TSTP Solution File: SEU025+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU025+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n011.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 3.89s 4.08s
% Output : Proof 3.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SEU025+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.14 % Command : run_zenon %s %d
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 16:03:09 EDT 2022
% 0.14/0.36 % CPUTime :
% 3.89/4.08 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 3.89/4.08 (* PROOF-FOUND *)
% 3.89/4.08 % SZS status Theorem
% 3.89/4.08 (* BEGIN-PROOF *)
% 3.89/4.08 % SZS output start Proof
% 3.89/4.08 Theorem t58_funct_1 : (forall A : zenon_U, (((relation A)/\(function A))->((one_to_one A)->(((relation_dom (relation_composition A (function_inverse A))) = (relation_dom A))/\((relation_rng (relation_composition A (function_inverse A))) = (relation_dom A)))))).
% 3.89/4.08 Proof.
% 3.89/4.08 assert (zenon_L1_ : forall (zenon_TA_bt : zenon_U), (relation zenon_TA_bt) -> (function zenon_TA_bt) -> (~(relation (function_inverse zenon_TA_bt))) -> False).
% 3.89/4.08 do 1 intro. intros zenon_H2a zenon_H2b zenon_H2c.
% 3.89/4.08 generalize (dt_k2_funct_1 zenon_TA_bt). zenon_intro zenon_H2e.
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 3.89/4.08 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 3.89/4.08 exact (zenon_H32 zenon_H2a).
% 3.89/4.08 exact (zenon_H31 zenon_H2b).
% 3.89/4.08 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 3.89/4.08 exact (zenon_H2c zenon_H34).
% 3.89/4.08 (* end of lemma zenon_L1_ *)
% 3.89/4.08 assert (zenon_L2_ : forall (zenon_TA_bt : zenon_U), (forall x : zenon_U, (subset x x)) -> (~(subset (relation_dom (function_inverse zenon_TA_bt)) (relation_rng zenon_TA_bt))) -> ((relation_rng zenon_TA_bt) = (relation_dom (function_inverse zenon_TA_bt))) -> False).
% 3.89/4.08 do 1 intro. intros zenon_H35 zenon_H36 zenon_H37.
% 3.89/4.08 generalize (zenon_H35 (relation_dom (function_inverse zenon_TA_bt))). zenon_intro zenon_H38.
% 3.89/4.08 cut ((subset (relation_dom (function_inverse zenon_TA_bt)) (relation_dom (function_inverse zenon_TA_bt))) = (subset (relation_dom (function_inverse zenon_TA_bt)) (relation_rng zenon_TA_bt))).
% 3.89/4.08 intro zenon_D_pnotp.
% 3.89/4.08 apply zenon_H36.
% 3.89/4.08 rewrite <- zenon_D_pnotp.
% 3.89/4.08 exact zenon_H38.
% 3.89/4.08 cut (((relation_dom (function_inverse zenon_TA_bt)) = (relation_rng zenon_TA_bt))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 3.89/4.08 cut (((relation_dom (function_inverse zenon_TA_bt)) = (relation_dom (function_inverse zenon_TA_bt)))); [idtac | apply NNPP; zenon_intro zenon_H3a].
% 3.89/4.08 congruence.
% 3.89/4.08 apply zenon_H3a. apply refl_equal.
% 3.89/4.08 apply zenon_H39. apply sym_equal. exact zenon_H37.
% 3.89/4.08 (* end of lemma zenon_L2_ *)
% 3.89/4.08 apply NNPP. intro zenon_G.
% 3.89/4.08 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_H35 | zenon_intro zenon_H3b ].
% 3.89/4.08 apply (zenon_notallex_s (fun A : zenon_U => (((relation A)/\(function A))->((one_to_one A)->(((relation_dom (relation_composition A (function_inverse A))) = (relation_dom A))/\((relation_rng (relation_composition A (function_inverse A))) = (relation_dom A)))))) zenon_G); [ zenon_intro zenon_H3c; idtac ].
% 3.89/4.08 elim zenon_H3c. zenon_intro zenon_TA_bt. zenon_intro zenon_H3d.
% 3.89/4.08 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e.
% 3.89/4.08 apply (zenon_notimply_s _ _ zenon_H3e). zenon_intro zenon_H41. zenon_intro zenon_H40.
% 3.89/4.08 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H2a. zenon_intro zenon_H2b.
% 3.89/4.08 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ].
% 3.89/4.08 generalize (t46_relat_1 zenon_TA_bt). zenon_intro zenon_H44.
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ].
% 3.89/4.08 exact (zenon_H32 zenon_H2a).
% 3.89/4.08 generalize (t55_funct_1 zenon_TA_bt). zenon_intro zenon_H46.
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H30 | zenon_intro zenon_H47 ].
% 3.89/4.08 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 3.89/4.08 exact (zenon_H32 zenon_H2a).
% 3.89/4.08 exact (zenon_H31 zenon_H2b).
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 3.89/4.08 exact (zenon_H49 zenon_H41).
% 3.89/4.08 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H37. zenon_intro zenon_H4a.
% 3.89/4.08 generalize (zenon_H45 (function_inverse zenon_TA_bt)). zenon_intro zenon_H4b.
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H2c | zenon_intro zenon_H4c ].
% 3.89/4.08 apply (zenon_L1_ zenon_TA_bt); trivial.
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ].
% 3.89/4.08 generalize (zenon_H35 (relation_rng zenon_TA_bt)). zenon_intro zenon_H4f.
% 3.89/4.08 cut ((subset (relation_rng zenon_TA_bt) (relation_rng zenon_TA_bt)) = (subset (relation_rng zenon_TA_bt) (relation_dom (function_inverse zenon_TA_bt)))).
% 3.89/4.08 intro zenon_D_pnotp.
% 3.89/4.08 apply zenon_H4e.
% 3.89/4.08 rewrite <- zenon_D_pnotp.
% 3.89/4.08 exact zenon_H4f.
% 3.89/4.08 cut (((relation_rng zenon_TA_bt) = (relation_dom (function_inverse zenon_TA_bt)))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 3.89/4.08 cut (((relation_rng zenon_TA_bt) = (relation_rng zenon_TA_bt))); [idtac | apply NNPP; zenon_intro zenon_H51].
% 3.89/4.08 congruence.
% 3.89/4.08 apply zenon_H51. apply refl_equal.
% 3.89/4.08 exact (zenon_H50 zenon_H37).
% 3.89/4.08 exact (zenon_H43 zenon_H4d).
% 3.89/4.08 generalize (t47_relat_1 (function_inverse zenon_TA_bt)). zenon_intro zenon_H52.
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H2c | zenon_intro zenon_H53 ].
% 3.89/4.08 apply (zenon_L1_ zenon_TA_bt); trivial.
% 3.89/4.08 generalize (t55_funct_1 zenon_TA_bt). zenon_intro zenon_H46.
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H30 | zenon_intro zenon_H47 ].
% 3.89/4.08 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 3.89/4.08 exact (zenon_H32 zenon_H2a).
% 3.89/4.08 exact (zenon_H31 zenon_H2b).
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 3.89/4.08 exact (zenon_H49 zenon_H41).
% 3.89/4.08 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H37. zenon_intro zenon_H4a.
% 3.89/4.08 generalize (zenon_H53 zenon_TA_bt). zenon_intro zenon_H54.
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H32 | zenon_intro zenon_H55 ].
% 3.89/4.08 exact (zenon_H32 zenon_H2a).
% 3.89/4.08 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H36 | zenon_intro zenon_H56 ].
% 3.89/4.08 apply (zenon_L2_ zenon_TA_bt); trivial.
% 3.89/4.08 elim (classic ((relation_dom zenon_TA_bt) = (relation_dom zenon_TA_bt))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ].
% 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_dom zenon_TA_bt)) = ((relation_rng (relation_composition zenon_TA_bt (function_inverse zenon_TA_bt))) = (relation_dom zenon_TA_bt))).
% 3.89/4.08 intro zenon_D_pnotp.
% 3.89/4.08 apply zenon_H42.
% 3.89/4.08 rewrite <- zenon_D_pnotp.
% 3.89/4.08 exact zenon_H57.
% 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_dom zenon_TA_bt))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_rng (relation_composition zenon_TA_bt (function_inverse zenon_TA_bt))))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 3.89/4.08 congruence.
% 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_rng (function_inverse zenon_TA_bt))) = ((relation_dom zenon_TA_bt) = (relation_rng (relation_composition zenon_TA_bt (function_inverse zenon_TA_bt))))).
% 3.89/4.08 intro zenon_D_pnotp.
% 3.89/4.08 apply zenon_H59.
% 3.89/4.08 rewrite <- zenon_D_pnotp.
% 3.89/4.08 exact zenon_H4a.
% 3.89/4.08 cut (((relation_rng (function_inverse zenon_TA_bt)) = (relation_rng (relation_composition zenon_TA_bt (function_inverse zenon_TA_bt))))); [idtac | apply NNPP; zenon_intro zenon_H5a].
% 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_dom zenon_TA_bt))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 3.89/4.08 congruence.
% 3.89/4.08 apply zenon_H58. apply refl_equal.
% 3.89/4.08 apply zenon_H5a. apply sym_equal. exact zenon_H56.
% 3.89/4.08 apply zenon_H58. apply refl_equal.
% 3.89/4.08 apply zenon_H58. apply refl_equal.
% 3.89/4.08 apply zenon_H3b. zenon_intro zenon_Tx_dn. apply NNPP. zenon_intro zenon_H5c.
% 3.89/4.08 generalize (reflexivity_r1_tarski zenon_Tx_dn). zenon_intro zenon_H0.
% 3.89/4.08 generalize (zenon_H0 zenon_E). zenon_intro zenon_H5d.
% 3.89/4.08 exact (zenon_H5c zenon_H5d).
% 3.89/4.08 Qed.
% 3.89/4.08 % SZS output end Proof
% 3.89/4.08 (* END-PROOF *)
% 3.89/4.08 nodes searched: 94387
% 3.89/4.08 max branch formulas: 3355
% 3.89/4.08 proof nodes created: 5388
% 3.89/4.08 formulas created: 189716
% 3.89/4.08
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