TSTP Solution File: NUM316+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : NUM316+1 : TPTP v8.1.0. Released v3.1.0.
% 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 15:54:50 EDT 2022
% Result : Theorem 1.58s 1.77s
% Output : Proof 1.58s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM316+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % 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 : Thu Jul 7 02:11:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.58/1.77 (* PROOF-FOUND *)
% 1.58/1.77 % SZS status Theorem
% 1.58/1.77 (* BEGIN-PROOF *)
% 1.58/1.77 % SZS output start Proof
% 1.58/1.77 Theorem sum_n2_nn5_nn3 : (sum (n2) (nn5) (nn3)).
% 1.58/1.77 Proof.
% 1.58/1.77 assert (zenon_L1_ : (~(rdn_positive_less (rdnn (n3)) (rdnn (n5)))) -> False).
% 1.58/1.77 do 0 intro. intros zenon_H192.
% 1.58/1.77 generalize (rdn_positive_less_transitivity (n3)). zenon_intro zenon_H193.
% 1.58/1.77 generalize (zenon_H193 (n4)). zenon_intro zenon_H194.
% 1.58/1.77 generalize (zenon_H194 (n5)). zenon_intro zenon_H195.
% 1.58/1.77 apply (zenon_imply_s _ _ zenon_H195); [ zenon_intro zenon_H197 | zenon_intro zenon_H196 ].
% 1.58/1.77 apply (zenon_notand_s _ _ zenon_H197); [ zenon_intro zenon_H199 | zenon_intro zenon_H198 ].
% 1.58/1.77 exact (zenon_H199 rdn_positive_less34).
% 1.58/1.77 exact (zenon_H198 rdn_positive_less45).
% 1.58/1.77 exact (zenon_H192 zenon_H196).
% 1.58/1.77 (* end of lemma zenon_L1_ *)
% 1.58/1.77 assert (zenon_L2_ : (sum (n2) (nn5) (nn3)) -> (~(difference (nn3) (n2) (nn5))) -> False).
% 1.58/1.77 do 0 intro. intros zenon_H19a zenon_H19b.
% 1.58/1.77 generalize (minus_entry_point (nn3)). zenon_intro zenon_H19c.
% 1.58/1.77 generalize (zenon_H19c (n2)). zenon_intro zenon_H19d.
% 1.58/1.77 generalize (zenon_H19d (nn5)). zenon_intro zenon_H19e.
% 1.58/1.77 apply (zenon_equiv_s _ _ zenon_H19e); [ zenon_intro zenon_G; zenon_intro zenon_H19b | zenon_intro zenon_H19a; zenon_intro zenon_H19f ].
% 1.58/1.77 exact (zenon_G zenon_H19a).
% 1.58/1.77 exact (zenon_H19b zenon_H19f).
% 1.58/1.77 (* end of lemma zenon_L2_ *)
% 1.58/1.77 assert (zenon_L3_ : (forall RDN_Y : zenon_U, (forall RDN_Z : zenon_U, (((rdn_translate (n2) (rdn_pos (rdnn (n2))))/\((rdn_translate (nn5) (rdn_neg RDN_Y))/\((rdn_positive_less (rdnn (n2)) RDN_Y)/\((rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) RDN_Z RDN_Y)/\(rdn_translate (nn3) (rdn_neg RDN_Z))))))->(sum (n2) (nn5) (nn3))))) -> (~(difference (nn3) (n2) (nn5))) -> (rdn_positive_less (rdnn (n2)) (rdnn (n5))) -> False).
% 1.58/1.77 do 0 intro. intros zenon_H1a0 zenon_H19b zenon_H1a1.
% 1.58/1.77 generalize (zenon_H1a0 (rdnn (n5))). zenon_intro zenon_H1a2.
% 1.58/1.77 generalize (zenon_H1a2 (rdnn (n3))). zenon_intro zenon_H1a3.
% 1.58/1.77 apply (zenon_imply_s _ _ zenon_H1a3); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H19a ].
% 1.58/1.77 apply (zenon_notand_s _ _ zenon_H1a4); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1a5 ].
% 1.58/1.77 exact (zenon_H1a6 rdn2).
% 1.58/1.77 apply (zenon_notand_s _ _ zenon_H1a5); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a7 ].
% 1.58/1.77 exact (zenon_H1a8 rdnn5).
% 1.58/1.77 apply (zenon_notand_s _ _ zenon_H1a7); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1a9 ].
% 1.58/1.77 exact (zenon_H1aa zenon_H1a1).
% 1.58/1.77 apply (zenon_notand_s _ _ zenon_H1a9); [ zenon_intro zenon_H1ac | zenon_intro zenon_H1ab ].
% 1.58/1.77 generalize (add_digit_digit_digit (n0)). zenon_intro zenon_H1ad.
% 1.58/1.77 generalize (zenon_H1ad (n2)). zenon_intro zenon_H1ae.
% 1.58/1.77 generalize (zenon_H1ae (n3)). zenon_intro zenon_H1af.
% 1.58/1.77 generalize (zenon_H1af (n5)). zenon_intro zenon_H1b0.
% 1.58/1.77 generalize (zenon_H1b0 (n5)). zenon_intro zenon_H1b1.
% 1.58/1.77 apply (zenon_imply_s _ _ zenon_H1b1); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1b2 ].
% 1.58/1.77 apply (zenon_notand_s _ _ zenon_H1b3); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H1b4 ].
% 1.58/1.77 exact (zenon_H1b5 rdn_digit_add_n2_n3_n5_n0).
% 1.58/1.77 exact (zenon_H1b4 rdn_digit_add_n5_n0_n5_n0).
% 1.58/1.77 exact (zenon_H1ac zenon_H1b2).
% 1.58/1.77 exact (zenon_H1ab rdnn3).
% 1.58/1.77 apply (zenon_L2_); trivial.
% 1.58/1.77 (* end of lemma zenon_L3_ *)
% 1.58/1.77 assert (zenon_L4_ : (forall RDN_X : zenon_U, (forall RDN_Y : zenon_U, (forall RDN_Z : zenon_U, (((rdn_translate (n2) (rdn_pos RDN_X))/\((rdn_translate (nn5) (rdn_neg RDN_Y))/\((rdn_positive_less RDN_X RDN_Y)/\((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Z RDN_Y)/\(rdn_translate (nn3) (rdn_neg RDN_Z))))))->(sum (n2) (nn5) (nn3)))))) -> (rdn_positive_less (rdnn (n2)) (rdnn (n5))) -> (~(difference (nn3) (n2) (nn5))) -> False).
% 1.58/1.77 do 0 intro. intros zenon_H1b6 zenon_H1a1 zenon_H19b.
% 1.58/1.77 generalize (zenon_H1b6 (rdnn (n2))). zenon_intro zenon_H1a0.
% 1.58/1.77 apply (zenon_L3_); trivial.
% 1.58/1.77 (* end of lemma zenon_L4_ *)
% 1.58/1.77 apply NNPP. intro zenon_G.
% 1.58/1.77 generalize (minus_entry_point (nn3)). zenon_intro zenon_H19c.
% 1.58/1.77 generalize (zenon_H19c (n2)). zenon_intro zenon_H19d.
% 1.58/1.77 generalize (zenon_H19d (nn5)). zenon_intro zenon_H19e.
% 1.58/1.77 apply (zenon_equiv_s _ _ zenon_H19e); [ zenon_intro zenon_G; zenon_intro zenon_H19b | zenon_intro zenon_H19a; zenon_intro zenon_H19f ].
% 1.58/1.77 generalize (sum_entry_point_pos_neg_1 (n2)). zenon_intro zenon_H1b7.
% 1.58/1.77 generalize (zenon_H1b7 (nn5)). zenon_intro zenon_H1b8.
% 1.58/1.77 generalize (zenon_H1b8 (nn3)). zenon_intro zenon_H1b6.
% 1.58/1.77 generalize (rdn_positive_less_transitivity (n2)). zenon_intro zenon_H1b9.
% 1.58/1.77 generalize (zenon_H1b9 (n3)). zenon_intro zenon_H1ba.
% 1.58/1.77 generalize (zenon_H1ba (n5)). zenon_intro zenon_H1bb.
% 1.58/1.77 apply (zenon_imply_s _ _ zenon_H1bb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1a1 ].
% 1.58/1.77 apply (zenon_notand_s _ _ zenon_H1bc); [ zenon_intro zenon_H1bd | zenon_intro zenon_H192 ].
% 1.58/1.77 exact (zenon_H1bd rdn_positive_less23).
% 1.58/1.77 apply (zenon_L1_); trivial.
% 1.58/1.77 apply (zenon_L4_); trivial.
% 1.58/1.77 exact (zenon_G zenon_H19a).
% 1.58/1.77 Qed.
% 1.58/1.77 % SZS output end Proof
% 1.58/1.77 (* END-PROOF *)
% 1.58/1.77 nodes searched: 209145
% 1.58/1.77 max branch formulas: 4481
% 1.58/1.77 proof nodes created: 3296
% 1.58/1.77 formulas created: 238806
% 1.58/1.77
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