%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV027+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.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 23:02:44 EDT 2022 % Result : Theorem 0.20s 0.54s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWV027+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n010.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 15 05:27:24 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.54 (* PROOF-FOUND *) % 0.20/0.54 % SZS status Theorem % 0.20/0.54 (* BEGIN-PROOF *) % 0.20/0.54 % SZS output start Proof % 0.20/0.54 Theorem gauss_init_0021 : ((((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) (pv20))/\((leq (n0) (pv1376))/\((leq (s_best7) (n3))/\((leq (s_sworst7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv19) (minus (n410) (n1)))/\((leq (pv20) (minus (n330) (n1)))/\((leq (pv1376) (n3))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init))))/\((forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init))))/\((forall E : zenon_U, (((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 (n0) (pv20))/\((leq (n0) (pv1376))/\((leq (s_best7) (n3))/\((leq (s_sworst7) (n3))/\((leq (s_worst7) (n3))/\((leq (pv19) (minus (n410) (n1)))/\((leq (pv20) (minus (n330) (n1)))/\((leq (pv1376) (n3))/\((forall A : zenon_U, (((leq (n0) A)/\(leq A (n2)))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (n3)))->((a_select3 (simplex7_init) B A) = (init))))))/\((forall C : zenon_U, (((leq (n0) C)/\(leq C (n3)))->((a_select2 (s_values7_init) C) = (init))))/\((forall D : zenon_U, (((leq (n0) D)/\(leq D (n2)))->((a_select2 (s_center7_init) D) = (init))))/\((forall E : zenon_U, (((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)))))))))))))))))))))))))). % 0.20/0.54 Proof. % 0.20/0.54 assert (zenon_L1_ : (~((init) = (init))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H64. % 0.20/0.54 apply zenon_H64. apply refl_equal. % 0.20/0.54 (* end of lemma zenon_L1_ *) % 0.20/0.54 assert (zenon_L2_ : (gt (succ (s_best7)) (n0)) -> (~(leq (n0) (s_best7))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H65 zenon_H66. % 0.20/0.54 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.20/0.54 generalize (zenon_H67 (s_best7)). zenon_intro zenon_H68. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H66; zenon_intro zenon_H6a | zenon_intro zenon_H69; zenon_intro zenon_H65 ]. % 0.20/0.54 exact (zenon_H6a zenon_H65). % 0.20/0.54 exact (zenon_H66 zenon_H69). % 0.20/0.54 (* end of lemma zenon_L2_ *) % 0.20/0.54 assert (zenon_L3_ : (gt (succ (s_sworst7)) (n0)) -> (~(leq (n0) (s_sworst7))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H6b zenon_H6c. % 0.20/0.54 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.20/0.54 generalize (zenon_H67 (s_sworst7)). zenon_intro zenon_H6d. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H6d); [ zenon_intro zenon_H6c; zenon_intro zenon_H6f | zenon_intro zenon_H6e; zenon_intro zenon_H6b ]. % 0.20/0.54 exact (zenon_H6f zenon_H6b). % 0.20/0.54 exact (zenon_H6c zenon_H6e). % 0.20/0.54 (* end of lemma zenon_L3_ *) % 0.20/0.54 assert (zenon_L4_ : (gt (succ (s_worst7)) (n0)) -> (~(leq (n0) (s_worst7))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H70 zenon_H71. % 0.20/0.54 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.20/0.54 generalize (zenon_H67 (s_worst7)). zenon_intro zenon_H72. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H71; zenon_intro zenon_H74 | zenon_intro zenon_H73; zenon_intro zenon_H70 ]. % 0.20/0.54 exact (zenon_H74 zenon_H70). % 0.20/0.54 exact (zenon_H71 zenon_H73). % 0.20/0.54 (* end of lemma zenon_L4_ *) % 0.20/0.54 assert (zenon_L5_ : (gt (succ (pv19)) (n0)) -> (~(leq (n0) (pv19))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H75 zenon_H76. % 0.20/0.54 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.20/0.54 generalize (zenon_H67 (pv19)). zenon_intro zenon_H77. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H77); [ zenon_intro zenon_H76; zenon_intro zenon_H79 | zenon_intro zenon_H78; zenon_intro zenon_H75 ]. % 0.20/0.54 exact (zenon_H79 zenon_H75). % 0.20/0.54 exact (zenon_H76 zenon_H78). % 0.20/0.54 (* end of lemma zenon_L5_ *) % 0.20/0.54 assert (zenon_L6_ : (gt (succ (pv20)) (n0)) -> (~(leq (n0) (pv20))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H7a zenon_H7b. % 0.20/0.54 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.20/0.54 generalize (zenon_H67 (pv20)). zenon_intro zenon_H7c. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H7b; zenon_intro zenon_H7e | zenon_intro zenon_H7d; zenon_intro zenon_H7a ]. % 0.20/0.54 exact (zenon_H7e zenon_H7a). % 0.20/0.54 exact (zenon_H7b zenon_H7d). % 0.20/0.54 (* end of lemma zenon_L6_ *) % 0.20/0.54 assert (zenon_L7_ : (gt (succ (pv1376)) (n0)) -> (~(leq (n0) (pv1376))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H7f zenon_H80. % 0.20/0.54 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H67. % 0.20/0.54 generalize (zenon_H67 (pv1376)). zenon_intro zenon_H81. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H80; zenon_intro zenon_H83 | zenon_intro zenon_H82; zenon_intro zenon_H7f ]. % 0.20/0.54 exact (zenon_H83 zenon_H7f). % 0.20/0.54 exact (zenon_H80 zenon_H82). % 0.20/0.54 (* end of lemma zenon_L7_ *) % 0.20/0.54 assert (zenon_L8_ : (gt (succ (n3)) (s_best7)) -> (~(leq (s_best7) (n3))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H84 zenon_H85. % 0.20/0.54 generalize (leq_succ_gt_equiv (s_best7)). zenon_intro zenon_H86. % 0.20/0.54 generalize (zenon_H86 (n3)). zenon_intro zenon_H87. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H87); [ zenon_intro zenon_H85; zenon_intro zenon_H89 | zenon_intro zenon_H88; zenon_intro zenon_H84 ]. % 0.20/0.54 exact (zenon_H89 zenon_H84). % 0.20/0.54 exact (zenon_H85 zenon_H88). % 0.20/0.54 (* end of lemma zenon_L8_ *) % 0.20/0.54 assert (zenon_L9_ : (gt (succ (n3)) (s_sworst7)) -> (~(leq (s_sworst7) (n3))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H8a zenon_H8b. % 0.20/0.54 generalize (leq_succ_gt_equiv (s_sworst7)). zenon_intro zenon_H8c. % 0.20/0.54 generalize (zenon_H8c (n3)). zenon_intro zenon_H8d. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H8d); [ zenon_intro zenon_H8b; zenon_intro zenon_H8f | zenon_intro zenon_H8e; zenon_intro zenon_H8a ]. % 0.20/0.54 exact (zenon_H8f zenon_H8a). % 0.20/0.54 exact (zenon_H8b zenon_H8e). % 0.20/0.54 (* end of lemma zenon_L9_ *) % 0.20/0.54 assert (zenon_L10_ : (gt (succ (n3)) (s_worst7)) -> (~(leq (s_worst7) (n3))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H90 zenon_H91. % 0.20/0.54 generalize (leq_succ_gt_equiv (s_worst7)). zenon_intro zenon_H92. % 0.20/0.54 generalize (zenon_H92 (n3)). zenon_intro zenon_H93. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H93); [ zenon_intro zenon_H91; zenon_intro zenon_H95 | zenon_intro zenon_H94; zenon_intro zenon_H90 ]. % 0.20/0.54 exact (zenon_H95 zenon_H90). % 0.20/0.54 exact (zenon_H91 zenon_H94). % 0.20/0.54 (* end of lemma zenon_L10_ *) % 0.20/0.54 assert (zenon_L11_ : (gt (succ (minus (n410) (n1))) (pv19)) -> (~(leq (pv19) (minus (n410) (n1)))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H96 zenon_H97. % 0.20/0.54 generalize (leq_succ_gt_equiv (pv19)). zenon_intro zenon_H98. % 0.20/0.54 generalize (zenon_H98 (minus (n410) (n1))). zenon_intro zenon_H99. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H99); [ zenon_intro zenon_H97; zenon_intro zenon_H9b | zenon_intro zenon_H9a; zenon_intro zenon_H96 ]. % 0.20/0.54 exact (zenon_H9b zenon_H96). % 0.20/0.54 exact (zenon_H97 zenon_H9a). % 0.20/0.54 (* end of lemma zenon_L11_ *) % 0.20/0.54 assert (zenon_L12_ : (gt (succ (minus (n330) (n1))) (pv20)) -> (~(leq (pv20) (minus (n330) (n1)))) -> False). % 0.20/0.54 do 0 intro. intros zenon_H9c zenon_H9d. % 0.20/0.54 generalize (leq_succ_gt_equiv (pv20)). zenon_intro zenon_H9e. % 0.20/0.54 generalize (zenon_H9e (minus (n330) (n1))). zenon_intro zenon_H9f. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H9f); [ zenon_intro zenon_H9d; zenon_intro zenon_Ha1 | zenon_intro zenon_Ha0; zenon_intro zenon_H9c ]. % 0.20/0.54 exact (zenon_Ha1 zenon_H9c). % 0.20/0.54 exact (zenon_H9d zenon_Ha0). % 0.20/0.54 (* end of lemma zenon_L12_ *) % 0.20/0.54 assert (zenon_L13_ : (gt (succ (n3)) (pv1376)) -> (~(leq (pv1376) (n3))) -> False). % 0.20/0.54 do 0 intro. intros zenon_Ha2 zenon_Ha3. % 0.20/0.54 generalize (leq_succ_gt_equiv (pv1376)). zenon_intro zenon_Ha4. % 0.20/0.54 generalize (zenon_Ha4 (n3)). zenon_intro zenon_Ha5. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_Ha5); [ zenon_intro zenon_Ha3; zenon_intro zenon_Ha7 | zenon_intro zenon_Ha6; zenon_intro zenon_Ha2 ]. % 0.20/0.54 exact (zenon_Ha7 zenon_Ha2). % 0.20/0.54 exact (zenon_Ha3 zenon_Ha6). % 0.20/0.54 (* end of lemma zenon_L13_ *) % 0.20/0.54 apply NNPP. intro zenon_G. % 0.20/0.54 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8. % 0.20/0.54 exact (zenon_Ha8 zenon_Ha9). % 0.20/0.54 Qed. % 0.20/0.54 % SZS output end Proof % 0.20/0.54 (* END-PROOF *) % 0.20/0.54 nodes searched: 110 % 0.20/0.54 max branch formulas: 146 % 0.20/0.54 proof nodes created: 59 % 0.20/0.54 formulas created: 3049 % 0.20/0.54 %------------------------------------------------------------------------------