%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV109+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n003.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 23:02:59 EDT 2022 % Result : Theorem 0.19s 0.49s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV109+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n003.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 : Tue Jun 14 18:48:10 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.49 (* PROOF-FOUND *) % 0.19/0.49 % SZS status Theorem % 0.19/0.49 (* BEGIN-PROOF *) % 0.19/0.49 % SZS output start Proof % 0.19/0.49 Theorem quaternion_ds1_symm_0002 : (((leq (n0) (pv5))/\((leq (n0) (pv47))/\((leq (pv5) (minus (n999) (n1)))/\((leq (pv47) (minus (n6) (n1)))/\((forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (minus (n6) (n1)))/\(leq B (minus (n6) (n1))))))->((a_select3 (q_ds1_filter) A B) = (a_select3 (q_ds1_filter) B A)))))/\((forall C : zenon_U, (forall D : zenon_U, (((leq (n0) C)/\((leq (n0) D)/\((leq C (minus (n3) (n1)))/\(leq D (minus (n3) (n1))))))->((a_select3 (r_ds1_filter) C D) = (a_select3 (r_ds1_filter) D C)))))/\((forall E : zenon_U, (forall F : zenon_U, (((leq (n0) E)/\((leq (n0) F)/\((leq E (minus (n6) (n1)))/\(leq F (minus (n6) (n1))))))->((a_select3 (pminus_ds1_filter) E F) = (a_select3 (pminus_ds1_filter) F E)))))/\((forall E : zenon_U, (forall F : zenon_U, (((leq (n0) E)/\((leq (n0) F)/\((leq E (minus (n6) (n1)))/\(leq F (minus (n6) (n1))))))->((a_select3 (pminus_ds1_filter) E F) = (a_select3 (pminus_ds1_filter) F E)))))/\(forall I : zenon_U, (((leq (n0) I)/\(leq I (minus (n6) (n1))))->(forall J : zenon_U, (((leq (n0) J)/\(leq J (minus (n6) (n1))))->((a_select3 (id_ds1_filter) I J) = (a_select3 (id_ds1_filter) J I))))))))))))))->((leq (n0) (pv5))/\((leq (pv5) (minus (n999) (n1)))/\((forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (minus (n6) (n1)))/\(leq B (minus (n6) (n1))))))->((a_select3 (q_ds1_filter) A B) = (a_select3 (q_ds1_filter) B A)))))/\((forall C : zenon_U, (forall D : zenon_U, (((leq (n0) C)/\((leq (n0) D)/\((leq C (minus (n3) (n1)))/\(leq D (minus (n3) (n1))))))->((a_select3 (r_ds1_filter) C D) = (a_select3 (r_ds1_filter) D C)))))/\((forall E : zenon_U, (forall F : zenon_U, (((leq (n0) E)/\((leq (n0) F)/\((leq E (minus (n6) (n1)))/\(leq F (minus (n6) (n1))))))->((a_select3 (pminus_ds1_filter) E F) = (a_select3 (pminus_ds1_filter) F E)))))/\((forall E : zenon_U, (forall F : zenon_U, (((leq (n0) E)/\((leq (n0) F)/\((leq E (minus (n6) (n1)))/\(leq F (minus (n6) (n1))))))->((a_select3 (pminus_ds1_filter) E F) = (a_select3 (pminus_ds1_filter) F E)))))/\(forall I : zenon_U, (((leq (n0) I)/\(leq I (minus (n6) (n1))))->(forall J : zenon_U, (((leq (n0) J)/\(leq J (minus (n6) (n1))))->((a_select3 (id_ds1_filter) I J) = (a_select3 (id_ds1_filter) J I))))))))))))). % 0.19/0.49 Proof. % 0.19/0.49 apply NNPP. intro zenon_G. % 0.19/0.49 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H67. zenon_intro zenon_H66. % 0.19/0.49 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H69. zenon_intro zenon_H68. % 0.19/0.49 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 0.19/0.49 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c. % 0.19/0.49 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 0.19/0.49 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70. % 0.19/0.49 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 0.19/0.49 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 0.19/0.49 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H75. zenon_intro zenon_H76. % 0.19/0.49 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H77. % 0.19/0.49 generalize (zenon_H77 (pv5)). zenon_intro zenon_H78. % 0.19/0.49 apply (zenon_equiv_s _ _ zenon_H78); [ zenon_intro zenon_H7b; zenon_intro zenon_H7a | zenon_intro zenon_H69; zenon_intro zenon_H79 ]. % 0.19/0.49 exact (zenon_H7b zenon_H69). % 0.19/0.49 generalize (leq_succ_gt_equiv (pv5)). zenon_intro zenon_H7c. % 0.19/0.49 generalize (zenon_H7c (minus (n999) (n1))). zenon_intro zenon_H7d. % 0.19/0.49 apply (zenon_equiv_s _ _ zenon_H7d); [ zenon_intro zenon_H80; zenon_intro zenon_H7f | zenon_intro zenon_H6d; zenon_intro zenon_H7e ]. % 0.19/0.49 exact (zenon_H80 zenon_H6d). % 0.19/0.49 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H7b | zenon_intro zenon_H81 ]. % 0.19/0.49 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H77. % 0.19/0.49 generalize (zenon_H77 (pv5)). zenon_intro zenon_H78. % 0.19/0.49 apply (zenon_equiv_s _ _ zenon_H78); [ zenon_intro zenon_H7b; zenon_intro zenon_H7a | zenon_intro zenon_H69; zenon_intro zenon_H79 ]. % 0.19/0.49 exact (zenon_H7a zenon_H79). % 0.19/0.49 exact (zenon_H7b zenon_H69). % 0.19/0.49 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H80 | zenon_intro zenon_H82 ]. % 0.19/0.49 generalize (leq_succ_gt_equiv (pv5)). zenon_intro zenon_H7c. % 0.19/0.49 generalize (zenon_H7c (minus (n999) (n1))). zenon_intro zenon_H7d. % 0.19/0.49 apply (zenon_equiv_s _ _ zenon_H7d); [ zenon_intro zenon_H80; zenon_intro zenon_H7f | zenon_intro zenon_H6d; zenon_intro zenon_H7e ]. % 0.19/0.49 exact (zenon_H7f zenon_H7e). % 0.19/0.49 exact (zenon_H80 zenon_H6d). % 0.19/0.49 apply (zenon_notand_s _ _ zenon_H82); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 0.19/0.49 exact (zenon_H84 zenon_H71). % 0.19/0.49 apply (zenon_notand_s _ _ zenon_H83); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 0.19/0.49 exact (zenon_H86 zenon_H73). % 0.19/0.49 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 0.19/0.49 exact (zenon_H88 zenon_H75). % 0.19/0.49 apply (zenon_notand_s _ _ zenon_H87); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 0.19/0.49 exact (zenon_H88 zenon_H75). % 0.19/0.49 exact (zenon_H89 zenon_H76). % 0.19/0.49 Qed. % 0.19/0.49 % SZS output end Proof % 0.19/0.49 (* END-PROOF *) % 0.19/0.49 nodes searched: 61 % 0.19/0.49 max branch formulas: 124 % 0.19/0.49 proof nodes created: 13 % 0.19/0.49 formulas created: 1896 % 0.19/0.49 %------------------------------------------------------------------------------