%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM330+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 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 14:41:44 EDT 2022 % Result : Theorem 0.60s 0.80s % Output : Proof 0.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : NUM330+1 : TPTP v8.1.0. Released v3.1.0. % 0.04/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Thu Jul 7 18:50:09 EDT 2022 % 0.13/0.35 % CPUTime : % 0.60/0.80 % SZS status Theorem % 0.60/0.80 (* PROOF-FOUND *) % 0.60/0.80 (* BEGIN-PROOF *) % 0.60/0.80 % SZS output start Proof % 0.60/0.80 1. (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (-. (rdn_translate (n4) (rdn_pos (rdnn (n4))))) ### Axiom % 0.60/0.80 2. (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (-. (rdn_translate (n4) (rdn_pos (rdnn (n4))))) ### Axiom % 0.60/0.80 3. (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (-. (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0)))) ### Axiom % 0.60/0.80 4. (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (-. (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0)))) ### Axiom % 0.60/0.80 5. (-. (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn (n8)))) (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn (n8))) ### Axiom % 0.60/0.80 6. (((rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) /\ (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn (n8)))) (-. (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn (n8)))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) ### DisjTree 3 4 5 % 0.60/0.80 7. (All ID, (((rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn (n8)) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn (n8))))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (-. (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn (n8)))) ### All 6 % 0.60/0.80 8. (All RD, (All ID, (((rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn RD))))) (-. (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn (n8)))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) ### All 7 % 0.60/0.80 9. (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (-. (rdn_translate (n8) (rdn_pos (rdnn (n8))))) ### Axiom % 0.60/0.80 10. (-. (difference (n8) (n4) (n4))) (difference (n8) (n4) (n4)) ### Axiom % 0.60/0.80 11. (sum (n4) (n4) (n8)) (-. (difference (n8) (n4) (n4))) ### Extension/test/minus_entry_point 10 % 0.60/0.80 12. (((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn (n8))) /\ (rdn_translate (n8) (rdn_pos (rdnn (n8))))))) => (sum (n4) (n4) (n8))) (-. (difference (n8) (n4) (n4))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (All RD, (All ID, (((rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn RD))))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) ### DisjTree 1 2 8 9 11 % 0.60/0.80 13. (All RDN_Z, (((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) RDN_Z) /\ (rdn_translate (n8) (rdn_pos RDN_Z))))) => (sum (n4) (n4) (n8)))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (All RD, (All ID, (((rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) (rdnn RD))))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (-. (difference (n8) (n4) (n4))) ### All 12 % 0.60/0.80 14. (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn (n4)) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn D2) (rdnn RD)))))) (-. (difference (n8) (n4) (n4))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (All RDN_Z, (((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) RDN_Z) /\ (rdn_translate (n8) (rdn_pos RDN_Z))))) => (sum (n4) (n4) (n8)))) ### All 13 % 0.60/0.80 15. (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn D1) (rdnn D2) (rdnn RD))))))) (All RDN_Z, (((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) RDN_Z) /\ (rdn_translate (n8) (rdn_pos RDN_Z))))) => (sum (n4) (n4) (n8)))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (-. (difference (n8) (n4) (n4))) ### All 14 % 0.60/0.80 16. (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) (-. (difference (n8) (n4) (n4))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (All RDN_Z, (((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) (rdnn (n4)) RDN_Z) /\ (rdn_translate (n8) (rdn_pos RDN_Z))))) => (sum (n4) (n4) (n8)))) ### All 15 % 0.60/0.80 17. (All RDN_Y, (All RDN_Z, (((rdn_translate (n4) (rdn_pos (rdnn (n4)))) /\ ((rdn_translate (n4) (rdn_pos RDN_Y)) /\ ((rdn_add_with_carry (rdnn (n0)) (rdnn (n4)) RDN_Y RDN_Z) /\ (rdn_translate (n8) (rdn_pos RDN_Z))))) => (sum (n4) (n4) (n8))))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (-. (difference (n8) (n4) (n4))) (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) ### All 16 % 0.60/0.80 18. (All RDN_X, (All RDN_Y, (All RDN_Z, (((rdn_translate (n4) (rdn_pos RDN_X)) /\ ((rdn_translate (n4) (rdn_pos RDN_Y)) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Y RDN_Z) /\ (rdn_translate (n8) (rdn_pos RDN_Z))))) => (sum (n4) (n4) (n8)))))) (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) (-. (difference (n8) (n4) (n4))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) ### All 17 % 0.60/0.80 19. (All Z, (All RDN_X, (All RDN_Y, (All RDN_Z, (((rdn_translate (n4) (rdn_pos RDN_X)) /\ ((rdn_translate (n4) (rdn_pos RDN_Y)) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Y RDN_Z) /\ (rdn_translate Z (rdn_pos RDN_Z))))) => (sum (n4) (n4) Z)))))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (-. (difference (n8) (n4) (n4))) (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) ### All 18 % 0.60/0.80 20. (All Y, (All Z, (All RDN_X, (All RDN_Y, (All RDN_Z, (((rdn_translate (n4) (rdn_pos RDN_X)) /\ ((rdn_translate Y (rdn_pos RDN_Y)) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Y RDN_Z) /\ (rdn_translate Z (rdn_pos RDN_Z))))) => (sum (n4) Y Z))))))) (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) (-. (difference (n8) (n4) (n4))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) ### All 19 % 0.60/0.80 21. (All X, (All Y, (All Z, (All RDN_X, (All RDN_Y, (All RDN_Z, (((rdn_translate X (rdn_pos RDN_X)) /\ ((rdn_translate Y (rdn_pos RDN_Y)) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Y RDN_Z) /\ (rdn_translate Z (rdn_pos RDN_Z))))) => (sum X Y Z)))))))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (-. (difference (n8) (n4) (n4))) (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) ### All 20 % 0.60/0.80 22. (-. (sum (n4) (n4) (n8))) (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (All X, (All Y, (All Z, (All RDN_X, (All RDN_Y, (All RDN_Z, (((rdn_translate X (rdn_pos RDN_X)) /\ ((rdn_translate Y (rdn_pos RDN_Y)) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Y RDN_Z) /\ (rdn_translate Z (rdn_pos RDN_Z))))) => (sum X Y Z)))))))) ### Extension/test/not_minus_entry_point 21 % 0.60/0.80 23. ((n4) != (n4)) ### NotEqual % 0.60/0.80 24. (-. ((sum (n4) (n4) (n8)) /\ (((n4) = (n4)) /\ ((n4) = (n4))))) (All X, (All Y, (All Z, (All RDN_X, (All RDN_Y, (All RDN_Z, (((rdn_translate X (rdn_pos RDN_X)) /\ ((rdn_translate Y (rdn_pos RDN_Y)) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Y RDN_Z) /\ (rdn_translate Z (rdn_pos RDN_Z))))) => (sum X Y Z)))))))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) ### DisjTree 22 23 23 % 0.60/0.80 25. (-. (Ex Y, ((sum (n4) Y (n8)) /\ (((n4) = (n4)) /\ (Y = (n4)))))) (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (All X, (All Y, (All Z, (All RDN_X, (All RDN_Y, (All RDN_Z, (((rdn_translate X (rdn_pos RDN_X)) /\ ((rdn_translate Y (rdn_pos RDN_Y)) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Y RDN_Z) /\ (rdn_translate Z (rdn_pos RDN_Z))))) => (sum X Y Z)))))))) ### NotExists 24 % 0.60/0.80 26. (-. (Ex X, (Ex Y, ((sum X Y (n8)) /\ ((X = (n4)) /\ (Y = (n4))))))) (All X, (All Y, (All Z, (All RDN_X, (All RDN_Y, (All RDN_Z, (((rdn_translate X (rdn_pos RDN_X)) /\ ((rdn_translate Y (rdn_pos RDN_Y)) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Y RDN_Z) /\ (rdn_translate Z (rdn_pos RDN_Z))))) => (sum X Y Z)))))))) (rdn_translate (n4) (rdn_pos (rdnn (n4)))) (rdn_digit_add (rdnn (n8)) (rdnn (n0)) (rdnn (n8)) (rdnn (n0))) (rdn_digit_add (rdnn (n4)) (rdnn (n4)) (rdnn (n8)) (rdnn (n0))) (rdn_translate (n8) (rdn_pos (rdnn (n8)))) (All C, (All D1, (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn D1) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn C) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn C) (rdnn D1) (rdnn D2) (rdnn RD)))))))) ### NotExists 25 % 0.60/0.80 % SZS output end Proof % 0.60/0.80 (* END-PROOF *) %------------------------------------------------------------------------------