TSTP Solution File: SEU219+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU219+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n009.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 16:00:20 EDT 2022
% Result : Theorem 0.84s 1.04s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU219+3 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n009.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 : Sun Jun 19 19:30:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.84/1.04 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.84/1.04 (* PROOF-FOUND *)
% 0.84/1.04 % SZS status Theorem
% 0.84/1.04 (* BEGIN-PROOF *)
% 0.84/1.04 % SZS output start Proof
% 0.84/1.04 Theorem t55_funct_1 : (forall A : zenon_U, (((relation A)/\(function A))->((one_to_one A)->(((relation_rng A) = (relation_dom (function_inverse A)))/\((relation_dom A) = (relation_rng (function_inverse A))))))).
% 0.84/1.04 Proof.
% 0.84/1.04 assert (zenon_L1_ : forall (zenon_TA_bq : zenon_U), (~((relation_rng (relation_inverse (relation_inverse zenon_TA_bq))) = (relation_rng zenon_TA_bq))) -> ((relation_inverse (relation_inverse zenon_TA_bq)) = zenon_TA_bq) -> False).
% 0.84/1.04 do 1 intro. intros zenon_H28 zenon_H29.
% 0.84/1.04 cut (((relation_inverse (relation_inverse zenon_TA_bq)) = zenon_TA_bq)); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 0.84/1.04 congruence.
% 0.84/1.04 exact (zenon_H2b zenon_H29).
% 0.84/1.04 (* end of lemma zenon_L1_ *)
% 0.84/1.04 apply NNPP. intro zenon_G.
% 0.84/1.04 apply (zenon_notallex_s (fun A : zenon_U => (((relation A)/\(function A))->((one_to_one A)->(((relation_rng A) = (relation_dom (function_inverse A)))/\((relation_dom A) = (relation_rng (function_inverse A))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ].
% 0.84/1.04 elim zenon_H2c. zenon_intro zenon_TA_bq. zenon_intro zenon_H2d.
% 0.84/1.04 apply (zenon_notimply_s _ _ zenon_H2d). zenon_intro zenon_H2f. zenon_intro zenon_H2e.
% 0.84/1.04 apply (zenon_notimply_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30.
% 0.84/1.04 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H33. zenon_intro zenon_H32.
% 0.84/1.04 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.84/1.04 generalize (involutiveness_k4_relat_1 zenon_TA_bq). zenon_intro zenon_H36.
% 0.84/1.04 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H37 | zenon_intro zenon_H29 ].
% 0.84/1.04 exact (zenon_H37 zenon_H33).
% 0.84/1.04 generalize (t37_relat_1 (relation_inverse zenon_TA_bq)). zenon_intro zenon_H38.
% 0.84/1.04 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 0.84/1.04 generalize (dt_k4_relat_1 zenon_TA_bq). zenon_intro zenon_H3b.
% 0.84/1.04 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H37 | zenon_intro zenon_H3c ].
% 0.84/1.04 exact (zenon_H37 zenon_H33).
% 0.84/1.04 exact (zenon_H3a zenon_H3c).
% 0.84/1.04 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 0.84/1.04 elim (classic ((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ].
% 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq))) = ((relation_rng zenon_TA_bq) = (relation_dom (function_inverse zenon_TA_bq)))).
% 0.84/1.04 intro zenon_D_pnotp.
% 0.84/1.04 apply zenon_H35.
% 0.84/1.04 rewrite <- zenon_D_pnotp.
% 0.84/1.04 exact zenon_H3f.
% 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H40].
% 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_rng zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H41].
% 0.84/1.04 congruence.
% 0.84/1.04 cut (((relation_dom (relation_inverse zenon_TA_bq)) = (relation_rng (relation_inverse (relation_inverse zenon_TA_bq)))) = ((relation_dom (function_inverse zenon_TA_bq)) = (relation_rng zenon_TA_bq))).
% 0.84/1.04 intro zenon_D_pnotp.
% 0.84/1.04 apply zenon_H41.
% 0.84/1.04 rewrite <- zenon_D_pnotp.
% 0.84/1.04 exact zenon_H3d.
% 0.84/1.04 cut (((relation_rng (relation_inverse (relation_inverse zenon_TA_bq))) = (relation_rng zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 0.84/1.04 cut (((relation_dom (relation_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H42].
% 0.84/1.04 congruence.
% 0.84/1.04 elim (classic ((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ].
% 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq))) = ((relation_dom (relation_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))).
% 0.84/1.04 intro zenon_D_pnotp.
% 0.84/1.04 apply zenon_H42.
% 0.84/1.04 rewrite <- zenon_D_pnotp.
% 0.84/1.04 exact zenon_H3f.
% 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H40].
% 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (relation_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H43].
% 0.84/1.04 congruence.
% 0.84/1.04 cut (((function_inverse zenon_TA_bq) = (relation_inverse zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H44].
% 0.84/1.04 congruence.
% 0.84/1.04 generalize (d9_funct_1 zenon_TA_bq). zenon_intro zenon_H45.
% 0.84/1.04 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.84/1.04 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H37 | zenon_intro zenon_H48 ].
% 0.84/1.04 exact (zenon_H37 zenon_H33).
% 0.84/1.04 exact (zenon_H48 zenon_H32).
% 0.84/1.04 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 0.84/1.04 exact (zenon_H4a zenon_H31).
% 0.84/1.04 exact (zenon_H44 zenon_H49).
% 0.84/1.04 apply zenon_H40. apply refl_equal.
% 0.84/1.04 apply zenon_H40. apply refl_equal.
% 0.84/1.04 apply (zenon_L1_ zenon_TA_bq); trivial.
% 0.84/1.04 apply zenon_H40. apply refl_equal.
% 0.84/1.04 apply zenon_H40. apply refl_equal.
% 0.84/1.04 generalize (t37_relat_1 zenon_TA_bq). zenon_intro zenon_H4b.
% 0.84/1.04 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H37 | zenon_intro zenon_H4c ].
% 0.84/1.04 exact (zenon_H37 zenon_H33).
% 0.84/1.04 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 0.84/1.04 generalize (d9_funct_1 zenon_TA_bq). zenon_intro zenon_H45.
% 0.84/1.04 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.84/1.04 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H37 | zenon_intro zenon_H48 ].
% 0.84/1.04 exact (zenon_H37 zenon_H33).
% 0.84/1.04 exact (zenon_H48 zenon_H32).
% 0.84/1.04 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 0.84/1.04 exact (zenon_H4a zenon_H31).
% 0.84/1.04 cut (((relation_dom zenon_TA_bq) = (relation_rng (relation_inverse zenon_TA_bq))) = ((relation_dom zenon_TA_bq) = (relation_rng (function_inverse zenon_TA_bq)))).
% 0.84/1.04 intro zenon_D_pnotp.
% 0.84/1.04 apply zenon_H34.
% 0.84/1.04 rewrite <- zenon_D_pnotp.
% 0.84/1.04 exact zenon_H4d.
% 0.84/1.04 cut (((relation_rng (relation_inverse zenon_TA_bq)) = (relation_rng (function_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 0.84/1.04 cut (((relation_dom zenon_TA_bq) = (relation_dom zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 0.84/1.04 congruence.
% 0.84/1.04 apply zenon_H50. apply refl_equal.
% 0.84/1.04 cut (((relation_inverse zenon_TA_bq) = (function_inverse zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H51].
% 0.84/1.04 congruence.
% 0.84/1.04 apply zenon_H51. apply sym_equal. exact zenon_H49.
% 0.84/1.04 Qed.
% 0.84/1.04 % SZS output end Proof
% 0.84/1.04 (* END-PROOF *)
% 0.84/1.04 nodes searched: 8258
% 0.84/1.04 max branch formulas: 2063
% 0.84/1.04 proof nodes created: 566
% 0.84/1.04 formulas created: 30027
% 0.84/1.04
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