TSTP Solution File: SET014+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0.
% 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 06:32:23 EDT 2022
% Result : Theorem 0.42s 0.59s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.15 % Command : run_zenon %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 12:37:48 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.42/0.59 (* PROOF-FOUND *)
% 0.42/0.59 % SZS status Theorem
% 0.42/0.59 (* BEGIN-PROOF *)
% 0.42/0.59 % SZS output start Proof
% 0.42/0.59 Theorem prove_union_subset : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset D C))->(subset (union B D) C))))).
% 0.42/0.59 Proof.
% 0.42/0.59 apply NNPP. intro zenon_G.
% 0.42/0.59 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset D C))->(subset (union B D) C))))) zenon_G); [ zenon_intro zenon_H6; idtac ].
% 0.42/0.59 elim zenon_H6. zenon_intro zenon_TB_h. zenon_intro zenon_H8.
% 0.42/0.59 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TB_h C)/\(subset D C))->(subset (union zenon_TB_h D) C)))) zenon_H8); [ zenon_intro zenon_H9; idtac ].
% 0.42/0.59 elim zenon_H9. zenon_intro zenon_TC_k. zenon_intro zenon_Hb.
% 0.42/0.59 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TB_h zenon_TC_k)/\(subset D zenon_TC_k))->(subset (union zenon_TB_h D) zenon_TC_k))) zenon_Hb); [ zenon_intro zenon_Hc; idtac ].
% 0.42/0.59 elim zenon_Hc. zenon_intro zenon_TD_n. zenon_intro zenon_He.
% 0.42/0.59 apply (zenon_notimply_s _ _ zenon_He). zenon_intro zenon_H10. zenon_intro zenon_Hf.
% 0.42/0.59 apply (zenon_and_s _ _ zenon_H10). zenon_intro zenon_H12. zenon_intro zenon_H11.
% 0.42/0.59 generalize (subset_defn zenon_TB_h). zenon_intro zenon_H13.
% 0.42/0.59 generalize (zenon_H13 zenon_TC_k). zenon_intro zenon_H14.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H17; zenon_intro zenon_H16 | zenon_intro zenon_H12; zenon_intro zenon_H15 ].
% 0.42/0.59 exact (zenon_H17 zenon_H12).
% 0.42/0.59 generalize (subset_defn zenon_TD_n). zenon_intro zenon_H18.
% 0.42/0.59 generalize (zenon_H18 zenon_TC_k). zenon_intro zenon_H19.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H11; zenon_intro zenon_H1a ].
% 0.42/0.59 exact (zenon_H1c zenon_H11).
% 0.42/0.59 generalize (subset_defn (union zenon_TB_h zenon_TD_n)). zenon_intro zenon_H1d.
% 0.42/0.59 generalize (zenon_H1d zenon_TC_k). zenon_intro zenon_H1e.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_Hf; zenon_intro zenon_H21 | zenon_intro zenon_H20; zenon_intro zenon_H1f ].
% 0.42/0.59 apply (zenon_notallex_s (fun D : zenon_U => ((member D (union zenon_TB_h zenon_TD_n))->(member D zenon_TC_k))) zenon_H21); [ zenon_intro zenon_H22; idtac ].
% 0.42/0.59 elim zenon_H22. zenon_intro zenon_TD_bj. zenon_intro zenon_H24.
% 0.42/0.59 apply (zenon_notimply_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25.
% 0.42/0.59 generalize (zenon_H15 zenon_TD_bj). zenon_intro zenon_H27.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.42/0.59 generalize (zenon_H1a zenon_TD_bj). zenon_intro zenon_H2a.
% 0.42/0.59 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2b | zenon_intro zenon_H28 ].
% 0.42/0.59 generalize (commutativity_of_union zenon_TD_n). zenon_intro zenon_H2c.
% 0.42/0.59 generalize (union_defn zenon_TD_n). zenon_intro zenon_H2d.
% 0.42/0.59 generalize (zenon_H2d zenon_TB_h). zenon_intro zenon_H2e.
% 0.42/0.59 generalize (zenon_H2c zenon_TB_h). zenon_intro zenon_H2f.
% 0.42/0.59 generalize (zenon_H2e zenon_TD_bj). zenon_intro zenon_H30.
% 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H30); [ zenon_intro zenon_H34; zenon_intro zenon_H33 | zenon_intro zenon_H32; zenon_intro zenon_H31 ].
% 0.42/0.59 cut ((member zenon_TD_bj (union zenon_TB_h zenon_TD_n)) = (member zenon_TD_bj (union zenon_TD_n zenon_TB_h))).
% 0.42/0.59 intro zenon_D_pnotp.
% 0.42/0.59 apply zenon_H34.
% 0.42/0.59 rewrite <- zenon_D_pnotp.
% 0.42/0.59 exact zenon_H26.
% 0.42/0.59 cut (((union zenon_TB_h zenon_TD_n) = (union zenon_TD_n zenon_TB_h))); [idtac | apply NNPP; zenon_intro zenon_H35].
% 0.42/0.59 cut ((zenon_TD_bj = zenon_TD_bj)); [idtac | apply NNPP; zenon_intro zenon_H36].
% 0.42/0.59 congruence.
% 0.42/0.59 apply zenon_H36. apply refl_equal.
% 0.42/0.59 apply zenon_H35. apply sym_equal. exact zenon_H2f.
% 0.42/0.59 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ].
% 0.42/0.59 exact (zenon_H2b zenon_H38).
% 0.42/0.59 exact (zenon_H29 zenon_H37).
% 0.42/0.59 exact (zenon_H25 zenon_H28).
% 0.42/0.59 exact (zenon_H25 zenon_H28).
% 0.42/0.59 exact (zenon_Hf zenon_H20).
% 0.42/0.59 Qed.
% 0.42/0.59 % SZS output end Proof
% 0.42/0.59 (* END-PROOF *)
% 0.42/0.59 nodes searched: 812
% 0.42/0.59 max branch formulas: 371
% 0.42/0.59 proof nodes created: 84
% 0.42/0.59 formulas created: 3590
% 0.42/0.59
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