%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM324+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 : n008.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 14:41:42 EDT 2022 % Result : Theorem 28.81s 29.01s % Output : Proof 28.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM324+1 : TPTP v8.1.0. Released v3.1.0. % 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n008.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 08:54:23 EDT 2022 % 0.12/0.33 % CPUTime : % 28.81/29.01 % SZS status Theorem % 28.81/29.01 (* PROOF-FOUND *) % 28.81/29.01 (* BEGIN-PROOF *) % 28.81/29.01 % SZS output start Proof % 28.81/29.01 1. (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (-. (rdn_translate (n2) (rdn_pos (rdnn (n2))))) ### Axiom % 28.81/29.01 2. (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (-. (rdn_translate (nn5) (rdn_neg (rdnn (n5))))) ### Axiom % 28.81/29.01 3. (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n3)))) ### Axiom % 28.81/29.01 4. (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (-. (rdn_positive_less (rdnn (n3)) (rdnn (n4)))) ### Axiom % 28.81/29.01 5. (rdn_positive_less (rdnn (n2)) (rdnn (n4))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n4)))) ### Axiom % 28.81/29.01 6. (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (-. (rdn_positive_less (rdnn (n4)) (rdnn (n5)))) ### Axiom % 28.81/29.01 7. (-. (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) (rdn_positive_less (rdnn (n2)) (rdnn (n5))) ### Axiom % 28.81/29.01 8. (((rdn_positive_less (rdnn (n2)) (rdnn (n4))) /\ (rdn_positive_less (rdnn (n4)) (rdnn (n5)))) => (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n2)) (rdnn (n4))) ### DisjTree 5 6 7 % 28.81/29.01 9. (All Z, (((rdn_positive_less (rdnn (n2)) (rdnn (n4))) /\ (rdn_positive_less (rdnn (n4)) (rdnn Z))) => (rdn_positive_less (rdnn (n2)) (rdnn Z)))) (rdn_positive_less (rdnn (n2)) (rdnn (n4))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) ### All 8 % 28.81/29.01 10. (((rdn_positive_less (rdnn (n2)) (rdnn (n3))) /\ (rdn_positive_less (rdnn (n3)) (rdnn (n4)))) => (rdn_positive_less (rdnn (n2)) (rdnn (n4)))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (All Z, (((rdn_positive_less (rdnn (n2)) (rdnn (n4))) /\ (rdn_positive_less (rdnn (n4)) (rdnn Z))) => (rdn_positive_less (rdnn (n2)) (rdnn Z)))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) ### DisjTree 3 4 9 % 28.81/29.01 11. (All Z, (((rdn_positive_less (rdnn (n2)) (rdnn (n3))) /\ (rdn_positive_less (rdnn (n3)) (rdnn Z))) => (rdn_positive_less (rdnn (n2)) (rdnn Z)))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (All Z, (((rdn_positive_less (rdnn (n2)) (rdnn (n4))) /\ (rdn_positive_less (rdnn (n4)) (rdnn Z))) => (rdn_positive_less (rdnn (n2)) (rdnn Z)))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) ### All 10 % 28.81/29.01 12. (All Y, (All Z, (((rdn_positive_less (rdnn (n2)) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn (n2)) (rdnn Z))))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (All Z, (((rdn_positive_less (rdnn (n2)) (rdnn (n3))) /\ (rdn_positive_less (rdnn (n3)) (rdnn Z))) => (rdn_positive_less (rdnn (n2)) (rdnn Z)))) ### All 11 % 28.81/29.01 13. (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) (All Y, (All Z, (((rdn_positive_less (rdnn (n2)) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn (n2)) (rdnn Z))))) ### All 12 % 28.81/29.01 14. (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) ### All 13 % 28.81/29.01 15. (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (-. (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0)))) ### Axiom % 28.81/29.01 16. (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (-. (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0)))) ### Axiom % 28.81/29.01 17. (-. (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5)))) (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5))) ### Axiom % 28.81/29.01 18. (((rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) /\ (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5)))) (-. (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5)))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) ### DisjTree 15 16 17 % 28.81/29.01 19. (All ID, (((rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn (n5)) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5))))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (-. (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5)))) ### All 18 % 28.81/29.01 20. (All RD, (All ID, (((rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn RD))))) (-. (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5)))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) ### All 19 % 28.81/29.01 21. (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn (n2)) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn D2) (rdnn RD)))))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (-. (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5)))) ### All 20 % 28.81/29.01 22. (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (-. (rdn_translate (nn3) (rdn_neg (rdnn (n3))))) ### Axiom % 28.81/29.01 23. (-. (difference (nn3) (n2) (nn5))) (difference (nn3) (n2) (nn5)) ### Axiom % 28.81/29.01 24. (sum (n2) (nn5) (nn3)) (-. (difference (nn3) (n2) (nn5))) ### Definition-Pseudo(sum) 23 % 28.81/29.01 25. (((rdn_translate (n2) (rdn_pos (rdnn (n2)))) /\ ((rdn_translate (nn5) (rdn_neg (rdnn (n5)))) /\ ((rdn_positive_less (rdnn (n2)) (rdnn (n5))) /\ ((rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn (n3)) (rdnn (n5))) /\ (rdn_translate (nn3) (rdn_neg (rdnn (n3)))))))) => (sum (n2) (nn5) (nn3))) (-. (difference (nn3) (n2) (nn5))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn (n2)) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn D2) (rdnn RD)))))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) ### DisjTree 1 2 14 21 22 24 % 28.81/29.01 26. (All RDN_Z, (((rdn_translate (n2) (rdn_pos (rdnn (n2)))) /\ ((rdn_translate (nn5) (rdn_neg (rdnn (n5)))) /\ ((rdn_positive_less (rdnn (n2)) (rdnn (n5))) /\ ((rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) RDN_Z (rdnn (n5))) /\ (rdn_translate (nn3) (rdn_neg RDN_Z)))))) => (sum (n2) (nn5) (nn3)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn (n2)) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn D2) (rdnn RD)))))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (-. (difference (nn3) (n2) (nn5))) ### All 25 % 28.81/29.01 27. (All RDN_Y, (All RDN_Z, (((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_translate (nn3) (rdn_neg (rdnn (n3)))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn (n2)) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn D2) (rdnn RD)))))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) ### All 26 % 28.81/29.01 28. (All RDN_X, (All RDN_Y, (All RDN_Z, (((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_translate (n2) (rdn_pos (rdnn (n2)))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (All D2, (All RD, (All ID, (((rdn_digit_add (rdnn (n2)) (rdnn D2) (rdnn ID) (rdnn (n0))) /\ (rdn_digit_add (rdnn ID) (rdnn (n0)) (rdnn RD) (rdnn (n0)))) => (rdn_add_with_carry (rdnn (n0)) (rdnn (n2)) (rdnn D2) (rdnn RD)))))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (-. (difference (nn3) (n2) (nn5))) ### All 27 % 28.81/29.01 29. (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))))))) (-. (difference (nn3) (n2) (nn5))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (All RDN_X, (All RDN_Y, (All RDN_Z, (((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)))))) ### All 28 % 28.81/29.01 30. (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 RDN_X, (All RDN_Y, (All RDN_Z, (((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_translate (n2) (rdn_pos (rdnn (n2)))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (-. (difference (nn3) (n2) (nn5))) ### All 29 % 28.81/29.01 31. (All Z, (All RDN_X, (All RDN_Y, (All RDN_Z, (((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 Z (rdn_neg RDN_Z)))))) => (sum (n2) (nn5) Z)))))) (-. (difference (nn3) (n2) (nn5))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (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 30 % 28.81/29.01 32. (All Y, (All Z, (All RDN_X, (All RDN_Y, (All RDN_Z, (((rdn_translate (n2) (rdn_pos RDN_X)) /\ ((rdn_translate Y (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 Z (rdn_neg RDN_Z)))))) => (sum (n2) 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)))))))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (-. (difference (nn3) (n2) (nn5))) ### All 31 % 28.81/29.01 33. (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_neg RDN_Y)) /\ ((rdn_positive_less RDN_X RDN_Y) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Z RDN_Y) /\ (rdn_translate Z (rdn_neg RDN_Z)))))) => (sum X Y Z)))))))) (-. (difference (nn3) (n2) (nn5))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (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 32 % 28.81/29.01 34. (-. (sum (n2) (nn5) (nn3))) (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 (n2) (rdn_pos (rdnn (n2)))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (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_neg RDN_Y)) /\ ((rdn_positive_less RDN_X RDN_Y) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Z RDN_Y) /\ (rdn_translate Z (rdn_neg RDN_Z)))))) => (sum X Y Z)))))))) ### Definition-Pseudo(sum) 33 % 28.86/29.02 35. (-. (Ex X, (sum X (nn5) (nn3)))) (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_neg RDN_Y)) /\ ((rdn_positive_less RDN_X RDN_Y) /\ ((rdn_add_with_carry (rdnn (n0)) RDN_X RDN_Z RDN_Y) /\ (rdn_translate Z (rdn_neg RDN_Z)))))) => (sum X Y Z)))))))) (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (All X, (All Y, (All Z, (((rdn_positive_less (rdnn X) (rdnn Y)) /\ (rdn_positive_less (rdnn Y) (rdnn Z))) => (rdn_positive_less (rdnn X) (rdnn Z)))))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (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 34 % 28.86/29.02 % SZS output end Proof % 28.86/29.02 (* END-PROOF *) %------------------------------------------------------------------------------