%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN726+1 : TPTP v8.1.0. Released v2.5.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 13:55:19 EDT 2022 % Result : Theorem 0.45s 0.71s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SYN726+1 : TPTP v8.1.0. Released v2.5.0. % 0.00/0.09 % Command : run_zenon %s %d % 0.09/0.29 % Computer : n017.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 600 % 0.09/0.29 % DateTime : Tue Jul 12 02:41:49 EDT 2022 % 0.09/0.29 % CPUTime : % 0.45/0.71 (* PROOF-FOUND *) % 0.45/0.71 % SZS status Theorem % 0.45/0.71 (* BEGIN-PROOF *) % 0.45/0.71 % SZS output start Proof % 0.45/0.71 Theorem thm400 : ((((forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((p X Y)/\(p Y Z))->(p X Z)))))/\((forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((q X Y)/\(q Y Z))->(q X Z)))))/\((forall X : zenon_U, (forall Y : zenon_U, ((q X Y)->(q Y X))))/\(forall X : zenon_U, (forall Y : zenon_U, ((p X Y)\/(q X Y)))))))->(forall X : zenon_U, (forall Y : zenon_U, (p X Y))))\/(forall X : zenon_U, (forall Y : zenon_U, (q X Y)))). % 0.45/0.71 Proof. % 0.45/0.71 assert (zenon_L1_ : forall (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U), (forall X : zenon_U, (forall Y : zenon_U, ((q X Y)->(q Y X)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((q x y)->((q y z)->(q x z)))))) -> (~(p zenon_TX_j zenon_TY_i)) -> (~(q zenon_TX_h zenon_TY_i)) -> (~(p zenon_TX_j zenon_TX_h)) -> (forall Y : zenon_U, ((p zenon_TX_j Y)\/(q zenon_TX_j Y))) -> False). % 0.45/0.71 do 3 intro. intros zenon_H1 zenon_H2 zenon_H3 zenon_H4 zenon_H5 zenon_H6. % 0.45/0.71 generalize (zenon_H6 zenon_TY_i). zenon_intro zenon_Ha. % 0.45/0.71 apply (zenon_or_s _ _ zenon_Ha); [ zenon_intro zenon_Hc | zenon_intro zenon_Hb ]. % 0.45/0.71 exact (zenon_H3 zenon_Hc). % 0.45/0.71 elim (classic ((~(zenon_TX_h = zenon_TX_j))/\(~(q zenon_TX_h zenon_TX_j)))); [ zenon_intro zenon_Hd | zenon_intro zenon_He ]. % 0.45/0.71 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_H10. zenon_intro zenon_Hf. % 0.45/0.71 generalize (zenon_H6 zenon_TX_h). zenon_intro zenon_H11. % 0.45/0.71 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ]. % 0.45/0.71 exact (zenon_H5 zenon_H13). % 0.45/0.71 generalize (zenon_H1 zenon_TX_j). zenon_intro zenon_H14. % 0.45/0.71 generalize (zenon_H14 zenon_TX_h). zenon_intro zenon_H15. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.45/0.71 exact (zenon_H17 zenon_H12). % 0.45/0.71 exact (zenon_Hf zenon_H16). % 0.45/0.71 cut ((q zenon_TX_j zenon_TY_i) = (q zenon_TX_h zenon_TY_i)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H4. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_Hb. % 0.45/0.71 cut ((zenon_TY_i = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_H18]. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H19]. % 0.45/0.71 congruence. % 0.45/0.71 apply (zenon_notand_s _ _ zenon_He); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.45/0.71 apply zenon_H1b. zenon_intro zenon_H1c. % 0.45/0.71 elim (classic (zenon_TX_h = zenon_TX_h)); [ zenon_intro zenon_H1d | zenon_intro zenon_H1e ]. % 0.45/0.71 cut ((zenon_TX_h = zenon_TX_h) = (zenon_TX_j = zenon_TX_h)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H19. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_H1d. % 0.45/0.71 cut ((zenon_TX_h = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 0.45/0.71 cut ((zenon_TX_h = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H10]. % 0.45/0.71 congruence. % 0.45/0.71 exact (zenon_H10 zenon_H1c). % 0.45/0.71 apply zenon_H1e. apply refl_equal. % 0.45/0.71 apply zenon_H1e. apply refl_equal. % 0.45/0.71 apply zenon_H1a. zenon_intro zenon_H16. % 0.45/0.71 generalize (zenon_H2 zenon_TX_h). zenon_intro zenon_H1f. % 0.45/0.71 generalize (zenon_H1f zenon_TX_j). zenon_intro zenon_H20. % 0.45/0.71 generalize (zenon_H20 zenon_TY_i). zenon_intro zenon_H21. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_Hf | zenon_intro zenon_H22 ]. % 0.45/0.71 exact (zenon_Hf zenon_H16). % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 0.45/0.71 exact (zenon_H24 zenon_Hb). % 0.45/0.71 exact (zenon_H4 zenon_H23). % 0.45/0.71 apply zenon_H18. apply refl_equal. % 0.45/0.71 (* end of lemma zenon_L1_ *) % 0.45/0.71 assert (zenon_L2_ : forall (zenon_TY_bp : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_h : zenon_U), (forall X : zenon_U, (forall Y : zenon_U, ((q X Y)->(q Y X)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((q x y)->((q y z)->(q x z)))))) -> (~(q zenon_TX_h zenon_TY_i)) -> (forall Y : zenon_U, ((p zenon_TX_j Y)\/(q zenon_TX_j Y))) -> (p zenon_TX_h zenon_TY_i) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((p x y)->((p y z)->(p x z)))))) -> (~(p zenon_TX_j zenon_TY_bp)) -> (p zenon_TY_i zenon_TY_bp) -> False). % 0.45/0.71 do 4 intro. intros zenon_H1 zenon_H2 zenon_H4 zenon_H6 zenon_H25 zenon_H26 zenon_H27 zenon_H28. % 0.45/0.71 elim (classic ((~(zenon_TX_j = zenon_TY_i))/\(~(p zenon_TX_j zenon_TY_i)))); [ zenon_intro zenon_H2a | zenon_intro zenon_H2b ]. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2c. zenon_intro zenon_H3. % 0.45/0.71 elim (classic ((~(zenon_TX_j = zenon_TX_h))/\(~(p zenon_TX_j zenon_TX_h)))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ]. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H19. zenon_intro zenon_H5. % 0.45/0.71 apply (zenon_L1_ zenon_TX_h zenon_TY_i zenon_TX_j); trivial. % 0.45/0.71 cut ((p zenon_TX_h zenon_TY_i) = (p zenon_TX_j zenon_TY_i)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H3. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_H25. % 0.45/0.71 cut ((zenon_TY_i = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_H18]. % 0.45/0.71 cut ((zenon_TX_h = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H10]. % 0.45/0.71 congruence. % 0.45/0.71 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.45/0.71 apply zenon_H30. zenon_intro zenon_H31. % 0.45/0.71 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ]. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_h = zenon_TX_j)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H10. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_H32. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H33]. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H19]. % 0.45/0.71 congruence. % 0.45/0.71 exact (zenon_H19 zenon_H31). % 0.45/0.71 apply zenon_H33. apply refl_equal. % 0.45/0.71 apply zenon_H33. apply refl_equal. % 0.45/0.71 apply zenon_H2f. zenon_intro zenon_H13. % 0.45/0.71 generalize (zenon_H26 zenon_TX_j). zenon_intro zenon_H34. % 0.45/0.71 generalize (zenon_H34 zenon_TX_h). zenon_intro zenon_H35. % 0.45/0.71 generalize (zenon_H35 zenon_TY_i). zenon_intro zenon_H36. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H5 | zenon_intro zenon_H37 ]. % 0.45/0.71 exact (zenon_H5 zenon_H13). % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H38 | zenon_intro zenon_Hc ]. % 0.45/0.71 exact (zenon_H38 zenon_H25). % 0.45/0.71 exact (zenon_H3 zenon_Hc). % 0.45/0.71 apply zenon_H18. apply refl_equal. % 0.45/0.71 cut ((p zenon_TY_i zenon_TY_bp) = (p zenon_TX_j zenon_TY_bp)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H27. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_H28. % 0.45/0.71 cut ((zenon_TY_bp = zenon_TY_bp)); [idtac | apply NNPP; zenon_intro zenon_H39]. % 0.45/0.71 cut ((zenon_TY_i = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 0.45/0.71 congruence. % 0.45/0.71 apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.45/0.71 apply zenon_H3c. zenon_intro zenon_H3d. % 0.45/0.71 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ]. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_i = zenon_TX_j)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H3a. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_H32. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H33]. % 0.45/0.71 cut ((zenon_TX_j = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 0.45/0.71 congruence. % 0.45/0.71 exact (zenon_H2c zenon_H3d). % 0.45/0.71 apply zenon_H33. apply refl_equal. % 0.45/0.71 apply zenon_H33. apply refl_equal. % 0.45/0.71 apply zenon_H3b. zenon_intro zenon_Hc. % 0.45/0.71 generalize (zenon_H26 zenon_TX_j). zenon_intro zenon_H34. % 0.45/0.71 generalize (zenon_H34 zenon_TY_i). zenon_intro zenon_H3e. % 0.45/0.71 generalize (zenon_H3e zenon_TY_bp). zenon_intro zenon_H3f. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H3 | zenon_intro zenon_H40 ]. % 0.45/0.71 exact (zenon_H3 zenon_Hc). % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.45/0.71 exact (zenon_H42 zenon_H28). % 0.45/0.71 exact (zenon_H27 zenon_H41). % 0.45/0.71 apply zenon_H39. apply refl_equal. % 0.45/0.71 (* end of lemma zenon_L2_ *) % 0.45/0.71 assert (zenon_L3_ : forall (zenon_TX_j : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_h : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((q x y)->((q y z)->(q x z)))))) -> (forall X : zenon_U, (forall Y : zenon_U, ((q X Y)->(q Y X)))) -> (~(q zenon_TX_h zenon_TY_i)) -> (forall X : zenon_U, (forall Y : zenon_U, ((p X Y)\/(q X Y)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((p x y)->((p y z)->(p x z)))))) -> (~(p zenon_TX_j zenon_TX_h)) -> (p zenon_TY_i zenon_TX_h) -> False). % 0.45/0.71 do 3 intro. intros zenon_H2 zenon_H1 zenon_H4 zenon_H43 zenon_H26 zenon_H5 zenon_H44. % 0.45/0.71 elim (classic ((~(zenon_TX_j = zenon_TY_i))/\(~(p zenon_TX_j zenon_TY_i)))); [ zenon_intro zenon_H2a | zenon_intro zenon_H2b ]. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2c. zenon_intro zenon_H3. % 0.45/0.71 generalize (zenon_H43 zenon_TX_j). zenon_intro zenon_H6. % 0.45/0.71 apply (zenon_L1_ zenon_TX_h zenon_TY_i zenon_TX_j); trivial. % 0.45/0.71 cut ((p zenon_TY_i zenon_TX_h) = (p zenon_TX_j zenon_TX_h)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H5. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_H44. % 0.45/0.71 cut ((zenon_TX_h = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 0.45/0.71 cut ((zenon_TY_i = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 0.45/0.71 congruence. % 0.45/0.71 apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.45/0.71 apply zenon_H3c. zenon_intro zenon_H3d. % 0.45/0.71 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ]. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_i = zenon_TX_j)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H3a. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_H32. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H33]. % 0.45/0.71 cut ((zenon_TX_j = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 0.45/0.71 congruence. % 0.45/0.71 exact (zenon_H2c zenon_H3d). % 0.45/0.71 apply zenon_H33. apply refl_equal. % 0.45/0.71 apply zenon_H33. apply refl_equal. % 0.45/0.71 apply zenon_H3b. zenon_intro zenon_Hc. % 0.45/0.71 generalize (zenon_H26 zenon_TX_j). zenon_intro zenon_H34. % 0.45/0.71 generalize (zenon_H34 zenon_TY_i). zenon_intro zenon_H3e. % 0.45/0.71 generalize (zenon_H3e zenon_TX_h). zenon_intro zenon_H45. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H3 | zenon_intro zenon_H46 ]. % 0.45/0.71 exact (zenon_H3 zenon_Hc). % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H47 | zenon_intro zenon_H13 ]. % 0.45/0.71 exact (zenon_H47 zenon_H44). % 0.45/0.71 exact (zenon_H5 zenon_H13). % 0.45/0.71 apply zenon_H1e. apply refl_equal. % 0.45/0.71 (* end of lemma zenon_L3_ *) % 0.45/0.71 assert (zenon_L4_ : forall (zenon_TY_bp : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_h : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((q x y)->((q y z)->(q x z)))))) -> (forall X : zenon_U, (forall Y : zenon_U, ((q X Y)->(q Y X)))) -> (forall X : zenon_U, (forall Y : zenon_U, ((p X Y)\/(q X Y)))) -> (~(q zenon_TX_h zenon_TY_i)) -> (p zenon_TY_i zenon_TX_h) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((p x y)->((p y z)->(p x z)))))) -> (~(p zenon_TX_j zenon_TY_bp)) -> (p zenon_TX_h zenon_TY_bp) -> False). % 0.45/0.71 do 4 intro. intros zenon_H2 zenon_H1 zenon_H43 zenon_H4 zenon_H44 zenon_H26 zenon_H27 zenon_H48. % 0.45/0.71 elim (classic ((~(zenon_TX_j = zenon_TX_h))/\(~(p zenon_TX_j zenon_TX_h)))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ]. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H19. zenon_intro zenon_H5. % 0.45/0.71 apply (zenon_L3_ zenon_TX_j zenon_TY_i zenon_TX_h); trivial. % 0.45/0.71 cut ((p zenon_TX_h zenon_TY_bp) = (p zenon_TX_j zenon_TY_bp)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H27. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_H48. % 0.45/0.71 cut ((zenon_TY_bp = zenon_TY_bp)); [idtac | apply NNPP; zenon_intro zenon_H39]. % 0.45/0.71 cut ((zenon_TX_h = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H10]. % 0.45/0.71 congruence. % 0.45/0.71 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.45/0.71 apply zenon_H30. zenon_intro zenon_H31. % 0.45/0.71 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ]. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_h = zenon_TX_j)). % 0.45/0.71 intro zenon_D_pnotp. % 0.45/0.71 apply zenon_H10. % 0.45/0.71 rewrite <- zenon_D_pnotp. % 0.45/0.71 exact zenon_H32. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H33]. % 0.45/0.71 cut ((zenon_TX_j = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H19]. % 0.45/0.71 congruence. % 0.45/0.71 exact (zenon_H19 zenon_H31). % 0.45/0.71 apply zenon_H33. apply refl_equal. % 0.45/0.71 apply zenon_H33. apply refl_equal. % 0.45/0.71 apply zenon_H2f. zenon_intro zenon_H13. % 0.45/0.71 generalize (zenon_H26 zenon_TX_j). zenon_intro zenon_H34. % 0.45/0.71 generalize (zenon_H34 zenon_TX_h). zenon_intro zenon_H35. % 0.45/0.71 generalize (zenon_H35 zenon_TY_bp). zenon_intro zenon_H49. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H5 | zenon_intro zenon_H4a ]. % 0.45/0.71 exact (zenon_H5 zenon_H13). % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H4b | zenon_intro zenon_H41 ]. % 0.45/0.71 exact (zenon_H4b zenon_H48). % 0.45/0.71 exact (zenon_H27 zenon_H41). % 0.45/0.71 apply zenon_H39. apply refl_equal. % 0.45/0.71 (* end of lemma zenon_L4_ *) % 0.45/0.71 apply NNPP. intro zenon_G. % 0.45/0.71 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((q x y)->((q y z)->(q x z))))))); [ zenon_intro zenon_H2 | zenon_intro zenon_H4c ]. % 0.45/0.71 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((p x y)->((p y z)->(p x z))))))); [ zenon_intro zenon_H26 | zenon_intro zenon_H4d ]. % 0.45/0.71 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 0.45/0.71 apply (zenon_notimply_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H55. zenon_intro zenon_H54. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H1. zenon_intro zenon_H43. % 0.45/0.71 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (p X Y))) zenon_H50); [ zenon_intro zenon_H56; idtac ]. % 0.45/0.71 elim zenon_H56. zenon_intro zenon_TX_j. zenon_intro zenon_H57. % 0.45/0.71 apply (zenon_notallex_s (fun Y : zenon_U => (p zenon_TX_j Y)) zenon_H57); [ zenon_intro zenon_H58; idtac ]. % 0.45/0.71 elim zenon_H58. zenon_intro zenon_TY_bp. zenon_intro zenon_H27. % 0.45/0.71 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (q X Y))) zenon_H4e); [ zenon_intro zenon_H59; idtac ]. % 0.45/0.71 elim zenon_H59. zenon_intro zenon_TX_h. zenon_intro zenon_H5a. % 0.45/0.71 apply (zenon_notallex_s (fun Y : zenon_U => (q zenon_TX_h Y)) zenon_H5a); [ zenon_intro zenon_H5b; idtac ]. % 0.45/0.71 elim zenon_H5b. zenon_intro zenon_TY_i. zenon_intro zenon_H4. % 0.45/0.71 generalize (zenon_H43 zenon_TY_i). zenon_intro zenon_H5c. % 0.45/0.71 generalize (zenon_H43 zenon_TX_h). zenon_intro zenon_H5d. % 0.45/0.71 generalize (zenon_H5c zenon_TX_h). zenon_intro zenon_H5e. % 0.45/0.71 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H44 | zenon_intro zenon_H5f ]. % 0.45/0.71 generalize (zenon_H5d zenon_TY_i). zenon_intro zenon_H60. % 0.45/0.71 apply (zenon_or_s _ _ zenon_H60); [ zenon_intro zenon_H25 | zenon_intro zenon_H23 ]. % 0.45/0.71 generalize (zenon_H43 zenon_TX_j). zenon_intro zenon_H6. % 0.45/0.71 generalize (zenon_H5c zenon_TY_bp). zenon_intro zenon_H61. % 0.45/0.71 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H28 | zenon_intro zenon_H62 ]. % 0.45/0.71 apply (zenon_L2_ zenon_TY_bp zenon_TX_j zenon_TY_i zenon_TX_h); trivial. % 0.45/0.71 generalize (zenon_H1 zenon_TY_i). zenon_intro zenon_H63. % 0.45/0.71 generalize (zenon_H63 zenon_TX_h). zenon_intro zenon_H64. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H65 | zenon_intro zenon_H23 ]. % 0.45/0.71 elim (classic (q zenon_TY_bp zenon_TX_h)); [ zenon_intro zenon_H66 | zenon_intro zenon_H67 ]. % 0.45/0.71 generalize (zenon_H2 zenon_TY_i). zenon_intro zenon_H68. % 0.45/0.71 generalize (zenon_H68 zenon_TY_bp). zenon_intro zenon_H69. % 0.45/0.71 generalize (zenon_H69 zenon_TX_h). zenon_intro zenon_H6a. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 0.45/0.71 exact (zenon_H6c zenon_H62). % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H67 | zenon_intro zenon_H5f ]. % 0.45/0.71 exact (zenon_H67 zenon_H66). % 0.45/0.71 exact (zenon_H65 zenon_H5f). % 0.45/0.71 generalize (zenon_H5d zenon_TY_bp). zenon_intro zenon_H6d. % 0.45/0.71 apply (zenon_or_s _ _ zenon_H6d); [ zenon_intro zenon_H48 | zenon_intro zenon_H6e ]. % 0.45/0.71 apply (zenon_L4_ zenon_TY_bp zenon_TX_j zenon_TY_i zenon_TX_h); trivial. % 0.45/0.71 generalize (zenon_H1 zenon_TX_h). zenon_intro zenon_H6f. % 0.45/0.71 generalize (zenon_H6f zenon_TY_bp). zenon_intro zenon_H70. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H71 | zenon_intro zenon_H66 ]. % 0.45/0.71 exact (zenon_H71 zenon_H6e). % 0.45/0.71 exact (zenon_H67 zenon_H66). % 0.45/0.71 exact (zenon_H4 zenon_H23). % 0.45/0.71 exact (zenon_H4 zenon_H23). % 0.45/0.71 generalize (zenon_H1 zenon_TY_i). zenon_intro zenon_H63. % 0.45/0.71 generalize (zenon_H63 zenon_TX_h). zenon_intro zenon_H64. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H65 | zenon_intro zenon_H23 ]. % 0.45/0.71 exact (zenon_H65 zenon_H5f). % 0.45/0.71 exact (zenon_H4 zenon_H23). % 0.45/0.71 apply zenon_H4d. zenon_intro zenon_Tx_ek. apply NNPP. zenon_intro zenon_H73. % 0.45/0.71 apply zenon_H73. zenon_intro zenon_Ty_em. apply NNPP. zenon_intro zenon_H75. % 0.45/0.71 apply zenon_H75. zenon_intro zenon_Tz_eo. apply NNPP. zenon_intro zenon_H77. % 0.45/0.71 apply (zenon_notimply_s _ _ zenon_H77). zenon_intro zenon_H79. zenon_intro zenon_H78. % 0.45/0.71 apply (zenon_notimply_s _ _ zenon_H78). zenon_intro zenon_H7b. zenon_intro zenon_H7a. % 0.45/0.71 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 0.45/0.71 apply (zenon_notimply_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52. % 0.45/0.71 generalize (zenon_H53 zenon_Tx_ek). zenon_intro zenon_H7c. % 0.45/0.71 generalize (zenon_H7c zenon_Ty_em). zenon_intro zenon_H7d. % 0.45/0.71 generalize (zenon_H7d zenon_Tz_eo). zenon_intro zenon_H7e. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H7e); [ zenon_intro zenon_H80 | zenon_intro zenon_H7f ]. % 0.45/0.71 apply (zenon_notand_s _ _ zenon_H80); [ zenon_intro zenon_H82 | zenon_intro zenon_H81 ]. % 0.45/0.71 exact (zenon_H82 zenon_H79). % 0.45/0.71 exact (zenon_H81 zenon_H7b). % 0.45/0.71 exact (zenon_H7a zenon_H7f). % 0.45/0.71 apply zenon_H4c. zenon_intro zenon_Tx_fb. apply NNPP. zenon_intro zenon_H84. % 0.45/0.71 apply zenon_H84. zenon_intro zenon_Ty_fd. apply NNPP. zenon_intro zenon_H86. % 0.45/0.71 apply zenon_H86. zenon_intro zenon_Tz_ff. apply NNPP. zenon_intro zenon_H88. % 0.45/0.71 apply (zenon_notimply_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 0.45/0.71 apply (zenon_notimply_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b. % 0.45/0.71 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 0.45/0.71 apply (zenon_notimply_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52. % 0.45/0.71 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H55. zenon_intro zenon_H54. % 0.45/0.71 generalize (zenon_H55 zenon_Tx_fb). zenon_intro zenon_H8d. % 0.45/0.71 generalize (zenon_H8d zenon_Ty_fd). zenon_intro zenon_H8e. % 0.45/0.71 generalize (zenon_H8e zenon_Tz_ff). zenon_intro zenon_H8f. % 0.45/0.71 apply (zenon_imply_s _ _ zenon_H8f); [ zenon_intro zenon_H91 | zenon_intro zenon_H90 ]. % 0.45/0.71 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 0.45/0.71 exact (zenon_H93 zenon_H8a). % 0.45/0.71 exact (zenon_H92 zenon_H8c). % 0.45/0.71 exact (zenon_H8b zenon_H90). % 0.45/0.71 Qed. % 0.45/0.71 % SZS output end Proof % 0.45/0.71 (* END-PROOF *) % 0.45/0.71 nodes searched: 19772 % 0.45/0.71 max branch formulas: 573 % 0.45/0.71 proof nodes created: 561 % 0.45/0.71 formulas created: 12811 % 0.45/0.71 %------------------------------------------------------------------------------