TSTP Solution File: RNG067+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : RNG067+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n019.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 20:48:23 EDT 2022
% Result : Theorem 0.21s 0.60s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG067+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon May 30 15:06:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.60 (* PROOF-FOUND *)
% 0.21/0.60 % SZS status Theorem
% 0.21/0.60 (* BEGIN-PROOF *)
% 0.21/0.60 % SZS output start Proof
% 0.21/0.60 Theorem m__ : (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN))).
% 0.21/0.60 Proof.
% 0.21/0.60 assert (zenon_L1_ : (~(aScalar0 (sdtasdt0 (xP) (xP)))) -> (aScalar0 (xP)) -> False).
% 0.21/0.60 do 0 intro. intros zenon_H3b zenon_H3c.
% 0.21/0.60 generalize (mMulSc (xP)). zenon_intro zenon_H3d.
% 0.21/0.60 generalize (zenon_H3d (xP)). zenon_intro zenon_H3e.
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H41 | zenon_intro zenon_H41 ].
% 0.21/0.60 exact (zenon_H41 zenon_H3c).
% 0.21/0.60 exact (zenon_H41 zenon_H3c).
% 0.21/0.60 exact (zenon_H3b zenon_H3f).
% 0.21/0.60 (* end of lemma zenon_L1_ *)
% 0.21/0.60 assert (zenon_L2_ : (~(aScalar0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))))) -> (aScalar0 (xP)) -> False).
% 0.21/0.60 do 0 intro. intros zenon_H42 zenon_H3c.
% 0.21/0.60 generalize (mSumSc (sdtasdt0 (xP) (xP))). zenon_intro zenon_H43.
% 0.21/0.60 generalize (zenon_H43 (sdtasdt0 (xP) (xP))). zenon_intro zenon_H44.
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H3b ].
% 0.21/0.60 apply (zenon_L1_); trivial.
% 0.21/0.60 apply (zenon_L1_); trivial.
% 0.21/0.60 exact (zenon_H42 zenon_H45).
% 0.21/0.60 (* end of lemma zenon_L2_ *)
% 0.21/0.60 assert (zenon_L3_ : (~(aScalar0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))))) -> (aScalar0 (xS)) -> (aScalar0 (xR)) -> False).
% 0.21/0.60 do 0 intro. intros zenon_H47 zenon_H48 zenon_H49.
% 0.21/0.60 generalize (mSumSc (sdtasdt0 (xR) (xR))). zenon_intro zenon_H4a.
% 0.21/0.60 generalize (zenon_H4a (sdtasdt0 (xS) (xS))). zenon_intro zenon_H4b.
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ].
% 0.21/0.60 generalize (mMulSc (xR)). zenon_intro zenon_H50.
% 0.21/0.60 generalize (zenon_H50 (xR)). zenon_intro zenon_H51.
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H54 | zenon_intro zenon_H54 ].
% 0.21/0.60 exact (zenon_H54 zenon_H49).
% 0.21/0.60 exact (zenon_H54 zenon_H49).
% 0.21/0.60 exact (zenon_H4f zenon_H52).
% 0.21/0.60 generalize (mMulSc (xS)). zenon_intro zenon_H55.
% 0.21/0.60 generalize (zenon_H55 (xS)). zenon_intro zenon_H56.
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H58); [ zenon_intro zenon_H59 | zenon_intro zenon_H59 ].
% 0.21/0.60 exact (zenon_H59 zenon_H48).
% 0.21/0.60 exact (zenon_H59 zenon_H48).
% 0.21/0.60 exact (zenon_H4e zenon_H57).
% 0.21/0.60 exact (zenon_H47 zenon_H4c).
% 0.21/0.60 (* end of lemma zenon_L3_ *)
% 0.21/0.60 apply NNPP. intro zenon_G.
% 0.21/0.60 apply (zenon_and_s _ _ m__1892). zenon_intro zenon_H49. zenon_intro zenon_H5a.
% 0.21/0.60 apply (zenon_and_s _ _ m__1911). zenon_intro zenon_H3c. zenon_intro zenon_H5b.
% 0.21/0.60 apply (zenon_and_s _ _ m__1930). zenon_intro zenon_H48. zenon_intro zenon_H5c.
% 0.21/0.60 apply (zenon_and_s _ _ m__1949). zenon_intro zenon_H5e. zenon_intro zenon_H5d.
% 0.21/0.60 generalize (mLEMon (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP)))). zenon_intro zenon_H5f.
% 0.21/0.60 generalize (zenon_H5f (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN))). zenon_intro zenon_H60.
% 0.21/0.60 generalize (zenon_H60 (sdtasdt0 (xP) (xP))). zenon_intro zenon_H61.
% 0.21/0.60 generalize (zenon_H61 (xN)). zenon_intro zenon_H62.
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ].
% 0.21/0.60 generalize (mSumSc (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP)))). zenon_intro zenon_H67.
% 0.21/0.60 generalize (zenon_H67 (sdtasdt0 (xP) (xP))). zenon_intro zenon_H68.
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H42 | zenon_intro zenon_H3b ].
% 0.21/0.60 apply (zenon_L2_); trivial.
% 0.21/0.60 apply (zenon_L1_); trivial.
% 0.21/0.60 exact (zenon_H66 zenon_H69).
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ].
% 0.21/0.60 generalize (mSumSc (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))). zenon_intro zenon_H6d.
% 0.21/0.60 generalize (zenon_H6d (xN)). zenon_intro zenon_H6e.
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H70 | zenon_intro zenon_H6f ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H70); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ].
% 0.21/0.60 apply (zenon_L3_); trivial.
% 0.21/0.60 exact (zenon_H71 zenon_H5e).
% 0.21/0.60 exact (zenon_H6c zenon_H6f).
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H3b | zenon_intro zenon_H71 ].
% 0.21/0.60 apply (zenon_L1_); trivial.
% 0.21/0.60 exact (zenon_H71 zenon_H5e).
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H73); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ].
% 0.21/0.60 generalize (mLEMon (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP)))). zenon_intro zenon_H76.
% 0.21/0.60 generalize (zenon_H76 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))). zenon_intro zenon_H77.
% 0.21/0.60 generalize (zenon_H77 (sdtasdt0 (xP) (xP))). zenon_intro zenon_H78.
% 0.21/0.60 generalize (zenon_H78 (xN)). zenon_intro zenon_H79.
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H7b | zenon_intro zenon_H7a ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H7b); [ zenon_intro zenon_H42 | zenon_intro zenon_H7c ].
% 0.21/0.60 apply (zenon_L2_); trivial.
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H47 | zenon_intro zenon_H6b ].
% 0.21/0.60 apply (zenon_L3_); trivial.
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H3b | zenon_intro zenon_H71 ].
% 0.21/0.60 apply (zenon_L1_); trivial.
% 0.21/0.60 exact (zenon_H71 zenon_H5e).
% 0.21/0.60 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ].
% 0.21/0.60 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H7f | zenon_intro zenon_H74 ].
% 0.21/0.60 exact (zenon_H7f m__2104).
% 0.21/0.60 exact (zenon_H74 m__2004).
% 0.21/0.60 exact (zenon_H75 zenon_H7d).
% 0.21/0.60 exact (zenon_H74 m__2004).
% 0.21/0.60 exact (zenon_G zenon_H72).
% 0.21/0.60 Qed.
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 (* END-PROOF *)
% 0.21/0.60 nodes searched: 1260
% 0.21/0.60 max branch formulas: 629
% 0.21/0.60 proof nodes created: 76
% 0.21/0.60 formulas created: 13261
% 0.21/0.60
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