%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL674+1.015 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:32:45 PM UTC 2026 % Result : Theorem 13.87s 14.14s % Output : Proof 13.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL674+1.015 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.35 % Computer : n019.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 21:30:23 UTC 2026 % 0.09/0.35 % CPUTime : % 13.87/14.14 (* PROOF-FOUND *) % 13.87/14.14 % SZS status Theorem % 13.87/14.14 (* BEGIN-PROOF *) % 13.87/14.14 % SZS output start Proof % 13.87/14.14 Theorem main : (~(exists X : zenon_U, (~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p7 Y))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p16 X))/\((~(p116 X))/\(p115 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p16 X)/\((~(p116 X))/\(p115 X))))))))\/(~((~(p115 Y))/\(p114 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p15 X))/\((~(p115 X))/\(p114 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p15 X)/\((~(p115 X))/\(p114 X))))))))\/(~((~(p114 Y))/\(p113 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p14 X))/\((~(p114 X))/\(p113 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p14 X)/\((~(p114 X))/\(p113 X))))))))\/(~((~(p113 Y))/\(p112 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p13 X))/\((~(p113 X))/\(p112 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p13 X)/\((~(p113 X))/\(p112 X))))))))\/(~((~(p112 Y))/\(p111 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p12 X))/\((~(p112 X))/\(p111 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p12 X)/\((~(p112 X))/\(p111 X))))))))\/(~((~(p111 Y))/\(p110 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p11 X))/\((~(p111 X))/\(p110 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p11 X)/\((~(p111 X))/\(p110 X))))))))\/(~((~(p110 Y))/\(p109 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p10 X))/\((~(p110 X))/\(p109 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p10 X)/\((~(p110 X))/\(p109 X))))))))\/(~((~(p109 Y))/\(p108 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p9 X))/\((~(p109 X))/\(p108 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p9 X)/\((~(p109 X))/\(p108 X))))))))\/(~((~(p108 Y))/\(p107 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p8 X))/\((~(p108 X))/\(p107 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p8 X)/\((~(p108 X))/\(p107 X))))))))\/(~((~(p107 Y))/\(p106 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p7 X))/\((~(p107 X))/\(p106 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p7 X)/\((~(p107 X))/\(p106 X))))))))\/(~((~(p106 Y))/\(p105 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p6 X))/\((~(p106 X))/\(p105 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p6 X)/\((~(p106 X))/\(p105 X))))))))\/(~((~(p105 Y))/\(p104 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p5 X))/\((~(p105 X))/\(p104 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p5 X)/\((~(p105 X))/\(p104 X))))))))\/(~((~(p104 Y))/\(p103 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p4 X))/\((~(p104 X))/\(p103 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p4 X)/\((~(p104 X))/\(p103 X))))))))\/(~((~(p103 Y))/\(p102 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p3 X))/\((~(p103 X))/\(p102 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p3 X)/\((~(p103 X))/\(p102 X))))))))\/(~((~(p102 Y))/\(p101 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p2 X))/\((~(p102 X))/\(p101 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p2 X)/\((~(p102 X))/\(p101 X))))))))\/(~((~(p101 Y))/\(p100 Y))))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p16 X))\/(~(p115 X)))))\/(p16 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p16 X)\/(~(p115 X)))))\/(~(p16 Y))))\/(~(p115 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p15 X))\/(~(p114 X)))))\/(p15 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p15 X)\/(~(p114 X)))))\/(~(p15 Y))))\/(~(p114 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p14 X))\/(~(p113 X)))))\/(p14 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p14 X)\/(~(p113 X)))))\/(~(p14 Y))))\/(~(p113 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p13 X))\/(~(p112 X)))))\/(p13 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p13 X)\/(~(p112 X)))))\/(~(p13 Y))))\/(~(p112 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p12 X))\/(~(p111 X)))))\/(p12 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p12 X)\/(~(p111 X)))))\/(~(p12 Y))))\/(~(p111 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p11 X))\/(~(p110 X)))))\/(p11 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p11 X)\/(~(p110 X)))))\/(~(p11 Y))))\/(~(p110 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p10 X))\/(~(p109 X)))))\/(p10 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p10 X)\/(~(p109 X)))))\/(~(p10 Y))))\/(~(p109 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p9 X))\/(~(p108 X)))))\/(p9 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p9 X)\/(~(p108 X)))))\/(~(p9 Y))))\/(~(p108 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p8 X))\/(~(p107 X)))))\/(p8 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p8 X)\/(~(p107 X)))))\/(~(p8 Y))))\/(~(p107 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p7 X))\/(~(p106 X)))))\/(p7 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p7 X)\/(~(p106 X)))))\/(~(p7 Y))))\/(~(p106 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p6 X))\/(~(p105 X)))))\/(p6 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p6 X)\/(~(p105 X)))))\/(~(p6 Y))))\/(~(p105 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p5 X))\/(~(p104 X)))))\/(p5 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p5 X)\/(~(p104 X)))))\/(~(p5 Y))))\/(~(p104 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p4 X))\/(~(p103 X)))))\/(p4 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p4 X)\/(~(p103 X)))))\/(~(p4 Y))))\/(~(p103 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p3 X))\/(~(p102 X)))))\/(p3 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p3 X)\/(~(p102 X)))))\/(~(p3 Y))))\/(~(p102 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p2 X))\/(~(p101 X)))))\/(p2 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(p101 X)))))\/(~(p2 Y))))\/(~(p101 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p1 X))\/(~(p100 X)))))\/(p1 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(p100 X)))))\/(~(p1 Y))))\/(~(p100 Y)))/\(((p115 Y)\/(~(p116 Y)))/\(((p114 Y)\/(~(p115 Y)))/\(((p113 Y)\/(~(p114 Y)))/\(((p112 Y)\/(~(p113 Y)))/\(((p111 Y)\/(~(p112 Y)))/\(((p110 Y)\/(~(p111 Y)))/\(((p109 Y)\/(~(p110 Y)))/\(((p108 Y)\/(~(p109 Y)))/\(((p107 Y)\/(~(p108 Y)))/\(((p106 Y)\/(~(p107 Y)))/\(((p105 Y)\/(~(p106 Y)))/\(((p104 Y)\/(~(p105 Y)))/\(((p103 Y)\/(~(p104 Y)))/\(((p102 Y)\/(~(p103 Y)))/\(((p101 Y)\/(~(p102 Y)))/\((p100 Y)\/(~(p101 Y)))))))))))))))))))))))))))))))))))))))))))))))))))/\((~(p101 X))/\(p100 X)))))))). % 13.87/14.14 Proof. % 13.87/14.14 assert (zenon_L1_ : forall (zenon_TX_h : zenon_U) (zenon_TX_i : zenon_U) (zenon_TX_j : zenon_U), (r1 zenon_TX_j zenon_TX_i) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_h)) -> (r1 zenon_TX_i zenon_TX_h) -> False). % 13.87/14.14 do 3 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6. % 13.87/14.14 elim (classic ((~(zenon_TX_j = zenon_TX_i))/\(~(r1 zenon_TX_j zenon_TX_i)))); [ zenon_intro zenon_Ha | zenon_intro zenon_Hb ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 13.87/14.14 exact (zenon_Hc zenon_H3). % 13.87/14.14 cut ((r1 zenon_TX_i zenon_TX_h) = (r1 zenon_TX_j zenon_TX_h)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_H5. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H6. % 13.87/14.14 cut ((zenon_TX_h = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_He]. % 13.87/14.14 cut ((zenon_TX_i = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 13.87/14.14 congruence. % 13.87/14.14 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 13.87/14.14 apply zenon_H11. zenon_intro zenon_H12. % 13.87/14.14 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_i = zenon_TX_j)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_Hf. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H13. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_i)); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 13.87/14.14 congruence. % 13.87/14.14 exact (zenon_Hd zenon_H12). % 13.87/14.14 apply zenon_H14. apply refl_equal. % 13.87/14.14 apply zenon_H14. apply refl_equal. % 13.87/14.14 apply zenon_H10. zenon_intro zenon_H3. % 13.87/14.14 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 13.87/14.14 generalize (zenon_H15 zenon_TX_i). zenon_intro zenon_H16. % 13.87/14.14 generalize (zenon_H16 zenon_TX_h). zenon_intro zenon_H17. % 13.87/14.14 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_Hc | zenon_intro zenon_H18 ]. % 13.87/14.14 exact (zenon_Hc zenon_H3). % 13.87/14.14 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 13.87/14.14 exact (zenon_H1a zenon_H6). % 13.87/14.14 exact (zenon_H5 zenon_H19). % 13.87/14.14 apply zenon_He. apply refl_equal. % 13.87/14.14 (* end of lemma zenon_L1_ *) % 13.87/14.14 assert (zenon_L2_ : forall (zenon_TX_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TX_i : zenon_U) (zenon_TX_j : zenon_U), (r1 zenon_TX_j zenon_TX_i) -> (r1 zenon_TX_i zenon_TX_h) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_bd)) -> (r1 zenon_TX_h zenon_TX_bd) -> False). % 13.87/14.14 do 4 intro. intros zenon_H3 zenon_H6 zenon_H4 zenon_H1b zenon_H1c. % 13.87/14.14 elim (classic ((~(zenon_TX_j = zenon_TX_h))/\(~(r1 zenon_TX_j zenon_TX_h)))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H5. % 13.87/14.14 apply (zenon_L1_ zenon_TX_h zenon_TX_i zenon_TX_j); trivial. % 13.87/14.14 cut ((r1 zenon_TX_h zenon_TX_bd) = (r1 zenon_TX_j zenon_TX_bd)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_H1b. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H1c. % 13.87/14.14 cut ((zenon_TX_bd = zenon_TX_bd)); [idtac | apply NNPP; zenon_intro zenon_H21]. % 13.87/14.14 cut ((zenon_TX_h = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H22]. % 13.87/14.14 congruence. % 13.87/14.14 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 13.87/14.14 apply zenon_H24. zenon_intro zenon_H25. % 13.87/14.14 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_h = zenon_TX_j)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_H22. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H13. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H20]. % 13.87/14.14 congruence. % 13.87/14.14 exact (zenon_H20 zenon_H25). % 13.87/14.14 apply zenon_H14. apply refl_equal. % 13.87/14.14 apply zenon_H14. apply refl_equal. % 13.87/14.14 apply zenon_H23. zenon_intro zenon_H19. % 13.87/14.14 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 13.87/14.14 generalize (zenon_H15 zenon_TX_h). zenon_intro zenon_H26. % 13.87/14.14 generalize (zenon_H26 zenon_TX_bd). zenon_intro zenon_H27. % 13.87/14.14 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H5 | zenon_intro zenon_H28 ]. % 13.87/14.14 exact (zenon_H5 zenon_H19). % 13.87/14.14 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 13.87/14.14 exact (zenon_H2a zenon_H1c). % 13.87/14.14 exact (zenon_H1b zenon_H29). % 13.87/14.14 apply zenon_H21. apply refl_equal. % 13.87/14.14 (* end of lemma zenon_L2_ *) % 13.87/14.14 assert (zenon_L3_ : forall (zenon_TX_bt : zenon_U) (zenon_TX_bd : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TX_i : zenon_U), (r1 zenon_TX_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TX_i) -> (r1 zenon_TX_h zenon_TX_bd) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_bt)) -> (r1 zenon_TX_bd zenon_TX_bt) -> False). % 13.87/14.14 do 5 intro. intros zenon_H6 zenon_H3 zenon_H1c zenon_H4 zenon_H2b zenon_H2c. % 13.87/14.14 elim (classic ((~(zenon_TX_j = zenon_TX_bd))/\(~(r1 zenon_TX_j zenon_TX_bd)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H1b. % 13.87/14.14 apply (zenon_L2_ zenon_TX_bd zenon_TX_h zenon_TX_i zenon_TX_j); trivial. % 13.87/14.14 cut ((r1 zenon_TX_bd zenon_TX_bt) = (r1 zenon_TX_j zenon_TX_bt)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_H2b. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H2c. % 13.87/14.14 cut ((zenon_TX_bt = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H31]. % 13.87/14.14 cut ((zenon_TX_bd = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H32]. % 13.87/14.14 congruence. % 13.87/14.14 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 13.87/14.14 apply zenon_H34. zenon_intro zenon_H35. % 13.87/14.14 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_bd = zenon_TX_j)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_H32. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H13. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_bd)); [idtac | apply NNPP; zenon_intro zenon_H30]. % 13.87/14.14 congruence. % 13.87/14.14 exact (zenon_H30 zenon_H35). % 13.87/14.14 apply zenon_H14. apply refl_equal. % 13.87/14.14 apply zenon_H14. apply refl_equal. % 13.87/14.14 apply zenon_H33. zenon_intro zenon_H29. % 13.87/14.14 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 13.87/14.14 generalize (zenon_H15 zenon_TX_bd). zenon_intro zenon_H36. % 13.87/14.14 generalize (zenon_H36 zenon_TX_bt). zenon_intro zenon_H37. % 13.87/14.14 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H1b | zenon_intro zenon_H38 ]. % 13.87/14.14 exact (zenon_H1b zenon_H29). % 13.87/14.14 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 13.87/14.14 exact (zenon_H3a zenon_H2c). % 13.87/14.14 exact (zenon_H2b zenon_H39). % 13.87/14.14 apply zenon_H31. apply refl_equal. % 13.87/14.14 (* end of lemma zenon_L3_ *) % 13.87/14.14 assert (zenon_L4_ : forall (zenon_TX_cj : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TX_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_bd : zenon_U) (zenon_TX_h : zenon_U), (r1 zenon_TX_h zenon_TX_bd) -> (r1 zenon_TX_j zenon_TX_i) -> (r1 zenon_TX_i zenon_TX_h) -> (r1 zenon_TX_bd zenon_TX_bt) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_cj)) -> (r1 zenon_TX_bt zenon_TX_cj) -> False). % 13.87/14.14 do 6 intro. intros zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4 zenon_H3b zenon_H3c. % 13.87/14.14 elim (classic ((~(zenon_TX_j = zenon_TX_bt))/\(~(r1 zenon_TX_j zenon_TX_bt)))); [ zenon_intro zenon_H3e | zenon_intro zenon_H3f ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H2b. % 13.87/14.14 apply (zenon_L3_ zenon_TX_bt zenon_TX_bd zenon_TX_j zenon_TX_h zenon_TX_i); trivial. % 13.87/14.14 cut ((r1 zenon_TX_bt zenon_TX_cj) = (r1 zenon_TX_j zenon_TX_cj)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_H3b. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H3c. % 13.87/14.14 cut ((zenon_TX_cj = zenon_TX_cj)); [idtac | apply NNPP; zenon_intro zenon_H41]. % 13.87/14.14 cut ((zenon_TX_bt = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H42]. % 13.87/14.14 congruence. % 13.87/14.14 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 13.87/14.14 apply zenon_H44. zenon_intro zenon_H45. % 13.87/14.14 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_bt = zenon_TX_j)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_H42. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H13. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H40]. % 13.87/14.14 congruence. % 13.87/14.14 exact (zenon_H40 zenon_H45). % 13.87/14.14 apply zenon_H14. apply refl_equal. % 13.87/14.14 apply zenon_H14. apply refl_equal. % 13.87/14.14 apply zenon_H43. zenon_intro zenon_H39. % 13.87/14.14 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 13.87/14.14 generalize (zenon_H15 zenon_TX_bt). zenon_intro zenon_H46. % 13.87/14.14 generalize (zenon_H46 zenon_TX_cj). zenon_intro zenon_H47. % 13.87/14.14 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H2b | zenon_intro zenon_H48 ]. % 13.87/14.14 exact (zenon_H2b zenon_H39). % 13.87/14.14 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 13.87/14.14 exact (zenon_H4a zenon_H3c). % 13.87/14.14 exact (zenon_H3b zenon_H49). % 13.87/14.14 apply zenon_H41. apply refl_equal. % 13.87/14.14 (* end of lemma zenon_L4_ *) % 13.87/14.14 apply NNPP. intro zenon_G. % 13.87/14.14 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z))))))); [ zenon_intro zenon_H4 | zenon_intro zenon_H4b ]. % 13.87/14.14 apply zenon_G. zenon_intro zenon_H4c. % 13.87/14.14 elim zenon_H4c. zenon_intro zenon_TX_j. zenon_intro zenon_H4d. % 13.87/14.14 apply (zenon_notor_s _ _ zenon_H4d). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 13.87/14.14 apply zenon_H4e. zenon_intro zenon_H50. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H52. zenon_intro zenon_H51. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 13.87/14.14 apply zenon_H4f. zenon_intro zenon_H55. % 13.87/14.14 generalize (zenon_H52 zenon_TX_j). zenon_intro zenon_H56. % 13.87/14.14 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ]. % 13.87/14.14 generalize (reflexivity zenon_TX_j). zenon_intro zenon_H59. % 13.87/14.14 exact (zenon_H58 zenon_H59). % 13.87/14.14 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5b. zenon_intro zenon_H5a. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H61. zenon_intro zenon_H60. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H63. zenon_intro zenon_H62. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H65. zenon_intro zenon_H64. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H67. zenon_intro zenon_H66. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76. % 13.87/14.14 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H79 | zenon_intro zenon_H78 ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H79). zenon_intro zenon_H7b. zenon_intro zenon_H7a. % 13.87/14.14 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_j X))\/(~((~(p2 X))/\((~(p102 X))/\(p101 X)))))) zenon_H7b); [ zenon_intro zenon_H7c; idtac ]. % 13.87/14.14 elim zenon_H7c. zenon_intro zenon_TX_i. zenon_intro zenon_H7d. % 13.87/14.14 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H10. zenon_intro zenon_H7e. % 13.87/14.14 apply zenon_H7e. zenon_intro zenon_H7f. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 13.87/14.14 apply zenon_H10. zenon_intro zenon_H3. % 13.87/14.14 generalize (zenon_H52 zenon_TX_i). zenon_intro zenon_H84. % 13.87/14.14 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_Hc | zenon_intro zenon_H85 ]. % 13.87/14.14 exact (zenon_Hc zenon_H3). % 13.87/14.14 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H87. zenon_intro zenon_H86. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H89. zenon_intro zenon_H88. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8d. zenon_intro zenon_H8c. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H97. zenon_intro zenon_H96. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H99. zenon_intro zenon_H98. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H98). zenon_intro zenon_H9b. zenon_intro zenon_H9a. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9f. zenon_intro zenon_H9e. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0. % 13.87/14.14 apply (zenon_or_s _ _ zenon_Ha1); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Ha2 ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Ha3). zenon_intro zenon_Ha5. zenon_intro zenon_Ha4. % 13.87/14.14 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_i X))\/(~((p3 X)/\((~(p103 X))/\(p102 X)))))) zenon_Ha4); [ zenon_intro zenon_Ha6; idtac ]. % 13.87/14.14 elim zenon_Ha6. zenon_intro zenon_TX_h. zenon_intro zenon_Ha7. % 13.87/14.14 apply (zenon_notor_s _ _ zenon_Ha7). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8. % 13.87/14.14 apply zenon_Ha8. zenon_intro zenon_Haa. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Haa). zenon_intro zenon_Hac. zenon_intro zenon_Hab. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hab). zenon_intro zenon_Hae. zenon_intro zenon_Had. % 13.87/14.14 apply zenon_Ha9. zenon_intro zenon_H6. % 13.87/14.14 generalize (zenon_H52 zenon_TX_h). zenon_intro zenon_Haf. % 13.87/14.14 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_H5 | zenon_intro zenon_Hb0 ]. % 13.87/14.14 apply (zenon_L1_ zenon_TX_h zenon_TX_i zenon_TX_j); trivial. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hb0). zenon_intro zenon_Hb2. zenon_intro zenon_Hb1. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hb4. zenon_intro zenon_Hb3. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Hb6. zenon_intro zenon_Hb5. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_Hb8. zenon_intro zenon_Hb7. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hb7). zenon_intro zenon_Hba. zenon_intro zenon_Hb9. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hb9). zenon_intro zenon_Hbc. zenon_intro zenon_Hbb. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hc0. zenon_intro zenon_Hbf. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hbf). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hc4. zenon_intro zenon_Hc3. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc6. zenon_intro zenon_Hc5. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 13.87/14.14 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_Hce. zenon_intro zenon_Hcd. % 13.87/14.14 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_h X))\/(~((~(p4 X))/\((~(p104 X))/\(p103 X)))))) zenon_Hce); [ zenon_intro zenon_Hcf; idtac ]. % 13.87/14.14 elim zenon_Hcf. zenon_intro zenon_TX_bd. zenon_intro zenon_Hd0. % 13.87/14.14 apply (zenon_notor_s _ _ zenon_Hd0). zenon_intro zenon_Hd2. zenon_intro zenon_Hd1. % 13.87/14.14 apply zenon_Hd1. zenon_intro zenon_Hd3. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hd3). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_Hd7. zenon_intro zenon_Hd6. % 13.87/14.14 apply zenon_Hd2. zenon_intro zenon_H1c. % 13.87/14.14 generalize (zenon_H52 zenon_TX_bd). zenon_intro zenon_Hd8. % 13.87/14.14 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H1b | zenon_intro zenon_Hd9 ]. % 13.87/14.14 apply (zenon_L2_ zenon_TX_bd zenon_TX_h zenon_TX_i zenon_TX_j); trivial. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hd9). zenon_intro zenon_Hdb. zenon_intro zenon_Hda. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hda). zenon_intro zenon_Hdd. zenon_intro zenon_Hdc. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hdc). zenon_intro zenon_Hdf. zenon_intro zenon_Hde. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hde). zenon_intro zenon_He1. zenon_intro zenon_He0. % 13.87/14.14 apply (zenon_and_s _ _ zenon_He0). zenon_intro zenon_He3. zenon_intro zenon_He2. % 13.87/14.14 apply (zenon_and_s _ _ zenon_He2). zenon_intro zenon_He5. zenon_intro zenon_He4. % 13.87/14.14 apply (zenon_and_s _ _ zenon_He4). zenon_intro zenon_He7. zenon_intro zenon_He6. % 13.87/14.14 apply (zenon_and_s _ _ zenon_He6). zenon_intro zenon_He9. zenon_intro zenon_He8. % 13.87/14.14 apply (zenon_and_s _ _ zenon_He8). zenon_intro zenon_Heb. zenon_intro zenon_Hea. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hed. zenon_intro zenon_Hec. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hec). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Hf1. zenon_intro zenon_Hf0. % 13.87/14.14 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hf3 | zenon_intro zenon_Hf2 ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hf3). zenon_intro zenon_Hf5. zenon_intro zenon_Hf4. % 13.87/14.14 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_bd X))\/(~((~(p5 X))/\((~(p105 X))/\(p104 X)))))) zenon_Hf5); [ zenon_intro zenon_Hf6; idtac ]. % 13.87/14.14 elim zenon_Hf6. zenon_intro zenon_TX_bt. zenon_intro zenon_Hf7. % 13.87/14.14 apply (zenon_notor_s _ _ zenon_Hf7). zenon_intro zenon_Hf9. zenon_intro zenon_Hf8. % 13.87/14.14 apply zenon_Hf8. zenon_intro zenon_Hfa. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hfa). zenon_intro zenon_Hfc. zenon_intro zenon_Hfb. % 13.87/14.14 apply (zenon_and_s _ _ zenon_Hfb). zenon_intro zenon_Hfe. zenon_intro zenon_Hfd. % 13.87/14.14 apply zenon_Hf9. zenon_intro zenon_H2c. % 13.87/14.14 generalize (zenon_H52 zenon_TX_bt). zenon_intro zenon_Hff. % 13.87/14.14 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H2b | zenon_intro zenon_H100 ]. % 13.87/14.14 apply (zenon_L3_ zenon_TX_bt zenon_TX_bd zenon_TX_j zenon_TX_h zenon_TX_i); trivial. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H100). zenon_intro zenon_H102. zenon_intro zenon_H101. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H101). zenon_intro zenon_H104. zenon_intro zenon_H103. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H103). zenon_intro zenon_H106. zenon_intro zenon_H105. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H105). zenon_intro zenon_H108. zenon_intro zenon_H107. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H10a. zenon_intro zenon_H109. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H109). zenon_intro zenon_H10c. zenon_intro zenon_H10b. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H10b). zenon_intro zenon_H10e. zenon_intro zenon_H10d. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H10d). zenon_intro zenon_H110. zenon_intro zenon_H10f. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H10f). zenon_intro zenon_H112. zenon_intro zenon_H111. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H111). zenon_intro zenon_H114. zenon_intro zenon_H113. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H113). zenon_intro zenon_H116. zenon_intro zenon_H115. % 13.87/14.14 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H118 | zenon_intro zenon_H117 ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H118). zenon_intro zenon_H11a. zenon_intro zenon_H119. % 13.87/14.14 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_bt X))\/(~((p6 X)/\((~(p106 X))/\(p105 X)))))) zenon_H119); [ zenon_intro zenon_H11b; idtac ]. % 13.87/14.14 elim zenon_H11b. zenon_intro zenon_TX_cj. zenon_intro zenon_H11c. % 13.87/14.14 apply (zenon_notor_s _ _ zenon_H11c). zenon_intro zenon_H11e. zenon_intro zenon_H11d. % 13.87/14.14 apply zenon_H11d. zenon_intro zenon_H11f. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H11f). zenon_intro zenon_H121. zenon_intro zenon_H120. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H120). zenon_intro zenon_H123. zenon_intro zenon_H122. % 13.87/14.14 apply zenon_H11e. zenon_intro zenon_H3c. % 13.87/14.14 generalize (zenon_H52 zenon_TX_cj). zenon_intro zenon_H124. % 13.87/14.14 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H3b | zenon_intro zenon_H125 ]. % 13.87/14.14 apply (zenon_L4_ zenon_TX_cj zenon_TX_bt zenon_TX_i zenon_TX_j zenon_TX_bd zenon_TX_h); trivial. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H125). zenon_intro zenon_H127. zenon_intro zenon_H126. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H126). zenon_intro zenon_H129. zenon_intro zenon_H128. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H128). zenon_intro zenon_H12b. zenon_intro zenon_H12a. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H12a). zenon_intro zenon_H12d. zenon_intro zenon_H12c. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H12f. zenon_intro zenon_H12e. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H12e). zenon_intro zenon_H131. zenon_intro zenon_H130. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H133. zenon_intro zenon_H132. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H132). zenon_intro zenon_H135. zenon_intro zenon_H134. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H134). zenon_intro zenon_H137. zenon_intro zenon_H136. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H136). zenon_intro zenon_H139. zenon_intro zenon_H138. % 13.87/14.14 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H13b | zenon_intro zenon_H13a ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H13b). zenon_intro zenon_H13d. zenon_intro zenon_H13c. % 13.87/14.14 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_cj X))\/(~((~(p7 X))/\((~(p107 X))/\(p106 X)))))) zenon_H13d); [ zenon_intro zenon_H13e; idtac ]. % 13.87/14.14 elim zenon_H13e. zenon_intro zenon_TX_mh. zenon_intro zenon_H140. % 13.87/14.14 apply (zenon_notor_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 13.87/14.14 apply zenon_H141. zenon_intro zenon_H143. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H144. % 13.87/14.14 apply zenon_H142. zenon_intro zenon_H146. % 13.87/14.14 generalize (zenon_H55 zenon_TX_mh). zenon_intro zenon_H147. % 13.87/14.14 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 13.87/14.14 elim (classic ((~(zenon_TX_j = zenon_TX_cj))/\(~(r1 zenon_TX_j zenon_TX_cj)))); [ zenon_intro zenon_H14a | zenon_intro zenon_H14b ]. % 13.87/14.14 apply (zenon_and_s _ _ zenon_H14a). zenon_intro zenon_H14c. zenon_intro zenon_H3b. % 13.87/14.14 apply (zenon_L4_ zenon_TX_cj zenon_TX_bt zenon_TX_i zenon_TX_j zenon_TX_bd zenon_TX_h); trivial. % 13.87/14.14 cut ((r1 zenon_TX_cj zenon_TX_mh) = (r1 zenon_TX_j zenon_TX_mh)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_H149. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H146. % 13.87/14.14 cut ((zenon_TX_mh = zenon_TX_mh)); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 13.87/14.14 cut ((zenon_TX_cj = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 13.87/14.14 congruence. % 13.87/14.14 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H150 | zenon_intro zenon_H14f ]. % 13.87/14.14 apply zenon_H150. zenon_intro zenon_H151. % 13.87/14.14 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_cj = zenon_TX_j)). % 13.87/14.14 intro zenon_D_pnotp. % 13.87/14.14 apply zenon_H14e. % 13.87/14.14 rewrite <- zenon_D_pnotp. % 13.87/14.14 exact zenon_H13. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 13.87/14.14 cut ((zenon_TX_j = zenon_TX_cj)); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 13.87/14.16 congruence. % 13.87/14.16 exact (zenon_H14c zenon_H151). % 13.87/14.16 apply zenon_H14. apply refl_equal. % 13.87/14.16 apply zenon_H14. apply refl_equal. % 13.87/14.16 apply zenon_H14f. zenon_intro zenon_H49. % 13.87/14.16 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 13.87/14.16 generalize (zenon_H15 zenon_TX_cj). zenon_intro zenon_H152. % 13.87/14.16 generalize (zenon_H152 zenon_TX_mh). zenon_intro zenon_H153. % 13.87/14.16 apply (zenon_imply_s _ _ zenon_H153); [ zenon_intro zenon_H3b | zenon_intro zenon_H154 ]. % 13.87/14.16 exact (zenon_H3b zenon_H49). % 13.87/14.16 apply (zenon_imply_s _ _ zenon_H154); [ zenon_intro zenon_H156 | zenon_intro zenon_H155 ]. % 13.87/14.16 exact (zenon_H156 zenon_H146). % 13.87/14.16 exact (zenon_H149 zenon_H155). % 13.87/14.16 apply zenon_H14d. apply refl_equal. % 13.87/14.16 exact (zenon_H145 zenon_H148). % 13.87/14.16 apply (zenon_notand_s _ _ zenon_H13a); [ zenon_intro zenon_H158 | zenon_intro zenon_H157 ]. % 13.87/14.16 exact (zenon_H158 zenon_H123). % 13.87/14.16 exact (zenon_H157 zenon_H122). % 13.87/14.16 apply (zenon_notand_s _ _ zenon_H117); [ zenon_intro zenon_H15a | zenon_intro zenon_H159 ]. % 13.87/14.16 exact (zenon_H15a zenon_Hfe). % 13.87/14.16 exact (zenon_H159 zenon_Hfd). % 13.87/14.16 apply (zenon_notand_s _ _ zenon_Hf2); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ]. % 13.87/14.16 exact (zenon_H15c zenon_Hd7). % 13.87/14.16 exact (zenon_H15b zenon_Hd6). % 13.87/14.16 apply (zenon_notand_s _ _ zenon_Hcb); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ]. % 13.87/14.16 exact (zenon_H15e zenon_Hae). % 13.87/14.16 exact (zenon_H15d zenon_Had). % 13.87/14.16 apply (zenon_notand_s _ _ zenon_Ha2); [ zenon_intro zenon_H160 | zenon_intro zenon_H15f ]. % 13.87/14.16 exact (zenon_H160 zenon_H83). % 13.87/14.16 exact (zenon_H15f zenon_H82). % 13.87/14.16 apply (zenon_notand_s _ _ zenon_H78); [ zenon_intro zenon_H162 | zenon_intro zenon_H161 ]. % 13.87/14.16 exact (zenon_H162 zenon_H54). % 13.87/14.16 exact (zenon_H161 zenon_H53). % 13.87/14.16 apply zenon_H4b. zenon_intro zenon_Tx_nr. apply NNPP. zenon_intro zenon_H164. % 13.87/14.16 apply zenon_H164. zenon_intro zenon_Ty_nt. apply NNPP. zenon_intro zenon_H166. % 13.87/14.16 apply zenon_H166. zenon_intro zenon_Tz_nv. apply NNPP. zenon_intro zenon_H168. % 13.87/14.16 apply (zenon_notimply_s _ _ zenon_H168). zenon_intro zenon_H16a. zenon_intro zenon_H169. % 13.87/14.16 apply (zenon_notimply_s _ _ zenon_H169). zenon_intro zenon_H16c. zenon_intro zenon_H16b. % 13.87/14.16 generalize (transitivity zenon_Tx_nr). zenon_intro zenon_H16d. % 13.87/14.16 generalize (zenon_H16d zenon_Ty_nt). zenon_intro zenon_H16e. % 13.87/14.16 generalize (zenon_H16e zenon_Tz_nv). zenon_intro zenon_H16f. % 13.87/14.16 apply (zenon_imply_s _ _ zenon_H16f); [ zenon_intro zenon_H171 | zenon_intro zenon_H170 ]. % 13.87/14.16 apply (zenon_notand_s _ _ zenon_H171); [ zenon_intro zenon_H173 | zenon_intro zenon_H172 ]. % 13.87/14.16 exact (zenon_H173 zenon_H16a). % 13.87/14.16 exact (zenon_H172 zenon_H16c). % 13.87/14.16 exact (zenon_H16b zenon_H170). % 13.87/14.16 Qed. % 13.87/14.16 % SZS output end Proof % 13.87/14.16 (* END-PROOF *) % 13.87/14.16 nodes searched: 246496 % 13.87/14.16 max branch formulas: 22699 % 13.87/14.16 proof nodes created: 11626 % 13.87/14.16 formulas created: 738242 % 13.87/14.16 %------------------------------------------------------------------------------