%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 15:59:05 EDT 2022 % Result : Theorem 38.56s 38.72s % Output : Proof 38.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n006.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 19:07:55 EDT 2022 % 0.12/0.33 % CPUTime : % 38.56/38.72 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 38.56/38.72 (* PROOF-FOUND *) % 38.56/38.72 % SZS status Theorem % 38.56/38.72 (* BEGIN-PROOF *) % 38.56/38.72 % SZS output start Proof % 38.56/38.72 Theorem t65_funct_1 : (forall A : zenon_U, (((relation A)/\(function A))->((one_to_one A)->((function_inverse (function_inverse A)) = A)))). % 38.56/38.72 Proof. % 38.56/38.72 assert (zenon_L1_ : forall (zenon_TA_bv : zenon_U), (relation zenon_TA_bv) -> (function zenon_TA_bv) -> (~(relation (function_inverse zenon_TA_bv))) -> False). % 38.56/38.72 do 1 intro. intros zenon_H2c zenon_H2d zenon_H2e. % 38.56/38.72 generalize (dt_k2_funct_1 zenon_TA_bv). zenon_intro zenon_H30. % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 38.56/38.72 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 38.56/38.72 exact (zenon_H34 zenon_H2c). % 38.56/38.72 exact (zenon_H33 zenon_H2d). % 38.56/38.72 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H36. zenon_intro zenon_H35. % 38.56/38.72 exact (zenon_H2e zenon_H36). % 38.56/38.72 (* end of lemma zenon_L1_ *) % 38.56/38.72 assert (zenon_L2_ : forall (zenon_TA_bv : zenon_U), (relation zenon_TA_bv) -> (function zenon_TA_bv) -> (~(function (function_inverse zenon_TA_bv))) -> False). % 38.56/38.72 do 1 intro. intros zenon_H2c zenon_H2d zenon_H37. % 38.56/38.72 generalize (dt_k2_funct_1 zenon_TA_bv). zenon_intro zenon_H30. % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 38.56/38.72 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 38.56/38.72 exact (zenon_H34 zenon_H2c). % 38.56/38.72 exact (zenon_H33 zenon_H2d). % 38.56/38.72 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H36. zenon_intro zenon_H35. % 38.56/38.72 exact (zenon_H37 zenon_H35). % 38.56/38.72 (* end of lemma zenon_L2_ *) % 38.56/38.72 apply NNPP. intro zenon_G. % 38.56/38.72 apply (zenon_notallex_s (fun A : zenon_U => (((relation A)/\(function A))->((one_to_one A)->((function_inverse (function_inverse A)) = A)))) zenon_G); [ zenon_intro zenon_H38; idtac ]. % 38.56/38.72 elim zenon_H38. zenon_intro zenon_TA_bv. zenon_intro zenon_H39. % 38.56/38.72 apply (zenon_notimply_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 38.56/38.72 apply (zenon_notimply_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 38.56/38.72 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H2c. zenon_intro zenon_H2d. % 38.56/38.72 generalize (t55_funct_1 zenon_TA_bv). zenon_intro zenon_H3e. % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H32 | zenon_intro zenon_H3f ]. % 38.56/38.72 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 38.56/38.72 exact (zenon_H34 zenon_H2c). % 38.56/38.72 exact (zenon_H33 zenon_H2d). % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 38.56/38.72 exact (zenon_H41 zenon_H3d). % 38.56/38.72 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H43. zenon_intro zenon_H42. % 38.56/38.72 generalize (t62_funct_1 zenon_TA_bv). zenon_intro zenon_H44. % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 38.56/38.72 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 38.56/38.72 exact (zenon_H34 zenon_H2c). % 38.56/38.72 exact (zenon_H33 zenon_H2d). % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H41 | zenon_intro zenon_H46 ]. % 38.56/38.72 exact (zenon_H41 zenon_H3d). % 38.56/38.72 generalize (t63_funct_1 (function_inverse zenon_TA_bv)). zenon_intro zenon_H47. % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 38.56/38.72 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H2e | zenon_intro zenon_H37 ]. % 38.56/38.72 apply (zenon_L1_ zenon_TA_bv); trivial. % 38.56/38.72 apply (zenon_L2_ zenon_TA_bv); trivial. % 38.56/38.72 generalize (zenon_H48 zenon_TA_bv). zenon_intro zenon_H4a. % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H32 | zenon_intro zenon_H4b ]. % 38.56/38.72 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 38.56/38.72 exact (zenon_H34 zenon_H2c). % 38.56/38.72 exact (zenon_H33 zenon_H2d). % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ]. % 38.56/38.72 apply (zenon_notand_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 38.56/38.72 exact (zenon_H4f zenon_H46). % 38.56/38.72 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 38.56/38.72 apply zenon_H51. apply sym_equal. exact zenon_H42. % 38.56/38.72 generalize (t61_funct_1 zenon_TA_bv). zenon_intro zenon_H52. % 38.56/38.72 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H32 | zenon_intro zenon_H53 ]. % 38.58/38.72 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 38.58/38.72 exact (zenon_H34 zenon_H2c). % 38.58/38.72 exact (zenon_H33 zenon_H2d). % 38.58/38.72 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H41 | zenon_intro zenon_H54 ]. % 38.58/38.72 exact (zenon_H41 zenon_H3d). % 38.58/38.72 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H56. zenon_intro zenon_H55. % 38.58/38.72 cut (((relation_composition (function_inverse zenon_TA_bv) zenon_TA_bv) = (identity_relation (relation_rng zenon_TA_bv))) = ((relation_composition (function_inverse zenon_TA_bv) zenon_TA_bv) = (identity_relation (relation_dom (function_inverse zenon_TA_bv))))). % 38.58/38.72 intro zenon_D_pnotp. % 38.58/38.72 apply zenon_H50. % 38.58/38.72 rewrite <- zenon_D_pnotp. % 38.58/38.72 exact zenon_H55. % 38.58/38.72 cut (((identity_relation (relation_rng zenon_TA_bv)) = (identity_relation (relation_dom (function_inverse zenon_TA_bv))))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 38.58/38.72 cut (((relation_composition (function_inverse zenon_TA_bv) zenon_TA_bv) = (relation_composition (function_inverse zenon_TA_bv) zenon_TA_bv))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 38.58/38.72 congruence. % 38.58/38.72 apply zenon_H58. apply refl_equal. % 38.58/38.72 cut (((relation_rng zenon_TA_bv) = (relation_dom (function_inverse zenon_TA_bv)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 38.58/38.72 congruence. % 38.58/38.72 exact (zenon_H59 zenon_H43). % 38.58/38.72 apply zenon_H3c. apply sym_equal. exact zenon_H4c. % 38.58/38.72 Qed. % 38.58/38.72 % SZS output end Proof % 38.58/38.72 (* END-PROOF *) % 38.58/38.72 nodes searched: 398245 % 38.58/38.72 max branch formulas: 4816 % 38.58/38.72 proof nodes created: 21830 % 38.58/38.72 formulas created: 862319 % 38.58/38.72 %------------------------------------------------------------------------------