TSTP Solution File: SET185+3 by Zenon---0.7.1
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% File : Zenon---0.7.1
% Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% 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 06:34:44 EDT 2022
% Result : Theorem 0.19s 0.54s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% 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 Jul 10 10:41:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.54 (* PROOF-FOUND *)
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54 (* BEGIN-PROOF *)
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 Theorem prove_subset_union : (forall B : zenon_U, (forall C : zenon_U, ((subset B C)->((union B C) = C)))).
% 0.19/0.54 Proof.
% 0.19/0.54 apply NNPP. intro zenon_G.
% 0.19/0.54 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((subset B C)->((union B C) = C)))) zenon_G); [ zenon_intro zenon_H7; idtac ].
% 0.19/0.54 elim zenon_H7. zenon_intro zenon_TB_i. zenon_intro zenon_H9.
% 0.19/0.54 apply (zenon_notallex_s (fun C : zenon_U => ((subset zenon_TB_i C)->((union zenon_TB_i C) = C))) zenon_H9); [ zenon_intro zenon_Ha; idtac ].
% 0.19/0.54 elim zenon_Ha. zenon_intro zenon_TC_l. zenon_intro zenon_Hc.
% 0.19/0.54 apply (zenon_notimply_s _ _ zenon_Hc). zenon_intro zenon_He. zenon_intro zenon_Hd.
% 0.19/0.54 generalize (subset_defn zenon_TB_i). zenon_intro zenon_Hf.
% 0.19/0.54 generalize (zenon_Hf zenon_TC_l). zenon_intro zenon_H10.
% 0.19/0.54 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_H13; zenon_intro zenon_H12 | zenon_intro zenon_He; zenon_intro zenon_H11 ].
% 0.19/0.54 exact (zenon_H13 zenon_He).
% 0.19/0.54 generalize (equal_member_defn zenon_TC_l). zenon_intro zenon_H14.
% 0.19/0.54 generalize (commutativity_of_union zenon_TC_l). zenon_intro zenon_H15.
% 0.19/0.54 generalize (zenon_H14 (union zenon_TB_i zenon_TC_l)). zenon_intro zenon_H16.
% 0.19/0.54 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H1a; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_H17 ].
% 0.19/0.54 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TC_l)<->(member D (union zenon_TB_i zenon_TC_l)))) zenon_H19); [ zenon_intro zenon_H1b; idtac ].
% 0.19/0.54 elim zenon_H1b. zenon_intro zenon_TD_bc. zenon_intro zenon_H1d.
% 0.19/0.54 apply (zenon_notequiv_s _ _ zenon_H1d); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ].
% 0.19/0.54 generalize (zenon_H11 zenon_TD_bc). zenon_intro zenon_H22.
% 0.19/0.54 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H23 | zenon_intro zenon_H1f ].
% 0.19/0.54 generalize (union_defn zenon_TC_l). zenon_intro zenon_H24.
% 0.19/0.54 generalize (zenon_H15 zenon_TB_i). zenon_intro zenon_H25.
% 0.19/0.54 generalize (zenon_H24 zenon_TB_i). zenon_intro zenon_H26.
% 0.19/0.54 generalize (zenon_H26 zenon_TD_bc). zenon_intro zenon_H27.
% 0.19/0.54 apply (zenon_equiv_s _ _ zenon_H27); [ zenon_intro zenon_H2b; zenon_intro zenon_H2a | zenon_intro zenon_H29; zenon_intro zenon_H28 ].
% 0.19/0.54 cut ((member zenon_TD_bc (union zenon_TB_i zenon_TC_l)) = (member zenon_TD_bc (union zenon_TC_l zenon_TB_i))).
% 0.19/0.54 intro zenon_D_pnotp.
% 0.19/0.54 apply zenon_H2b.
% 0.19/0.54 rewrite <- zenon_D_pnotp.
% 0.19/0.54 exact zenon_H20.
% 0.19/0.54 cut (((union zenon_TB_i zenon_TC_l) = (union zenon_TC_l zenon_TB_i))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 0.19/0.54 cut ((zenon_TD_bc = zenon_TD_bc)); [idtac | apply NNPP; zenon_intro zenon_H2d].
% 0.19/0.54 congruence.
% 0.19/0.54 apply zenon_H2d. apply refl_equal.
% 0.19/0.54 apply zenon_H2c. apply sym_equal. exact zenon_H25.
% 0.19/0.54 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H1f | zenon_intro zenon_H2e ].
% 0.19/0.54 exact (zenon_H21 zenon_H1f).
% 0.19/0.54 exact (zenon_H23 zenon_H2e).
% 0.19/0.54 exact (zenon_H21 zenon_H1f).
% 0.19/0.54 generalize (union_defn zenon_TB_i). zenon_intro zenon_H2f.
% 0.19/0.54 generalize (zenon_H2f zenon_TC_l). zenon_intro zenon_H30.
% 0.19/0.54 generalize (zenon_H30 zenon_TD_bc). zenon_intro zenon_H31.
% 0.19/0.54 apply (zenon_equiv_s _ _ zenon_H31); [ zenon_intro zenon_H1e; zenon_intro zenon_H33 | zenon_intro zenon_H20; zenon_intro zenon_H32 ].
% 0.19/0.54 apply (zenon_notor_s _ _ zenon_H33). zenon_intro zenon_H23. zenon_intro zenon_H21.
% 0.19/0.54 exact (zenon_H21 zenon_H1f).
% 0.19/0.54 exact (zenon_H1e zenon_H20).
% 0.19/0.54 apply zenon_Hd. apply sym_equal. exact zenon_H18.
% 0.19/0.54 Qed.
% 0.19/0.54 % SZS output end Proof
% 0.19/0.54 (* END-PROOF *)
% 0.19/0.54 nodes searched: 1059
% 0.19/0.54 max branch formulas: 425
% 0.19/0.54 proof nodes created: 98
% 0.19/0.54 formulas created: 4257
% 0.19/0.54
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