%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV222+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 23:03:21 EDT 2022 % Result : Theorem 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWV222+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.12/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n012.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 05:32:25 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.50 (* PROOF-FOUND *) % 0.19/0.50 % SZS status Theorem % 0.19/0.50 (* BEGIN-PROOF *) % 0.19/0.50 % SZS output start Proof % 0.19/0.50 Theorem quaternion_ds1_symm_0441 : (((forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (n5))/\(leq B (n5)))))->((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 (n2))/\(leq D (n2)))))->((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 (n5))/\(leq F (n5)))))->(((~(((n0) = E)/\((n1) = F)))/\((~(((n0) = E)/\((n2) = F)))/\((~(((n0) = E)/\((n3) = F)))/\((~(((n0) = E)/\((n4) = F)))/\((~(((n0) = E)/\((n5) = F)))/\((~(((n0) = F)/\((n1) = E)))/\((~(((n0) = F)/\((n2) = E)))/\((~(((n0) = F)/\((n3) = E)))/\((~(((n0) = F)/\((n4) = E)))/\((~(((n0) = F)/\((n5) = E)))/\((~(((n1) = E)/\((n1) = F)))/\((~(((n1) = E)/\((n2) = F)))/\((~(((n1) = E)/\((n3) = F)))/\((~(((n1) = E)/\((n4) = F)))/\((~(((n1) = E)/\((n5) = F)))/\((~(((n1) = F)/\((n2) = E)))/\((~(((n1) = F)/\((n3) = E)))/\((~(((n1) = F)/\((n4) = E)))/\((~(((n1) = F)/\((n5) = E)))/\((~(((n2) = E)/\((n2) = F)))/\((~(((n2) = E)/\((n3) = F)))/\((~(((n2) = E)/\((n4) = F)))/\((~(((n2) = E)/\((n5) = F)))/\((~(((n2) = F)/\((n3) = E)))/\((~(((n2) = F)/\((n4) = E)))/\((~(((n2) = F)/\((n5) = E)))/\((~(((n3) = E)/\((n3) = F)))/\((~(((n3) = E)/\((n4) = F)))/\((~(((n3) = E)/\((n5) = F)))/\((~(((n3) = F)/\((n4) = E)))/\((~(((n3) = F)/\((n5) = E)))/\((~(((n4) = E)/\((n4) = F)))/\((~(((n4) = E)/\((n5) = F)))/\((~(((n4) = F)/\((n5) = E)))/\((~(((n5) = E)/\((n5) = F)))/\(((n0) = E)/\(((n0) = F)/\(((n1) = E)/\((n3) = F)))))))))))))))))))))))))))))))))))))))->((a_select2 (xinit_noise) (n0)) = (n0))))))). % 0.19/0.50 Proof. % 0.19/0.50 apply NNPP. intro zenon_G. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H56. zenon_intro zenon_H55. % 0.19/0.50 apply (zenon_notallex_s (fun E : zenon_U => (forall F : zenon_U, (((leq (n0) E)/\((leq (n0) F)/\((leq E (n5))/\(leq F (n5)))))->(((~(((n0) = E)/\((n1) = F)))/\((~(((n0) = E)/\((n2) = F)))/\((~(((n0) = E)/\((n3) = F)))/\((~(((n0) = E)/\((n4) = F)))/\((~(((n0) = E)/\((n5) = F)))/\((~(((n0) = F)/\((n1) = E)))/\((~(((n0) = F)/\((n2) = E)))/\((~(((n0) = F)/\((n3) = E)))/\((~(((n0) = F)/\((n4) = E)))/\((~(((n0) = F)/\((n5) = E)))/\((~(((n1) = E)/\((n1) = F)))/\((~(((n1) = E)/\((n2) = F)))/\((~(((n1) = E)/\((n3) = F)))/\((~(((n1) = E)/\((n4) = F)))/\((~(((n1) = E)/\((n5) = F)))/\((~(((n1) = F)/\((n2) = E)))/\((~(((n1) = F)/\((n3) = E)))/\((~(((n1) = F)/\((n4) = E)))/\((~(((n1) = F)/\((n5) = E)))/\((~(((n2) = E)/\((n2) = F)))/\((~(((n2) = E)/\((n3) = F)))/\((~(((n2) = E)/\((n4) = F)))/\((~(((n2) = E)/\((n5) = F)))/\((~(((n2) = F)/\((n3) = E)))/\((~(((n2) = F)/\((n4) = E)))/\((~(((n2) = F)/\((n5) = E)))/\((~(((n3) = E)/\((n3) = F)))/\((~(((n3) = E)/\((n4) = F)))/\((~(((n3) = E)/\((n5) = F)))/\((~(((n3) = F)/\((n4) = E)))/\((~(((n3) = F)/\((n5) = E)))/\((~(((n4) = E)/\((n4) = F)))/\((~(((n4) = E)/\((n5) = F)))/\((~(((n4) = F)/\((n5) = E)))/\((~(((n5) = E)/\((n5) = F)))/\(((n0) = E)/\(((n0) = F)/\(((n1) = E)/\((n3) = F)))))))))))))))))))))))))))))))))))))))->((a_select2 (xinit_noise) (n0)) = (n0)))))) zenon_H55); [ zenon_intro zenon_H57; idtac ]. % 0.19/0.50 elim zenon_H57. zenon_intro zenon_TE_dk. zenon_intro zenon_H59. % 0.19/0.50 apply (zenon_notallex_s (fun F : zenon_U => (((leq (n0) zenon_TE_dk)/\((leq (n0) F)/\((leq zenon_TE_dk (n5))/\(leq F (n5)))))->(((~(((n0) = zenon_TE_dk)/\((n1) = F)))/\((~(((n0) = zenon_TE_dk)/\((n2) = F)))/\((~(((n0) = zenon_TE_dk)/\((n3) = F)))/\((~(((n0) = zenon_TE_dk)/\((n4) = F)))/\((~(((n0) = zenon_TE_dk)/\((n5) = F)))/\((~(((n0) = F)/\((n1) = zenon_TE_dk)))/\((~(((n0) = F)/\((n2) = zenon_TE_dk)))/\((~(((n0) = F)/\((n3) = zenon_TE_dk)))/\((~(((n0) = F)/\((n4) = zenon_TE_dk)))/\((~(((n0) = F)/\((n5) = zenon_TE_dk)))/\((~(((n1) = zenon_TE_dk)/\((n1) = F)))/\((~(((n1) = zenon_TE_dk)/\((n2) = F)))/\((~(((n1) = zenon_TE_dk)/\((n3) = F)))/\((~(((n1) = zenon_TE_dk)/\((n4) = F)))/\((~(((n1) = zenon_TE_dk)/\((n5) = F)))/\((~(((n1) = F)/\((n2) = zenon_TE_dk)))/\((~(((n1) = F)/\((n3) = zenon_TE_dk)))/\((~(((n1) = F)/\((n4) = zenon_TE_dk)))/\((~(((n1) = F)/\((n5) = zenon_TE_dk)))/\((~(((n2) = zenon_TE_dk)/\((n2) = F)))/\((~(((n2) = zenon_TE_dk)/\((n3) = F)))/\((~(((n2) = zenon_TE_dk)/\((n4) = F)))/\((~(((n2) = zenon_TE_dk)/\((n5) = F)))/\((~(((n2) = F)/\((n3) = zenon_TE_dk)))/\((~(((n2) = F)/\((n4) = zenon_TE_dk)))/\((~(((n2) = F)/\((n5) = zenon_TE_dk)))/\((~(((n3) = zenon_TE_dk)/\((n3) = F)))/\((~(((n3) = zenon_TE_dk)/\((n4) = F)))/\((~(((n3) = zenon_TE_dk)/\((n5) = F)))/\((~(((n3) = F)/\((n4) = zenon_TE_dk)))/\((~(((n3) = F)/\((n5) = zenon_TE_dk)))/\((~(((n4) = zenon_TE_dk)/\((n4) = F)))/\((~(((n4) = zenon_TE_dk)/\((n5) = F)))/\((~(((n4) = F)/\((n5) = zenon_TE_dk)))/\((~(((n5) = zenon_TE_dk)/\((n5) = F)))/\(((n0) = zenon_TE_dk)/\(((n0) = F)/\(((n1) = zenon_TE_dk)/\((n3) = F)))))))))))))))))))))))))))))))))))))))->((a_select2 (xinit_noise) (n0)) = (n0))))) zenon_H59); [ zenon_intro zenon_H5a; idtac ]. % 0.19/0.50 elim zenon_H5a. zenon_intro zenon_TF_dn. zenon_intro zenon_H5c. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_H5c). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H7a. zenon_intro zenon_H79. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H79). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H7d. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H82. zenon_intro zenon_H81. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H81). zenon_intro zenon_H84. zenon_intro zenon_H83. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H88. zenon_intro zenon_H87. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H8b). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H93). zenon_intro zenon_H96. zenon_intro zenon_H95. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H95). zenon_intro zenon_H98. zenon_intro zenon_H97. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H97). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H9c. zenon_intro zenon_H9b. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_Ha0. zenon_intro zenon_H9f. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H9f). zenon_intro zenon_Ha2. zenon_intro zenon_Ha1. % 0.19/0.50 apply (zenon_and_s _ _ zenon_Ha1). zenon_intro zenon_Ha4. zenon_intro zenon_Ha3. % 0.19/0.50 apply (zenon_and_s _ _ zenon_Ha3). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5. % 0.19/0.50 apply (zenon_and_s _ _ zenon_Ha5). zenon_intro zenon_Ha8. zenon_intro zenon_Ha7. % 0.19/0.50 apply (zenon_and_s _ _ zenon_Ha7). zenon_intro zenon_Haa. zenon_intro zenon_Ha9. % 0.19/0.51 apply (zenon_and_s _ _ zenon_Ha9). zenon_intro zenon_Hac. zenon_intro zenon_Hab. % 0.19/0.51 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_Hae | zenon_intro zenon_Had ]. % 0.19/0.51 exact (zenon_Hae zenon_Ha8). % 0.19/0.51 exact (zenon_Had zenon_Hab). % 0.19/0.51 Qed. % 0.19/0.51 % SZS output end Proof % 0.19/0.51 (* END-PROOF *) % 0.19/0.51 nodes searched: 15 % 0.19/0.51 max branch formulas: 137 % 0.19/0.51 proof nodes created: 7 % 0.19/0.51 formulas created: 1747 % 0.19/0.51 %------------------------------------------------------------------------------