TSTP Solution File: SET978+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n012.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 06:40:00 EDT 2022
% Result : Theorem 0.19s 0.52s
% 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
% 0.07/0.13 % Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 16:00:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.52 (* PROOF-FOUND *)
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 (* BEGIN-PROOF *)
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 Theorem t131_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((~(A = B))->((disjoint (cartesian_product2 (singleton A) C) (cartesian_product2 (singleton B) D))/\(disjoint (cartesian_product2 C (singleton A)) (cartesian_product2 D (singleton B))))))))).
% 0.19/0.52 Proof.
% 0.19/0.52 assert (zenon_L1_ : forall (zenon_TA_i : zenon_U) (zenon_TB_j : zenon_U), (~(disjoint (singleton zenon_TB_j) (singleton zenon_TA_i))) -> (~(zenon_TA_i = zenon_TB_j)) -> False).
% 0.19/0.52 do 2 intro. intros zenon_H6 zenon_H7.
% 0.19/0.52 generalize (t17_zfmisc_1 zenon_TA_i). zenon_intro zenon_Ha.
% 0.19/0.52 generalize (zenon_Ha zenon_TB_j). zenon_intro zenon_Hb.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_Hb); [ zenon_intro zenon_Hd | zenon_intro zenon_Hc ].
% 0.19/0.52 exact (zenon_Hd zenon_H7).
% 0.19/0.52 generalize (symmetry_r1_xboole_0 (singleton zenon_TA_i)). zenon_intro zenon_He.
% 0.19/0.52 generalize (zenon_He (singleton zenon_TB_j)). zenon_intro zenon_Hf.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ].
% 0.19/0.52 exact (zenon_H11 zenon_Hc).
% 0.19/0.52 exact (zenon_H6 zenon_H10).
% 0.19/0.52 (* end of lemma zenon_L1_ *)
% 0.19/0.52 apply NNPP. intro zenon_G.
% 0.19/0.52 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((~(A = B))->((disjoint (cartesian_product2 (singleton A) C) (cartesian_product2 (singleton B) D))/\(disjoint (cartesian_product2 C (singleton A)) (cartesian_product2 D (singleton B))))))))) zenon_G); [ zenon_intro zenon_H12; idtac ].
% 0.19/0.52 elim zenon_H12. zenon_intro zenon_TA_i. zenon_intro zenon_H13.
% 0.19/0.52 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((~(zenon_TA_i = B))->((disjoint (cartesian_product2 (singleton zenon_TA_i) C) (cartesian_product2 (singleton B) D))/\(disjoint (cartesian_product2 C (singleton zenon_TA_i)) (cartesian_product2 D (singleton B)))))))) zenon_H13); [ zenon_intro zenon_H14; idtac ].
% 0.19/0.52 elim zenon_H14. zenon_intro zenon_TB_j. zenon_intro zenon_H15.
% 0.19/0.52 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((~(zenon_TA_i = zenon_TB_j))->((disjoint (cartesian_product2 (singleton zenon_TA_i) C) (cartesian_product2 (singleton zenon_TB_j) D))/\(disjoint (cartesian_product2 C (singleton zenon_TA_i)) (cartesian_product2 D (singleton zenon_TB_j))))))) zenon_H15); [ zenon_intro zenon_H16; idtac ].
% 0.19/0.52 elim zenon_H16. zenon_intro zenon_TC_x. zenon_intro zenon_H18.
% 0.19/0.52 apply (zenon_notallex_s (fun D : zenon_U => ((~(zenon_TA_i = zenon_TB_j))->((disjoint (cartesian_product2 (singleton zenon_TA_i) zenon_TC_x) (cartesian_product2 (singleton zenon_TB_j) D))/\(disjoint (cartesian_product2 zenon_TC_x (singleton zenon_TA_i)) (cartesian_product2 D (singleton zenon_TB_j)))))) zenon_H18); [ zenon_intro zenon_H19; idtac ].
% 0.19/0.52 elim zenon_H19. zenon_intro zenon_TD_ba. zenon_intro zenon_H1b.
% 0.19/0.52 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H7. zenon_intro zenon_H1c.
% 0.19/0.52 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 0.19/0.52 generalize (t127_zfmisc_1 (singleton zenon_TB_j)). zenon_intro zenon_H1f.
% 0.19/0.52 generalize (zenon_H1f (singleton zenon_TA_i)). zenon_intro zenon_H20.
% 0.19/0.52 generalize (zenon_H20 zenon_TD_ba). zenon_intro zenon_H21.
% 0.19/0.52 generalize (zenon_H21 zenon_TC_x). zenon_intro zenon_H22.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ].
% 0.19/0.52 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H6. zenon_intro zenon_H25.
% 0.19/0.52 apply (zenon_L1_ zenon_TA_i zenon_TB_j); trivial.
% 0.19/0.52 generalize (symmetry_r1_xboole_0 (cartesian_product2 (singleton zenon_TB_j) zenon_TD_ba)). zenon_intro zenon_H26.
% 0.19/0.52 generalize (zenon_H26 (cartesian_product2 (singleton zenon_TA_i) zenon_TC_x)). zenon_intro zenon_H27.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.19/0.52 exact (zenon_H29 zenon_H23).
% 0.19/0.52 exact (zenon_H1e zenon_H28).
% 0.19/0.52 generalize (t127_zfmisc_1 zenon_TD_ba). zenon_intro zenon_H2a.
% 0.19/0.52 generalize (zenon_H2a zenon_TC_x). zenon_intro zenon_H2b.
% 0.19/0.52 generalize (zenon_H2b (singleton zenon_TB_j)). zenon_intro zenon_H2c.
% 0.19/0.52 generalize (zenon_H2c (singleton zenon_TA_i)). zenon_intro zenon_H2d.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 0.19/0.52 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H25. zenon_intro zenon_H6.
% 0.19/0.52 apply (zenon_L1_ zenon_TA_i zenon_TB_j); trivial.
% 0.19/0.52 generalize (symmetry_r1_xboole_0 (cartesian_product2 zenon_TD_ba (singleton zenon_TB_j))). zenon_intro zenon_H30.
% 0.19/0.52 generalize (zenon_H30 (cartesian_product2 zenon_TC_x (singleton zenon_TA_i))). zenon_intro zenon_H31.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 0.19/0.52 exact (zenon_H33 zenon_H2e).
% 0.19/0.52 exact (zenon_H1d zenon_H32).
% 0.19/0.52 Qed.
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52 (* END-PROOF *)
% 0.19/0.52 nodes searched: 363
% 0.19/0.52 max branch formulas: 169
% 0.19/0.52 proof nodes created: 58
% 0.19/0.52 formulas created: 2305
% 0.19/0.52
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