TSTP Solution File: SEU264+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n017.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 16:00:42 EDT 2022
% Result : Theorem 0.36s 0.52s
% Output : Proof 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.32 % Computer : n017.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jun 19 16:19:13 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.36/0.52 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.36/0.52 (* PROOF-FOUND *)
% 0.36/0.52 % SZS status Theorem
% 0.36/0.52 (* BEGIN-PROOF *)
% 0.36/0.52 % SZS output start Proof
% 0.36/0.52 Theorem t16_relset_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((relation_of2_as_subset D C A)->((subset A B)->(relation_of2_as_subset D C B))))))).
% 0.36/0.52 Proof.
% 0.36/0.52 assert (zenon_L1_ : forall (zenon_TA_p : zenon_U) (zenon_TC_q : zenon_U) (zenon_TD_r : zenon_U), (relation_of2 zenon_TD_r zenon_TC_q zenon_TA_p) -> (~(relation_of2_as_subset zenon_TD_r zenon_TC_q zenon_TA_p)) -> False).
% 0.36/0.52 do 3 intro. intros zenon_Hd zenon_He.
% 0.36/0.52 generalize (redefinition_m2_relset_1 zenon_TC_q). zenon_intro zenon_H12.
% 0.36/0.52 generalize (zenon_H12 zenon_TA_p). zenon_intro zenon_H13.
% 0.36/0.52 generalize (zenon_H13 zenon_TD_r). zenon_intro zenon_H14.
% 0.36/0.52 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_He; zenon_intro zenon_H16 | zenon_intro zenon_H15; zenon_intro zenon_Hd ].
% 0.36/0.52 exact (zenon_H16 zenon_Hd).
% 0.36/0.52 exact (zenon_He zenon_H15).
% 0.36/0.52 (* end of lemma zenon_L1_ *)
% 0.36/0.52 assert (zenon_L2_ : forall (zenon_TB_z : zenon_U) (zenon_TC_q : zenon_U) (zenon_TD_r : zenon_U), (relation_of2_as_subset zenon_TD_r zenon_TC_q zenon_TB_z) -> (~(relation_of2 zenon_TD_r zenon_TC_q zenon_TB_z)) -> False).
% 0.36/0.53 do 3 intro. intros zenon_H17 zenon_H18.
% 0.36/0.53 generalize (redefinition_m2_relset_1 zenon_TC_q). zenon_intro zenon_H12.
% 0.36/0.53 generalize (zenon_H12 zenon_TB_z). zenon_intro zenon_H1a.
% 0.36/0.53 generalize (zenon_H1a zenon_TD_r). zenon_intro zenon_H1b.
% 0.36/0.53 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1d; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H1c ].
% 0.36/0.53 exact (zenon_H1d zenon_H17).
% 0.36/0.53 exact (zenon_H18 zenon_H1c).
% 0.36/0.53 (* end of lemma zenon_L2_ *)
% 0.36/0.53 apply NNPP. intro zenon_G.
% 0.36/0.53 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_H1e | zenon_intro zenon_H1f ].
% 0.36/0.53 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((relation_of2_as_subset D C A)->((subset A B)->(relation_of2_as_subset D C B))))))) zenon_G); [ zenon_intro zenon_H20; idtac ].
% 0.36/0.53 elim zenon_H20. zenon_intro zenon_TA_p. zenon_intro zenon_H21.
% 0.36/0.53 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((relation_of2_as_subset D C zenon_TA_p)->((subset zenon_TA_p B)->(relation_of2_as_subset D C B)))))) zenon_H21); [ zenon_intro zenon_H22; idtac ].
% 0.36/0.53 elim zenon_H22. zenon_intro zenon_TB_z. zenon_intro zenon_H23.
% 0.36/0.53 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((relation_of2_as_subset D C zenon_TA_p)->((subset zenon_TA_p zenon_TB_z)->(relation_of2_as_subset D C zenon_TB_z))))) zenon_H23); [ zenon_intro zenon_H24; idtac ].
% 0.36/0.53 elim zenon_H24. zenon_intro zenon_TC_q. zenon_intro zenon_H25.
% 0.36/0.53 apply (zenon_notallex_s (fun D : zenon_U => ((relation_of2_as_subset D zenon_TC_q zenon_TA_p)->((subset zenon_TA_p zenon_TB_z)->(relation_of2_as_subset D zenon_TC_q zenon_TB_z)))) zenon_H25); [ zenon_intro zenon_H26; idtac ].
% 0.36/0.53 elim zenon_H26. zenon_intro zenon_TD_r. zenon_intro zenon_H27.
% 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H27). zenon_intro zenon_H15. zenon_intro zenon_H28.
% 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H28). zenon_intro zenon_H29. zenon_intro zenon_H1d.
% 0.36/0.53 generalize (redefinition_m2_relset_1 zenon_TC_q). zenon_intro zenon_H12.
% 0.36/0.53 generalize (zenon_H12 zenon_TA_p). zenon_intro zenon_H13.
% 0.36/0.53 generalize (zenon_H13 zenon_TD_r). zenon_intro zenon_H14.
% 0.36/0.53 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_He; zenon_intro zenon_H16 | zenon_intro zenon_H15; zenon_intro zenon_Hd ].
% 0.36/0.53 exact (zenon_He zenon_H15).
% 0.36/0.53 generalize (redefinition_m2_relset_1 zenon_TC_q). zenon_intro zenon_H12.
% 0.36/0.53 generalize (zenon_H12 zenon_TB_z). zenon_intro zenon_H1a.
% 0.36/0.53 generalize (zenon_H1a zenon_TD_r). zenon_intro zenon_H1b.
% 0.36/0.53 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1d; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H1c ].
% 0.36/0.53 generalize (t14_relset_1 zenon_TA_p). zenon_intro zenon_H2a.
% 0.36/0.53 generalize (zenon_H2a zenon_TB_z). zenon_intro zenon_H2b.
% 0.36/0.53 generalize (zenon_H2b zenon_TC_q). zenon_intro zenon_H2c.
% 0.36/0.53 generalize (zenon_H2c zenon_TD_r). zenon_intro zenon_H2d.
% 0.36/0.53 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_He | zenon_intro zenon_H2e ].
% 0.36/0.53 apply (zenon_L1_ zenon_TA_p zenon_TC_q zenon_TD_r); trivial.
% 0.36/0.53 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H2f | zenon_intro zenon_H17 ].
% 0.36/0.53 elim (classic ((~((relation_rng zenon_TD_r) = zenon_TA_p))/\(~(subset (relation_rng zenon_TD_r) zenon_TA_p)))); [ zenon_intro zenon_H30 | zenon_intro zenon_H31 ].
% 0.36/0.53 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H33. zenon_intro zenon_H32.
% 0.36/0.53 generalize (t12_relset_1 zenon_TC_q). zenon_intro zenon_H34.
% 0.36/0.53 generalize (zenon_H34 zenon_TA_p). zenon_intro zenon_H35.
% 0.36/0.53 generalize (zenon_H35 zenon_TD_r). zenon_intro zenon_H36.
% 0.36/0.53 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_He | zenon_intro zenon_H37 ].
% 0.36/0.53 apply (zenon_L1_ zenon_TA_p zenon_TC_q zenon_TD_r); trivial.
% 0.36/0.53 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 0.36/0.53 exact (zenon_H32 zenon_H38).
% 0.36/0.53 cut ((subset zenon_TA_p zenon_TB_z) = (subset (relation_rng zenon_TD_r) zenon_TB_z)).
% 0.36/0.53 intro zenon_D_pnotp.
% 0.36/0.53 apply zenon_H2f.
% 0.36/0.53 rewrite <- zenon_D_pnotp.
% 0.36/0.53 exact zenon_H29.
% 0.36/0.53 cut ((zenon_TB_z = zenon_TB_z)); [idtac | apply NNPP; zenon_intro zenon_H3a].
% 0.36/0.53 cut ((zenon_TA_p = (relation_rng zenon_TD_r))); [idtac | apply NNPP; zenon_intro zenon_H3b].
% 0.36/0.53 congruence.
% 0.36/0.53 apply (zenon_notand_s _ _ zenon_H31); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 0.36/0.53 apply zenon_H3d. zenon_intro zenon_H3e.
% 0.36/0.53 elim (classic ((relation_rng zenon_TD_r) = (relation_rng zenon_TD_r))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ].
% 0.36/0.53 cut (((relation_rng zenon_TD_r) = (relation_rng zenon_TD_r)) = (zenon_TA_p = (relation_rng zenon_TD_r))).
% 0.36/0.53 intro zenon_D_pnotp.
% 0.36/0.53 apply zenon_H3b.
% 0.36/0.53 rewrite <- zenon_D_pnotp.
% 0.36/0.53 exact zenon_H3f.
% 0.36/0.53 cut (((relation_rng zenon_TD_r) = (relation_rng zenon_TD_r))); [idtac | apply NNPP; zenon_intro zenon_H40].
% 0.36/0.53 cut (((relation_rng zenon_TD_r) = zenon_TA_p)); [idtac | apply NNPP; zenon_intro zenon_H33].
% 0.36/0.53 congruence.
% 0.36/0.53 exact (zenon_H33 zenon_H3e).
% 0.36/0.53 apply zenon_H40. apply refl_equal.
% 0.36/0.53 apply zenon_H40. apply refl_equal.
% 0.36/0.53 apply zenon_H3c. zenon_intro zenon_H38.
% 0.36/0.53 generalize (zenon_H1e (relation_rng zenon_TD_r)). zenon_intro zenon_H41.
% 0.36/0.53 generalize (zenon_H41 zenon_TA_p). zenon_intro zenon_H42.
% 0.36/0.53 generalize (zenon_H42 zenon_TB_z). zenon_intro zenon_H43.
% 0.36/0.53 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H32 | zenon_intro zenon_H44 ].
% 0.36/0.53 exact (zenon_H32 zenon_H38).
% 0.36/0.53 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 0.36/0.53 exact (zenon_H46 zenon_H29).
% 0.36/0.53 exact (zenon_H2f zenon_H45).
% 0.36/0.53 apply zenon_H3a. apply refl_equal.
% 0.36/0.53 apply (zenon_L2_ zenon_TB_z zenon_TC_q zenon_TD_r); trivial.
% 0.36/0.53 exact (zenon_H1d zenon_H17).
% 0.36/0.53 apply zenon_H1f. zenon_intro zenon_Tx_ct. apply NNPP. zenon_intro zenon_H48.
% 0.36/0.53 apply zenon_H48. zenon_intro zenon_Ty_cv. apply NNPP. zenon_intro zenon_H4a.
% 0.36/0.53 apply zenon_H4a. zenon_intro zenon_Tz_cx. apply NNPP. zenon_intro zenon_H4c.
% 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f.
% 0.36/0.53 generalize (t1_xboole_1 zenon_Tx_ct). zenon_intro zenon_H51.
% 0.36/0.53 generalize (zenon_H51 zenon_Ty_cv). zenon_intro zenon_H52.
% 0.36/0.53 generalize (zenon_H52 zenon_Tz_cx). zenon_intro zenon_H53.
% 0.36/0.53 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.36/0.53 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 0.36/0.53 exact (zenon_H57 zenon_H4e).
% 0.36/0.53 exact (zenon_H56 zenon_H50).
% 0.36/0.53 exact (zenon_H4f zenon_H54).
% 0.36/0.53 Qed.
% 0.36/0.53 % SZS output end Proof
% 0.36/0.53 (* END-PROOF *)
% 0.36/0.53 nodes searched: 1481
% 0.36/0.53 max branch formulas: 457
% 0.36/0.53 proof nodes created: 136
% 0.36/0.53 formulas created: 3413
% 0.36/0.53
%------------------------------------------------------------------------------