%------------------------------------------------------------------------------ % 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 : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----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 %------------------------------------------------------------------------------