TSTP Solution File: SEU167+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n003.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 15:59:56 EDT 2022
% Result : Theorem 2.00s 2.25s
% Output : Proof 2.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n003.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 : Sun Jun 19 07:10:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.00/2.25 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 2.00/2.25 (* PROOF-FOUND *)
% 2.00/2.25 % SZS status Theorem
% 2.00/2.25 (* BEGIN-PROOF *)
% 2.00/2.25 % SZS output start Proof
% 2.00/2.25 Theorem t119_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset A B)/\(subset C D))->(subset (cartesian_product2 A C) (cartesian_product2 B D))))))).
% 2.00/2.25 Proof.
% 2.00/2.25 apply NNPP. intro zenon_G.
% 2.00/2.25 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((subset x y)->((subset y z)->(subset x z))))))); [ zenon_intro zenon_H6 | zenon_intro zenon_H7 ].
% 2.00/2.25 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset A B)/\(subset C D))->(subset (cartesian_product2 A C) (cartesian_product2 B D))))))) zenon_G); [ zenon_intro zenon_H8; idtac ].
% 2.00/2.25 elim zenon_H8. zenon_intro zenon_TA_j. zenon_intro zenon_Ha.
% 2.00/2.25 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset zenon_TA_j B)/\(subset C D))->(subset (cartesian_product2 zenon_TA_j C) (cartesian_product2 B D)))))) zenon_Ha); [ zenon_intro zenon_Hb; idtac ].
% 2.00/2.25 elim zenon_Hb. zenon_intro zenon_TB_m. zenon_intro zenon_Hd.
% 2.00/2.25 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TA_j zenon_TB_m)/\(subset C D))->(subset (cartesian_product2 zenon_TA_j C) (cartesian_product2 zenon_TB_m D))))) zenon_Hd); [ zenon_intro zenon_He; idtac ].
% 2.00/2.25 elim zenon_He. zenon_intro zenon_TC_p. zenon_intro zenon_H10.
% 2.00/2.25 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TA_j zenon_TB_m)/\(subset zenon_TC_p D))->(subset (cartesian_product2 zenon_TA_j zenon_TC_p) (cartesian_product2 zenon_TB_m D)))) zenon_H10); [ zenon_intro zenon_H11; idtac ].
% 2.00/2.25 elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13.
% 2.00/2.25 apply (zenon_notimply_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14.
% 2.00/2.25 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 2.00/2.25 generalize (t118_zfmisc_1 zenon_TC_p). zenon_intro zenon_H18.
% 2.00/2.25 generalize (zenon_H18 zenon_TD_s). zenon_intro zenon_H19.
% 2.00/2.25 generalize (zenon_H19 zenon_TB_m). zenon_intro zenon_H1a.
% 2.00/2.25 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 2.00/2.25 exact (zenon_H1c zenon_H16).
% 2.00/2.25 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1e. zenon_intro zenon_H1d.
% 2.00/2.25 elim (classic ((~((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TB_m zenon_TC_p)))/\(~(subset (cartesian_product2 zenon_TA_j zenon_TC_p) (cartesian_product2 zenon_TB_m zenon_TC_p))))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ].
% 2.00/2.25 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H22. zenon_intro zenon_H21.
% 2.00/2.25 generalize (t118_zfmisc_1 zenon_TA_j). zenon_intro zenon_H23.
% 2.00/2.25 generalize (zenon_H23 zenon_TB_m). zenon_intro zenon_H24.
% 2.00/2.25 generalize (zenon_H24 zenon_TC_p). zenon_intro zenon_H25.
% 2.00/2.25 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ].
% 2.00/2.25 exact (zenon_H27 zenon_H17).
% 2.00/2.25 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H29. zenon_intro zenon_H28.
% 2.00/2.25 exact (zenon_H21 zenon_H29).
% 2.00/2.25 cut ((subset (cartesian_product2 zenon_TB_m zenon_TC_p) (cartesian_product2 zenon_TB_m zenon_TD_s)) = (subset (cartesian_product2 zenon_TA_j zenon_TC_p) (cartesian_product2 zenon_TB_m zenon_TD_s))).
% 2.00/2.25 intro zenon_D_pnotp.
% 2.00/2.25 apply zenon_H14.
% 2.00/2.25 rewrite <- zenon_D_pnotp.
% 2.00/2.25 exact zenon_H1d.
% 2.00/2.25 cut (((cartesian_product2 zenon_TB_m zenon_TD_s) = (cartesian_product2 zenon_TB_m zenon_TD_s))); [idtac | apply NNPP; zenon_intro zenon_H2a].
% 2.00/2.25 cut (((cartesian_product2 zenon_TB_m zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 2.00/2.25 congruence.
% 2.00/2.25 apply (zenon_notand_s _ _ zenon_H20); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 2.00/2.25 apply zenon_H2d. zenon_intro zenon_H2e.
% 2.00/2.25 elim (classic ((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ].
% 2.00/2.25 cut (((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p)) = ((cartesian_product2 zenon_TB_m zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p))).
% 2.09/2.26 intro zenon_D_pnotp.
% 2.09/2.26 apply zenon_H2b.
% 2.09/2.26 rewrite <- zenon_D_pnotp.
% 2.09/2.26 exact zenon_H2f.
% 2.09/2.26 cut (((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 2.09/2.26 cut (((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TB_m zenon_TC_p))); [idtac | apply NNPP; zenon_intro zenon_H22].
% 2.09/2.26 congruence.
% 2.09/2.26 exact (zenon_H22 zenon_H2e).
% 2.09/2.26 apply zenon_H30. apply refl_equal.
% 2.09/2.26 apply zenon_H30. apply refl_equal.
% 2.09/2.26 apply zenon_H2c. zenon_intro zenon_H29.
% 2.09/2.26 generalize (zenon_H6 (cartesian_product2 zenon_TA_j zenon_TC_p)). zenon_intro zenon_H31.
% 2.09/2.26 generalize (zenon_H31 (cartesian_product2 zenon_TB_m zenon_TC_p)). zenon_intro zenon_H32.
% 2.09/2.26 generalize (zenon_H32 (cartesian_product2 zenon_TB_m zenon_TD_s)). zenon_intro zenon_H33.
% 2.09/2.26 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H21 | zenon_intro zenon_H34 ].
% 2.09/2.26 exact (zenon_H21 zenon_H29).
% 2.09/2.26 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 2.09/2.26 exact (zenon_H36 zenon_H1d).
% 2.09/2.26 exact (zenon_H14 zenon_H35).
% 2.09/2.26 apply zenon_H2a. apply refl_equal.
% 2.09/2.26 apply zenon_H7. zenon_intro zenon_Tx_cd. apply NNPP. zenon_intro zenon_H38.
% 2.09/2.26 apply zenon_H38. zenon_intro zenon_Ty_cf. apply NNPP. zenon_intro zenon_H3a.
% 2.09/2.26 apply zenon_H3a. zenon_intro zenon_Tz_ch. apply NNPP. zenon_intro zenon_H3c.
% 2.09/2.26 apply (zenon_notimply_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 2.09/2.26 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H40. zenon_intro zenon_H3f.
% 2.09/2.26 generalize (t1_xboole_1 zenon_Tx_cd). zenon_intro zenon_H41.
% 2.09/2.26 generalize (zenon_H41 zenon_Ty_cf). zenon_intro zenon_H42.
% 2.09/2.26 generalize (zenon_H42 zenon_Tz_ch). zenon_intro zenon_H43.
% 2.09/2.26 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 2.09/2.26 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 2.09/2.26 exact (zenon_H47 zenon_H3e).
% 2.09/2.26 exact (zenon_H46 zenon_H40).
% 2.09/2.26 exact (zenon_H3f zenon_H44).
% 2.09/2.26 Qed.
% 2.09/2.26 % SZS output end Proof
% 2.09/2.26 (* END-PROOF *)
% 2.09/2.26 nodes searched: 337301
% 2.09/2.26 max branch formulas: 2544
% 2.09/2.26 proof nodes created: 923
% 2.09/2.26 formulas created: 96038
% 2.09/2.26
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