TSTP Solution File: KRS082+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : KRS082+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n027.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 : Sun Jul 17 03:39:24 EDT 2022
% Result : Unsatisfiable 1.07s 1.29s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : KRS082+1 : TPTP v8.1.0. Released v3.1.0.
% 0.09/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n027.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 : Tue Jun 7 18:38:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.07/1.29 (* PROOF-FOUND *)
% 1.07/1.29 % SZS status Unsatisfiable
% 1.07/1.29 (* BEGIN-PROOF *)
% 1.07/1.29 % SZS output start Proof
% 1.07/1.29 Theorem zenon_thm : False.
% 1.07/1.29 Proof.
% 1.07/1.29 assert (zenon_L1_ : forall (zenon_TW_o : zenon_U) (zenon_TZ_p : zenon_U) (zenon_TY_q : zenon_U), (rp zenon_TY_q zenon_TZ_p) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (~(rp zenon_TY_q zenon_TW_o)) -> (rp zenon_TZ_p zenon_TW_o) -> False).
% 1.07/1.29 do 3 intro. intros zenon_Ha zenon_Hb zenon_Hc zenon_Hd.
% 1.07/1.29 elim (classic ((~(zenon_TY_q = zenon_TZ_p))/\(~(rp zenon_TY_q zenon_TZ_p)))); [ zenon_intro zenon_H11 | zenon_intro zenon_H12 ].
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H11). zenon_intro zenon_H14. zenon_intro zenon_H13.
% 1.07/1.29 exact (zenon_H13 zenon_Ha).
% 1.07/1.29 cut ((rp zenon_TZ_p zenon_TW_o) = (rp zenon_TY_q zenon_TW_o)).
% 1.07/1.29 intro zenon_D_pnotp.
% 1.07/1.29 apply zenon_Hc.
% 1.07/1.29 rewrite <- zenon_D_pnotp.
% 1.07/1.29 exact zenon_Hd.
% 1.07/1.29 cut ((zenon_TW_o = zenon_TW_o)); [idtac | apply NNPP; zenon_intro zenon_H15].
% 1.07/1.29 cut ((zenon_TZ_p = zenon_TY_q)); [idtac | apply NNPP; zenon_intro zenon_H16].
% 1.07/1.29 congruence.
% 1.07/1.29 apply (zenon_notand_s _ _ zenon_H12); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 1.07/1.29 apply zenon_H18. zenon_intro zenon_H19.
% 1.07/1.29 elim (classic (zenon_TY_q = zenon_TY_q)); [ zenon_intro zenon_H1a | zenon_intro zenon_H1b ].
% 1.07/1.29 cut ((zenon_TY_q = zenon_TY_q) = (zenon_TZ_p = zenon_TY_q)).
% 1.07/1.29 intro zenon_D_pnotp.
% 1.07/1.29 apply zenon_H16.
% 1.07/1.29 rewrite <- zenon_D_pnotp.
% 1.07/1.29 exact zenon_H1a.
% 1.07/1.29 cut ((zenon_TY_q = zenon_TY_q)); [idtac | apply NNPP; zenon_intro zenon_H1b].
% 1.07/1.29 cut ((zenon_TY_q = zenon_TZ_p)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 1.07/1.29 congruence.
% 1.07/1.29 exact (zenon_H14 zenon_H19).
% 1.07/1.29 apply zenon_H1b. apply refl_equal.
% 1.07/1.29 apply zenon_H1b. apply refl_equal.
% 1.07/1.29 apply zenon_H17. zenon_intro zenon_Ha.
% 1.07/1.29 generalize (zenon_Hb zenon_TY_q). zenon_intro zenon_H1c.
% 1.07/1.29 generalize (zenon_H1c zenon_TZ_p). zenon_intro zenon_H1d.
% 1.07/1.29 generalize (zenon_H1d zenon_TW_o). zenon_intro zenon_H1e.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H13 | zenon_intro zenon_H1f ].
% 1.07/1.29 exact (zenon_H13 zenon_Ha).
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 1.07/1.29 exact (zenon_H21 zenon_Hd).
% 1.07/1.29 exact (zenon_Hc zenon_H20).
% 1.07/1.29 apply zenon_H15. apply refl_equal.
% 1.07/1.29 (* end of lemma zenon_L1_ *)
% 1.07/1.29 assert (zenon_L2_ : forall (zenon_TY_q : zenon_U), (forall W : zenon_U, ((rinvS zenon_TY_q W)->(~(ca W)))) -> (rs (i2003_11_14_17_19_28752) zenon_TY_q) -> False).
% 1.07/1.29 do 1 intro. intros zenon_H22 zenon_H23.
% 1.07/1.29 generalize (axiom_3 (i2003_11_14_17_19_28752)). zenon_intro zenon_H24.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ].
% 1.07/1.29 exact (zenon_H26 axiom_9).
% 1.07/1.29 generalize (zenon_H22 (i2003_11_14_17_19_28752)). zenon_intro zenon_H27.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 1.07/1.29 generalize (axiom_7 zenon_TY_q). zenon_intro zenon_H2a.
% 1.07/1.29 generalize (zenon_H2a (i2003_11_14_17_19_28752)). zenon_intro zenon_H2b.
% 1.07/1.29 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H29; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H23 ].
% 1.07/1.29 exact (zenon_H2d zenon_H23).
% 1.07/1.29 exact (zenon_H29 zenon_H2c).
% 1.07/1.29 exact (zenon_H28 zenon_H25).
% 1.07/1.29 (* end of lemma zenon_L2_ *)
% 1.07/1.29 assert (zenon_L3_ : forall (zenon_TZ_p : zenon_U) (zenon_TY_q : zenon_U) (zenon_TW_o : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (forall Z : zenon_U, ((rinvP zenon_TW_o Z)->(forall W : zenon_U, ((rinvS Z W)->(~(ca W)))))) -> (rp zenon_TY_q zenon_TZ_p) -> (rp zenon_TZ_p zenon_TW_o) -> (rs (i2003_11_14_17_19_28752) zenon_TY_q) -> False).
% 1.07/1.29 do 3 intro. intros zenon_Hb zenon_H2e zenon_Ha zenon_Hd zenon_H23.
% 1.07/1.29 generalize (zenon_H2e zenon_TY_q). zenon_intro zenon_H2f.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H30 | zenon_intro zenon_H22 ].
% 1.07/1.29 generalize (axiom_5 zenon_TW_o). zenon_intro zenon_H31.
% 1.07/1.29 generalize (zenon_H31 zenon_TY_q). zenon_intro zenon_H32.
% 1.07/1.29 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H30; zenon_intro zenon_Hc | zenon_intro zenon_H33; zenon_intro zenon_H20 ].
% 1.07/1.29 apply (zenon_L1_ zenon_TW_o zenon_TZ_p zenon_TY_q); trivial.
% 1.07/1.29 exact (zenon_H30 zenon_H33).
% 1.07/1.29 apply (zenon_L2_ zenon_TY_q); trivial.
% 1.07/1.29 (* end of lemma zenon_L3_ *)
% 1.07/1.29 assert (zenon_L4_ : forall (zenon_TZ_p : zenon_U) (zenon_TY_q : zenon_U) (zenon_TW_o : zenon_U) (zenon_TW_cc : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (cc zenon_TW_cc) -> (rr zenon_TW_o zenon_TW_cc) -> (rp zenon_TY_q zenon_TZ_p) -> (rp zenon_TZ_p zenon_TW_o) -> (rs (i2003_11_14_17_19_28752) zenon_TY_q) -> False).
% 1.07/1.29 do 4 intro. intros zenon_Hb zenon_H34 zenon_H35 zenon_Ha zenon_Hd zenon_H23.
% 1.07/1.29 generalize (axiom_4 zenon_TW_cc). zenon_intro zenon_H37.
% 1.07/1.29 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3a; zenon_intro zenon_H39 | zenon_intro zenon_H34; zenon_intro zenon_H38 ].
% 1.07/1.29 exact (zenon_H3a zenon_H34).
% 1.07/1.29 generalize (zenon_H38 zenon_TW_o). zenon_intro zenon_H3b.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_H2e ].
% 1.07/1.29 generalize (axiom_6 zenon_TW_cc). zenon_intro zenon_H3d.
% 1.07/1.29 generalize (zenon_H3d zenon_TW_o). zenon_intro zenon_H3e.
% 1.07/1.29 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3c; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H35 ].
% 1.07/1.29 exact (zenon_H40 zenon_H35).
% 1.07/1.29 exact (zenon_H3c zenon_H3f).
% 1.07/1.29 apply (zenon_L3_ zenon_TZ_p zenon_TY_q zenon_TW_o); trivial.
% 1.07/1.29 (* end of lemma zenon_L4_ *)
% 1.07/1.29 assert (zenon_L5_ : forall (zenon_TY_q : zenon_U) (zenon_TZ_p : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (exists W : zenon_U, ((rp zenon_TZ_p W)/\(cowlThing W))) -> (forall Z : zenon_U, ((rp zenon_TY_q Z)->(exists W : zenon_U, ((rr Z W)/\(cowlThing W))))) -> (rp zenon_TY_q zenon_TZ_p) -> (forall Z : zenon_U, ((rp zenon_TY_q Z)->(forall W : zenon_U, ((rr Z W)->(cc W))))) -> (rs (i2003_11_14_17_19_28752) zenon_TY_q) -> False).
% 1.07/1.29 do 2 intro. intros zenon_Hb zenon_H41 zenon_H42 zenon_Ha zenon_H43 zenon_H23.
% 1.07/1.29 elim zenon_H41. zenon_intro zenon_TW_o. zenon_intro zenon_H44.
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_Hd. zenon_intro zenon_H45.
% 1.07/1.29 generalize (zenon_H42 zenon_TW_o). zenon_intro zenon_H46.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_Hc | zenon_intro zenon_H47 ].
% 1.07/1.29 apply (zenon_L1_ zenon_TW_o zenon_TZ_p zenon_TY_q); trivial.
% 1.07/1.29 elim zenon_H47. zenon_intro zenon_TW_cc. zenon_intro zenon_H48.
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H35. zenon_intro zenon_H49.
% 1.07/1.29 generalize (zenon_H43 zenon_TW_o). zenon_intro zenon_H4a.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_Hc | zenon_intro zenon_H4b ].
% 1.07/1.29 apply (zenon_L1_ zenon_TW_o zenon_TZ_p zenon_TY_q); trivial.
% 1.07/1.29 generalize (zenon_H4b zenon_TW_cc). zenon_intro zenon_H4c.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H40 | zenon_intro zenon_H34 ].
% 1.07/1.29 exact (zenon_H40 zenon_H35).
% 1.07/1.29 apply (zenon_L4_ zenon_TZ_p zenon_TY_q zenon_TW_o zenon_TW_cc); trivial.
% 1.07/1.29 (* end of lemma zenon_L5_ *)
% 1.07/1.29 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z))))))); [ zenon_intro zenon_Hb | zenon_intro zenon_H4d ].
% 1.07/1.29 generalize (axiom_2 (i2003_11_14_17_19_28752)). zenon_intro zenon_H4e.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H26 | zenon_intro zenon_H4f ].
% 1.07/1.29 exact (zenon_H26 axiom_9).
% 1.07/1.29 elim zenon_H4f. zenon_intro zenon_TY_q. zenon_intro zenon_H50.
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H23. zenon_intro zenon_H51.
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52.
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H55. zenon_intro zenon_H54.
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H42. zenon_intro zenon_H56.
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H58. zenon_intro zenon_H57.
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H43. zenon_intro zenon_H59.
% 1.07/1.29 elim zenon_H53. zenon_intro zenon_TZ_p. zenon_intro zenon_H5a.
% 1.07/1.29 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_Ha. zenon_intro zenon_H5b.
% 1.07/1.29 generalize (zenon_H58 zenon_TZ_p). zenon_intro zenon_H5c.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H13 | zenon_intro zenon_H41 ].
% 1.07/1.29 exact (zenon_H13 zenon_Ha).
% 1.07/1.29 apply (zenon_L5_ zenon_TY_q zenon_TZ_p); trivial.
% 1.07/1.29 apply zenon_H4d. zenon_intro zenon_Tx_dp. apply NNPP. zenon_intro zenon_H5e.
% 1.07/1.29 apply zenon_H5e. zenon_intro zenon_Ty_dr. apply NNPP. zenon_intro zenon_H60.
% 1.07/1.29 apply zenon_H60. zenon_intro zenon_Tz_dt. apply NNPP. zenon_intro zenon_H62.
% 1.07/1.29 apply (zenon_notimply_s _ _ zenon_H62). zenon_intro zenon_H64. zenon_intro zenon_H63.
% 1.07/1.29 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 1.07/1.29 generalize (axiom_8 zenon_Tx_dp). zenon_intro zenon_H67.
% 1.07/1.29 generalize (zenon_H67 zenon_Ty_dr). zenon_intro zenon_H68.
% 1.07/1.29 generalize (zenon_H68 zenon_Tz_dt). zenon_intro zenon_H69.
% 1.07/1.29 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ].
% 1.07/1.29 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H6d | zenon_intro zenon_H6c ].
% 1.07/1.29 exact (zenon_H6d zenon_H64).
% 1.07/1.29 exact (zenon_H6c zenon_H66).
% 1.07/1.29 exact (zenon_H65 zenon_H6a).
% 1.07/1.29 Qed.
% 1.07/1.29 % SZS output end Proof
% 1.07/1.29 (* END-PROOF *)
% 1.07/1.29 nodes searched: 34986
% 1.07/1.29 max branch formulas: 2724
% 1.07/1.29 proof nodes created: 545
% 1.07/1.29 formulas created: 67825
% 1.07/1.29
%------------------------------------------------------------------------------