%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM327+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 15:54:54 EDT 2022 % Result : Theorem 0.83s 1.00s % Output : Proof 0.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM327+1 : TPTP v8.1.0. Released v3.1.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jul 6 00:25:22 EDT 2022 % 0.13/0.34 % CPUTime : % 0.83/1.00 (* PROOF-FOUND *) % 0.83/1.00 % SZS status Theorem % 0.83/1.00 (* BEGIN-PROOF *) % 0.83/1.00 % SZS output start Proof % 0.83/1.00 Theorem sum_zero_identity : (exists X : zenon_U, (sum X (n0) X)). % 0.83/1.00 Proof. % 0.83/1.00 assert (zenon_L1_ : (sum (n0) (n0) (n0)) -> (~(difference (n0) (n0) (n0))) -> False). % 0.83/1.00 do 0 intro. intros zenon_H192 zenon_H193. % 0.83/1.00 generalize (minus_entry_point (n0)). zenon_intro zenon_H194. % 0.83/1.00 generalize (zenon_H194 (n0)). zenon_intro zenon_H195. % 0.83/1.00 generalize (zenon_H195 (n0)). zenon_intro zenon_H196. % 0.83/1.00 apply (zenon_equiv_s _ _ zenon_H196); [ zenon_intro zenon_H198; zenon_intro zenon_H193 | zenon_intro zenon_H192; zenon_intro zenon_H197 ]. % 0.83/1.00 exact (zenon_H198 zenon_H192). % 0.83/1.00 exact (zenon_H193 zenon_H197). % 0.83/1.00 (* end of lemma zenon_L1_ *) % 0.83/1.00 apply NNPP. intro zenon_G. % 0.83/1.00 apply zenon_G. exists (n0). apply NNPP. zenon_intro zenon_H198. % 0.83/1.00 generalize (minus_entry_point (n0)). zenon_intro zenon_H194. % 0.83/1.00 generalize (zenon_H194 (n0)). zenon_intro zenon_H195. % 0.83/1.00 generalize (zenon_H195 (n0)). zenon_intro zenon_H196. % 0.83/1.00 apply (zenon_equiv_s _ _ zenon_H196); [ zenon_intro zenon_H198; zenon_intro zenon_H193 | zenon_intro zenon_H192; zenon_intro zenon_H197 ]. % 0.83/1.00 generalize (sum_entry_point_pos_pos (n0)). zenon_intro zenon_H199. % 0.83/1.00 generalize (zenon_H199 (n0)). zenon_intro zenon_H19a. % 0.83/1.00 generalize (zenon_H19a (n0)). zenon_intro zenon_H19b. % 0.83/1.00 generalize (zenon_H19b (rdnn (n0))). zenon_intro zenon_H19c. % 0.83/1.00 generalize (zenon_H19c (rdnn (n0))). zenon_intro zenon_H19d. % 0.83/1.00 generalize (zenon_H19d (rdnn (n0))). zenon_intro zenon_H19e. % 0.83/1.00 apply (zenon_imply_s _ _ zenon_H19e); [ zenon_intro zenon_H19f | zenon_intro zenon_H192 ]. % 0.83/1.00 apply (zenon_notand_s _ _ zenon_H19f); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H1a0 ]. % 0.83/1.00 exact (zenon_H1a1 rdn0). % 0.83/1.00 apply (zenon_notand_s _ _ zenon_H1a0); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H1a2 ]. % 0.83/1.00 exact (zenon_H1a1 rdn0). % 0.83/1.00 apply (zenon_notand_s _ _ zenon_H1a2); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ]. % 0.83/1.00 generalize (add_digit_digit_digit (n0)). zenon_intro zenon_H1a4. % 0.83/1.00 generalize (zenon_H1a4 (n0)). zenon_intro zenon_H1a5. % 0.83/1.00 generalize (zenon_H1a5 (n0)). zenon_intro zenon_H1a6. % 0.83/1.00 generalize (zenon_H1a6 (n0)). zenon_intro zenon_H1a7. % 0.83/1.00 generalize (zenon_H1a7 (n0)). zenon_intro zenon_H1a8. % 0.83/1.00 apply (zenon_imply_s _ _ zenon_H1a8); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1a9 ]. % 0.83/1.00 apply (zenon_notand_s _ _ zenon_H1aa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1ab ]. % 0.83/1.00 exact (zenon_H1ab rdn_digit_add_n0_n0_n0_n0). % 0.83/1.00 exact (zenon_H1ab rdn_digit_add_n0_n0_n0_n0). % 0.83/1.00 exact (zenon_H1a3 zenon_H1a9). % 0.83/1.00 exact (zenon_H1a1 rdn0). % 0.83/1.00 apply (zenon_L1_); trivial. % 0.83/1.00 exact (zenon_H198 zenon_H192). % 0.83/1.00 Qed. % 0.83/1.00 % SZS output end Proof % 0.83/1.00 (* END-PROOF *) % 0.83/1.00 nodes searched: 15784 % 0.83/1.00 max branch formulas: 4291 % 0.83/1.00 proof nodes created: 438 % 0.83/1.00 formulas created: 140484 % 0.83/1.00 %------------------------------------------------------------------------------