%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWV028+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 : n016.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 21:49:46 EDT 2022 % Result : Theorem 2.43s 2.65s % Output : Proof 2.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV028+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n016.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 : Wed Jun 15 03:43:32 EDT 2022 % 0.12/0.33 % CPUTime : % 2.43/2.65 % SZS status Theorem % 2.43/2.65 (* PROOF-FOUND *) % 2.43/2.65 (* BEGIN-PROOF *) % 2.43/2.65 % SZS output start Proof % 2.43/2.65 1. ((init) != (init)) ### NotEqual % 2.43/2.65 2. ((s_best7_init) = (init)) ((s_best7_init) != (init)) ### Axiom % 2.43/2.65 3. ((s_sworst7_init) = (init)) ((s_sworst7_init) != (init)) ### Axiom % 2.43/2.65 4. ((s_worst7_init) = (init)) ((s_worst7_init) != (init)) ### Axiom % 2.43/2.65 5. (gt (succ (s_best7)) (n0)) (-. (gt (succ (s_best7)) (n0))) ### Axiom % 2.43/2.65 6. (-. (leq (n0) (s_best7))) (gt (succ (s_best7)) (n0)) ### Definition-Pseudo(leq) 5 % 2.43/2.65 7. (gt (succ (s_sworst7)) (n0)) (-. (gt (succ (s_sworst7)) (n0))) ### Axiom % 2.43/2.65 8. (-. (leq (n0) (s_sworst7))) (gt (succ (s_sworst7)) (n0)) ### Definition-Pseudo(leq) 7 % 2.43/2.65 9. (gt (succ (s_worst7)) (n0)) (-. (gt (succ (s_worst7)) (n0))) ### Axiom % 2.43/2.65 10. (-. (leq (n0) (s_worst7))) (gt (succ (s_worst7)) (n0)) ### Definition-Pseudo(leq) 9 % 2.43/2.65 11. (gt (succ (pv1376)) (n0)) (-. (gt (succ (pv1376)) (n0))) ### Axiom % 2.43/2.65 12. (-. (leq (n0) (pv1376))) (gt (succ (pv1376)) (n0)) ### Definition-Pseudo(leq) 11 % 2.43/2.65 13. (gt (succ (n3)) (s_best7)) (-. (gt (succ (n3)) (s_best7))) ### Axiom % 2.43/2.65 14. (-. (leq (s_best7) (n3))) (gt (succ (n3)) (s_best7)) ### Definition-Pseudo(leq) 13 % 2.43/2.65 15. (gt (succ (n3)) (s_sworst7)) (-. (gt (succ (n3)) (s_sworst7))) ### Axiom % 2.43/2.65 16. (-. (leq (s_sworst7) (n3))) (gt (succ (n3)) (s_sworst7)) ### Definition-Pseudo(leq) 15 % 2.43/2.65 17. (gt (succ (n3)) (s_worst7)) (-. (gt (succ (n3)) (s_worst7))) ### Axiom % 2.43/2.65 18. (-. (leq (s_worst7) (n3))) (gt (succ (n3)) (s_worst7)) ### Definition-Pseudo(leq) 17 % 2.43/2.65 19. (gt (succ (n3)) (pv1376)) (-. (gt (succ (n3)) (pv1376))) ### Axiom % 2.43/2.65 20. (-. (leq (pv1376) (n3))) (gt (succ (n3)) (pv1376)) ### Definition-Pseudo(leq) 19 % 2.43/2.65 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 % 2.43/2.65 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 % 2.43/2.65 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 % 2.43/2.65 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 % 2.43/2.65 25. (-. (gt (loopcounter) (n1))) (gt (loopcounter) (n1)) ### Axiom % 2.43/2.65 26. (-. ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))) (-. (gt (loopcounter) (n1))) ### NotImply 25 % 2.43/2.65 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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 (n3)) (pv1376)) (gt (succ (n3)) (s_worst7)) (gt (succ (n3)) (s_sworst7)) (gt (succ (n3)) (s_best7)) (gt (succ (pv1376)) (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 % 2.43/2.65 28. ((s_best7_init) = (init)) ((s_best7_init) != (init)) ### Axiom % 2.43/2.65 29. ((s_sworst7_init) = (init)) ((s_sworst7_init) != (init)) ### Axiom % 2.43/2.65 30. ((s_worst7_init) = (init)) ((s_worst7_init) != (init)) ### Axiom % 2.43/2.65 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 % 2.43/2.65 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 % 2.43/2.65 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 % 2.43/2.65 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 % 2.43/2.65 35. (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))) (-. (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init))))) ### Axiom % 2.43/2.65 36. (-. ((gt (loopcounter) (n1)) => (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))))) (((pvar1400_init) = (init)) /\ (((pvar1401_init) = (init)) /\ ((pvar1402_init) = (init)))) ### NotImply 35 % 2.43/2.65 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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 (n3)) (pv1376)) (gt (succ (n3)) (s_worst7)) (gt (succ (n3)) (s_sworst7)) (gt (succ (n3)) (s_best7)) (gt (succ (pv1376)) (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 % 2.43/2.65 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 (pv1376)) (n0)) (gt (succ (n3)) (s_best7)) (gt (succ (n3)) (s_sworst7)) (gt (succ (n3)) (s_worst7)) (gt (succ (n3)) (pv1376)) (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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 % 2.43/2.65 39. (leq (pv1376) (n3)) (-. (((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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 (pv1376)) (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 % 2.43/2.65 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 (pv1376)) (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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 (pv1376) (n3)) ### Definition-Pseudo(leq) 39 % 2.43/2.65 41. (leq (s_sworst7) (n3)) (leq (pv1376) (n3)) (-. (((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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 (pv1376)) (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 % 2.43/2.65 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 (pv1376)) (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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 (pv1376) (n3)) (leq (s_sworst7) (n3)) ### Definition-Pseudo(leq) 41 % 2.43/2.65 43. (leq (n0) (pv1376)) (leq (s_sworst7) (n3)) (leq (pv1376) (n3)) (-. (((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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 % 2.43/2.65 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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 (pv1376) (n3)) (leq (s_sworst7) (n3)) (leq (n0) (pv1376)) ### Definition-Pseudo(leq) 43 % 2.43/2.65 45. (leq (n0) (s_sworst7)) (leq (n0) (pv1376)) (leq (s_sworst7) (n3)) (leq (pv1376) (n3)) (-. (((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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 % 2.43/2.65 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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 (pv1376) (n3)) (leq (s_sworst7) (n3)) (leq (n0) (pv1376)) (leq (n0) (s_sworst7)) ### Definition-Pseudo(leq) 45 % 2.43/2.65 47. (-. ((((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 (n0) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv19) (minus (n410) (n1))) /\ ((leq (pv1376) (n3)) /\ ((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) (pv1376)) /\ ((leq (s_best7) (n3)) /\ ((leq (s_sworst7) (n3)) /\ ((leq (s_worst7) (n3)) /\ ((leq (pv1376) (n3)) /\ ((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 % 2.43/2.65 % SZS output end Proof % 2.43/2.65 (* END-PROOF *) %------------------------------------------------------------------------------