TSTP Solution File: NUM505+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n013.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 15:56:18 EDT 2022
% Result : Theorem 261.86s 262.06s
% Output : Proof 261.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : run_zenon %s %d
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jul 5 12:21:29 EDT 2022
% 0.15/0.36 % CPUTime :
% 261.86/262.06 (* PROOF-FOUND *)
% 261.86/262.06 % SZS status Theorem
% 261.86/262.06 (* BEGIN-PROOF *)
% 261.86/262.06 % SZS output start Proof
% 261.86/262.06 Theorem m__ : ((~(sdtlseqdt0 (xp) (xk)))->((~((xk) = (xp)))/\(sdtlseqdt0 (xk) (xp)))).
% 261.86/262.06 Proof.
% 261.86/262.06 assert (zenon_L1_ : (aNaturalNumber0 (xp)) -> ((xp) = (sz00)) -> (isPrime0 (xp)) -> False).
% 261.86/262.06 do 0 intro. intros zenon_H32 zenon_H33 zenon_H34.
% 261.86/262.06 generalize (mDefPrime (xp)). zenon_intro zenon_H35.
% 261.86/262.06 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 261.86/262.06 exact (zenon_H37 zenon_H32).
% 261.86/262.06 apply (zenon_equiv_s _ _ zenon_H36); [ zenon_intro zenon_H3a; zenon_intro zenon_H39 | zenon_intro zenon_H34; zenon_intro zenon_H38 ].
% 261.86/262.06 exact (zenon_H3a zenon_H34).
% 261.86/262.06 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H3c. zenon_intro zenon_H3b.
% 261.86/262.06 exact (zenon_H3c zenon_H33).
% 261.86/262.06 (* end of lemma zenon_L1_ *)
% 261.86/262.06 assert (zenon_L2_ : (forall W1 : zenon_U, (((aNaturalNumber0 (xp))/\(aNaturalNumber0 W1))->(((~((xp) = (sz00)))/\(doDivides0 (xp) W1))->(forall W2 : zenon_U, ((W2 = (sdtsldt0 W1 (xp)))<->((aNaturalNumber0 W2)/\(W1 = (sdtasdt0 (xp) W2)))))))) -> (aNaturalNumber0 (xp)) -> (aNaturalNumber0 (xm)) -> (aNaturalNumber0 (xn)) -> (isPrime0 (xp)) -> (doDivides0 (xp) (sdtasdt0 (xn) (xm))) -> (~(aNaturalNumber0 (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)))) -> False).
% 261.86/262.06 do 0 intro. intros zenon_H3d zenon_H32 zenon_H3e zenon_H3f zenon_H34 zenon_H40 zenon_H41.
% 261.86/262.06 generalize (zenon_H3d (sdtasdt0 (xn) (xm))). zenon_intro zenon_H42.
% 261.86/262.06 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 261.86/262.06 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H37 | zenon_intro zenon_H45 ].
% 261.86/262.06 exact (zenon_H37 zenon_H32).
% 261.86/262.06 generalize (mSortsB_02 (xn)). zenon_intro zenon_H46.
% 261.86/262.06 generalize (zenon_H46 (xm)). zenon_intro zenon_H47.
% 261.86/262.06 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 261.86/262.06 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 261.86/262.06 exact (zenon_H4b zenon_H3f).
% 261.86/262.06 exact (zenon_H4a zenon_H3e).
% 261.86/262.06 exact (zenon_H45 zenon_H48).
% 261.86/262.06 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 261.86/262.06 apply (zenon_notand_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ].
% 261.86/262.06 apply zenon_H4f. zenon_intro zenon_H33.
% 261.86/262.06 apply (zenon_L1_); trivial.
% 261.86/262.06 exact (zenon_H4e zenon_H40).
% 261.86/262.06 generalize (zenon_H4c (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp))). zenon_intro zenon_H50.
% 261.86/262.06 apply (zenon_equiv_s _ _ zenon_H50); [ zenon_intro zenon_H54; zenon_intro zenon_H53 | zenon_intro zenon_H52; zenon_intro zenon_H51 ].
% 261.86/262.06 apply zenon_H54. apply refl_equal.
% 261.86/262.06 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H56. zenon_intro zenon_H55.
% 261.86/262.06 exact (zenon_H41 zenon_H56).
% 261.86/262.06 (* end of lemma zenon_L2_ *)
% 261.86/262.06 assert (zenon_L3_ : (~(aNaturalNumber0 (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)))) -> (doDivides0 (xp) (sdtasdt0 (xn) (xm))) -> (isPrime0 (xp)) -> (aNaturalNumber0 (xn)) -> (aNaturalNumber0 (xm)) -> (aNaturalNumber0 (xp)) -> False).
% 261.86/262.06 do 0 intro. intros zenon_H41 zenon_H40 zenon_H34 zenon_H3f zenon_H3e zenon_H32.
% 261.86/262.06 generalize (mDefQuot (xp)). zenon_intro zenon_H3d.
% 261.86/262.06 apply (zenon_L2_); trivial.
% 261.86/262.06 (* end of lemma zenon_L3_ *)
% 261.86/262.06 assert (zenon_L4_ : (~((sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) = (xk))) -> False).
% 261.86/262.06 do 0 intro. intros zenon_H57.
% 261.86/262.06 apply (zenon_congruence_lr_s _ (fun zenon_Vi : _ => (~((sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) = zenon_Vi))) _ _ zenon_H57 m__2306). zenon_intro zenon_H54.
% 261.86/262.06 apply zenon_H54. apply refl_equal.
% 261.86/262.06 (* end of lemma zenon_L4_ *)
% 261.86/262.06 assert (zenon_L5_ : ((~((sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) = (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp))))/\(sdtlseqdt0 (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)))) -> False).
% 261.86/262.06 do 0 intro. intros zenon_H58.
% 261.86/262.06 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H54. zenon_intro zenon_H59.
% 261.86/262.06 apply zenon_H54. apply refl_equal.
% 261.86/262.06 (* end of lemma zenon_L5_ *)
% 261.86/262.06 assert (zenon_L6_ : (~((xp) = (xp))) -> False).
% 261.86/262.06 do 0 intro. intros zenon_H5a.
% 261.86/262.06 apply zenon_H5a. apply refl_equal.
% 261.86/262.06 (* end of lemma zenon_L6_ *)
% 261.86/262.06 apply NNPP. intro zenon_G.
% 261.86/262.06 apply (zenon_and_s _ _ m__1837). zenon_intro zenon_H3f. zenon_intro zenon_H5b.
% 261.86/262.06 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H3e. zenon_intro zenon_H32.
% 261.86/262.06 apply (zenon_and_s _ _ m__1860). zenon_intro zenon_H34. zenon_intro zenon_H40.
% 261.94/262.10 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 261.94/262.10 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ].
% 261.94/262.10 apply zenon_H5f. zenon_intro zenon_H60.
% 261.94/262.10 apply (zenon_congruence_lr_s _ (fun zenon_Vg : _ => (zenon_Vg = (xp))) _ _ zenon_H60 m__2306). zenon_intro zenon_H61.
% 261.94/262.10 generalize (mLETotal (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp))). zenon_intro zenon_H62.
% 261.94/262.10 generalize (zenon_H62 (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp))). zenon_intro zenon_H63.
% 261.94/262.10 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 261.94/262.10 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H41 | zenon_intro zenon_H41 ].
% 261.94/262.10 apply (zenon_L3_); trivial.
% 261.94/262.10 apply (zenon_L3_); trivial.
% 261.94/262.10 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ].
% 261.94/262.10 cut ((sdtlseqdt0 (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp))) = (sdtlseqdt0 (xp) (xk))).
% 261.94/262.10 intro zenon_D_pnotp.
% 261.94/262.10 apply zenon_H5d.
% 261.94/262.10 rewrite <- zenon_D_pnotp.
% 261.94/262.10 exact zenon_H59.
% 261.94/262.10 cut (((sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) = (xk))); [idtac | apply NNPP; zenon_intro zenon_H57].
% 261.94/262.10 cut (((sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) = (xp))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 261.94/262.10 congruence.
% 261.94/262.10 exact (zenon_H66 zenon_H61).
% 261.94/262.10 apply (zenon_L4_); trivial.
% 261.94/262.10 apply (zenon_L5_); trivial.
% 261.94/262.10 generalize (mLETotal (xp)). zenon_intro zenon_H67.
% 261.94/262.10 generalize (zenon_H67 (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp))). zenon_intro zenon_H68.
% 261.94/262.10 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ].
% 261.94/262.10 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H37 | zenon_intro zenon_H41 ].
% 261.94/262.10 exact (zenon_H37 zenon_H32).
% 261.94/262.10 apply (zenon_L3_); trivial.
% 261.94/262.10 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ].
% 261.94/262.10 cut ((sdtlseqdt0 (xp) (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp))) = (sdtlseqdt0 (xp) (xk))).
% 261.94/262.10 intro zenon_D_pnotp.
% 261.94/262.10 apply zenon_H5d.
% 261.94/262.10 rewrite <- zenon_D_pnotp.
% 261.94/262.10 exact zenon_H6c.
% 261.94/262.10 cut (((sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) = (xk))); [idtac | apply NNPP; zenon_intro zenon_H57].
% 261.94/262.10 cut (((xp) = (xp))); [idtac | apply NNPP; zenon_intro zenon_H5a].
% 261.94/262.10 congruence.
% 261.94/262.10 apply zenon_H5a. apply refl_equal.
% 261.94/262.10 apply (zenon_L4_); trivial.
% 261.94/262.10 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H66. zenon_intro zenon_H6d.
% 261.94/262.10 cut ((sdtlseqdt0 (sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) (xp)) = (sdtlseqdt0 (xk) (xp))).
% 261.94/262.10 intro zenon_D_pnotp.
% 261.94/262.10 apply zenon_H5e.
% 261.94/262.10 rewrite <- zenon_D_pnotp.
% 261.94/262.10 exact zenon_H6d.
% 261.94/262.10 cut (((xp) = (xp))); [idtac | apply NNPP; zenon_intro zenon_H5a].
% 261.94/262.10 cut (((sdtsldt0 (sdtasdt0 (xn) (xm)) (xp)) = (xk))); [idtac | apply NNPP; zenon_intro zenon_H57].
% 261.94/262.10 congruence.
% 261.94/262.10 apply (zenon_L4_); trivial.
% 261.94/262.10 apply zenon_H5a. apply refl_equal.
% 261.94/262.10 Qed.
% 261.94/262.10 % SZS output end Proof
% 261.94/262.10 (* END-PROOF *)
% 261.94/262.10 nodes searched: 1507066
% 261.94/262.10 max branch formulas: 41974
% 261.94/262.10 proof nodes created: 52223
% 261.94/262.10 formulas created: 7215103
% 261.94/262.10
%------------------------------------------------------------------------------