TSTP Solution File: SEU028+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n032.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 : Tue Jul 19 15:59:04 EDT 2022
% Result : Theorem 0.42s 0.59s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.08 % Command : run_zenon %s %d
% 0.07/0.26 % Computer : n032.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Mon Jun 20 09:21:03 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.42/0.59 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.42/0.59 (* PROOF-FOUND *)
% 0.42/0.59 % SZS status Theorem
% 0.42/0.59 (* BEGIN-PROOF *)
% 0.42/0.59 % SZS output start Proof
% 0.42/0.59 Theorem t61_funct_1 : (forall A : zenon_U, (((relation A)/\(function A))->((one_to_one A)->(((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A)))/\((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))).
% 0.42/0.59 Proof.
% 0.42/0.59 assert (zenon_L1_ : forall (zenon_TA_bw : zenon_U), (relation zenon_TA_bw) -> (function zenon_TA_bw) -> (~(relation (function_inverse zenon_TA_bw))) -> False).
% 0.42/0.59 do 1 intro. intros zenon_H2d zenon_H2e zenon_H2f.
% 0.42/0.59 generalize (dt_k2_funct_1 zenon_TA_bw). zenon_intro zenon_H31.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.42/0.59 exact (zenon_H35 zenon_H2d).
% 0.42/0.59 exact (zenon_H34 zenon_H2e).
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H37. zenon_intro zenon_H36.
% 0.42/0.59 exact (zenon_H2f zenon_H37).
% 0.42/0.59 (* end of lemma zenon_L1_ *)
% 0.42/0.59 assert (zenon_L2_ : forall (zenon_TA_bw : zenon_U), (relation zenon_TA_bw) -> (function zenon_TA_bw) -> (~(function (function_inverse zenon_TA_bw))) -> False).
% 0.42/0.59 do 1 intro. intros zenon_H2d zenon_H2e zenon_H38.
% 0.42/0.59 generalize (dt_k2_funct_1 zenon_TA_bw). zenon_intro zenon_H31.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.42/0.59 exact (zenon_H35 zenon_H2d).
% 0.42/0.59 exact (zenon_H34 zenon_H2e).
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H37. zenon_intro zenon_H36.
% 0.42/0.59 exact (zenon_H38 zenon_H36).
% 0.42/0.59 (* end of lemma zenon_L2_ *)
% 0.42/0.59 assert (zenon_L3_ : forall (zenon_TA_bw : zenon_U), (~(function (relation_composition (function_inverse zenon_TA_bw) zenon_TA_bw))) -> (function zenon_TA_bw) -> (relation zenon_TA_bw) -> False).
% 0.42/0.59 do 1 intro. intros zenon_H39 zenon_H2e zenon_H2d.
% 0.42/0.59 generalize (fc1_funct_1 (function_inverse zenon_TA_bw)). zenon_intro zenon_H3a.
% 0.42/0.59 generalize (zenon_H3a zenon_TA_bw). zenon_intro zenon_H3b.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H2f | zenon_intro zenon_H3e ].
% 0.42/0.59 apply (zenon_L1_ zenon_TA_bw); trivial.
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H38 | zenon_intro zenon_H33 ].
% 0.42/0.59 apply (zenon_L2_ zenon_TA_bw); trivial.
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.42/0.59 exact (zenon_H35 zenon_H2d).
% 0.42/0.59 exact (zenon_H34 zenon_H2e).
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H40. zenon_intro zenon_H3f.
% 0.42/0.59 exact (zenon_H39 zenon_H3f).
% 0.42/0.59 (* end of lemma zenon_L3_ *)
% 0.42/0.59 apply NNPP. intro zenon_G.
% 0.42/0.59 apply (zenon_notallex_s (fun A : zenon_U => (((relation A)/\(function A))->((one_to_one A)->(((relation_composition A (function_inverse A)) = (identity_relation (relation_dom A)))/\((relation_composition (function_inverse A) A) = (identity_relation (relation_rng A))))))) zenon_G); [ zenon_intro zenon_H41; idtac ].
% 0.42/0.59 elim zenon_H41. zenon_intro zenon_TA_bw. zenon_intro zenon_H42.
% 0.42/0.59 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43.
% 0.42/0.59 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45.
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H2d. zenon_intro zenon_H2e.
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ].
% 0.42/0.59 generalize (t34_funct_1 (relation_dom zenon_TA_bw)). zenon_intro zenon_H49.
% 0.42/0.59 generalize (t58_funct_1 zenon_TA_bw). zenon_intro zenon_H4a.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H33 | zenon_intro zenon_H4b ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.42/0.59 exact (zenon_H35 zenon_H2d).
% 0.42/0.59 exact (zenon_H34 zenon_H2e).
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 0.42/0.59 exact (zenon_H4d zenon_H46).
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e.
% 0.42/0.59 generalize (zenon_H49 (relation_composition zenon_TA_bw (function_inverse zenon_TA_bw))). zenon_intro zenon_H50.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ].
% 0.42/0.59 generalize (fc1_funct_1 zenon_TA_bw). zenon_intro zenon_H55.
% 0.42/0.59 generalize (zenon_H55 (function_inverse zenon_TA_bw)). zenon_intro zenon_H56.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H58); [ zenon_intro zenon_H35 | zenon_intro zenon_H59 ].
% 0.42/0.59 exact (zenon_H35 zenon_H2d).
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H34 | zenon_intro zenon_H5a ].
% 0.42/0.59 exact (zenon_H34 zenon_H2e).
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H5a); [ zenon_intro zenon_H2f | zenon_intro zenon_H38 ].
% 0.42/0.59 apply (zenon_L1_ zenon_TA_bw); trivial.
% 0.42/0.59 apply (zenon_L2_ zenon_TA_bw); trivial.
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5c. zenon_intro zenon_H5b.
% 0.42/0.59 exact (zenon_H54 zenon_H5c).
% 0.42/0.59 generalize (fc1_funct_1 zenon_TA_bw). zenon_intro zenon_H55.
% 0.42/0.59 generalize (zenon_H55 (function_inverse zenon_TA_bw)). zenon_intro zenon_H56.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H58); [ zenon_intro zenon_H35 | zenon_intro zenon_H59 ].
% 0.42/0.59 exact (zenon_H35 zenon_H2d).
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H34 | zenon_intro zenon_H5a ].
% 0.42/0.59 exact (zenon_H34 zenon_H2e).
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H5a); [ zenon_intro zenon_H2f | zenon_intro zenon_H38 ].
% 0.42/0.59 apply (zenon_L1_ zenon_TA_bw); trivial.
% 0.42/0.59 apply (zenon_L2_ zenon_TA_bw); trivial.
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5c. zenon_intro zenon_H5b.
% 0.42/0.59 exact (zenon_H53 zenon_H5b).
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H48; zenon_intro zenon_H5f | zenon_intro zenon_H5e; zenon_intro zenon_H5d ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ].
% 0.42/0.59 exact (zenon_H61 zenon_H4f).
% 0.42/0.59 apply (zenon_notallex_s (fun C : zenon_U => ((in C (relation_dom zenon_TA_bw))->((apply (relation_composition zenon_TA_bw (function_inverse zenon_TA_bw)) C) = C))) zenon_H60); [ zenon_intro zenon_H62; idtac ].
% 0.42/0.59 elim zenon_H62. zenon_intro zenon_TC_dv. zenon_intro zenon_H64.
% 0.42/0.59 apply (zenon_notimply_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 0.42/0.59 generalize (t56_funct_1 zenon_TC_dv). zenon_intro zenon_H67.
% 0.42/0.59 generalize (zenon_H67 zenon_TA_bw). zenon_intro zenon_H68.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H33 | zenon_intro zenon_H69 ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.42/0.59 exact (zenon_H35 zenon_H2d).
% 0.42/0.59 exact (zenon_H34 zenon_H2e).
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H4d | zenon_intro zenon_H6c ].
% 0.42/0.59 exact (zenon_H4d zenon_H46).
% 0.42/0.59 exact (zenon_H6c zenon_H66).
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 0.42/0.59 apply zenon_H65. apply sym_equal. exact zenon_H6d.
% 0.42/0.59 exact (zenon_H48 zenon_H5e).
% 0.42/0.59 generalize (t34_funct_1 (relation_rng zenon_TA_bw)). zenon_intro zenon_H6f.
% 0.42/0.59 generalize (t59_funct_1 zenon_TA_bw). zenon_intro zenon_H70.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H33 | zenon_intro zenon_H71 ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.42/0.59 exact (zenon_H35 zenon_H2d).
% 0.42/0.59 exact (zenon_H34 zenon_H2e).
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H4d | zenon_intro zenon_H72 ].
% 0.42/0.59 exact (zenon_H4d zenon_H46).
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73.
% 0.42/0.59 generalize (zenon_H6f (relation_composition (function_inverse zenon_TA_bw) zenon_TA_bw)). zenon_intro zenon_H75.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ].
% 0.42/0.59 apply (zenon_notand_s _ _ zenon_H77); [ zenon_intro zenon_H78 | zenon_intro zenon_H39 ].
% 0.42/0.59 generalize (dt_k5_relat_1 (function_inverse zenon_TA_bw)). zenon_intro zenon_H79.
% 0.42/0.59 generalize (zenon_H79 zenon_TA_bw). zenon_intro zenon_H7a.
% 0.42/0.60 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H7b | zenon_intro zenon_H40 ].
% 0.42/0.60 apply (zenon_notand_s _ _ zenon_H7b); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ].
% 0.42/0.60 apply (zenon_L1_ zenon_TA_bw); trivial.
% 0.42/0.60 exact (zenon_H35 zenon_H2d).
% 0.42/0.60 exact (zenon_H78 zenon_H40).
% 0.42/0.60 apply (zenon_L3_ zenon_TA_bw); trivial.
% 0.42/0.60 apply (zenon_equiv_s _ _ zenon_H76); [ zenon_intro zenon_H47; zenon_intro zenon_H7e | zenon_intro zenon_H7d; zenon_intro zenon_H7c ].
% 0.42/0.60 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H80 | zenon_intro zenon_H7f ].
% 0.42/0.60 exact (zenon_H80 zenon_H74).
% 0.42/0.60 apply (zenon_notallex_s (fun C : zenon_U => ((in C (relation_rng zenon_TA_bw))->((apply (relation_composition (function_inverse zenon_TA_bw) zenon_TA_bw) C) = C))) zenon_H7f); [ zenon_intro zenon_H81; idtac ].
% 0.42/0.60 elim zenon_H81. zenon_intro zenon_TC_fa. zenon_intro zenon_H83.
% 0.42/0.60 apply (zenon_notimply_s _ _ zenon_H83). zenon_intro zenon_H85. zenon_intro zenon_H84.
% 0.42/0.60 generalize (t57_funct_1 zenon_TC_fa). zenon_intro zenon_H86.
% 0.42/0.60 generalize (zenon_H86 zenon_TA_bw). zenon_intro zenon_H87.
% 0.42/0.60 apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H33 | zenon_intro zenon_H88 ].
% 0.42/0.60 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.42/0.60 exact (zenon_H35 zenon_H2d).
% 0.42/0.60 exact (zenon_H34 zenon_H2e).
% 0.42/0.60 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H8a | zenon_intro zenon_H89 ].
% 0.42/0.60 apply (zenon_notand_s _ _ zenon_H8a); [ zenon_intro zenon_H4d | zenon_intro zenon_H8b ].
% 0.42/0.60 exact (zenon_H4d zenon_H46).
% 0.42/0.60 exact (zenon_H8b zenon_H85).
% 0.42/0.60 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8d. zenon_intro zenon_H8c.
% 0.42/0.60 apply zenon_H84. apply sym_equal. exact zenon_H8c.
% 0.42/0.60 exact (zenon_H47 zenon_H7d).
% 0.42/0.60 Qed.
% 0.42/0.60 % SZS output end Proof
% 0.42/0.60 (* END-PROOF *)
% 0.42/0.60 nodes searched: 9370
% 0.42/0.60 max branch formulas: 1350
% 0.42/0.60 proof nodes created: 892
% 0.42/0.60 formulas created: 26843
% 0.42/0.60
%------------------------------------------------------------------------------