TSTP Solution File: SET200+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET200+3 : TPTP v8.1.0. Released v2.2.0.
% 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 06:34:52 EDT 2022
% Result : Theorem 0.56s 0.74s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET200+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.15/0.36 % Computer : n006.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 23:00:50 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.56/0.74 (* PROOF-FOUND *)
% 0.56/0.74 % SZS status Theorem
% 0.56/0.74 (* BEGIN-PROOF *)
% 0.56/0.74 % SZS output start Proof
% 0.56/0.74 Theorem prove_th34 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (forall E : zenon_U, (((subset B C)/\(subset D E))->(subset (union B D) (union C E))))))).
% 0.56/0.74 Proof.
% 0.56/0.74 apply NNPP. intro zenon_G.
% 0.56/0.74 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (forall E : zenon_U, (((subset B C)/\(subset D E))->(subset (union B D) (union C E))))))) zenon_G); [ zenon_intro zenon_H6; idtac ].
% 0.56/0.74 elim zenon_H6. zenon_intro zenon_TB_h. zenon_intro zenon_H8.
% 0.56/0.74 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (forall E : zenon_U, (((subset zenon_TB_h C)/\(subset D E))->(subset (union zenon_TB_h D) (union C E)))))) zenon_H8); [ zenon_intro zenon_H9; idtac ].
% 0.56/0.74 elim zenon_H9. zenon_intro zenon_TC_k. zenon_intro zenon_Hb.
% 0.56/0.74 apply (zenon_notallex_s (fun D : zenon_U => (forall E : zenon_U, (((subset zenon_TB_h zenon_TC_k)/\(subset D E))->(subset (union zenon_TB_h D) (union zenon_TC_k E))))) zenon_Hb); [ zenon_intro zenon_Hc; idtac ].
% 0.56/0.74 elim zenon_Hc. zenon_intro zenon_TD_n. zenon_intro zenon_He.
% 0.56/0.74 apply (zenon_notallex_s (fun E : zenon_U => (((subset zenon_TB_h zenon_TC_k)/\(subset zenon_TD_n E))->(subset (union zenon_TB_h zenon_TD_n) (union zenon_TC_k E)))) zenon_He); [ zenon_intro zenon_Hf; idtac ].
% 0.56/0.74 elim zenon_Hf. zenon_intro zenon_TE_q. zenon_intro zenon_H11.
% 0.56/0.74 apply (zenon_notimply_s _ _ zenon_H11). zenon_intro zenon_H13. zenon_intro zenon_H12.
% 0.56/0.74 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14.
% 0.56/0.74 generalize (subset_defn zenon_TB_h). zenon_intro zenon_H16.
% 0.56/0.74 generalize (zenon_H16 zenon_TC_k). zenon_intro zenon_H17.
% 0.56/0.74 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H1a; zenon_intro zenon_H19 | zenon_intro zenon_H15; zenon_intro zenon_H18 ].
% 0.56/0.74 exact (zenon_H1a zenon_H15).
% 0.56/0.74 generalize (subset_defn zenon_TD_n). zenon_intro zenon_H1b.
% 0.56/0.74 generalize (zenon_H1b zenon_TE_q). zenon_intro zenon_H1c.
% 0.56/0.74 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1f; zenon_intro zenon_H1e | zenon_intro zenon_H14; zenon_intro zenon_H1d ].
% 0.56/0.74 exact (zenon_H1f zenon_H14).
% 0.56/0.74 generalize (subset_defn (union zenon_TB_h zenon_TD_n)). zenon_intro zenon_H20.
% 0.56/0.74 generalize (zenon_H20 (union zenon_TC_k zenon_TE_q)). zenon_intro zenon_H21.
% 0.56/0.74 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H12; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ].
% 0.56/0.74 apply (zenon_notallex_s (fun D : zenon_U => ((member D (union zenon_TB_h zenon_TD_n))->(member D (union zenon_TC_k zenon_TE_q)))) zenon_H24); [ zenon_intro zenon_H25; idtac ].
% 0.56/0.74 elim zenon_H25. zenon_intro zenon_TD_bm. zenon_intro zenon_H27.
% 0.56/0.74 apply (zenon_notimply_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H28.
% 0.56/0.74 generalize (commutativity_of_union zenon_TD_n). zenon_intro zenon_H2a.
% 0.56/0.74 generalize (union_defn zenon_TC_k). zenon_intro zenon_H2b.
% 0.56/0.74 generalize (zenon_H2a zenon_TB_h). zenon_intro zenon_H2c.
% 0.56/0.74 generalize (zenon_H2b zenon_TE_q). zenon_intro zenon_H2d.
% 0.56/0.74 generalize (zenon_H2d zenon_TD_bm). zenon_intro zenon_H2e.
% 0.56/0.74 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H28; zenon_intro zenon_H31 | zenon_intro zenon_H30; zenon_intro zenon_H2f ].
% 0.56/0.74 apply (zenon_notor_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32.
% 0.56/0.74 generalize (union_defn zenon_TD_n). zenon_intro zenon_H34.
% 0.56/0.74 generalize (zenon_H1d zenon_TD_bm). zenon_intro zenon_H35.
% 0.56/0.74 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.56/0.74 generalize (zenon_H34 zenon_TB_h). zenon_intro zenon_H38.
% 0.56/0.74 generalize (zenon_H18 zenon_TD_bm). zenon_intro zenon_H39.
% 0.56/0.74 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 0.56/0.74 generalize (zenon_H38 zenon_TD_bm). zenon_intro zenon_H3c.
% 0.56/0.74 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H40; zenon_intro zenon_H3f | zenon_intro zenon_H3e; zenon_intro zenon_H3d ].
% 0.56/0.74 cut ((member zenon_TD_bm (union zenon_TB_h zenon_TD_n)) = (member zenon_TD_bm (union zenon_TD_n zenon_TB_h))).
% 0.56/0.74 intro zenon_D_pnotp.
% 0.56/0.74 apply zenon_H40.
% 0.56/0.74 rewrite <- zenon_D_pnotp.
% 0.56/0.74 exact zenon_H29.
% 0.56/0.74 cut (((union zenon_TB_h zenon_TD_n) = (union zenon_TD_n zenon_TB_h))); [idtac | apply NNPP; zenon_intro zenon_H41].
% 0.56/0.74 cut ((zenon_TD_bm = zenon_TD_bm)); [idtac | apply NNPP; zenon_intro zenon_H42].
% 0.56/0.74 congruence.
% 0.56/0.74 apply zenon_H42. apply refl_equal.
% 0.56/0.74 apply zenon_H41. apply sym_equal. exact zenon_H2c.
% 0.56/0.74 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.56/0.74 exact (zenon_H37 zenon_H44).
% 0.56/0.74 exact (zenon_H3b zenon_H43).
% 0.56/0.74 exact (zenon_H33 zenon_H3a).
% 0.56/0.74 exact (zenon_H32 zenon_H36).
% 0.56/0.74 exact (zenon_H28 zenon_H30).
% 0.56/0.74 exact (zenon_H12 zenon_H23).
% 0.56/0.74 Qed.
% 0.56/0.74 % SZS output end Proof
% 0.56/0.74 (* END-PROOF *)
% 0.56/0.74 nodes searched: 4918
% 0.56/0.74 max branch formulas: 1082
% 0.56/0.74 proof nodes created: 405
% 0.56/0.74 formulas created: 14306
% 0.56/0.74
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