TSTP Solution File: SEU126+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n015.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 15:59:31 EDT 2022
% Result : Theorem 1.02s 1.18s
% Output : Proof 1.02s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.32 % Computer : n015.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 23:09:15 EDT 2022
% 0.12/0.32 % CPUTime :
% 1.02/1.18 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0
% 1.02/1.18 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 1.02/1.18 (* PROOF-FOUND *)
% 1.02/1.18 % SZS status Theorem
% 1.02/1.18 (* BEGIN-PROOF *)
% 1.02/1.18 % SZS output start Proof
% 1.02/1.18 Theorem t12_xboole_1 : (forall A : zenon_U, (forall B : zenon_U, ((subset A B)->((set_union2 A B) = B)))).
% 1.02/1.18 Proof.
% 1.02/1.18 assert (zenon_L1_ : forall (zenon_TB_u : zenon_U) (zenon_TA_v : zenon_U) (zenon_TD_w : zenon_U), (~((in zenon_TD_w zenon_TA_v)\/(in zenon_TD_w zenon_TB_u))) -> (in zenon_TD_w zenon_TB_u) -> False).
% 1.02/1.18 do 3 intro. intros zenon_H12 zenon_H13.
% 1.02/1.18 apply (zenon_notor_s _ _ zenon_H12). zenon_intro zenon_H18. zenon_intro zenon_H17.
% 1.02/1.18 exact (zenon_H17 zenon_H13).
% 1.02/1.18 (* end of lemma zenon_L1_ *)
% 1.02/1.18 apply NNPP. intro zenon_G.
% 1.02/1.18 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((subset A B)->((set_union2 A B) = B)))) zenon_G); [ zenon_intro zenon_H19; idtac ].
% 1.02/1.18 elim zenon_H19. zenon_intro zenon_TA_v. zenon_intro zenon_H1a.
% 1.02/1.18 apply (zenon_notallex_s (fun B : zenon_U => ((subset zenon_TA_v B)->((set_union2 zenon_TA_v B) = B))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ].
% 1.02/1.18 elim zenon_H1b. zenon_intro zenon_TB_u. zenon_intro zenon_H1c.
% 1.02/1.18 apply (zenon_notimply_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H1d.
% 1.02/1.18 generalize (d3_tarski zenon_TA_v). zenon_intro zenon_H1f.
% 1.02/1.18 generalize (zenon_H1f zenon_TB_u). zenon_intro zenon_H20.
% 1.02/1.18 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H23; zenon_intro zenon_H22 | zenon_intro zenon_H1e; zenon_intro zenon_H21 ].
% 1.02/1.18 exact (zenon_H23 zenon_H1e).
% 1.02/1.18 generalize (d2_xboole_0 zenon_TA_v). zenon_intro zenon_H24.
% 1.02/1.18 generalize (zenon_H24 zenon_TB_u). zenon_intro zenon_H25.
% 1.02/1.18 generalize (zenon_H25 zenon_TB_u). zenon_intro zenon_H26.
% 1.02/1.18 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H2a; zenon_intro zenon_H29 | zenon_intro zenon_H28; zenon_intro zenon_H27 ].
% 1.02/1.18 apply (zenon_notallex_s (fun D : zenon_U => ((in D zenon_TB_u)<->((in D zenon_TA_v)\/(in D zenon_TB_u)))) zenon_H29); [ zenon_intro zenon_H2b; idtac ].
% 1.02/1.18 elim zenon_H2b. zenon_intro zenon_TD_w. zenon_intro zenon_H2c.
% 1.02/1.18 apply (zenon_notequiv_s _ _ zenon_H2c); [ zenon_intro zenon_H17; zenon_intro zenon_H2d | zenon_intro zenon_H13; zenon_intro zenon_H12 ].
% 1.02/1.18 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H2e | zenon_intro zenon_H13 ].
% 1.02/1.18 generalize (zenon_H21 zenon_TD_w). zenon_intro zenon_H2f.
% 1.02/1.18 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H18 | zenon_intro zenon_H13 ].
% 1.02/1.18 exact (zenon_H18 zenon_H2e).
% 1.02/1.18 exact (zenon_H17 zenon_H13).
% 1.02/1.18 exact (zenon_H17 zenon_H13).
% 1.02/1.18 apply (zenon_L1_ zenon_TB_u zenon_TA_v zenon_TD_w); trivial.
% 1.02/1.18 apply zenon_H1d. apply sym_equal. exact zenon_H28.
% 1.02/1.18 Qed.
% 1.02/1.18 % SZS output end Proof
% 1.02/1.18 (* END-PROOF *)
% 1.02/1.18 nodes searched: 19156
% 1.02/1.18 max branch formulas: 1233
% 1.02/1.18 proof nodes created: 1647
% 1.02/1.18 formulas created: 40455
% 1.02/1.18
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