TSTP Solution File: SET917+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET917+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n008.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 06:39:37 EDT 2022
% Result : Theorem 0.18s 0.50s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET917+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.13/0.32 % Computer : n008.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Sun Jul 10 12:21:53 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.18/0.50 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0
% 0.18/0.50 (* PROOF-FOUND *)
% 0.18/0.50 % SZS status Theorem
% 0.18/0.50 (* BEGIN-PROOF *)
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 Theorem t58_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, ((disjoint (singleton A) B)\/((set_intersection2 (singleton A) B) = (singleton A))))).
% 0.18/0.50 Proof.
% 0.18/0.50 apply NNPP. intro zenon_G.
% 0.18/0.50 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((disjoint (singleton A) B)\/((set_intersection2 (singleton A) B) = (singleton A))))) zenon_G); [ zenon_intro zenon_H9; idtac ].
% 0.18/0.50 elim zenon_H9. zenon_intro zenon_TA_k. zenon_intro zenon_Hb.
% 0.18/0.50 apply (zenon_notallex_s (fun B : zenon_U => ((disjoint (singleton zenon_TA_k) B)\/((set_intersection2 (singleton zenon_TA_k) B) = (singleton zenon_TA_k)))) zenon_Hb); [ zenon_intro zenon_Hc; idtac ].
% 0.18/0.50 elim zenon_Hc. zenon_intro zenon_TB_n. zenon_intro zenon_He.
% 0.18/0.50 apply (zenon_notor_s _ _ zenon_He). zenon_intro zenon_H10. zenon_intro zenon_Hf.
% 0.18/0.50 generalize (commutativity_k3_xboole_0 zenon_TB_n). zenon_intro zenon_H11.
% 0.18/0.50 generalize (l32_zfmisc_1 zenon_TA_k). zenon_intro zenon_H12.
% 0.18/0.50 generalize (zenon_H11 (singleton zenon_TA_k)). zenon_intro zenon_H13.
% 0.18/0.50 generalize (l28_zfmisc_1 zenon_TA_k). zenon_intro zenon_H14.
% 0.18/0.50 elim (classic ((singleton zenon_TA_k) = (singleton zenon_TA_k))); [ zenon_intro zenon_H15 | zenon_intro zenon_H16 ].
% 0.18/0.50 cut (((singleton zenon_TA_k) = (singleton zenon_TA_k)) = ((set_intersection2 (singleton zenon_TA_k) zenon_TB_n) = (singleton zenon_TA_k))).
% 0.18/0.50 intro zenon_D_pnotp.
% 0.18/0.50 apply zenon_Hf.
% 0.18/0.50 rewrite <- zenon_D_pnotp.
% 0.18/0.50 exact zenon_H15.
% 0.18/0.50 cut (((singleton zenon_TA_k) = (singleton zenon_TA_k))); [idtac | apply NNPP; zenon_intro zenon_H16].
% 0.18/0.50 cut (((singleton zenon_TA_k) = (set_intersection2 (singleton zenon_TA_k) zenon_TB_n))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 0.18/0.50 congruence.
% 0.18/0.50 cut (((set_intersection2 zenon_TB_n (singleton zenon_TA_k)) = (set_intersection2 (singleton zenon_TA_k) zenon_TB_n)) = ((singleton zenon_TA_k) = (set_intersection2 (singleton zenon_TA_k) zenon_TB_n))).
% 0.18/0.50 intro zenon_D_pnotp.
% 0.18/0.50 apply zenon_H17.
% 0.18/0.50 rewrite <- zenon_D_pnotp.
% 0.18/0.50 exact zenon_H13.
% 0.18/0.50 cut (((set_intersection2 (singleton zenon_TA_k) zenon_TB_n) = (set_intersection2 (singleton zenon_TA_k) zenon_TB_n))); [idtac | apply NNPP; zenon_intro zenon_H18].
% 0.18/0.50 cut (((set_intersection2 zenon_TB_n (singleton zenon_TA_k)) = (singleton zenon_TA_k))); [idtac | apply NNPP; zenon_intro zenon_H19].
% 0.18/0.50 congruence.
% 0.18/0.50 elim (classic ((singleton zenon_TA_k) = (singleton zenon_TA_k))); [ zenon_intro zenon_H15 | zenon_intro zenon_H16 ].
% 0.18/0.50 cut (((singleton zenon_TA_k) = (singleton zenon_TA_k)) = ((set_intersection2 zenon_TB_n (singleton zenon_TA_k)) = (singleton zenon_TA_k))).
% 0.18/0.50 intro zenon_D_pnotp.
% 0.18/0.50 apply zenon_H19.
% 0.18/0.50 rewrite <- zenon_D_pnotp.
% 0.18/0.50 exact zenon_H15.
% 0.18/0.50 cut (((singleton zenon_TA_k) = (singleton zenon_TA_k))); [idtac | apply NNPP; zenon_intro zenon_H16].
% 0.18/0.50 cut (((singleton zenon_TA_k) = (set_intersection2 zenon_TB_n (singleton zenon_TA_k)))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 0.18/0.50 congruence.
% 0.18/0.50 generalize (zenon_H12 zenon_TB_n). zenon_intro zenon_H1b.
% 0.18/0.50 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ].
% 0.18/0.50 generalize (zenon_H14 zenon_TB_n). zenon_intro zenon_H1e.
% 0.18/0.50 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ].
% 0.18/0.50 exact (zenon_H20 zenon_H1d).
% 0.18/0.50 exact (zenon_H10 zenon_H1f).
% 0.18/0.50 apply zenon_H1a. apply sym_equal. exact zenon_H1c.
% 0.18/0.50 apply zenon_H16. apply refl_equal.
% 0.18/0.50 apply zenon_H16. apply refl_equal.
% 0.18/0.50 apply zenon_H18. apply refl_equal.
% 0.18/0.50 apply zenon_H16. apply refl_equal.
% 0.18/0.50 apply zenon_H16. apply refl_equal.
% 0.18/0.50 Qed.
% 0.18/0.50 % SZS output end Proof
% 0.18/0.50 (* END-PROOF *)
% 0.18/0.50 nodes searched: 1425
% 0.18/0.50 max branch formulas: 381
% 0.18/0.50 proof nodes created: 138
% 0.18/0.50 formulas created: 3984
% 0.18/0.50
%------------------------------------------------------------------------------