TSTP Solution File: SEU089+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n015.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 15:59:19 EDT 2022
% Result : Theorem 0.78s 0.94s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : run_zenon %s %d
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 04:25:44 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.78/0.94 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.78/0.94 (* PROOF-FOUND *)
% 0.78/0.94 % SZS status Theorem
% 0.78/0.94 (* BEGIN-PROOF *)
% 0.78/0.94 % SZS output start Proof
% 0.78/0.94 Theorem t20_finset_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((finite A)/\((finite B)/\(finite C)))->(finite (cartesian_product3 A B C)))))).
% 0.78/0.94 Proof.
% 0.78/0.94 assert (zenon_L1_ : forall (zenon_TC_ck : zenon_U) (zenon_TB_cl : zenon_U) (zenon_TA_cm : zenon_U), (~(finite (cartesian_product3 zenon_TA_cm zenon_TB_cl zenon_TC_ck))) -> (finite (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)) -> False).
% 0.78/0.94 do 3 intro. intros zenon_H3c zenon_H3d.
% 0.78/0.94 cut ((finite (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)) = (finite (cartesian_product3 zenon_TA_cm zenon_TB_cl zenon_TC_ck))).
% 0.78/0.94 intro zenon_D_pnotp.
% 0.78/0.94 apply zenon_H3c.
% 0.78/0.94 rewrite <- zenon_D_pnotp.
% 0.78/0.94 exact zenon_H3d.
% 0.78/0.94 cut (((cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck) = (cartesian_product3 zenon_TA_cm zenon_TB_cl zenon_TC_ck))); [idtac | apply NNPP; zenon_intro zenon_H41].
% 0.78/0.94 congruence.
% 0.78/0.94 generalize (d3_zfmisc_1 zenon_TA_cm). zenon_intro zenon_H42.
% 0.78/0.94 generalize (zenon_H42 zenon_TB_cl). zenon_intro zenon_H43.
% 0.78/0.94 generalize (zenon_H43 zenon_TC_ck). zenon_intro zenon_H44.
% 0.78/0.94 apply (zenon_congruence_lr_s _ (fun zenon_Vg : _ => (~((cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck) = zenon_Vg))) _ _ zenon_H41 zenon_H44). zenon_intro zenon_H45.
% 0.78/0.94 apply zenon_H45. apply refl_equal.
% 0.78/0.94 (* end of lemma zenon_L1_ *)
% 0.78/0.94 apply NNPP. intro zenon_G.
% 0.78/0.94 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_H46 | zenon_intro zenon_H47 ].
% 0.78/0.94 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((finite A)/\((finite B)/\(finite C)))->(finite (cartesian_product3 A B C)))))) zenon_G); [ zenon_intro zenon_H48; idtac ].
% 0.78/0.94 elim zenon_H48. zenon_intro zenon_TA_cm. zenon_intro zenon_H49.
% 0.78/0.94 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((finite zenon_TA_cm)/\((finite B)/\(finite C)))->(finite (cartesian_product3 zenon_TA_cm B C))))) zenon_H49); [ zenon_intro zenon_H4a; idtac ].
% 0.78/0.94 elim zenon_H4a. zenon_intro zenon_TB_cl. zenon_intro zenon_H4b.
% 0.78/0.94 apply (zenon_notallex_s (fun C : zenon_U => (((finite zenon_TA_cm)/\((finite zenon_TB_cl)/\(finite C)))->(finite (cartesian_product3 zenon_TA_cm zenon_TB_cl C)))) zenon_H4b); [ zenon_intro zenon_H4c; idtac ].
% 0.78/0.94 elim zenon_H4c. zenon_intro zenon_TC_ck. zenon_intro zenon_H4d.
% 0.78/0.94 apply (zenon_notimply_s _ _ zenon_H4d). zenon_intro zenon_H4e. zenon_intro zenon_H3c.
% 0.78/0.94 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H50. zenon_intro zenon_H4f.
% 0.78/0.94 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51.
% 0.78/0.94 generalize (t3_subset (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H53.
% 0.78/0.94 generalize (cc2_finset_1 (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H54.
% 0.78/0.94 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ].
% 0.78/0.94 generalize (fc14_finset_1 (cartesian_product2 zenon_TA_cm zenon_TB_cl)). zenon_intro zenon_H57.
% 0.78/0.94 generalize (zenon_H57 zenon_TC_ck). zenon_intro zenon_H58.
% 0.78/0.94 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H59 | zenon_intro zenon_H3d ].
% 0.78/0.94 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ].
% 0.78/0.94 generalize (fc14_finset_1 zenon_TA_cm). zenon_intro zenon_H5c.
% 0.78/0.94 generalize (zenon_H5c zenon_TB_cl). zenon_intro zenon_H5d.
% 0.78/0.94 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ].
% 0.78/0.94 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ].
% 0.78/0.94 exact (zenon_H61 zenon_H50).
% 0.78/0.94 exact (zenon_H60 zenon_H52).
% 0.78/0.94 exact (zenon_H5b zenon_H5e).
% 0.78/0.94 exact (zenon_H5a zenon_H51).
% 0.78/0.94 exact (zenon_H56 zenon_H3d).
% 0.78/0.94 generalize (zenon_H55 (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H62.
% 0.78/0.94 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H63 | zenon_intro zenon_H3d ].
% 0.78/0.94 generalize (zenon_H53 (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H64.
% 0.78/0.94 apply (zenon_equiv_s _ _ zenon_H64); [ zenon_intro zenon_H63; zenon_intro zenon_H67 | zenon_intro zenon_H66; zenon_intro zenon_H65 ].
% 0.78/0.94 generalize (zenon_H46 (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H65.
% 0.78/0.94 exact (zenon_H67 zenon_H65).
% 0.78/0.94 exact (zenon_H63 zenon_H66).
% 0.78/0.94 apply (zenon_L1_ zenon_TC_ck zenon_TB_cl zenon_TA_cm); trivial.
% 0.78/0.94 apply zenon_H47. zenon_intro zenon_Tx_ea. apply NNPP. zenon_intro zenon_H69.
% 0.78/0.94 generalize (reflexivity_r1_tarski zenon_Tx_ea). zenon_intro zenon_H0.
% 0.78/0.94 generalize (zenon_H0 zenon_E). zenon_intro zenon_H6a.
% 0.78/0.94 exact (zenon_H69 zenon_H6a).
% 0.78/0.94 Qed.
% 0.78/0.94 % SZS output end Proof
% 0.78/0.94 (* END-PROOF *)
% 0.78/0.94 nodes searched: 21148
% 0.78/0.94 max branch formulas: 5532
% 0.78/0.94 proof nodes created: 579
% 0.78/0.94 formulas created: 55585
% 0.78/0.94
%------------------------------------------------------------------------------