%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWV034+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 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 : Wed Jul 20 21:49:47 EDT 2022 % Result : Theorem 2.73s 2.95s % Output : Proof 2.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWV034+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.07/0.14 % 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 Jun 16 04:38:21 EDT 2022 % 0.13/0.35 % CPUTime : % 2.73/2.95 % SZS status Theorem % 2.73/2.95 (* PROOF-FOUND *) % 2.73/2.95 (* BEGIN-PROOF *) % 2.73/2.95 % SZS output start Proof % 2.73/2.95 1. ((init) != (init)) ### NotEqual % 2.73/2.95 2. ((s_best7_init) = (init)) ((s_best7_init) != (init)) ### Axiom % 2.73/2.95 3. ((s_sworst7_init) = (init)) ((s_sworst7_init) != (init)) ### Axiom % 2.73/2.95 4. ((s_worst7_init) = (init)) ((s_worst7_init) != (init)) ### Axiom % 2.73/2.95 5. (gt (succ (s_best7)) (n0)) (-. (gt (succ (s_best7)) (n0))) ### Axiom % 2.73/2.95 6. (-. (leq (n0) (s_best7))) (gt (succ (s_best7)) (n0)) ### Definition-Pseudo(leq) 5 % 2.73/2.95 7. (gt (succ (s_sworst7)) (n0)) (-. (gt (succ (s_sworst7)) (n0))) ### Axiom % 2.73/2.95 8. (-. (leq (n0) (s_sworst7))) (gt (succ (s_sworst7)) (n0)) ### Definition-Pseudo(leq) 7 % 2.73/2.95 9. (gt (succ (s_worst7)) (n0)) (-. (gt (succ (s_worst7)) (n0))) ### Axiom % 2.73/2.95 10. (-. (leq (n0) (s_worst7))) (gt (succ (s_worst7)) (n0)) ### Definition-Pseudo(leq) 9 % 2.73/2.95 11. (gt (succ (pv19)) (n0)) (-. (gt (succ (pv19)) (n0))) ### Axiom % 2.73/2.95 12. (-. (leq (n0) (pv19))) (gt (succ (pv19)) (n0)) ### Definition-Pseudo(leq) 11 % 2.73/2.95 13. (gt (succ (n3)) (s_best7)) (-. (gt (succ (n3)) (s_best7))) ### Axiom % 2.73/2.95 14. (-. (leq (s_best7) (n3))) (gt (succ (n3)) (s_best7)) ### Definition-Pseudo(leq) 13 % 2.73/2.95 15. (gt (succ (n3)) (s_sworst7)) (-. (gt (succ (n3)) (s_sworst7))) ### Axiom % 2.73/2.95 16. (-. (leq (s_sworst7) (n3))) (gt (succ (n3)) (s_sworst7)) ### Definition-Pseudo(leq) 15 % 2.73/2.95 17. (gt (succ (n3)) (s_worst7)) (-. (gt (succ (n3)) (s_worst7))) ### Axiom % 2.73/2.95 18. (-. (leq (s_worst7) (n3))) (gt (succ (n3)) (s_worst7)) ### Definition-Pseudo(leq) 17 % 2.73/2.95 19. (gt (succ (minus (n410) (n1))) (pv19)) (-. (gt (succ (minus (n410) (n1))) (pv19))) ### Axiom % 2.73/2.95 20. (-. (leq (pv19) (minus (n410) (n1)))) (gt (succ (minus (n410) (n1))) (pv19)) ### Definition-Pseudo(leq) 19 % 2.73/2.95 21. (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (-. (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init))))))) ### Axiom % 2.73/2.95 22. (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (-. (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init))))) ### Axiom % 2.73/2.95 23. (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (-. (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init))))) ### Axiom % 2.73/2.95 24. (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (-. (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init))))) ### Axiom % 2.73/2.95 25. (-. (gt (loopcounter) (n1))) (gt (loopcounter) (n1)) ### Axiom % 2.73/2.95 26. (-. ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))) (-. (gt (loopcounter) (n1))) ### NotImply 25 % 2.73/2.95 27. (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (-. (gt (loopcounter) (n1))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (gt (succ (minus (n410) (n1))) (pv19)) (gt (succ (n3)) (s_worst7)) (gt (succ (n3)) (s_sworst7)) (gt (succ (n3)) (s_best7)) (gt (succ (pv19)) (n0)) (gt (succ (s_worst7)) (n0)) (gt (succ (s_sworst7)) (n0)) (gt (succ (s_best7)) (n0)) ((s_worst7_init) = (init)) ((s_sworst7_init) = (init)) ((s_best7_init) = (init)) ### DisjTree 1 2 3 4 6 8 10 12 14 16 18 20 21 22 23 24 26 % 2.73/2.95 28. ((s_best7_init) = (init)) ((s_best7_init) != (init)) ### Axiom % 2.73/2.95 29. ((s_sworst7_init) = (init)) ((s_sworst7_init) != (init)) ### Axiom % 2.73/2.95 30. ((s_worst7_init) = (init)) ((s_worst7_init) != (init)) ### Axiom % 2.73/2.95 31. (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (-. (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init))))))) ### Axiom % 2.73/2.95 32. (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (-. (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init))))) ### Axiom % 2.73/2.95 33. (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (-. (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init))))) ### Axiom % 2.73/2.95 34. (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (-. (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init))))) ### Axiom % 2.73/2.95 35. (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))) (-. (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) ### Axiom % 2.73/2.95 36. (-. ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))) (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))) ### NotImply 35 % 2.73/2.95 37. (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (gt (succ (minus (n410) (n1))) (pv19)) (gt (succ (n3)) (s_worst7)) (gt (succ (n3)) (s_sworst7)) (gt (succ (n3)) (s_best7)) (gt (succ (pv19)) (n0)) (gt (succ (s_worst7)) (n0)) (gt (succ (s_sworst7)) (n0)) (gt (succ (s_best7)) (n0)) ((s_worst7_init) = (init)) ((s_sworst7_init) = (init)) ((s_best7_init) = (init)) ### DisjTree 1 28 29 30 6 8 10 12 14 16 18 20 31 32 33 34 36 % 2.73/2.95 38. ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) ((s_best7_init) = (init)) ((s_sworst7_init) = (init)) ((s_worst7_init) = (init)) (gt (succ (s_best7)) (n0)) (gt (succ (s_sworst7)) (n0)) (gt (succ (s_worst7)) (n0)) (gt (succ (pv19)) (n0)) (gt (succ (n3)) (s_best7)) (gt (succ (n3)) (s_sworst7)) (gt (succ (n3)) (s_worst7)) (gt (succ (minus (n410) (n1))) (pv19)) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) ### Imply 27 37 % 2.73/2.95 39. (leq (pv19) (minus (n410) (n1))) (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (gt (succ (n3)) (s_worst7)) (gt (succ (n3)) (s_sworst7)) (gt (succ (n3)) (s_best7)) (gt (succ (pv19)) (n0)) (gt (succ (s_worst7)) (n0)) (gt (succ (s_sworst7)) (n0)) (gt (succ (s_best7)) (n0)) ((s_worst7_init) = (init)) ((s_sworst7_init) = (init)) ((s_best7_init) = (init)) ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) ### Definition-Pseudo(leq) 38 % 2.73/2.95 40. (leq (s_worst7) (n3)) ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) ((s_best7_init) = (init)) ((s_sworst7_init) = (init)) ((s_worst7_init) = (init)) (gt (succ (s_best7)) (n0)) (gt (succ (s_sworst7)) (n0)) (gt (succ (s_worst7)) (n0)) (gt (succ (pv19)) (n0)) (gt (succ (n3)) (s_best7)) (gt (succ (n3)) (s_sworst7)) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (leq (pv19) (minus (n410) (n1))) ### Definition-Pseudo(leq) 39 % 2.73/2.95 41. (leq (s_sworst7) (n3)) (leq (pv19) (minus (n410) (n1))) (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (gt (succ (n3)) (s_best7)) (gt (succ (pv19)) (n0)) (gt (succ (s_worst7)) (n0)) (gt (succ (s_sworst7)) (n0)) (gt (succ (s_best7)) (n0)) ((s_worst7_init) = (init)) ((s_sworst7_init) = (init)) ((s_best7_init) = (init)) ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) (leq (s_worst7) (n3)) ### Definition-Pseudo(leq) 40 % 2.73/2.95 42. (leq (s_best7) (n3)) (leq (s_worst7) (n3)) ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) ((s_best7_init) = (init)) ((s_sworst7_init) = (init)) ((s_worst7_init) = (init)) (gt (succ (s_best7)) (n0)) (gt (succ (s_sworst7)) (n0)) (gt (succ (s_worst7)) (n0)) (gt (succ (pv19)) (n0)) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (leq (pv19) (minus (n410) (n1))) (leq (s_sworst7) (n3)) ### Definition-Pseudo(leq) 41 % 2.73/2.95 43. (leq (n0) (pv19)) (leq (s_sworst7) (n3)) (leq (pv19) (minus (n410) (n1))) (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (gt (succ (s_worst7)) (n0)) (gt (succ (s_sworst7)) (n0)) (gt (succ (s_best7)) (n0)) ((s_worst7_init) = (init)) ((s_sworst7_init) = (init)) ((s_best7_init) = (init)) ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) (leq (s_worst7) (n3)) (leq (s_best7) (n3)) ### Definition-Pseudo(leq) 42 % 2.73/2.95 44. (leq (n0) (s_worst7)) (leq (s_best7) (n3)) (leq (s_worst7) (n3)) ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) ((s_best7_init) = (init)) ((s_sworst7_init) = (init)) ((s_worst7_init) = (init)) (gt (succ (s_best7)) (n0)) (gt (succ (s_sworst7)) (n0)) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (leq (pv19) (minus (n410) (n1))) (leq (s_sworst7) (n3)) (leq (n0) (pv19)) ### Definition-Pseudo(leq) 43 % 2.73/2.95 45. (leq (n0) (s_sworst7)) (leq (n0) (pv19)) (leq (s_sworst7) (n3)) (leq (pv19) (minus (n410) (n1))) (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (gt (succ (s_best7)) (n0)) ((s_worst7_init) = (init)) ((s_sworst7_init) = (init)) ((s_best7_init) = (init)) ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) (leq (s_worst7) (n3)) (leq (s_best7) (n3)) (leq (n0) (s_worst7)) ### Definition-Pseudo(leq) 44 % 2.73/2.95 46. (leq (n0) (s_best7)) (leq (n0) (s_worst7)) (leq (s_best7) (n3)) (leq (s_worst7) (n3)) ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) ((s_best7_init) = (init)) ((s_sworst7_init) = (init)) ((s_worst7_init) = (init)) (All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) (All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) (All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) (All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) (-. (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))))) (leq (pv19) (minus (n410) (n1))) (leq (s_sworst7) (n3)) (leq (n0) (pv19)) (leq (n0) (s_sworst7)) ### Definition-Pseudo(leq) 45 % 2.73/2.95 47. (-. ((((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))))))))))))))))) => (((init) = (init)) /\ (((s_best7_init) = (init)) /\ (((s_sworst7_init) = (init)) /\ (((s_worst7_init) = (init)) /\ ((leq (n0) (s_best7)) /\ ((leq (n0) (s_sworst7)) /\ ((leq (n0) (s_worst7)) /\ ((leq (n0) (pv19)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((All A, (((leq (n0) A) /\ (leq A (n2))) => (All B, (((leq (n0) B) /\ (leq B (n3))) => ((a_select3 (simplex7_init) B A) = (init)))))) /\ ((All C, (((leq (n0) C) /\ (leq C (n3))) => ((a_select2 (s_values7_init) C) = (init)))) /\ ((All D, (((leq (n0) D) /\ (leq D (n2))) => ((a_select2 (s_center7_init) D) = (init)))) /\ ((All E, (((leq (n0) E) /\ (leq E (minus (n3) (n1)))) => ((a_select2 (s_try7_init) E) = (init)))) /\ ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))))))))))))))))))))) ### ConjTree 46 % 2.73/2.96 % SZS output end Proof % 2.73/2.96 (* END-PROOF *) %------------------------------------------------------------------------------