%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUN067+1 : TPTP v8.1.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n028.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 : Mon Jul 18 16:42:13 EDT 2022 % Result : Theorem 0.40s 0.58s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : NUN067+1 : TPTP v8.1.0. Released v7.3.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n028.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Thu Jun 2 08:10:53 EDT 2022 % 0.12/0.34 % CPUTime : % 0.40/0.58 (* PROOF-FOUND *) % 0.40/0.58 % SZS status Theorem % 0.40/0.58 (* BEGIN-PROOF *) % 0.40/0.58 % SZS output start Proof % 0.40/0.58 Theorem nonzerosexistid : (exists Y1 : zenon_U, (forall Y2 : zenon_U, ((~(id Y1 Y2))\/(~(r1 Y2))))). % 0.40/0.58 Proof. % 0.40/0.58 assert (zenon_L1_ : forall (zenon_TY21_v : zenon_U) (zenon_TY24_w : zenon_U), ((~(r2 zenon_TY24_w zenon_TY21_v))/\(~(id zenon_TY21_v zenon_TY21_v))) -> False). % 0.40/0.58 do 2 intro. intros zenon_H14. % 0.40/0.58 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.40/0.58 generalize (axiom_5 zenon_TY21_v). zenon_intro zenon_H19. % 0.40/0.58 exact (zenon_H17 zenon_H19). % 0.40/0.58 (* end of lemma zenon_L1_ *) % 0.40/0.58 assert (zenon_L2_ : forall (zenon_TY24_w : zenon_U) (zenon_TY2_bg : zenon_U), (forall x : zenon_U, (forall y : zenon_U, ((id x y)->(id y x)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((id x y)->((id y z)->(id x z)))))) -> (~(r2 zenon_TY2_bg zenon_TY24_w)) -> (forall X19 : zenon_U, (((id X19 zenon_TY24_w)/\(r1 X19))\/((~(r1 X19))/\(~(id X19 zenon_TY24_w))))) -> (~(exists Y1 : zenon_U, (forall Y2 : zenon_U, ((~(id Y1 Y2))\/(~(r1 Y2)))))) -> (id zenon_TY2_bg zenon_TY24_w) -> (forall X31 : zenon_U, ((~(id zenon_TY2_bg zenon_TY24_w))\/((~(id zenon_TY24_w X31))\/(((~(r2 zenon_TY2_bg zenon_TY24_w))/\(~(r2 zenon_TY24_w X31)))\/((r2 zenon_TY2_bg zenon_TY24_w)/\(r2 zenon_TY24_w X31)))))) -> False). % 0.40/0.58 do 2 intro. intros zenon_H1a zenon_H1b zenon_H1c zenon_H1d zenon_G zenon_H1e zenon_H1f. % 0.40/0.58 generalize (axiom_2 zenon_TY24_w). zenon_intro zenon_H21. % 0.40/0.58 elim zenon_H21. zenon_intro zenon_TY21_v. zenon_intro zenon_H22. % 0.40/0.58 generalize (zenon_H22 zenon_TY21_v). zenon_intro zenon_H23. % 0.40/0.58 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H24 | zenon_intro zenon_H14 ]. % 0.40/0.58 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H19. zenon_intro zenon_H25. % 0.40/0.58 generalize (zenon_H1f zenon_TY21_v). zenon_intro zenon_H26. % 0.40/0.58 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.40/0.58 exact (zenon_H28 zenon_H1e). % 0.40/0.58 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.40/0.58 apply zenon_G. exists zenon_TY21_v. apply NNPP. zenon_intro zenon_H2b. % 0.40/0.58 apply (zenon_notallex_s (fun Y2 : zenon_U => ((~(id zenon_TY21_v Y2))\/(~(r1 Y2)))) zenon_H2b); [ zenon_intro zenon_H2c; idtac ]. % 0.40/0.58 elim zenon_H2c. zenon_intro zenon_TY2_bt. zenon_intro zenon_H2e. % 0.40/0.58 apply (zenon_notor_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.40/0.58 apply zenon_H30. zenon_intro zenon_H31. % 0.40/0.58 apply zenon_H2f. zenon_intro zenon_H32. % 0.40/0.58 generalize (zenon_H1a zenon_TY21_v). zenon_intro zenon_H33. % 0.40/0.58 generalize (zenon_H33 zenon_TY24_w). zenon_intro zenon_H34. % 0.40/0.58 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.40/0.58 elim (classic (id zenon_TY2_bt zenon_TY24_w)); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 0.40/0.58 generalize (zenon_H1b zenon_TY21_v). zenon_intro zenon_H39. % 0.40/0.58 generalize (zenon_H39 zenon_TY2_bt). zenon_intro zenon_H3a. % 0.40/0.58 generalize (zenon_H3a zenon_TY24_w). zenon_intro zenon_H3b. % 0.40/0.58 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 0.40/0.58 exact (zenon_H3d zenon_H31). % 0.40/0.58 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H38 | zenon_intro zenon_H3e ]. % 0.40/0.58 exact (zenon_H38 zenon_H37). % 0.40/0.58 exact (zenon_H36 zenon_H3e). % 0.40/0.58 generalize (zenon_H1d zenon_TY2_bt). zenon_intro zenon_H3f. % 0.40/0.58 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 0.40/0.58 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H37. zenon_intro zenon_H32. % 0.40/0.58 exact (zenon_H38 zenon_H37). % 0.40/0.58 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H38. % 0.40/0.58 exact (zenon_H42 zenon_H32). % 0.40/0.58 exact (zenon_H2a zenon_H35). % 0.40/0.58 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.40/0.58 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H1c. zenon_intro zenon_H18. % 0.40/0.58 exact (zenon_H18 zenon_H25). % 0.40/0.58 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H25. % 0.40/0.58 exact (zenon_H1c zenon_H45). % 0.40/0.58 apply (zenon_L1_ zenon_TY21_v zenon_TY24_w); trivial. % 0.40/0.58 (* end of lemma zenon_L2_ *) % 0.40/0.58 assert (zenon_L3_ : forall (zenon_TY24_w : zenon_U) (zenon_TY2_bg : zenon_U), ((r2 zenon_TY2_bg zenon_TY24_w)/\(r2 zenon_TY24_w zenon_TY24_w)) -> (~(r2 zenon_TY24_w zenon_TY24_w)) -> False). % 0.40/0.59 do 2 intro. intros zenon_H46 zenon_H47. % 0.40/0.59 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H45. zenon_intro zenon_H48. % 0.40/0.59 exact (zenon_H47 zenon_H48). % 0.40/0.59 (* end of lemma zenon_L3_ *) % 0.40/0.59 assert (zenon_L4_ : forall (zenon_TY24_w : zenon_U), ((~(r1 zenon_TY24_w))/\(~(id zenon_TY24_w zenon_TY24_w))) -> False). % 0.40/0.59 do 1 intro. intros zenon_H49. % 0.40/0.59 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 0.40/0.59 generalize (axiom_5 zenon_TY24_w). zenon_intro zenon_H4c. % 0.40/0.59 exact (zenon_H4a zenon_H4c). % 0.40/0.59 (* end of lemma zenon_L4_ *) % 0.40/0.59 assert (zenon_L5_ : forall (zenon_TY24_w : zenon_U), (r2 zenon_TY24_w zenon_TY24_w) -> (forall X19 : zenon_U, (((id X19 zenon_TY24_w)/\(r1 X19))\/((~(r1 X19))/\(~(id X19 zenon_TY24_w))))) -> False). % 0.40/0.59 do 1 intro. intros zenon_H48 zenon_H1d. % 0.40/0.59 generalize (axiom_7a zenon_TY24_w). zenon_intro zenon_H4d. % 0.40/0.59 generalize (zenon_H4d zenon_TY24_w). zenon_intro zenon_H4e. % 0.40/0.59 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H4f | zenon_intro zenon_H47 ]. % 0.40/0.59 generalize (zenon_H1d zenon_TY24_w). zenon_intro zenon_H50. % 0.40/0.59 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H51 | zenon_intro zenon_H49 ]. % 0.40/0.59 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H4c. zenon_intro zenon_H52. % 0.40/0.59 generalize (zenon_H4f zenon_TY24_w). zenon_intro zenon_H53. % 0.40/0.59 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 0.40/0.59 generalize (axiom_5 zenon_TY24_w). zenon_intro zenon_H4c. % 0.40/0.59 exact (zenon_H4a zenon_H4c). % 0.40/0.59 exact (zenon_H4b zenon_H52). % 0.40/0.59 apply (zenon_L4_ zenon_TY24_w); trivial. % 0.40/0.59 exact (zenon_H47 zenon_H48). % 0.40/0.59 (* end of lemma zenon_L5_ *) % 0.40/0.59 apply NNPP. intro zenon_G. % 0.40/0.59 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((id x y)->((id y z)->(id x z))))))); [ zenon_intro zenon_H1b | zenon_intro zenon_H54 ]. % 0.40/0.59 elim (classic (forall x : zenon_U, (forall y : zenon_U, ((id x y)->(id y x))))); [ zenon_intro zenon_H1a | zenon_intro zenon_H55 ]. % 0.40/0.59 elim axiom_1. zenon_intro zenon_TY24_w. zenon_intro zenon_H1d. % 0.40/0.59 apply (zenon_notallex_s (fun Y2 : zenon_U => ((~(id Zenon error: uncaught exception File "lltocoq.ml", line 117, characters 15-21: Assertion failed %------------------------------------------------------------------------------