%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYO604+1 : TPTP v8.1.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n008.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 : Thu Jul 21 21:06:46 EDT 2022 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO604+1 : TPTP v8.1.0. Released v7.0.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n008.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sat Jul 9 12:41:53 EDT 2022 % 0.12/0.34 % CPUTime : % 0.38/0.57 (* PROOF-FOUND *) % 0.38/0.57 % SZS status Theorem % 0.38/0.57 (* BEGIN-PROOF *) % 0.38/0.57 % SZS output start Proof % 0.38/0.57 Theorem nc3 : ((forall A : zenon_U, (exists B : zenon_U, (((g_true_only B A)/\(((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(((g_both B A)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/((g_false_only B A)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))))))))\/((exists A : zenon_U, ((exists B : zenon_U, ((g_both B A)/\((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))))/\(~(exists B : zenon_U, (((g_true_only B A)/\(((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(((g_both B A)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/((g_false_only B A)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))))))))))/\(~(exists A : zenon_U, (forall B : zenon_U, (((g_true_only B A)/\(forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B))))\/((g_false_only B A)/\(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))))))). % 0.38/0.57 Proof. % 0.38/0.57 assert (zenon_L1_ : forall (zenon_TA_h : zenon_U), (g_false_only zenon_TA_h zenon_TA_h) -> (~(g_false zenon_TA_h zenon_TA_h)) -> False). % 0.38/0.57 do 1 intro. intros zenon_H5 zenon_H6. % 0.38/0.57 generalize (false_only_g zenon_TA_h). zenon_intro zenon_H8. % 0.38/0.57 generalize (zenon_H8 zenon_TA_h). zenon_intro zenon_H9. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H9); [ zenon_intro zenon_Hc; zenon_intro zenon_Hb | zenon_intro zenon_H5; zenon_intro zenon_Ha ]. % 0.38/0.57 exact (zenon_Hc zenon_H5). % 0.38/0.57 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.38/0.57 exact (zenon_H6 zenon_He). % 0.38/0.57 (* end of lemma zenon_L1_ *) % 0.38/0.57 assert (zenon_L2_ : forall (zenon_TA_h : zenon_U), (~(~(g_false zenon_TA_h zenon_TA_h))) -> (~(g_false zenon_TA_h zenon_TA_h)) -> False). % 0.38/0.57 do 1 intro. intros zenon_Hf zenon_H6. % 0.38/0.57 exact (zenon_Hf zenon_H6). % 0.38/0.57 (* end of lemma zenon_L2_ *) % 0.38/0.57 assert (zenon_L3_ : forall (zenon_TA_h : zenon_U), (~((g_true zenon_TA_h zenon_TA_h)/\(~(g_false zenon_TA_h zenon_TA_h)))) -> (~(g_false zenon_TA_h zenon_TA_h)) -> (forall X_1 : zenon_U, ((g_true_only zenon_TA_h X_1)\/((g_both zenon_TA_h X_1)\/(g_false_only zenon_TA_h X_1)))) -> False). % 0.38/0.57 do 1 intro. intros zenon_H10 zenon_H6 zenon_H11. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H10); [ zenon_intro zenon_Hd | zenon_intro zenon_Hf ]. % 0.38/0.57 generalize (zenon_H11 zenon_TA_h). zenon_intro zenon_H12. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ]. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TA_h). zenon_intro zenon_H16. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H18; zenon_intro zenon_H10 | zenon_intro zenon_H14; zenon_intro zenon_H17 ]. % 0.38/0.57 exact (zenon_H18 zenon_H14). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H19. zenon_intro zenon_H6. % 0.38/0.57 exact (zenon_Hd zenon_H19). % 0.38/0.57 apply (zenon_or_s _ _ zenon_H13); [ zenon_intro zenon_H1a | zenon_intro zenon_H5 ]. % 0.38/0.57 generalize (both_g zenon_TA_h). zenon_intro zenon_H1b. % 0.38/0.57 generalize (zenon_H1b zenon_TA_h). zenon_intro zenon_H1c. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1f; zenon_intro zenon_H1e | zenon_intro zenon_H1a; zenon_intro zenon_H1d ]. % 0.38/0.57 exact (zenon_H1f zenon_H1a). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H19. zenon_intro zenon_He. % 0.38/0.57 exact (zenon_Hd zenon_H19). % 0.38/0.57 apply (zenon_L1_ zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_Hf zenon_H6). % 0.38/0.57 (* end of lemma zenon_L3_ *) % 0.38/0.57 assert (zenon_L4_ : forall (zenon_TA_h : zenon_U), (~(g_false zenon_TA_h zenon_TA_h)) -> (~((g_true zenon_TA_h zenon_TA_h)/\(~(g_false zenon_TA_h zenon_TA_h)))) -> False). % 0.38/0.57 do 1 intro. intros zenon_H6 zenon_H10. % 0.38/0.57 generalize (exhaustion_g zenon_TA_h). zenon_intro zenon_H11. % 0.38/0.57 apply (zenon_L3_ zenon_TA_h); trivial. % 0.38/0.57 (* end of lemma zenon_L4_ *) % 0.38/0.57 assert (zenon_L5_ : forall (zenon_TA_h : zenon_U), (~(~(g_true zenon_TA_h zenon_TA_h))) -> (~(g_true zenon_TA_h zenon_TA_h)) -> False). % 0.38/0.57 do 1 intro. intros zenon_H20 zenon_Hd. % 0.38/0.57 exact (zenon_H20 zenon_Hd). % 0.38/0.57 (* end of lemma zenon_L5_ *) % 0.38/0.57 assert (zenon_L6_ : forall (zenon_TA_h : zenon_U) (zenon_TC_bj : zenon_U), (g_both zenon_TC_bj zenon_TA_h) -> (~(g_false zenon_TC_bj zenon_TA_h)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H21 zenon_H22. % 0.38/0.57 generalize (both_g zenon_TC_bj). zenon_intro zenon_H24. % 0.38/0.57 generalize (zenon_H24 zenon_TA_h). zenon_intro zenon_H25. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H28; zenon_intro zenon_H27 | zenon_intro zenon_H21; zenon_intro zenon_H26 ]. % 0.38/0.57 exact (zenon_H28 zenon_H21). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.38/0.57 exact (zenon_H22 zenon_H29). % 0.38/0.57 (* end of lemma zenon_L6_ *) % 0.38/0.57 assert (zenon_L7_ : forall (zenon_TA_h : zenon_U) (zenon_TC_bj : zenon_U), (g_false_only zenon_TC_bj zenon_TA_h) -> (~(g_false zenon_TC_bj zenon_TA_h)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H2b zenon_H22. % 0.38/0.57 generalize (false_only_g zenon_TC_bj). zenon_intro zenon_H2c. % 0.38/0.57 generalize (zenon_H2c zenon_TA_h). zenon_intro zenon_H2d. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H30; zenon_intro zenon_H2f | zenon_intro zenon_H2b; zenon_intro zenon_H2e ]. % 0.38/0.57 exact (zenon_H30 zenon_H2b). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H29. zenon_intro zenon_H31. % 0.38/0.57 exact (zenon_H22 zenon_H29). % 0.38/0.57 (* end of lemma zenon_L7_ *) % 0.38/0.57 assert (zenon_L8_ : forall (zenon_TA_h : zenon_U) (zenon_TC_bj : zenon_U), (~(~(g_false zenon_TC_bj zenon_TA_h))) -> (~(g_false zenon_TC_bj zenon_TA_h)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H32 zenon_H22. % 0.38/0.57 exact (zenon_H32 zenon_H22). % 0.38/0.57 (* end of lemma zenon_L8_ *) % 0.38/0.57 assert (zenon_L9_ : forall (zenon_TA_h : zenon_U) (zenon_TC_bj : zenon_U), (~(g_false zenon_TC_bj zenon_TA_h)) -> (~(g_true_only zenon_TC_bj zenon_TA_h)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H22 zenon_H33. % 0.38/0.57 generalize (true_only_g zenon_TC_bj). zenon_intro zenon_H34. % 0.38/0.57 generalize (zenon_H34 zenon_TA_h). zenon_intro zenon_H35. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H35); [ zenon_intro zenon_H33; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H31 | zenon_intro zenon_H32 ]. % 0.38/0.57 generalize (exhaustion_g zenon_TC_bj). zenon_intro zenon_H39. % 0.38/0.57 generalize (zenon_H39 zenon_TA_h). zenon_intro zenon_H3a. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H37 | zenon_intro zenon_H3b ]. % 0.38/0.57 generalize (true_only_g zenon_TC_bj). zenon_intro zenon_H34. % 0.38/0.57 generalize (zenon_H34 zenon_TA_h). zenon_intro zenon_H35. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H35); [ zenon_intro zenon_H33; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 0.38/0.57 exact (zenon_H33 zenon_H37). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H2a. zenon_intro zenon_H22. % 0.38/0.57 exact (zenon_H31 zenon_H2a). % 0.38/0.57 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H21 | zenon_intro zenon_H2b ]. % 0.38/0.57 apply (zenon_L6_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_L7_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 exact (zenon_H32 zenon_H22). % 0.38/0.57 exact (zenon_H33 zenon_H37). % 0.38/0.57 (* end of lemma zenon_L9_ *) % 0.38/0.57 assert (zenon_L10_ : forall (zenon_TA_h : zenon_U) (zenon_TC_bj : zenon_U), (g_true zenon_TC_bj zenon_TA_h) -> (~(g_false zenon_TC_bj zenon_TA_h)) -> (~(g_true_only zenon_TC_bj zenon_TA_h)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H2a zenon_H22 zenon_H33. % 0.38/0.57 generalize (true_only_g zenon_TC_bj). zenon_intro zenon_H34. % 0.38/0.57 generalize (zenon_H34 zenon_TA_h). zenon_intro zenon_H35. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H35); [ zenon_intro zenon_H33; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H31 | zenon_intro zenon_H32 ]. % 0.38/0.57 exact (zenon_H31 zenon_H2a). % 0.38/0.57 exact (zenon_H32 zenon_H22). % 0.38/0.57 exact (zenon_H33 zenon_H37). % 0.38/0.57 (* end of lemma zenon_L10_ *) % 0.38/0.57 assert (zenon_L11_ : forall (zenon_TC_bj : zenon_U) (zenon_TA_h : zenon_U), ((g_true zenon_TA_h zenon_TC_bj)/\(~(g_false zenon_TA_h zenon_TC_bj))) -> (~(g_true_only zenon_TA_h zenon_TC_bj)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H3c zenon_H3d. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TC_bj). zenon_intro zenon_H3e. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3d; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3c ]. % 0.38/0.57 exact (zenon_H40 zenon_H3c). % 0.38/0.57 exact (zenon_H3d zenon_H3f). % 0.38/0.57 (* end of lemma zenon_L11_ *) % 0.38/0.57 assert (zenon_L12_ : forall (zenon_TC_bj : zenon_U) (zenon_TA_h : zenon_U), (g_both zenon_TA_h zenon_TC_bj) -> (~(g_false zenon_TA_h zenon_TC_bj)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H41 zenon_H42. % 0.38/0.57 generalize (both_g zenon_TA_h). zenon_intro zenon_H1b. % 0.38/0.57 generalize (zenon_H1b zenon_TC_bj). zenon_intro zenon_H43. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H46; zenon_intro zenon_H45 | zenon_intro zenon_H41; zenon_intro zenon_H44 ]. % 0.38/0.57 exact (zenon_H46 zenon_H41). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H48. zenon_intro zenon_H47. % 0.38/0.57 exact (zenon_H42 zenon_H47). % 0.38/0.57 (* end of lemma zenon_L12_ *) % 0.38/0.57 assert (zenon_L13_ : forall (zenon_TC_bj : zenon_U) (zenon_TA_h : zenon_U), (g_false_only zenon_TA_h zenon_TC_bj) -> (~(g_false zenon_TA_h zenon_TC_bj)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H49 zenon_H42. % 0.38/0.57 generalize (false_only_g zenon_TA_h). zenon_intro zenon_H8. % 0.38/0.57 generalize (zenon_H8 zenon_TC_bj). zenon_intro zenon_H4a. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H4d; zenon_intro zenon_H4c | zenon_intro zenon_H49; zenon_intro zenon_H4b ]. % 0.38/0.57 exact (zenon_H4d zenon_H49). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H47. zenon_intro zenon_H4e. % 0.38/0.57 exact (zenon_H42 zenon_H47). % 0.38/0.57 (* end of lemma zenon_L13_ *) % 0.38/0.57 assert (zenon_L14_ : forall (zenon_TA_h : zenon_U) (zenon_TC_bj : zenon_U), (~(exists C : zenon_U, ((g_true_only zenon_TC_bj C)/\(g_true_only C zenon_TC_bj)))) -> (g_true zenon_TC_bj zenon_TA_h) -> (~(g_false zenon_TC_bj zenon_TA_h)) -> (~(g_false zenon_TA_h zenon_TC_bj)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H4f zenon_H2a zenon_H22 zenon_H42. % 0.38/0.57 apply zenon_H4f. exists zenon_TA_h. apply NNPP. zenon_intro zenon_H50. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 0.38/0.57 apply (zenon_L10_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 generalize (exhaustion_g zenon_TA_h). zenon_intro zenon_H11. % 0.38/0.57 generalize (zenon_H11 zenon_TC_bj). zenon_intro zenon_H51. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H3f | zenon_intro zenon_H52 ]. % 0.38/0.57 exact (zenon_H3d zenon_H3f). % 0.38/0.57 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H41 | zenon_intro zenon_H49 ]. % 0.38/0.57 apply (zenon_L12_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_L13_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 (* end of lemma zenon_L14_ *) % 0.38/0.57 assert (zenon_L15_ : forall (zenon_TA_h : zenon_U) (zenon_TC_bj : zenon_U), (~(g_false zenon_TC_bj zenon_TA_h)) -> (~(g_false zenon_TA_h zenon_TC_bj)) -> (~(exists B : zenon_U, (((g_true_only B zenon_TA_h)/\(((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(((g_both B zenon_TA_h)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/((g_false_only B zenon_TA_h)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B))))))))))) -> False). % 0.38/0.57 do 2 intro. intros zenon_H22 zenon_H42 zenon_H53. % 0.38/0.57 generalize (exhaustion_g zenon_TC_bj). zenon_intro zenon_H39. % 0.38/0.57 apply zenon_H53. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H54. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H54). zenon_intro zenon_H56. zenon_intro zenon_H55. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H56); [ zenon_intro zenon_H33 | zenon_intro zenon_H57 ]. % 0.38/0.57 apply (zenon_L9_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H57). zenon_intro zenon_H58. zenon_intro zenon_H4f. % 0.38/0.57 generalize (zenon_H39 zenon_TA_h). zenon_intro zenon_H3a. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H37 | zenon_intro zenon_H3b ]. % 0.38/0.57 generalize (true_only_g zenon_TC_bj). zenon_intro zenon_H34. % 0.38/0.57 generalize (zenon_H34 zenon_TA_h). zenon_intro zenon_H35. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H35); [ zenon_intro zenon_H33; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 0.38/0.57 exact (zenon_H33 zenon_H37). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H2a. zenon_intro zenon_H22. % 0.38/0.57 apply (zenon_L14_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H21 | zenon_intro zenon_H2b ]. % 0.38/0.57 apply (zenon_L6_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_L7_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 (* end of lemma zenon_L15_ *) % 0.38/0.57 assert (zenon_L16_ : forall (zenon_TC_bj : zenon_U) (zenon_TA_h : zenon_U), (g_false_only zenon_TA_h zenon_TC_bj) -> (g_true zenon_TA_h zenon_TC_bj) -> False). % 0.38/0.57 do 2 intro. intros zenon_H49 zenon_H48. % 0.38/0.57 generalize (false_only_g zenon_TA_h). zenon_intro zenon_H8. % 0.38/0.57 generalize (zenon_H8 zenon_TC_bj). zenon_intro zenon_H4a. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H4d; zenon_intro zenon_H4c | zenon_intro zenon_H49; zenon_intro zenon_H4b ]. % 0.38/0.57 exact (zenon_H4d zenon_H49). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H47. zenon_intro zenon_H4e. % 0.38/0.57 exact (zenon_H4e zenon_H48). % 0.38/0.57 (* end of lemma zenon_L16_ *) % 0.38/0.57 assert (zenon_L17_ : forall (zenon_TA_h : zenon_U) (zenon_TC_dn : zenon_U), ((g_true zenon_TC_dn zenon_TA_h)/\(~(g_false zenon_TC_dn zenon_TA_h))) -> (~(g_true_only zenon_TC_dn zenon_TA_h)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H59 zenon_H5a. % 0.38/0.57 generalize (true_only_g zenon_TC_dn). zenon_intro zenon_H5c. % 0.38/0.57 generalize (zenon_H5c zenon_TA_h). zenon_intro zenon_H5d. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5a; zenon_intro zenon_H5f | zenon_intro zenon_H5e; zenon_intro zenon_H59 ]. % 0.38/0.57 exact (zenon_H5f zenon_H59). % 0.38/0.57 exact (zenon_H5a zenon_H5e). % 0.38/0.57 (* end of lemma zenon_L17_ *) % 0.38/0.57 assert (zenon_L18_ : forall (zenon_TA_h : zenon_U), (exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h))) -> (~(exists B : zenon_U, (((g_true_only B zenon_TA_h)/\(((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(((g_both B zenon_TA_h)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/((g_false_only B zenon_TA_h)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B))))))))))) -> False). % 0.38/0.57 do 1 intro. intros zenon_H60 zenon_H53. % 0.38/0.57 elim zenon_H60. zenon_intro zenon_TC_dn. zenon_intro zenon_H61. % 0.38/0.57 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H62. zenon_intro zenon_H5e. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TC_dn). zenon_intro zenon_H63. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H66; zenon_intro zenon_H65 | zenon_intro zenon_H62; zenon_intro zenon_H64 ]. % 0.38/0.57 exact (zenon_H66 zenon_H62). % 0.38/0.57 generalize (true_only_g zenon_TC_dn). zenon_intro zenon_H5c. % 0.38/0.57 generalize (zenon_H5c zenon_TA_h). zenon_intro zenon_H5d. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5a; zenon_intro zenon_H5f | zenon_intro zenon_H5e; zenon_intro zenon_H59 ]. % 0.38/0.57 exact (zenon_H5a zenon_H5e). % 0.38/0.57 apply zenon_H53. exists zenon_TC_dn. apply NNPP. zenon_intro zenon_H67. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H67). zenon_intro zenon_H69. zenon_intro zenon_H68. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H69); [ zenon_intro zenon_H5a | zenon_intro zenon_H6a ]. % 0.38/0.57 apply (zenon_L17_ zenon_TA_h zenon_TC_dn); trivial. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H6a). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 0.38/0.57 apply zenon_H6b. exists zenon_TA_h. apply NNPP. zenon_intro zenon_H6d. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H5a | zenon_intro zenon_H66 ]. % 0.38/0.57 apply (zenon_L17_ zenon_TA_h zenon_TC_dn); trivial. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TC_dn). zenon_intro zenon_H63. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H66; zenon_intro zenon_H65 | zenon_intro zenon_H62; zenon_intro zenon_H64 ]. % 0.38/0.57 exact (zenon_H65 zenon_H64). % 0.38/0.57 exact (zenon_H66 zenon_H62). % 0.38/0.57 (* end of lemma zenon_L18_ *) % 0.38/0.57 assert (zenon_L19_ : forall (zenon_TA_h : zenon_U), (~(~(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h))))) -> (~(exists B : zenon_U, (((g_true_only B zenon_TA_h)/\(((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(((g_both B zenon_TA_h)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/((g_false_only B zenon_TA_h)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B))))))))))) -> False). % 0.38/0.57 do 1 intro. intros zenon_H6e zenon_H53. % 0.38/0.57 apply zenon_H6e. zenon_intro zenon_H60. % 0.38/0.57 apply (zenon_L18_ zenon_TA_h); trivial. % 0.38/0.57 (* end of lemma zenon_L19_ *) % 0.38/0.57 assert (zenon_L20_ : forall (zenon_TA_h : zenon_U) (zenon_TC_bj : zenon_U), (g_false_only zenon_TC_bj zenon_TA_h) -> (g_true zenon_TC_bj zenon_TA_h) -> False). % 0.38/0.57 do 2 intro. intros zenon_H2b zenon_H2a. % 0.38/0.57 generalize (false_only_g zenon_TC_bj). zenon_intro zenon_H2c. % 0.38/0.57 generalize (zenon_H2c zenon_TA_h). zenon_intro zenon_H2d. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H30; zenon_intro zenon_H2f | zenon_intro zenon_H2b; zenon_intro zenon_H2e ]. % 0.38/0.57 exact (zenon_H30 zenon_H2b). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H29. zenon_intro zenon_H31. % 0.38/0.57 exact (zenon_H31 zenon_H2a). % 0.38/0.57 (* end of lemma zenon_L20_ *) % 0.38/0.57 assert (zenon_L21_ : forall (zenon_TC_bj : zenon_U) (zenon_TA_h : zenon_U), (g_true zenon_TA_h zenon_TC_bj) -> (~(g_false zenon_TC_bj zenon_TA_h)) -> (~(exists C : zenon_U, (((g_both zenon_TA_h C)\/(g_both C zenon_TA_h))/\((~(g_false_only zenon_TA_h C))/\(~(g_false_only C zenon_TA_h)))))) -> (~(g_true_only zenon_TA_h zenon_TC_bj)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H48 zenon_H22 zenon_H6f zenon_H3d. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TC_bj). zenon_intro zenon_H3e. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3d; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3c ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H4e | zenon_intro zenon_H70 ]. % 0.38/0.57 exact (zenon_H4e zenon_H48). % 0.38/0.57 apply zenon_H70. zenon_intro zenon_H47. % 0.38/0.57 apply zenon_H6f. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H71. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H46. zenon_intro zenon_H28. % 0.38/0.57 generalize (both_g zenon_TA_h). zenon_intro zenon_H1b. % 0.38/0.57 generalize (zenon_H1b zenon_TC_bj). zenon_intro zenon_H43. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H46; zenon_intro zenon_H45 | zenon_intro zenon_H41; zenon_intro zenon_H44 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H4e | zenon_intro zenon_H42 ]. % 0.38/0.57 exact (zenon_H4e zenon_H48). % 0.38/0.57 exact (zenon_H42 zenon_H47). % 0.38/0.57 exact (zenon_H46 zenon_H41). % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 0.38/0.57 apply zenon_H75. zenon_intro zenon_H49. % 0.38/0.57 apply (zenon_L16_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H74. zenon_intro zenon_H2b. % 0.38/0.57 apply (zenon_L7_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 exact (zenon_H3d zenon_H3f). % 0.38/0.57 (* end of lemma zenon_L21_ *) % 0.38/0.57 assert (zenon_L22_ : forall (zenon_TA_h : zenon_U), (forall X_1 : zenon_U, ((g_true_only zenon_TA_h X_1)\/((g_both zenon_TA_h X_1)\/(g_false_only zenon_TA_h X_1)))) -> (~(g_false zenon_TA_h zenon_TA_h)) -> (~(g_true_only zenon_TA_h zenon_TA_h)) -> False). % 0.38/0.57 do 1 intro. intros zenon_H11 zenon_H6 zenon_H18. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TA_h). zenon_intro zenon_H16. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H18; zenon_intro zenon_H10 | zenon_intro zenon_H14; zenon_intro zenon_H17 ]. % 0.38/0.57 apply (zenon_L3_ zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_H18 zenon_H14). % 0.38/0.57 (* end of lemma zenon_L22_ *) % 0.38/0.57 assert (zenon_L23_ : forall (zenon_TA_h : zenon_U), (~(g_false zenon_TA_h zenon_TA_h)) -> (~(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h)))) -> False). % 0.38/0.57 do 1 intro. intros zenon_H6 zenon_H76. % 0.38/0.57 generalize (exhaustion_g zenon_TA_h). zenon_intro zenon_H11. % 0.38/0.57 apply zenon_H76. exists zenon_TA_h. apply NNPP. zenon_intro zenon_H77. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H77); [ zenon_intro zenon_H18 | zenon_intro zenon_H18 ]. % 0.38/0.57 apply (zenon_L22_ zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_L22_ zenon_TA_h); trivial. % 0.38/0.57 (* end of lemma zenon_L23_ *) % 0.38/0.57 assert (zenon_L24_ : forall (zenon_TC_bj : zenon_U) (zenon_TA_h : zenon_U), (~(exists C : zenon_U, (((g_both zenon_TA_h C)\/(g_both C zenon_TA_h))/\((~(g_false_only zenon_TA_h C))/\(~(g_false_only C zenon_TA_h)))))) -> ((g_true zenon_TA_h zenon_TC_bj)/\(~(g_false zenon_TA_h zenon_TC_bj))) -> (~(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h)))) -> (g_true zenon_TC_bj zenon_TA_h) -> (g_true zenon_TA_h zenon_TC_bj) -> False). % 0.38/0.57 do 2 intro. intros zenon_H6f zenon_H3c zenon_H76 zenon_H2a zenon_H48. % 0.38/0.57 apply zenon_H6f. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H71. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H46. zenon_intro zenon_H28. % 0.38/0.57 generalize (both_g zenon_TC_bj). zenon_intro zenon_H24. % 0.38/0.57 generalize (zenon_H24 zenon_TA_h). zenon_intro zenon_H25. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H28; zenon_intro zenon_H27 | zenon_intro zenon_H21; zenon_intro zenon_H26 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H31 | zenon_intro zenon_H22 ]. % 0.38/0.57 exact (zenon_H31 zenon_H2a). % 0.38/0.57 apply zenon_H76. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H78. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H78); [ zenon_intro zenon_H3d | zenon_intro zenon_H33 ]. % 0.38/0.57 apply (zenon_L11_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_L10_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 exact (zenon_H28 zenon_H21). % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 0.38/0.57 apply zenon_H75. zenon_intro zenon_H49. % 0.38/0.57 apply (zenon_L16_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H74. zenon_intro zenon_H2b. % 0.38/0.57 apply (zenon_L20_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 (* end of lemma zenon_L24_ *) % 0.38/0.57 assert (zenon_L25_ : forall (zenon_TC_bj : zenon_U) (zenon_TA_h : zenon_U), (forall X_1 : zenon_U, ((g_true_only zenon_TA_h X_1)\/((g_both zenon_TA_h X_1)\/(g_false_only zenon_TA_h X_1)))) -> (~(exists C : zenon_U, (((g_both zenon_TA_h C)\/(g_both C zenon_TA_h))/\((~(g_false_only zenon_TA_h C))/\(~(g_false_only C zenon_TA_h)))))) -> (~(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h)))) -> (g_true zenon_TC_bj zenon_TA_h) -> (~(g_false zenon_TA_h zenon_TC_bj)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H11 zenon_H6f zenon_H76 zenon_H2a zenon_H42. % 0.38/0.57 generalize (zenon_H11 zenon_TC_bj). zenon_intro zenon_H51. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H3f | zenon_intro zenon_H52 ]. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TC_bj). zenon_intro zenon_H3e. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3d; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3c ]. % 0.38/0.57 exact (zenon_H3d zenon_H3f). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H48. zenon_intro zenon_H42. % 0.38/0.57 apply (zenon_L24_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H41 | zenon_intro zenon_H49 ]. % 0.38/0.57 apply (zenon_L12_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_L13_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 (* end of lemma zenon_L25_ *) % 0.38/0.57 assert (zenon_L26_ : forall (zenon_TA_h : zenon_U) (zenon_TC_bj : zenon_U), (~(~(g_true zenon_TC_bj zenon_TA_h))) -> (~(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h)))) -> (~(exists C : zenon_U, (((g_both zenon_TA_h C)\/(g_both C zenon_TA_h))/\((~(g_false_only zenon_TA_h C))/\(~(g_false_only C zenon_TA_h)))))) -> (~((g_false zenon_TA_h zenon_TC_bj)/\(~(g_true zenon_TA_h zenon_TC_bj)))) -> False). % 0.38/0.57 do 2 intro. intros zenon_H79 zenon_H76 zenon_H6f zenon_H4c. % 0.38/0.57 apply zenon_H79. zenon_intro zenon_H2a. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H42 | zenon_intro zenon_H7a ]. % 0.38/0.57 generalize (exhaustion_g zenon_TA_h). zenon_intro zenon_H11. % 0.38/0.57 apply (zenon_L25_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H7a. zenon_intro zenon_H48. % 0.38/0.57 generalize (exhaustion_g zenon_TA_h). zenon_intro zenon_H11. % 0.38/0.57 generalize (zenon_H11 zenon_TC_bj). zenon_intro zenon_H51. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H3f | zenon_intro zenon_H52 ]. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TC_bj). zenon_intro zenon_H3e. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3d; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3c ]. % 0.38/0.57 exact (zenon_H3d zenon_H3f). % 0.38/0.57 apply (zenon_L24_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H41 | zenon_intro zenon_H49 ]. % 0.38/0.57 generalize (both_g zenon_TA_h). zenon_intro zenon_H1b. % 0.38/0.57 generalize (zenon_H1b zenon_TC_bj). zenon_intro zenon_H43. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H46; zenon_intro zenon_H45 | zenon_intro zenon_H41; zenon_intro zenon_H44 ]. % 0.38/0.57 exact (zenon_H46 zenon_H41). % 0.38/0.57 apply zenon_H6f. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H71. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H46. zenon_intro zenon_H28. % 0.38/0.57 generalize (both_g zenon_TA_h). zenon_intro zenon_H1b. % 0.38/0.57 generalize (zenon_H1b zenon_TC_bj). zenon_intro zenon_H43. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H46; zenon_intro zenon_H45 | zenon_intro zenon_H41; zenon_intro zenon_H44 ]. % 0.38/0.57 exact (zenon_H45 zenon_H44). % 0.38/0.57 exact (zenon_H46 zenon_H41). % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 0.38/0.57 apply zenon_H75. zenon_intro zenon_H49. % 0.38/0.57 apply (zenon_L16_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H74. zenon_intro zenon_H2b. % 0.38/0.57 apply (zenon_L20_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_L16_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 (* end of lemma zenon_L26_ *) % 0.38/0.57 assert (zenon_L27_ : forall (zenon_TA_h : zenon_U), (~(forall C : zenon_U, ((g_false_only zenon_TA_h C)\/(g_false_only C zenon_TA_h)))) -> (~(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h)))) -> (~(exists C : zenon_U, (((g_both zenon_TA_h C)\/(g_both C zenon_TA_h))/\((~(g_false_only zenon_TA_h C))/\(~(g_false_only C zenon_TA_h)))))) -> False). % 0.38/0.57 do 1 intro. intros zenon_H7b zenon_H76 zenon_H6f. % 0.38/0.57 apply (zenon_notallex_s (fun C : zenon_U => ((g_false_only zenon_TA_h C)\/(g_false_only C zenon_TA_h))) zenon_H7b); [ zenon_intro zenon_H7c; idtac ]. % 0.38/0.57 elim zenon_H7c. zenon_intro zenon_TC_bj. zenon_intro zenon_H7d. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H4d. zenon_intro zenon_H30. % 0.38/0.57 generalize (false_only_g zenon_TA_h). zenon_intro zenon_H8. % 0.38/0.57 generalize (zenon_H8 zenon_TC_bj). zenon_intro zenon_H4a. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H4d; zenon_intro zenon_H4c | zenon_intro zenon_H49; zenon_intro zenon_H4b ]. % 0.38/0.57 generalize (false_only_g zenon_TC_bj). zenon_intro zenon_H2c. % 0.38/0.57 generalize (zenon_H2c zenon_TA_h). zenon_intro zenon_H2d. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H30; zenon_intro zenon_H2f | zenon_intro zenon_H2b; zenon_intro zenon_H2e ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H22 | zenon_intro zenon_H79 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H42 | zenon_intro zenon_H7a ]. % 0.38/0.57 generalize (exhaustion_g zenon_TC_bj). zenon_intro zenon_H39. % 0.38/0.57 generalize (exhaustion_g zenon_TA_h). zenon_intro zenon_H11. % 0.38/0.57 generalize (zenon_H39 zenon_TA_h). zenon_intro zenon_H3a. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H37 | zenon_intro zenon_H3b ]. % 0.38/0.57 generalize (true_only_g zenon_TC_bj). zenon_intro zenon_H34. % 0.38/0.57 generalize (zenon_H34 zenon_TA_h). zenon_intro zenon_H35. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H35); [ zenon_intro zenon_H33; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 0.38/0.57 exact (zenon_H33 zenon_H37). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H2a. zenon_intro zenon_H22. % 0.38/0.57 apply (zenon_L25_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H21 | zenon_intro zenon_H2b ]. % 0.38/0.57 apply (zenon_L6_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_L7_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply zenon_H7a. zenon_intro zenon_H48. % 0.38/0.57 apply zenon_H76. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H78. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H78); [ zenon_intro zenon_H3d | zenon_intro zenon_H33 ]. % 0.38/0.57 apply (zenon_L21_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_L9_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_L26_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 exact (zenon_H30 zenon_H2b). % 0.38/0.57 exact (zenon_H4d zenon_H49). % 0.38/0.57 (* end of lemma zenon_L27_ *) % 0.38/0.57 assert (zenon_L28_ : forall (zenon_TA_h : zenon_U), (~(~(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h))))) -> (~(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h)))) -> False). % 0.38/0.57 do 1 intro. intros zenon_H6e zenon_H76. % 0.38/0.57 exact (zenon_H6e zenon_H76). % 0.38/0.57 (* end of lemma zenon_L28_ *) % 0.38/0.57 assert (zenon_L29_ : forall (zenon_TA_h : zenon_U), (~(exists B : zenon_U, (((g_true_only B zenon_TA_h)/\(((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(((g_both B zenon_TA_h)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/((g_false_only B zenon_TA_h)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B))))))))))) -> (~(g_both zenon_TA_h zenon_TA_h)) -> False). % 0.38/0.57 do 1 intro. intros zenon_H53 zenon_H1f. % 0.38/0.57 generalize (both_g zenon_TA_h). zenon_intro zenon_H1b. % 0.38/0.57 generalize (zenon_H1b zenon_TA_h). zenon_intro zenon_H1c. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1f; zenon_intro zenon_H1e | zenon_intro zenon_H1a; zenon_intro zenon_H1d ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H1e); [ zenon_intro zenon_Hd | zenon_intro zenon_H6 ]. % 0.38/0.57 apply zenon_H53. exists zenon_TA_h. apply NNPP. zenon_intro zenon_H7e. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H7f). zenon_intro zenon_H82. zenon_intro zenon_H81. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H80); [ zenon_intro zenon_H18 | zenon_intro zenon_H83 ]. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TA_h). zenon_intro zenon_H16. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H18; zenon_intro zenon_H10 | zenon_intro zenon_H14; zenon_intro zenon_H17 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_Hc | zenon_intro zenon_H84 ]. % 0.38/0.57 generalize (false_only_g zenon_TA_h). zenon_intro zenon_H8. % 0.38/0.57 generalize (zenon_H8 zenon_TA_h). zenon_intro zenon_H9. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H9); [ zenon_intro zenon_Hc; zenon_intro zenon_Hb | zenon_intro zenon_H5; zenon_intro zenon_Ha ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H6 | zenon_intro zenon_H20 ]. % 0.38/0.57 apply (zenon_L4_ zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_H20 zenon_Hd). % 0.38/0.57 exact (zenon_Hc zenon_H5). % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H84). zenon_intro zenon_H7b. zenon_intro zenon_H85. % 0.38/0.57 apply (zenon_notallex_s (fun C : zenon_U => ((g_false_only zenon_TA_h C)\/(g_false_only C zenon_TA_h))) zenon_H7b); [ zenon_intro zenon_H7c; idtac ]. % 0.38/0.57 elim zenon_H7c. zenon_intro zenon_TC_bj. zenon_intro zenon_H7d. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H4d. zenon_intro zenon_H30. % 0.38/0.57 generalize (false_only_g zenon_TA_h). zenon_intro zenon_H8. % 0.38/0.57 generalize (zenon_H8 zenon_TC_bj). zenon_intro zenon_H4a. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H4d; zenon_intro zenon_H4c | zenon_intro zenon_H49; zenon_intro zenon_H4b ]. % 0.38/0.57 generalize (false_only_g zenon_TC_bj). zenon_intro zenon_H2c. % 0.38/0.57 generalize (zenon_H2c zenon_TA_h). zenon_intro zenon_H2d. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H30; zenon_intro zenon_H2f | zenon_intro zenon_H2b; zenon_intro zenon_H2e ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H22 | zenon_intro zenon_H79 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H42 | zenon_intro zenon_H7a ]. % 0.38/0.57 apply (zenon_L15_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply zenon_H7a. zenon_intro zenon_H48. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 0.38/0.57 apply zenon_H6f. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H71. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H46. zenon_intro zenon_H28. % 0.38/0.57 generalize (both_g zenon_TA_h). zenon_intro zenon_H1b. % 0.38/0.57 generalize (zenon_H1b zenon_TC_bj). zenon_intro zenon_H43. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H46; zenon_intro zenon_H45 | zenon_intro zenon_H41; zenon_intro zenon_H44 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H4e | zenon_intro zenon_H42 ]. % 0.38/0.57 exact (zenon_H4e zenon_H48). % 0.38/0.57 apply (zenon_L15_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 exact (zenon_H46 zenon_H41). % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 0.38/0.57 apply zenon_H75. zenon_intro zenon_H49. % 0.38/0.57 apply (zenon_L16_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H74. zenon_intro zenon_H2b. % 0.38/0.57 apply (zenon_L7_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_L19_ zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H79. zenon_intro zenon_H2a. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H42 | zenon_intro zenon_H7a ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 0.38/0.57 apply zenon_H6f. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H71. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H46. zenon_intro zenon_H28. % 0.38/0.57 generalize (both_g zenon_TC_bj). zenon_intro zenon_H24. % 0.38/0.57 generalize (zenon_H24 zenon_TA_h). zenon_intro zenon_H25. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H28; zenon_intro zenon_H27 | zenon_intro zenon_H21; zenon_intro zenon_H26 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H31 | zenon_intro zenon_H22 ]. % 0.38/0.57 exact (zenon_H31 zenon_H2a). % 0.38/0.57 apply zenon_H53. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H54. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H54). zenon_intro zenon_H56. zenon_intro zenon_H55. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H56); [ zenon_intro zenon_H33 | zenon_intro zenon_H57 ]. % 0.38/0.57 apply (zenon_L10_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H57). zenon_intro zenon_H58. zenon_intro zenon_H4f. % 0.38/0.57 apply (zenon_L14_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 exact (zenon_H28 zenon_H21). % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 0.38/0.57 apply zenon_H75. zenon_intro zenon_H49. % 0.38/0.57 apply (zenon_L13_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H74. zenon_intro zenon_H2b. % 0.38/0.57 apply (zenon_L20_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_L19_ zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H7a. zenon_intro zenon_H48. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 0.38/0.57 apply zenon_H6f. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H71. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H46. zenon_intro zenon_H28. % 0.38/0.57 generalize (both_g zenon_TC_bj). zenon_intro zenon_H24. % 0.38/0.57 generalize (zenon_H24 zenon_TA_h). zenon_intro zenon_H25. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H28; zenon_intro zenon_H27 | zenon_intro zenon_H21; zenon_intro zenon_H26 ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H31 | zenon_intro zenon_H22 ]. % 0.38/0.57 exact (zenon_H31 zenon_H2a). % 0.38/0.57 apply zenon_H53. exists zenon_TC_bj. apply NNPP. zenon_intro zenon_H54. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H54). zenon_intro zenon_H56. zenon_intro zenon_H55. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H56); [ zenon_intro zenon_H33 | zenon_intro zenon_H57 ]. % 0.38/0.57 apply (zenon_L10_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H57). zenon_intro zenon_H58. zenon_intro zenon_H4f. % 0.38/0.57 apply zenon_H4f. exists zenon_TA_h. apply NNPP. zenon_intro zenon_H50. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 0.38/0.57 apply (zenon_L10_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_L21_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_H28 zenon_H21). % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 0.38/0.57 apply zenon_H75. zenon_intro zenon_H49. % 0.38/0.57 apply (zenon_L16_ zenon_TC_bj zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H74. zenon_intro zenon_H2b. % 0.38/0.57 apply (zenon_L20_ zenon_TA_h zenon_TC_bj); trivial. % 0.38/0.57 apply (zenon_L19_ zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_H30 zenon_H2b). % 0.38/0.57 exact (zenon_H4d zenon_H49). % 0.38/0.57 exact (zenon_H18 zenon_H14). % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H85. zenon_intro zenon_H76. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_Hc | zenon_intro zenon_H84 ]. % 0.38/0.57 generalize (false_only_g zenon_TA_h). zenon_intro zenon_H8. % 0.38/0.57 generalize (zenon_H8 zenon_TA_h). zenon_intro zenon_H9. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H9); [ zenon_intro zenon_Hc; zenon_intro zenon_Hb | zenon_intro zenon_H5; zenon_intro zenon_Ha ]. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H6 | zenon_intro zenon_H20 ]. % 0.38/0.57 apply (zenon_L23_ zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_H20 zenon_Hd). % 0.38/0.57 exact (zenon_Hc zenon_H5). % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H84). zenon_intro zenon_H7b. zenon_intro zenon_H85. % 0.38/0.57 apply (zenon_L27_ zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_H6e zenon_H76). % 0.38/0.57 apply zenon_H53. exists zenon_TA_h. apply NNPP. zenon_intro zenon_H7e. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H80); [ zenon_intro zenon_H18 | zenon_intro zenon_H83 ]. % 0.38/0.57 generalize (true_only_g zenon_TA_h). zenon_intro zenon_H15. % 0.38/0.57 generalize (zenon_H15 zenon_TA_h). zenon_intro zenon_H16. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H18; zenon_intro zenon_H10 | zenon_intro zenon_H14; zenon_intro zenon_H17 ]. % 0.38/0.57 apply (zenon_L4_ zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_H18 zenon_H14). % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H85. zenon_intro zenon_H76. % 0.38/0.57 apply (zenon_L23_ zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_H1f zenon_H1a). % 0.38/0.57 (* end of lemma zenon_L29_ *) % 0.38/0.57 assert (zenon_L30_ : forall (zenon_TA_h : zenon_U), (~((forall C : zenon_U, ((g_false_only zenon_TA_h C)\/(g_false_only C zenon_TA_h)))\/(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h))))) -> (~(exists C : zenon_U, ((g_true_only zenon_TA_h C)/\(g_true_only C zenon_TA_h)))) -> (~(exists C : zenon_U, (((g_both zenon_TA_h C)\/(g_both C zenon_TA_h))/\((~(g_false_only zenon_TA_h C))/\(~(g_false_only C zenon_TA_h)))))) -> False). % 0.38/0.57 do 1 intro. intros zenon_H86 zenon_H76 zenon_H6f. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H7b. zenon_intro zenon_H76. % 0.38/0.57 apply (zenon_L27_ zenon_TA_h); trivial. % 0.38/0.57 (* end of lemma zenon_L30_ *) % 0.38/0.57 assert (zenon_L31_ : forall (zenon_TA_fh : zenon_U), (g_false_only zenon_TA_fh zenon_TA_fh) -> (~(g_false zenon_TA_fh zenon_TA_fh)) -> False). % 0.38/0.57 do 1 intro. intros zenon_H87 zenon_H88. % 0.38/0.57 generalize (false_only_g zenon_TA_fh). zenon_intro zenon_H8a. % 0.38/0.57 generalize (zenon_H8a zenon_TA_fh). zenon_intro zenon_H8b. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H8b); [ zenon_intro zenon_H8e; zenon_intro zenon_H8d | zenon_intro zenon_H87; zenon_intro zenon_H8c ]. % 0.38/0.57 exact (zenon_H8e zenon_H87). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 0.38/0.57 exact (zenon_H88 zenon_H90). % 0.38/0.57 (* end of lemma zenon_L31_ *) % 0.38/0.57 assert (zenon_L32_ : forall (zenon_TA_fh : zenon_U) (zenon_TC_fr : zenon_U), (g_false_only zenon_TC_fr zenon_TA_fh) -> (~(g_false zenon_TC_fr zenon_TA_fh)) -> False). % 0.38/0.57 do 2 intro. intros zenon_H91 zenon_H92. % 0.38/0.57 generalize (false_only_g zenon_TC_fr). zenon_intro zenon_H94. % 0.38/0.57 generalize (zenon_H94 zenon_TA_fh). zenon_intro zenon_H95. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_H95); [ zenon_intro zenon_H98; zenon_intro zenon_H97 | zenon_intro zenon_H91; zenon_intro zenon_H96 ]. % 0.38/0.57 exact (zenon_H98 zenon_H91). % 0.38/0.57 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 0.38/0.57 exact (zenon_H92 zenon_H9a). % 0.38/0.57 (* end of lemma zenon_L32_ *) % 0.38/0.57 assert (zenon_L33_ : forall (zenon_TA_fh : zenon_U), (exists C : zenon_U, ((g_true_only zenon_TA_fh C)/\(g_true_only C zenon_TA_fh))) -> (forall B : zenon_U, (((g_true_only B zenon_TA_fh)/\(forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B))))\/((g_false_only B zenon_TA_fh)/\(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))) -> False). % 0.38/0.57 do 1 intro. intros zenon_H9b zenon_H9c. % 0.38/0.57 elim zenon_H9b. zenon_intro zenon_TC_fr. zenon_intro zenon_H9d. % 0.38/0.57 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H9f. zenon_intro zenon_H9e. % 0.38/0.57 generalize (true_only_g zenon_TA_fh). zenon_intro zenon_Ha0. % 0.38/0.57 generalize (zenon_Ha0 zenon_TC_fr). zenon_intro zenon_Ha1. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_Ha1); [ zenon_intro zenon_Ha4; zenon_intro zenon_Ha3 | zenon_intro zenon_H9f; zenon_intro zenon_Ha2 ]. % 0.38/0.57 exact (zenon_Ha4 zenon_H9f). % 0.38/0.57 apply (zenon_and_s _ _ zenon_Ha2). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5. % 0.38/0.57 generalize (true_only_g zenon_TC_fr). zenon_intro zenon_Ha7. % 0.38/0.57 generalize (zenon_Ha7 zenon_TA_fh). zenon_intro zenon_Ha8. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_Ha8); [ zenon_intro zenon_Hab; zenon_intro zenon_Haa | zenon_intro zenon_H9e; zenon_intro zenon_Ha9 ]. % 0.38/0.57 exact (zenon_Hab zenon_H9e). % 0.38/0.57 apply (zenon_and_s _ _ zenon_Ha9). zenon_intro zenon_Hac. zenon_intro zenon_H92. % 0.38/0.57 generalize (zenon_H9c zenon_TC_fr). zenon_intro zenon_Had. % 0.38/0.57 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_Haf | zenon_intro zenon_Hae ]. % 0.38/0.57 apply (zenon_and_s _ _ zenon_Haf). zenon_intro zenon_H9e. zenon_intro zenon_Hb0. % 0.38/0.57 generalize (zenon_Hb0 zenon_TA_fh). zenon_intro zenon_Hb1. % 0.38/0.57 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb2 ]. % 0.38/0.57 apply (zenon_L32_ zenon_TA_fh zenon_TC_fr); trivial. % 0.38/0.57 generalize (false_only_g zenon_TA_fh). zenon_intro zenon_H8a. % 0.38/0.57 generalize (zenon_H8a zenon_TC_fr). zenon_intro zenon_Hb3. % 0.38/0.57 apply (zenon_equiv_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6; zenon_intro zenon_Hb5 | zenon_intro zenon_Hb2; zenon_intro zenon_Hb4 ]. % 0.38/0.57 exact (zenon_Hb6 zenon_Hb2). % 0.38/0.57 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_Hb8. zenon_intro zenon_Hb7. % 0.38/0.57 exact (zenon_Ha5 zenon_Hb8). % 0.38/0.57 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H91. zenon_intro zenon_Hb9. % 0.38/0.57 apply (zenon_L32_ zenon_TA_fh zenon_TC_fr); trivial. % 0.38/0.57 (* end of lemma zenon_L33_ *) % 0.38/0.57 assert (zenon_L34_ : forall (zenon_TA_fh : zenon_U), ((g_false_only zenon_TA_fh zenon_TA_fh)/\(exists C : zenon_U, ((g_true_only zenon_TA_fh C)/\(g_true_only C zenon_TA_fh)))) -> (forall B : zenon_U, (((g_true_only B zenon_TA_fh)/\(forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B))))\/((g_false_only B zenon_TA_fh)/\(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))) -> False). % 0.38/0.57 do 1 intro. intros zenon_Hba zenon_H9c. % 0.38/0.57 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_H87. zenon_intro zenon_H9b. % 0.38/0.57 apply (zenon_L33_ zenon_TA_fh); trivial. % 0.38/0.57 (* end of lemma zenon_L34_ *) % 0.38/0.57 apply NNPP. intro zenon_G. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_Hbc. zenon_intro zenon_Hbb. % 0.38/0.57 apply (zenon_notallex_s (fun A : zenon_U => (exists B : zenon_U, (((g_true_only B A)/\(((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/(((g_both B A)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B)))))\/((g_false_only B A)/\((forall C : zenon_U, ((g_false_only B C)\/(g_false_only C B)))\/((exists C : zenon_U, (((g_both B C)\/(g_both C B))/\((~(g_false_only B C))/\(~(g_false_only C B)))))/\(~(exists C : zenon_U, ((g_true_only B C)/\(g_true_only C B))))))))))) zenon_Hbc); [ zenon_intro zenon_Hbd; idtac ]. % 0.38/0.57 elim zenon_Hbd. zenon_intro zenon_TA_h. zenon_intro zenon_H53. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hbe ]. % 0.38/0.57 apply zenon_Hbf. exists zenon_TA_h. apply NNPP. zenon_intro zenon_Hc0. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_Hc0); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hc1 ]. % 0.38/0.57 apply zenon_Hc2. exists zenon_TA_h. apply NNPP. zenon_intro zenon_Hc3. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_Hc3); [ zenon_intro zenon_H1f | zenon_intro zenon_H85 ]. % 0.38/0.57 apply (zenon_L29_ zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 0.38/0.57 apply zenon_H53. exists zenon_TA_h. apply NNPP. zenon_intro zenon_H7e. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H7f). zenon_intro zenon_H82. zenon_intro zenon_H81. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H82); [ zenon_intro zenon_H1f | zenon_intro zenon_H86 ]. % 0.38/0.57 apply (zenon_L29_ zenon_TA_h); trivial. % 0.38/0.57 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H7b. zenon_intro zenon_H76. % 0.38/0.57 apply (zenon_L30_ zenon_TA_h); trivial. % 0.38/0.57 apply zenon_H6e. zenon_intro zenon_H60. % 0.38/0.57 apply (zenon_L18_ zenon_TA_h); trivial. % 0.38/0.57 exact (zenon_Hc1 zenon_H53). % 0.38/0.57 apply zenon_Hbe. zenon_intro zenon_Hc4. % 0.38/0.57 elim zenon_Hc4. zenon_intro zenon_TA_fh. zenon_intro zenon_H9c. % 0.38/0.57 generalize (zenon_H9c zenon_TA_fh). zenon_intro zenon_Hc5. % 0.38/0.57 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hba ]. % 0.38/0.58 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 0.38/0.58 generalize (true_only_g zenon_TA_fh). zenon_intro zenon_Ha0. % 0.38/0.58 generalize (zenon_Ha0 zenon_TA_fh). zenon_intro zenon_Hc9. % 0.38/0.58 apply (zenon_equiv_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcc; zenon_intro zenon_Hcb | zenon_intro zenon_Hc8; zenon_intro zenon_Hca ]. % 0.38/0.58 exact (zenon_Hcc zenon_Hc8). % 0.38/0.58 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_Hcd. zenon_intro zenon_H88. % 0.38/0.58 generalize (zenon_Hc7 zenon_TA_fh). zenon_intro zenon_Hce. % 0.38/0.58 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H87 | zenon_intro zenon_H87 ]. % 0.38/0.58 apply (zenon_L31_ zenon_TA_fh); trivial. % 0.38/0.58 apply (zenon_L31_ zenon_TA_fh); trivial. % 0.38/0.58 apply (zenon_L34_ zenon_TA_fh); trivial. % 0.38/0.58 Qed. % 0.38/0.58 % SZS output end Proof % 0.38/0.58 (* END-PROOF *) % 0.38/0.58 nodes searched: 3880 % 0.38/0.58 max branch formulas: 619 % 0.38/0.58 proof nodes created: 476 % 0.38/0.58 formulas created: 8911 % 0.38/0.58 %------------------------------------------------------------------------------