TSTP Solution File: RNG109+4 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : RNG109+4 : TPTP v8.1.0. Released v4.0.0.
% 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 : Mon Jul 18 20:48:29 EDT 2022
% Result : Theorem 20.39s 20.59s
% Output : Proof 20.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG109+4 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n017.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 : Mon May 30 16:44:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 20.39/20.59 (* PROOF-FOUND *)
% 20.39/20.59 % SZS status Theorem
% 20.39/20.59 (* BEGIN-PROOF *)
% 20.39/20.59 % SZS output start Proof
% 20.39/20.59 Theorem m__ : (exists W0 : zenon_U, (((forall W0 : zenon_U, ((aElementOf0 W0 (slsdtgt0 (xa)))<->(exists W1 : zenon_U, ((aElement0 W1)/\((sdtasdt0 (xa) W1) = W0)))))->((forall W0 : zenon_U, ((aElementOf0 W0 (slsdtgt0 (xb)))<->(exists W1 : zenon_U, ((aElement0 W1)/\((sdtasdt0 (xb) W1) = W0)))))->((exists W1 : zenon_U, (exists W2 : zenon_U, ((aElementOf0 W1 (slsdtgt0 (xa)))/\((aElementOf0 W2 (slsdtgt0 (xb)))/\((sdtpldt0 W1 W2) = W0)))))\/(aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))))))/\(~(W0 = (sz00))))).
% 20.39/20.59 Proof.
% 20.39/20.59 assert (zenon_L1_ : (~((xa) = (xa))) -> False).
% 20.39/20.59 do 0 intro. intros zenon_H2c.
% 20.39/20.59 apply zenon_H2c. apply refl_equal.
% 20.39/20.59 (* end of lemma zenon_L1_ *)
% 20.39/20.59 assert (zenon_L2_ : (~((xb) = (xb))) -> False).
% 20.39/20.59 do 0 intro. intros zenon_H2d.
% 20.39/20.59 apply zenon_H2d. apply refl_equal.
% 20.39/20.59 (* end of lemma zenon_L2_ *)
% 20.39/20.59 assert (zenon_L3_ : (((sdtpldt0 (xb) (sz00)) = (xb))/\((xb) = (sdtpldt0 (sz00) (xb)))) -> (~(exists W0 : zenon_U, (((forall W0 : zenon_U, ((aElementOf0 W0 (slsdtgt0 (xa)))<->(exists W1 : zenon_U, ((aElement0 W1)/\((sdtasdt0 (xa) W1) = W0)))))->((forall W0 : zenon_U, ((aElementOf0 W0 (slsdtgt0 (xb)))<->(exists W1 : zenon_U, ((aElement0 W1)/\((sdtasdt0 (xb) W1) = W0)))))->((exists W1 : zenon_U, (exists W2 : zenon_U, ((aElementOf0 W1 (slsdtgt0 (xa)))/\((aElementOf0 W2 (slsdtgt0 (xb)))/\((sdtpldt0 W1 W2) = W0)))))\/(aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))))))/\(~(W0 = (sz00)))))) -> (aElementOf0 (sz00) (slsdtgt0 (xa))) -> (aElementOf0 (xb) (slsdtgt0 (xb))) -> (~((xb) = (sz00))) -> False).
% 20.39/20.59 do 0 intro. intros zenon_H2e zenon_G zenon_H2f zenon_H30 zenon_H31.
% 20.39/20.59 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H33. zenon_intro zenon_H32.
% 20.39/20.59 cut (((xb) = (sdtpldt0 (sz00) (xb))) = ((xb) = (sz00))).
% 20.39/20.59 intro zenon_D_pnotp.
% 20.39/20.59 apply zenon_H31.
% 20.39/20.59 rewrite <- zenon_D_pnotp.
% 20.39/20.59 exact zenon_H32.
% 20.39/20.59 cut (((sdtpldt0 (sz00) (xb)) = (sz00))); [idtac | apply NNPP; zenon_intro zenon_H34].
% 20.39/20.59 cut (((xb) = (xb))); [idtac | apply NNPP; zenon_intro zenon_H2d].
% 20.39/20.59 congruence.
% 20.39/20.59 apply zenon_H2d. apply refl_equal.
% 20.39/20.59 apply zenon_G. exists (sdtpldt0 (sz00) (xb)). apply NNPP. zenon_intro zenon_H35.
% 20.39/20.59 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 20.39/20.59 apply (zenon_notimply_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 20.39/20.59 apply (zenon_notimply_s _ _ zenon_H38). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 20.39/20.59 apply (zenon_notor_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c.
% 20.39/20.59 apply zenon_H3d. exists (sz00). apply NNPP. zenon_intro zenon_H3e.
% 20.39/20.59 apply zenon_H3e. exists (xb). apply NNPP. zenon_intro zenon_H3f.
% 20.39/20.59 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ].
% 20.39/20.59 exact (zenon_H41 zenon_H2f).
% 20.39/20.59 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ].
% 20.39/20.59 exact (zenon_H43 zenon_H30).
% 20.39/20.59 apply zenon_H42. apply refl_equal.
% 20.39/20.59 exact (zenon_H36 zenon_H34).
% 20.39/20.59 (* end of lemma zenon_L3_ *)
% 20.39/20.59 assert (zenon_L4_ : (aElement0 (xb)) -> (~(exists W0 : zenon_U, (((forall W0 : zenon_U, ((aElementOf0 W0 (slsdtgt0 (xa)))<->(exists W1 : zenon_U, ((aElement0 W1)/\((sdtasdt0 (xa) W1) = W0)))))->((forall W0 : zenon_U, ((aElementOf0 W0 (slsdtgt0 (xb)))<->(exists W1 : zenon_U, ((aElement0 W1)/\((sdtasdt0 (xb) W1) = W0)))))->((exists W1 : zenon_U, (exists W2 : zenon_U, ((aElementOf0 W1 (slsdtgt0 (xa)))/\((aElementOf0 W2 (slsdtgt0 (xb)))/\((sdtpldt0 W1 W2) = W0)))))\/(aElementOf0 W0 (sdtpldt1 (slsdtgt0 (xa)) (slsdtgt0 (xb)))))))/\(~(W0 = (sz00)))))) -> (aElementOf0 (sz00) (slsdtgt0 (xa))) -> (aElementOf0 (xb) (slsdtgt0 (xb))) -> (~((xb) = (sz00))) -> False).
% 20.39/20.59 do 0 intro. intros zenon_H44 zenon_G zenon_H2f zenon_H30 zenon_H31.
% 20.39/20.59 generalize (mAddZero (xb)). zenon_intro zenon_H45.
% 20.39/20.59 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H46 | zenon_intro zenon_H2e ].
% 20.39/20.59 exact (zenon_H46 zenon_H44).
% 20.39/20.59 apply (zenon_L3_); trivial.
% 20.39/20.59 (* end of lemma zenon_L4_ *)
% 20.39/20.59 apply NNPP. intro zenon_G.
% 20.39/20.59 apply (zenon_and_s _ _ m__2091). zenon_intro zenon_H47. zenon_intro zenon_H44.
% 20.39/20.59 apply (zenon_and_s _ _ m__2203). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 20.39/20.59 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H2f. zenon_intro zenon_H4a.
% 20.39/20.59 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H4c. zenon_intro zenon_H4b.
% 20.39/20.59 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 20.39/20.59 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f.
% 20.39/20.59 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51.
% 20.39/20.59 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H30.
% 20.39/20.59 apply (zenon_or_s _ _ m__2110); [ zenon_intro zenon_H54 | zenon_intro zenon_H31 ].
% 20.39/20.59 generalize (mAddZero (xa)). zenon_intro zenon_H55.
% 20.39/20.59 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 20.39/20.59 exact (zenon_H57 zenon_H47).
% 20.39/20.59 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H59. zenon_intro zenon_H58.
% 20.39/20.59 elim (classic ((sz00) = (sz00))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ].
% 20.39/20.59 cut (((sz00) = (sz00)) = ((xa) = (sz00))).
% 20.39/20.59 intro zenon_D_pnotp.
% 20.39/20.59 apply zenon_H54.
% 20.39/20.59 rewrite <- zenon_D_pnotp.
% 20.39/20.59 exact zenon_H5a.
% 20.39/20.59 cut (((sz00) = (sz00))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 20.39/20.59 cut (((sz00) = (xa))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 20.39/20.59 congruence.
% 20.39/20.59 cut (((sdtpldt0 (xa) (sz00)) = (xa)) = ((sz00) = (xa))).
% 20.39/20.59 intro zenon_D_pnotp.
% 20.39/20.59 apply zenon_H5c.
% 20.39/20.59 rewrite <- zenon_D_pnotp.
% 20.39/20.59 exact zenon_H59.
% 20.39/20.59 cut (((xa) = (xa))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 20.39/20.59 cut (((sdtpldt0 (xa) (sz00)) = (sz00))); [idtac | apply NNPP; zenon_intro zenon_H5d].
% 20.39/20.59 congruence.
% 20.39/20.59 elim (classic ((sz00) = (sz00))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ].
% 20.39/20.59 cut (((sz00) = (sz00)) = ((sdtpldt0 (xa) (sz00)) = (sz00))).
% 20.39/20.59 intro zenon_D_pnotp.
% 20.39/20.59 apply zenon_H5d.
% 20.39/20.59 rewrite <- zenon_D_pnotp.
% 20.39/20.59 exact zenon_H5a.
% 20.39/20.59 cut (((sz00) = (sz00))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 20.39/20.59 cut (((sz00) = (sdtpldt0 (xa) (sz00)))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 20.39/20.59 congruence.
% 20.39/20.59 apply zenon_G. exists (sdtpldt0 (xa) (sz00)). apply NNPP. zenon_intro zenon_H5f.
% 20.39/20.59 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ].
% 20.39/20.59 apply (zenon_notimply_s _ _ zenon_H61). zenon_intro zenon_H39. zenon_intro zenon_H62.
% 20.39/20.59 apply (zenon_notimply_s _ _ zenon_H62). zenon_intro zenon_H3b. zenon_intro zenon_H63.
% 20.39/20.59 apply (zenon_notor_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64.
% 20.39/20.59 apply zenon_H65. exists (xa). apply NNPP. zenon_intro zenon_H66.
% 20.39/20.59 apply zenon_H66. exists (sz00). apply NNPP. zenon_intro zenon_H67.
% 20.39/20.59 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ].
% 20.39/20.59 exact (zenon_H69 zenon_H4e).
% 20.39/20.59 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ].
% 20.39/20.59 exact (zenon_H6b zenon_H52).
% 20.39/20.59 apply zenon_H6a. apply refl_equal.
% 20.39/20.59 apply zenon_H60. zenon_intro zenon_H6c.
% 20.39/20.59 apply zenon_H5e. apply sym_equal. exact zenon_H6c.
% 20.39/20.59 apply zenon_H5b. apply refl_equal.
% 20.39/20.59 apply zenon_H5b. apply refl_equal.
% 20.39/20.59 apply zenon_H2c. apply refl_equal.
% 20.39/20.59 apply zenon_H5b. apply refl_equal.
% 20.39/20.59 apply zenon_H5b. apply refl_equal.
% 20.39/20.59 apply (zenon_L4_); trivial.
% 20.39/20.59 Qed.
% 20.39/20.59 % SZS output end Proof
% 20.39/20.59 (* END-PROOF *)
% 20.39/20.59 nodes searched: 543509
% 20.39/20.59 max branch formulas: 7437
% 20.39/20.59 proof nodes created: 15950
% 20.39/20.59 formulas created: 1327258
% 20.39/20.59
%------------------------------------------------------------------------------