
% 0.18/0.56 generalize (t37_xboole_1 (unordered_pair zenon_TA_n zenon_TB_m)). zenon_intro zenon_He.
% 0.18/0.56 generalize (zenon_He zenon_TC_l). zenon_intro zenon_Hf.
% 0.18/0.56 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H11; zenon_intro zenon_Ha | zenon_intro zenon_H9; zenon_intro zenon_H10 ].
% 0.18/0.56 exact (zenon_Ha zenon_H10).
% 0.18/0.56 exact (zenon_H11 zenon_H9).
% 0.18/0.56 apply (zenon_notand_s _ _ zenon_H18); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 0.18/0.56 generalize (t38_zfmisc_1 zenon_TA_n). zenon_intro zenon_H1a.
% 0.18/0.56 generalize (zenon_H1a zenon_TB_m). zenon_intro zenon_H1b.
% 0.18/0.56 generalize (zenon_H1b zenon_TC_l). zenon_intro zenon_H1c.
% 0.18/0.56 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_Ha; zenon_intro zenon_H18 | zenon_intro zenon_H10; zenon_intro zenon_H19 ].
% 0.18/0.56 apply (zenon_L1_ zenon_TC_l zenon_TB_m zenon_TA_n); trivial.
% 0.18/0.56 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H20. zenon_intro zenon_H1f.
% 0.18/0.56 exact (zenon_H1e zenon_H20).
% 0.18/0.56 generalize (t38_zfmisc_1 zenon_TA_n). zenon_intro zenon_H1a.
% 0.18/0.56 generalize (zenon_H1a zenon_TB_m). zenon_intro zenon_H1b.
% 0.18/0.56 generalize (zenon_H1b zenon_TC_l). zenon_intro zenon_H1c.
% 0.18/0.56 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_Ha; zenon_intro zenon_H18 | zenon_intro zenon_H10; zenon_intro zenon_H19 ].
% 0.18/0.56 apply (zenon_L1_ zenon_TC_l zenon_TB_m zenon_TA_n); trivial.
% 0.18/0.56 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H20. zenon_intro zenon_H1f.
% 0.18/0.56 exact (zenon_H1d zenon_H1f).
% 0.18/0.56 Qed.
% 0.18/0.56 % SZS output end Proof
% 0.18/0.56 (* END-PROOF *)
% 0.18/0.56 nodes searched: 1769
% 0.18/0.56 max branch formulas: 312
% 0.18/0.56 proof nodes created: 165
% 0.18/0.56 formulas created: 4355
% 0.18/0.56
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