TSTP Solution File: NUM306+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : NUM306+1 : TPTP v8.1.0. Released v3.1.0.
% 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 15:54:47 EDT 2022
% Result : Theorem 27.70s 27.87s
% Output : Proof 27.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM306+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n013.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 Jul 5 12:07:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 27.70/27.87 (* PROOF-FOUND *)
% 27.70/27.87 % SZS status Theorem
% 27.70/27.87 (* BEGIN-PROOF *)
% 27.70/27.87 % SZS output start Proof
% 27.70/27.87 Theorem sum_n23_n34_n57 : (sum (n23) (n34) (n57)).
% 27.70/27.87 Proof.
% 27.70/27.87 assert (zenon_L1_ : (~(rdn_non_zero (rdnn (n2)))) -> False).
% 27.70/27.87 do 0 intro. intros zenon_H192.
% 27.70/27.87 generalize (rdn_non_zero_by_digit (n2)). zenon_intro zenon_H193.
% 27.70/27.87 apply (zenon_imply_s _ _ zenon_H193); [ zenon_intro zenon_H195 | zenon_intro zenon_H194 ].
% 27.70/27.87 exact (zenon_H195 rdn_digit2).
% 27.70/27.87 exact (zenon_H192 zenon_H194).
% 27.70/27.87 (* end of lemma zenon_L1_ *)
% 27.70/27.87 assert (zenon_L2_ : (~(rdn_non_zero (rdnn (n3)))) -> False).
% 27.70/27.87 do 0 intro. intros zenon_H196.
% 27.70/27.87 generalize (rdn_non_zero_by_digit (n3)). zenon_intro zenon_H197.
% 27.70/27.87 apply (zenon_imply_s _ _ zenon_H197); [ zenon_intro zenon_H199 | zenon_intro zenon_H198 ].
% 27.70/27.87 exact (zenon_H199 rdn_digit3).
% 27.70/27.87 exact (zenon_H196 zenon_H198).
% 27.70/27.87 (* end of lemma zenon_L2_ *)
% 27.70/27.87 assert (zenon_L3_ : (~(rdn_non_zero (rdnn (n5)))) -> False).
% 27.70/27.87 do 0 intro. intros zenon_H19a.
% 27.70/27.87 generalize (rdn_non_zero_by_digit (n5)). zenon_intro zenon_H19b.
% 27.70/27.87 apply (zenon_imply_s _ _ zenon_H19b); [ zenon_intro zenon_H19d | zenon_intro zenon_H19c ].
% 27.70/27.87 exact (zenon_H19d rdn_digit5).
% 27.70/27.87 exact (zenon_H19a zenon_H19c).
% 27.70/27.87 (* end of lemma zenon_L3_ *)
% 27.70/27.87 assert (zenon_L4_ : (forall RC : zenon_U, (((rdn_digit_add (rdnn (n3)) (rdnn (n4)) (rdnn (n7)) (rdnn (n0)))/\((rdn_digit_add (rdnn (n7)) (rdnn (n0)) (rdnn (n7)) (rdnn (n0)))/\((rdn_digit_add (rdnn (n0)) (rdnn (n0)) (rdnn RC) (rdnn (n0)))/\((rdn_add_with_carry (rdnn RC) (rdnn (n2)) (rdnn (n3)) (rdnn (n5)))/\((rdn_non_zero (rdnn (n2)))/\((rdn_non_zero (rdnn (n3)))/\(rdn_non_zero (rdnn (n5)))))))))->(rdn_add_with_carry (rdnn (n0)) (rdn (rdnn (n3)) (rdnn (n2))) (rdn (rdnn (n4)) (rdnn (n3))) (rdn (rdnn (n7)) (rdnn (n5)))))) -> (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5))) -> (~(rdn_add_with_carry (rdnn (n0)) (rdn (rdnn (n3)) (rdnn (n2))) (rdn (rdnn (n4)) (rdnn (n3))) (rdn (rdnn (n7)) (rdnn (n5))))) -> False).
% 27.70/27.87 do 0 intro. intros zenon_H19e zenon_H19f zenon_H1a0.
% 27.70/27.87 generalize (zenon_H19e (n0)). zenon_intro zenon_H1a1.
% 27.70/27.87 apply (zenon_imply_s _ _ zenon_H1a1); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a2 ].
% 27.70/27.87 apply (zenon_notand_s _ _ zenon_H1a3); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H1a4 ].
% 27.70/27.87 exact (zenon_H1a5 rdn_digit_add_n3_n4_n7_n0).
% 27.70/27.87 apply (zenon_notand_s _ _ zenon_H1a4); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H1a6 ].
% 27.70/27.87 exact (zenon_H1a7 rdn_digit_add_n7_n0_n7_n0).
% 27.70/27.87 apply (zenon_notand_s _ _ zenon_H1a6); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H1a8 ].
% 27.70/27.87 exact (zenon_H1a9 rdn_digit_add_n0_n0_n0_n0).
% 27.70/27.87 apply (zenon_notand_s _ _ zenon_H1a8); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1aa ].
% 27.70/27.87 exact (zenon_H1ab zenon_H19f).
% 27.70/27.87 apply (zenon_notand_s _ _ zenon_H1aa); [ zenon_intro zenon_H192 | zenon_intro zenon_H1ac ].
% 27.70/27.87 apply (zenon_L1_); trivial.
% 27.70/27.87 apply (zenon_notand_s _ _ zenon_H1ac); [ zenon_intro zenon_H196 | zenon_intro zenon_H19a ].
% 27.70/27.87 apply (zenon_L2_); trivial.
% 27.70/27.87 apply (zenon_L3_); trivial.
% 27.70/27.87 exact (zenon_H1a0 zenon_H1a2).
% 27.70/27.87 (* end of lemma zenon_L4_ *)
% 27.70/27.87 assert (zenon_L5_ : (sum (n23) (n34) (n57)) -> (~(difference (n57) (n23) (n34))) -> False).
% 27.70/27.87 do 0 intro. intros zenon_H1ad zenon_H1ae.
% 27.70/27.87 generalize (minus_entry_point (n57)). zenon_intro zenon_H1af.
% 27.70/27.87 generalize (zenon_H1af (n23)). zenon_intro zenon_H1b0.
% 27.70/27.87 generalize (zenon_H1b0 (n34)). zenon_intro zenon_H1b1.
% 27.70/27.87 apply (zenon_equiv_s _ _ zenon_H1b1); [ zenon_intro zenon_G; zenon_intro zenon_H1ae | zenon_intro zenon_H1ad; zenon_intro zenon_H1b2 ].
% 27.70/27.87 exact (zenon_G zenon_H1ad).
% 27.70/27.87 exact (zenon_H1ae zenon_H1b2).
% 27.70/27.87 (* end of lemma zenon_L5_ *)
% 27.70/27.87 apply NNPP. intro zenon_G.
% 27.70/27.87 generalize (minus_entry_point (n57)). zenon_intro zenon_H1af.
% 27.70/27.87 generalize (zenon_H1af (n23)). zenon_intro zenon_H1b0.
% 27.70/27.87 generalize (zenon_H1b0 (n34)). zenon_intro zenon_H1b1.
% 27.70/27.87 apply (zenon_equiv_s _ _ zenon_H1b1); [ zenon_intro zenon_G; zenon_intro zenon_H1ae | zenon_intro zenon_H1ad; zenon_intro zenon_H1b2 ].
% 27.70/27.87 generalize (sum_entry_point_pos_pos (n23)). zenon_intro zenon_H1b3.
% 27.70/27.87 generalize (zenon_H1b3 (n34)). zenon_intro zenon_H1b4.
% 27.70/27.87 generalize (zenon_H1b4 (n57)). zenon_intro zenon_H1b5.
% 27.70/27.87 generalize (zenon_H1b5 (rdn (rdnn (n3)) (rdnn (n2)))). zenon_intro zenon_H1b6.
% 27.70/27.87 generalize (zenon_H1b6 (rdn (rdnn (n4)) (rdnn (n3)))). zenon_intro zenon_H1b7.
% 27.70/27.88 generalize (zenon_H1b7 (rdn (rdnn (n7)) (rdnn (n5)))). zenon_intro zenon_H1b8.
% 27.70/27.88 apply (zenon_imply_s _ _ zenon_H1b8); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ad ].
% 27.70/27.88 apply (zenon_notand_s _ _ zenon_H1b9); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1ba ].
% 27.70/27.88 exact (zenon_H1bb rdn23).
% 27.70/27.88 apply (zenon_notand_s _ _ zenon_H1ba); [ zenon_intro zenon_H1bd | zenon_intro zenon_H1bc ].
% 27.70/27.88 exact (zenon_H1bd rdn34).
% 27.70/27.88 apply (zenon_notand_s _ _ zenon_H1bc); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1be ].
% 27.70/27.88 generalize (add_rdn_rdn_rdn (n0)). zenon_intro zenon_H1bf.
% 27.70/27.88 generalize (zenon_H1bf (n3)). zenon_intro zenon_H1c0.
% 27.70/27.88 generalize (zenon_H1c0 (rdnn (n2))). zenon_intro zenon_H1c1.
% 27.70/27.88 generalize (zenon_H1c1 (n4)). zenon_intro zenon_H1c2.
% 27.70/27.88 generalize (zenon_H1c2 (rdnn (n3))). zenon_intro zenon_H1c3.
% 27.70/27.88 generalize (zenon_H1c3 (n7)). zenon_intro zenon_H1c4.
% 27.70/27.88 generalize (zenon_H1c4 (rdnn (n5))). zenon_intro zenon_H1c5.
% 27.70/27.88 generalize (zenon_H1c5 (n7)). zenon_intro zenon_H1c6.
% 27.70/27.88 generalize (zenon_H1c6 (n0)). zenon_intro zenon_H1c7.
% 27.70/27.88 generalize (zenon_H1c7 (n0)). zenon_intro zenon_H19e.
% 27.70/27.88 generalize (add_digit_digit_digit (n0)). zenon_intro zenon_H1c8.
% 27.70/27.88 generalize (zenon_H1c8 (n2)). zenon_intro zenon_H1c9.
% 27.70/27.88 generalize (zenon_H1c9 (n3)). zenon_intro zenon_H1ca.
% 27.70/27.88 generalize (zenon_H1ca (n5)). zenon_intro zenon_H1cb.
% 27.70/27.88 generalize (zenon_H1cb (n5)). zenon_intro zenon_H1cc.
% 27.70/27.88 apply (zenon_imply_s _ _ zenon_H1cc); [ zenon_intro zenon_H1cd | zenon_intro zenon_H19f ].
% 27.70/27.88 apply (zenon_notand_s _ _ zenon_H1cd); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1ce ].
% 27.70/27.88 exact (zenon_H1cf rdn_digit_add_n2_n3_n5_n0).
% 27.70/27.88 exact (zenon_H1ce rdn_digit_add_n5_n0_n5_n0).
% 27.70/27.88 apply (zenon_L4_); trivial.
% 27.70/27.88 exact (zenon_H1be rdn57).
% 27.70/27.88 apply (zenon_L5_); trivial.
% 27.70/27.88 exact (zenon_G zenon_H1ad).
% 27.70/27.88 Qed.
% 27.70/27.88 % SZS output end Proof
% 27.70/27.88 (* END-PROOF *)
% 27.70/27.88 nodes searched: 798203
% 27.70/27.88 max branch formulas: 88143
% 27.70/27.88 proof nodes created: 16857
% 27.70/27.88 formulas created: 3226897
% 27.70/27.88
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