TSTP Solution File: SET886+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n021.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 06:39:25 EDT 2022
% Result : Theorem 1.22s 1.45s
% Output : Proof 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 08:38:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.22/1.45 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 1.22/1.45 (* PROOF-FOUND *)
% 1.22/1.45 % SZS status Theorem
% 1.22/1.45 (* BEGIN-PROOF *)
% 1.22/1.45 % SZS output start Proof
% 1.22/1.45 Theorem t27_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, ((subset (unordered_pair A B) (singleton C))->((unordered_pair A B) = (singleton C)))))).
% 1.22/1.45 Proof.
% 1.22/1.45 assert (zenon_L1_ : forall (zenon_TC_m : zenon_U) (zenon_TB_n : zenon_U) (zenon_TA_o : zenon_U), (~((unordered_pair zenon_TA_o zenon_TB_n) = (singleton zenon_TC_m))) -> ((unordered_pair zenon_TC_m zenon_TC_m) = (singleton zenon_TC_m)) -> (zenon_TA_o = zenon_TC_m) -> (subset (unordered_pair zenon_TA_o zenon_TB_n) (singleton zenon_TC_m)) -> ((unordered_pair zenon_TB_n zenon_TA_o) = (unordered_pair zenon_TA_o zenon_TB_n)) -> False).
% 1.22/1.45 do 3 intro. intros zenon_H7 zenon_H8 zenon_H9 zenon_Ha zenon_Hb.
% 1.22/1.45 cut (((unordered_pair zenon_TC_m zenon_TC_m) = (singleton zenon_TC_m)) = ((unordered_pair zenon_TA_o zenon_TB_n) = (singleton zenon_TC_m))).
% 1.22/1.45 intro zenon_D_pnotp.
% 1.22/1.45 apply zenon_H7.
% 1.22/1.45 rewrite <- zenon_D_pnotp.
% 1.22/1.45 exact zenon_H8.
% 1.22/1.45 cut (((singleton zenon_TC_m) = (singleton zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_Hf].
% 1.22/1.45 cut (((unordered_pair zenon_TC_m zenon_TC_m) = (unordered_pair zenon_TA_o zenon_TB_n))); [idtac | apply NNPP; zenon_intro zenon_H10].
% 1.22/1.45 congruence.
% 1.22/1.45 elim (classic ((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TA_o zenon_TB_n))); [ zenon_intro zenon_H11 | zenon_intro zenon_H12 ].
% 1.22/1.45 cut (((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TA_o zenon_TB_n)) = ((unordered_pair zenon_TC_m zenon_TC_m) = (unordered_pair zenon_TA_o zenon_TB_n))).
% 1.22/1.45 intro zenon_D_pnotp.
% 1.22/1.45 apply zenon_H10.
% 1.22/1.45 rewrite <- zenon_D_pnotp.
% 1.22/1.45 exact zenon_H11.
% 1.22/1.45 cut (((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TA_o zenon_TB_n))); [idtac | apply NNPP; zenon_intro zenon_H12].
% 1.22/1.45 cut (((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TC_m zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_H13].
% 1.22/1.45 congruence.
% 1.22/1.45 cut ((zenon_TB_n = zenon_TC_m)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 1.22/1.45 cut ((zenon_TA_o = zenon_TC_m)); [idtac | apply NNPP; zenon_intro zenon_H15].
% 1.22/1.45 congruence.
% 1.22/1.45 exact (zenon_H15 zenon_H9).
% 1.22/1.45 generalize (t26_zfmisc_1 zenon_TB_n). zenon_intro zenon_H16.
% 1.22/1.45 generalize (zenon_H16 zenon_TA_o). zenon_intro zenon_H17.
% 1.22/1.45 generalize (zenon_H17 zenon_TC_m). zenon_intro zenon_H18.
% 1.22/1.45 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 1.22/1.45 cut ((subset (unordered_pair zenon_TA_o zenon_TB_n) (singleton zenon_TC_m)) = (subset (unordered_pair zenon_TB_n zenon_TA_o) (singleton zenon_TC_m))).
% 1.22/1.45 intro zenon_D_pnotp.
% 1.22/1.45 apply zenon_H1a.
% 1.22/1.45 rewrite <- zenon_D_pnotp.
% 1.22/1.45 exact zenon_Ha.
% 1.22/1.45 cut (((singleton zenon_TC_m) = (singleton zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_Hf].
% 1.22/1.45 cut (((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TB_n zenon_TA_o))); [idtac | apply NNPP; zenon_intro zenon_H1b].
% 1.22/1.45 congruence.
% 1.22/1.45 apply zenon_H1b. apply sym_equal. exact zenon_Hb.
% 1.22/1.45 apply zenon_Hf. apply refl_equal.
% 1.22/1.45 exact (zenon_H14 zenon_H19).
% 1.22/1.45 apply zenon_H12. apply refl_equal.
% 1.22/1.45 apply zenon_H12. apply refl_equal.
% 1.22/1.45 apply zenon_Hf. apply refl_equal.
% 1.22/1.45 (* end of lemma zenon_L1_ *)
% 1.22/1.45 apply NNPP. intro zenon_G.
% 1.22/1.45 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, ((subset (unordered_pair A B) (singleton C))->((unordered_pair A B) = (singleton C)))))) zenon_G); [ zenon_intro zenon_H1c; idtac ].
% 1.22/1.45 elim zenon_H1c. zenon_intro zenon_TA_o. zenon_intro zenon_H1d.
% 1.22/1.45 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((subset (unordered_pair zenon_TA_o B) (singleton C))->((unordered_pair zenon_TA_o B) = (singleton C))))) zenon_H1d); [ zenon_intro zenon_H1e; idtac ].
% 1.22/1.45 elim zenon_H1e. zenon_intro zenon_TB_n. zenon_intro zenon_H1f.
% 1.22/1.45 apply (zenon_notallex_s (fun C : zenon_U => ((subset (unordered_pair zenon_TA_o zenon_TB_n) (singleton C))->((unordered_pair zenon_TA_o zenon_TB_n) = (singleton C)))) zenon_H1f); [ zenon_intro zenon_H20; idtac ].
% 1.22/1.45 elim zenon_H20. zenon_intro zenon_TC_m. zenon_intro zenon_H21.
% 1.22/1.45 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_Ha. zenon_intro zenon_H7.
% 1.22/1.45 generalize (commutativity_k2_tarski zenon_TB_n). zenon_intro zenon_H22.
% 1.22/1.45 generalize (t69_enumset1 zenon_TC_m). zenon_intro zenon_H8.
% 1.22/1.45 generalize (zenon_H22 zenon_TA_o). zenon_intro zenon_Hb.
% 1.22/1.45 generalize (t26_zfmisc_1 zenon_TA_o). zenon_intro zenon_H23.
% 1.22/1.45 generalize (zenon_H23 zenon_TB_n). zenon_intro zenon_H24.
% 1.22/1.45 generalize (zenon_H24 zenon_TC_m). zenon_intro zenon_H25.
% 1.22/1.45 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H26 | zenon_intro zenon_H9 ].
% 1.22/1.45 exact (zenon_H26 zenon_Ha).
% 1.22/1.45 apply (zenon_L1_ zenon_TC_m zenon_TB_n zenon_TA_o); trivial.
% 1.22/1.45 Qed.
% 1.22/1.45 % SZS output end Proof
% 1.22/1.45 (* END-PROOF *)
% 1.22/1.45 nodes searched: 10573
% 1.22/1.45 max branch formulas: 1974
% 1.22/1.45 proof nodes created: 307
% 1.22/1.45 formulas created: 49601
% 1.22/1.45
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