%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL664+1.005 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n003.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 01:32:40 PM UTC 2026 % Result : Theorem 4.87s 5.15s % Output : Proof 4.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL664+1.005 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.09/0.35 % Computer : n003.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 01:41:35 UTC 2026 % 0.09/0.36 % CPUTime : % 4.87/5.15 (* PROOF-FOUND *) % 4.87/5.15 % SZS status Theorem % 4.87/5.15 (* BEGIN-PROOF *) % 4.87/5.15 % SZS output start Proof % 4.87/5.15 Theorem main : (~(exists X : zenon_U, (~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p56 Y))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p52 Y))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p56 Y)))/\(~(p46 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p56 Y)))/\(~(p44 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p56 Y)))/\(~(p42 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y)))/\(~(p46 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y)))/\(~(p44 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y)))/\(~(p42 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p52 Y)))/\(~(p46 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p52 Y)))/\(~(p44 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p52 Y)))/\(~(p42 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p46 X)))/\(~(p36 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p46 X)))/\(~(p32 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p55 Y)))/\(~(p45 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p53 Y)))/\(~(p45 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p51 Y)))/\(~(p45 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p44 X)))/\(~(p36 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p44 X)))/\(~(p32 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p55 Y)))/\(~(p43 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p53 Y)))/\(~(p43 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p51 Y)))/\(~(p43 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p42 X)))/\(~(p36 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p42 X)))/\(~(p32 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p55 Y)))/\(~(p41 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y)))/\(~(p41 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p53 Y)))/\(~(p41 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p51 Y)))/\(~(p41 X)))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p36 Y)))/\(~(p26 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p36 Y)))/\(~(p24 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p36 Y)))/\(~(p22 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p45 X)))/\(~(p35 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p43 X)))/\(~(p35 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p34 Y)))/\(~(p26 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p34 Y)))/\(~(p24 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p34 Y)))/\(~(p22 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p41 X)))/\(~(p34 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p45 X)))/\(~(p33 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p43 X)))/\(~(p33 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p32 Y)))/\(~(p26 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p32 Y)))/\(~(p24 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p32 Y)))/\(~(p22 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p45 X)))/\(~(p31 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p43 X)))/\(~(p31 Y)))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p26 X)))/\(~(p16 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p26 X)))/\(~(p14 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p35 Y)))/\(~(p25 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p33 Y)))/\(~(p25 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p31 Y)))/\(~(p25 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p24 X)))/\(~(p16 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p24 X)))/\(~(p14 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p35 Y)))/\(~(p23 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p33 Y)))/\(~(p23 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p31 Y)))/\(~(p23 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p22 X)))/\(~(p16 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p22 X)))/\(~(p14 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p35 Y)))/\(~(p21 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p34 Y)))/\(~(p21 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p33 Y)))/\(~(p21 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p31 Y)))/\(~(p21 X)))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p25 X)))/\(~(p15 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p23 X)))/\(~(p15 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p25 X)))/\(~(p13 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p23 X)))/\(~(p13 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p21 X)))/\(~(p12 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p25 X)))/\(~(p11 Y)))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p23 X)))/\(~(p11 Y)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p15 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p13 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p12 Y)))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p11 Y))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). % 4.87/5.15 Proof. % 4.87/5.15 assert (zenon_L1_ : forall (zenon_TX_f : zenon_U) (zenon_TY_g : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_g X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y))))) -> (r1 zenon_TY_g zenon_TX_f) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_f Y))\/(p54 Y)))) -> False). % 4.87/5.15 do 2 intro. intros zenon_H2 zenon_H3 zenon_H4. % 4.87/5.15 generalize (zenon_H2 zenon_TX_f). zenon_intro zenon_H7. % 4.87/5.15 apply (zenon_or_s _ _ zenon_H7); [ zenon_intro zenon_H9 | zenon_intro zenon_H8 ]. % 4.87/5.15 exact (zenon_H9 zenon_H3). % 4.87/5.15 exact (zenon_H4 zenon_H8). % 4.87/5.15 (* end of lemma zenon_L1_ *) % 4.87/5.15 assert (zenon_L2_ : forall (zenon_TX_f : zenon_U) (zenon_TY_g : zenon_U) (zenon_TX_m : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y))))))) -> (r1 zenon_TX_m zenon_TY_g) -> (r1 zenon_TY_g zenon_TX_f) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_f Y))\/(p54 Y)))) -> False). % 4.87/5.15 do 3 intro. intros zenon_Ha zenon_Hb zenon_H3 zenon_H4. % 4.87/5.15 generalize (zenon_Ha zenon_TY_g). zenon_intro zenon_Hd. % 4.87/5.15 apply (zenon_or_s _ _ zenon_Hd); [ zenon_intro zenon_He | zenon_intro zenon_H2 ]. % 4.87/5.15 exact (zenon_He zenon_Hb). % 4.87/5.15 apply (zenon_L1_ zenon_TX_f zenon_TY_g); trivial. % 4.87/5.15 (* end of lemma zenon_L2_ *) % 4.87/5.15 assert (zenon_L3_ : forall (zenon_TX_f : zenon_U) (zenon_TY_g : zenon_U) (zenon_TX_m : zenon_U) (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_t Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y))))))))))) -> (r1 zenon_TX_t zenon_TY_s) -> (r1 zenon_TY_s zenon_TX_m) -> (r1 zenon_TX_m zenon_TY_g) -> (r1 zenon_TY_g zenon_TX_f) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_f Y))\/(p54 Y)))) -> False). % 4.87/5.15 do 5 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_Hb zenon_H3 zenon_H4. % 4.87/5.15 generalize (zenon_Hf zenon_TY_s). zenon_intro zenon_H14. % 4.87/5.15 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 4.87/5.15 exact (zenon_H16 zenon_H10). % 4.87/5.15 generalize (zenon_H15 zenon_TX_m). zenon_intro zenon_H17. % 4.87/5.15 apply (zenon_or_s _ _ zenon_H17); [ zenon_intro zenon_H18 | zenon_intro zenon_Ha ]. % 4.87/5.15 exact (zenon_H18 zenon_H11). % 4.87/5.15 apply (zenon_L2_ zenon_TX_f zenon_TY_g zenon_TX_m); trivial. % 4.87/5.15 (* end of lemma zenon_L3_ *) % 4.87/5.15 assert (zenon_L4_ : forall (zenon_TX_m : zenon_U) (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U) (zenon_TX_f : zenon_U) (zenon_TY_g : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_g X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y)))/\(~(p41 X)))))) -> (r1 zenon_TY_g zenon_TX_f) -> (forall Y : zenon_U, ((~(r1 zenon_TX_t Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y))))))))))) -> (r1 zenon_TX_t zenon_TY_s) -> (r1 zenon_TY_s zenon_TX_m) -> (r1 zenon_TX_m zenon_TY_g) -> (~(p41 zenon_TX_f)) -> False). % 4.87/5.15 do 5 intro. intros zenon_H19 zenon_H3 zenon_Hf zenon_H10 zenon_H11 zenon_Hb zenon_H1a. % 4.87/5.15 generalize (zenon_H19 zenon_TX_f). zenon_intro zenon_H1b. % 4.87/5.15 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H9 | zenon_intro zenon_H1c ]. % 4.87/5.15 exact (zenon_H9 zenon_H3). % 4.87/5.15 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H4 | zenon_intro zenon_H1d ]. % 4.87/5.15 apply (zenon_L3_ zenon_TX_f zenon_TY_g zenon_TX_m zenon_TY_s zenon_TX_t); trivial. % 4.87/5.15 exact (zenon_H1d zenon_H1a). % 4.87/5.15 (* end of lemma zenon_L4_ *) % 4.87/5.15 assert (zenon_L5_ : forall (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U) (zenon_TX_f : zenon_U) (zenon_TY_g : zenon_U) (zenon_TX_m : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y)))/\(~(p41 X)))))))) -> (r1 zenon_TX_m zenon_TY_g) -> (r1 zenon_TY_g zenon_TX_f) -> (forall Y : zenon_U, ((~(r1 zenon_TX_t Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y))))))))))) -> (r1 zenon_TX_t zenon_TY_s) -> (r1 zenon_TY_s zenon_TX_m) -> (~(p41 zenon_TX_f)) -> False). % 4.87/5.15 do 5 intro. intros zenon_H1e zenon_Hb zenon_H3 zenon_Hf zenon_H10 zenon_H11 zenon_H1a. % 4.87/5.15 generalize (zenon_H1e zenon_TY_g). zenon_intro zenon_H1f. % 4.87/5.15 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_He | zenon_intro zenon_H19 ]. % 4.87/5.15 exact (zenon_He zenon_Hb). % 4.87/5.15 apply (zenon_L4_ zenon_TX_m zenon_TY_s zenon_TX_t zenon_TX_f zenon_TY_g); trivial. % 4.87/5.15 (* end of lemma zenon_L5_ *) % 4.87/5.15 assert (zenon_L6_ : forall (zenon_TX_m : zenon_U) (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U) (zenon_TY_g : zenon_U), (~(forall X : zenon_U, ((~(r1 zenon_TY_g X))\/(p41 X)))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_t Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y)))/\(~(p41 X)))))))))))) -> (r1 zenon_TX_t zenon_TY_s) -> (r1 zenon_TY_s zenon_TX_m) -> (r1 zenon_TX_m zenon_TY_g) -> (forall Y : zenon_U, ((~(r1 zenon_TX_t Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y))))))))))) -> False). % 4.87/5.15 do 4 intro. intros zenon_H20 zenon_H21 zenon_H10 zenon_H11 zenon_Hb zenon_Hf. % 4.87/5.15 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_g X))\/(p41 X))) zenon_H20); [ zenon_intro zenon_H22; idtac ]. % 4.87/5.15 elim zenon_H22. zenon_intro zenon_TX_f. zenon_intro zenon_H23. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H23). zenon_intro zenon_H24. zenon_intro zenon_H1a. % 4.87/5.15 apply zenon_H24. zenon_intro zenon_H3. % 4.87/5.15 generalize (zenon_H21 zenon_TY_s). zenon_intro zenon_H25. % 4.87/5.15 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H16 | zenon_intro zenon_H26 ]. % 4.87/5.15 exact (zenon_H16 zenon_H10). % 4.87/5.15 generalize (zenon_H26 zenon_TX_m). zenon_intro zenon_H27. % 4.87/5.15 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H18 | zenon_intro zenon_H1e ]. % 4.87/5.15 exact (zenon_H18 zenon_H11). % 4.87/5.15 apply (zenon_L5_ zenon_TY_s zenon_TX_t zenon_TX_f zenon_TY_g zenon_TX_m); trivial. % 4.87/5.15 (* end of lemma zenon_L6_ *) % 4.87/5.15 assert (zenon_L7_ : forall (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U) (zenon_TY_g : zenon_U) (zenon_TX_m : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p41 X)))/\(~(p34 Y)))))) -> (r1 zenon_TX_m zenon_TY_g) -> (forall Y : zenon_U, ((~(r1 zenon_TX_t Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y))))))))))) -> (r1 zenon_TY_s zenon_TX_m) -> (r1 zenon_TX_t zenon_TY_s) -> (forall Y : zenon_U, ((~(r1 zenon_TX_t Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p54 Y)))/\(~(p41 X)))))))))))) -> (~(p34 zenon_TY_g)) -> False). % 4.87/5.15 do 4 intro. intros zenon_H28 zenon_Hb zenon_Hf zenon_H11 zenon_H10 zenon_H21 zenon_H29. % 4.87/5.15 generalize (zenon_H28 zenon_TY_g). zenon_intro zenon_H2a. % 4.87/5.15 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_He | zenon_intro zenon_H2b ]. % 4.87/5.15 exact (zenon_He zenon_Hb). % 4.87/5.15 apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H20 | zenon_intro zenon_H2c ]. % 4.87/5.15 apply (zenon_L6_ zenon_TX_m zenon_TY_s zenon_TX_t zenon_TY_g); trivial. % 4.87/5.15 exact (zenon_H2c zenon_H29). % 4.87/5.15 (* end of lemma zenon_L7_ *) % 4.87/5.15 apply NNPP. intro zenon_G. % 4.87/5.15 apply zenon_G. zenon_intro zenon_H2d. % 4.87/5.15 elim zenon_H2d. zenon_intro zenon_TX_t. zenon_intro zenon_H2e. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H31). zenon_intro zenon_H32. zenon_intro zenon_H33. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H34). zenon_intro zenon_H37. zenon_intro zenon_H36. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H39. zenon_intro zenon_H38. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H38). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H3e). zenon_intro zenon_H41. zenon_intro zenon_H40. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H40). zenon_intro zenon_H43. zenon_intro zenon_H42. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H42). zenon_intro zenon_H45. zenon_intro zenon_H44. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H44). zenon_intro zenon_H47. zenon_intro zenon_H46. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H46). zenon_intro zenon_H49. zenon_intro zenon_H48. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H48). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H4a). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H4e). zenon_intro zenon_H51. zenon_intro zenon_H50. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H50). zenon_intro zenon_H53. zenon_intro zenon_H52. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H52). zenon_intro zenon_H55. zenon_intro zenon_H54. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H54). zenon_intro zenon_H57. zenon_intro zenon_H56. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H56). zenon_intro zenon_H59. zenon_intro zenon_H58. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H58). zenon_intro zenon_H5b. zenon_intro zenon_H5a. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H5a). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H5e). zenon_intro zenon_H61. zenon_intro zenon_H60. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H60). zenon_intro zenon_H63. zenon_intro zenon_H62. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H62). zenon_intro zenon_H65. zenon_intro zenon_H64. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H64). zenon_intro zenon_H67. zenon_intro zenon_H66. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H68). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H6c). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H76). zenon_intro zenon_H79. zenon_intro zenon_H78. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H78). zenon_intro zenon_H7b. zenon_intro zenon_H7a. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H7a). zenon_intro zenon_H7d. zenon_intro zenon_H7c. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H7c). zenon_intro zenon_H7f. zenon_intro zenon_H7e. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H81. zenon_intro zenon_H80. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H84). zenon_intro zenon_H87. zenon_intro zenon_H86. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H89. zenon_intro zenon_H88. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H88). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H8a). zenon_intro zenon_H8d. zenon_intro zenon_H8c. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H8c). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H94). zenon_intro zenon_H97. zenon_intro zenon_H96. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H96). zenon_intro zenon_H99. zenon_intro zenon_H98. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H98). zenon_intro zenon_H9b. zenon_intro zenon_H9a. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H9a). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H9c). zenon_intro zenon_H9f. zenon_intro zenon_H9e. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_H9e). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Ha0). zenon_intro zenon_Ha3. zenon_intro zenon_Ha2. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Ha2). zenon_intro zenon_Ha5. zenon_intro zenon_Ha4. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Ha4). zenon_intro zenon_Ha7. zenon_intro zenon_Ha6. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Ha6). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Ha8). zenon_intro zenon_Hab. zenon_intro zenon_Haa. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Haa). zenon_intro zenon_Had. zenon_intro zenon_Hac. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Hac). zenon_intro zenon_Haf. zenon_intro zenon_Hae. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Hae). zenon_intro zenon_Hb1. zenon_intro zenon_Hb0. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Hb0). zenon_intro zenon_Hb3. zenon_intro zenon_Hb2. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Hb2). zenon_intro zenon_Hb5. zenon_intro zenon_Hb4. % 4.87/5.15 apply (zenon_notor_s _ _ zenon_Hb4). zenon_intro zenon_Hb7. zenon_intro zenon_Hb6. % 4.87/5.17 apply (zenon_notor_s _ _ zenon_Hb6). zenon_intro zenon_Hb9. zenon_intro zenon_Hb8. % 4.87/5.17 apply (zenon_notor_s _ _ zenon_Hb8). zenon_intro zenon_Hbb. zenon_intro zenon_Hba. % 4.87/5.17 apply zenon_Hb1. zenon_intro zenon_Hbc. % 4.87/5.17 apply zenon_Ha3. zenon_intro zenon_Hbd. % 4.87/5.17 apply zenon_H79. zenon_intro zenon_Hbe. % 4.87/5.17 apply zenon_H63. zenon_intro zenon_H21. % 4.87/5.17 apply zenon_H32. zenon_intro zenon_Hf. % 4.87/5.17 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_t Y))\/(p12 Y))) zenon_Hbb); [ zenon_intro zenon_Hbf; idtac ]. % 4.87/5.17 elim zenon_Hbf. zenon_intro zenon_TY_s. zenon_intro zenon_Hc0. % 4.87/5.17 apply (zenon_notor_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 4.87/5.17 apply zenon_Hc2. zenon_intro zenon_H10. % 4.87/5.17 generalize (zenon_Hbc zenon_TY_s). zenon_intro zenon_Hc3. % 4.87/5.17 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H16 | zenon_intro zenon_Hc4 ]. % 4.87/5.17 exact (zenon_H16 zenon_H10). % 4.87/5.17 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc5 ]. % 4.87/5.17 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_s X))\/(p21 X))) zenon_Hc6); [ zenon_intro zenon_Hc7; idtac ]. % 4.87/5.17 elim zenon_Hc7. zenon_intro zenon_TX_m. zenon_intro zenon_Hc8. % 4.87/5.17 apply (zenon_notor_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 4.87/5.17 apply zenon_Hca. zenon_intro zenon_H11. % 4.87/5.17 generalize (zenon_Hbd zenon_TY_s). zenon_intro zenon_Hcb. % 4.87/5.17 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H16 | zenon_intro zenon_Hcc ]. % 4.87/5.17 exact (zenon_H16 zenon_H10). % 4.87/5.17 generalize (zenon_Hcc zenon_TX_m). zenon_intro zenon_Hcd. % 4.87/5.17 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H18 | zenon_intro zenon_Hce ]. % 4.87/5.17 exact (zenon_H18 zenon_H11). % 4.87/5.17 apply (zenon_notand_s _ _ zenon_Hce); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcf ]. % 4.87/5.17 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_m Y))\/(p34 Y))) zenon_Hd0); [ zenon_intro zenon_Hd1; idtac ]. % 4.87/5.17 elim zenon_Hd1. zenon_intro zenon_TY_g. zenon_intro zenon_Hd2. % 4.87/5.17 apply (zenon_notor_s _ _ zenon_Hd2). zenon_intro zenon_Hd3. zenon_intro zenon_H29. % 4.87/5.17 apply zenon_Hd3. zenon_intro zenon_Hb. % 4.87/5.17 generalize (zenon_Hbe zenon_TY_s). zenon_intro zenon_Hd4. % 4.87/5.17 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H16 | zenon_intro zenon_Hd5 ]. % 4.87/5.17 exact (zenon_H16 zenon_H10). % 4.87/5.17 generalize (zenon_Hd5 zenon_TX_m). zenon_intro zenon_Hd6. % 4.87/5.17 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H18 | zenon_intro zenon_H28 ]. % 4.87/5.17 exact (zenon_H18 zenon_H11). % 4.87/5.17 apply (zenon_L7_ zenon_TY_s zenon_TX_t zenon_TY_g zenon_TX_m); trivial. % 4.87/5.17 exact (zenon_Hcf zenon_Hc9). % 4.87/5.17 exact (zenon_Hc5 zenon_Hc1). % 4.87/5.17 Qed. % 4.87/5.17 % SZS output end Proof % 4.87/5.17 (* END-PROOF *) % 4.87/5.17 nodes searched: 57338 % 4.87/5.17 max branch formulas: 18887 % 4.87/5.17 proof nodes created: 3738 % 4.87/5.17 formulas created: 146612 % 4.87/5.17 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