TSTP Solution File: NUM316+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUM316+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 : n025.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 14:41:40 EDT 2022
% Result : Theorem 0.88s 1.06s
% Output : Proof 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM316+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n025.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 02:56:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.88/1.06 % SZS status Theorem
% 0.88/1.06 (* PROOF-FOUND *)
% 0.88/1.06 (* BEGIN-PROOF *)
% 0.88/1.06 % SZS output start Proof
% 0.88/1.06 1. (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n3)))) ### Axiom
% 0.88/1.06 2. (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (-. (rdn_positive_less (rdnn (n3)) (rdnn (n4)))) ### Axiom
% 0.88/1.06 3. (-. (rdn_positive_less (rdnn (n2)) (rdnn (n4)))) (rdn_positive_less (rdnn (n2)) (rdnn (n4))) ### Axiom
% 0.88/1.06 4. (((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 (n4)))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) ### DisjTree 1 2 3
% 0.88/1.06 5. (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))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n4)))) ### All 4
% 0.88/1.06 6. (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 (n4)))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) ### All 5
% 0.88/1.06 7. (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (-. (rdn_positive_less (rdnn (n4)) (rdnn (n5)))) ### Axiom
% 0.88/1.06 8. (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (-. (rdn_translate (n2) (rdn_pos (rdnn (n2))))) ### Axiom
% 0.88/1.06 9. (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (-. (rdn_translate (nn5) (rdn_neg (rdnn (n5))))) ### Axiom
% 0.88/1.06 10. (rdn_positive_less (rdnn (n2)) (rdnn (n5))) (-. (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) ### Axiom
% 0.88/1.06 11. (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0))) (-. (rdn_digit_add (rdnn (n2)) (rdnn (n3)) (rdnn (n5)) (rdnn (n0)))) ### Axiom
% 0.88/1.06 12. (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0))) (-. (rdn_digit_add (rdnn (n5)) (rdnn (n0)) (rdnn (n5)) (rdnn (n0)))) ### Axiom
% 0.88/1.06 13. (-. (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
% 0.88/1.06 14. (((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 11 12 13
% 0.88/1.06 15. (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 14
% 0.88/1.06 16. (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 15
% 0.88/1.06 17. (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 16
% 0.88/1.06 18. (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))))))) (-. (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 17
% 0.88/1.06 19. (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_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
% 0.88/1.06 20. (rdn_translate (nn3) (rdn_neg (rdnn (n3)))) (-. (rdn_translate (nn3) (rdn_neg (rdnn (n3))))) ### Axiom
% 0.88/1.06 21. (-. (difference (nn3) (n2) (nn5))) (difference (nn3) (n2) (nn5)) ### Axiom
% 0.88/1.06 22. (sum (n2) (nn5) (nn3)) (-. (difference (nn3) (n2) (nn5))) ### Extension/test/minus_entry_point 21
% 0.88/1.06 23. (((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 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_positive_less (rdnn (n2)) (rdnn (n5))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) ### DisjTree 8 9 10 19 20 22
% 0.88/1.06 24. (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)))) (rdn_positive_less (rdnn (n2)) (rdnn (n5))) (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_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 23
% 0.88/1.06 25. (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 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_positive_less (rdnn (n2)) (rdnn (n5))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) ### All 24
% 0.88/1.06 26. (((rdn_positive_less (rdnn (n2)) (rdnn (n4))) /\ (rdn_positive_less (rdnn (n4)) (rdnn (n5)))) => (rdn_positive_less (rdnn (n2)) (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (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_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 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))))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (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))))) ### DisjTree 6 7 25
% 0.88/1.06 27. (All Z, (((rdn_positive_less (rdnn (n2)) (rdnn (n4))) /\ (rdn_positive_less (rdnn (n4)) (rdnn Z))) => (rdn_positive_less (rdnn (n2)) (rdnn Z)))) (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 (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (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 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 (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) ### All 26
% 0.88/1.06 28. (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (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_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 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))))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (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 27
% 0.88/1.06 29. (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 (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (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 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 (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) ### All 28
% 0.88/1.06 30. (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 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_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))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (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)))))) ### All 29
% 0.88/1.06 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)))))) (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 (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (-. (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 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 (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) ### All 30
% 0.88/1.06 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))))))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (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_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))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (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)))))) ### All 31
% 0.88/1.06 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)))))))) (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 (n3)) (rdnn (n4))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (-. (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 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 (nn5) (rdn_neg (rdnn (n5)))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) ### All 32
% 0.88/1.06 34. (-. (sum (n2) (nn5) (nn3))) (rdn_translate (n2) (rdn_pos (rdnn (n2)))) (rdn_translate (nn5) (rdn_neg (rdnn (n5)))) (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_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)))) (rdn_positive_less (rdnn (n4)) (rdnn (n5))) (rdn_positive_less (rdnn (n2)) (rdnn (n3))) (rdn_positive_less (rdnn (n3)) (rdnn (n4))) (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)))))) (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)))))))) ### Extension/test/not_minus_entry_point 33
% 0.88/1.06 % SZS output end Proof
% 0.88/1.06 (* END-PROOF *)
%------------------------------------------------------------------------------