TSTP Solution File: SET173+3 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n013.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 06:34:38 EDT 2022
% Result : Theorem 226.79s 226.97s
% Output : Proof 226.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n013.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 09:47:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 226.79/226.97 (* PROOF-FOUND *)
% 226.79/226.97 % SZS status Theorem
% 226.79/226.97 (* BEGIN-PROOF *)
% 226.79/226.97 % SZS output start Proof
% 226.79/226.97 Theorem prove_absorbtion_for_intersection : (forall B : zenon_U, (forall C : zenon_U, ((intersection B (union B C)) = B))).
% 226.79/226.97 Proof.
% 226.79/226.97 apply NNPP. intro zenon_G.
% 226.79/226.97 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((intersection B (union B C)) = B))) zenon_G); [ zenon_intro zenon_H9; idtac ].
% 226.79/226.97 elim zenon_H9. zenon_intro zenon_TB_k. zenon_intro zenon_Hb.
% 226.79/226.97 apply (zenon_notallex_s (fun C : zenon_U => ((intersection zenon_TB_k (union zenon_TB_k C)) = zenon_TB_k)) zenon_Hb); [ zenon_intro zenon_Hc; idtac ].
% 226.79/226.97 elim zenon_Hc. zenon_intro zenon_TC_n. zenon_intro zenon_He.
% 226.79/226.97 generalize (equal_member_defn zenon_TB_k). zenon_intro zenon_Hf.
% 226.79/226.97 generalize (intersection_defn zenon_TB_k). zenon_intro zenon_H10.
% 226.79/226.97 generalize (zenon_Hf (intersection zenon_TB_k (union zenon_TB_k zenon_TC_n))). zenon_intro zenon_H11.
% 226.79/226.97 apply (zenon_equiv_s _ _ zenon_H11); [ zenon_intro zenon_H15; zenon_intro zenon_H14 | zenon_intro zenon_H13; zenon_intro zenon_H12 ].
% 226.79/226.97 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_k)<->(member D (intersection zenon_TB_k (union zenon_TB_k zenon_TC_n))))) zenon_H14); [ zenon_intro zenon_H16; idtac ].
% 226.79/226.97 elim zenon_H16. zenon_intro zenon_TD_x. zenon_intro zenon_H18.
% 226.79/226.97 apply (zenon_notequiv_s _ _ zenon_H18); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H1a; zenon_intro zenon_H19 ].
% 226.79/226.97 generalize (zenon_H10 (union zenon_TB_k zenon_TC_n)). zenon_intro zenon_H1d.
% 226.79/226.97 generalize (zenon_H1d zenon_TD_x). zenon_intro zenon_H1e.
% 226.79/226.97 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H19; zenon_intro zenon_H20 | zenon_intro zenon_H1b; zenon_intro zenon_H1f ].
% 226.79/226.97 exact (zenon_H19 zenon_H1b).
% 226.79/226.97 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H1a. zenon_intro zenon_H21.
% 226.79/226.97 exact (zenon_H1c zenon_H1a).
% 226.79/226.97 generalize (zenon_H10 (union zenon_TB_k zenon_TC_n)). zenon_intro zenon_H1d.
% 226.79/226.97 generalize (zenon_H1d zenon_TD_x). zenon_intro zenon_H1e.
% 226.79/226.97 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H19; zenon_intro zenon_H20 | zenon_intro zenon_H1b; zenon_intro zenon_H1f ].
% 226.79/226.97 apply (zenon_notand_s _ _ zenon_H20); [ zenon_intro zenon_H1c | zenon_intro zenon_H22 ].
% 226.79/226.97 exact (zenon_H1c zenon_H1a).
% 226.79/226.97 generalize (union_defn zenon_TB_k). zenon_intro zenon_H23.
% 226.79/226.97 generalize (zenon_H23 zenon_TC_n). zenon_intro zenon_H24.
% 226.79/226.97 generalize (zenon_H24 zenon_TD_x). zenon_intro zenon_H25.
% 226.79/226.97 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H22; zenon_intro zenon_H27 | zenon_intro zenon_H21; zenon_intro zenon_H26 ].
% 226.79/226.97 apply (zenon_notor_s _ _ zenon_H27). zenon_intro zenon_H1c. zenon_intro zenon_H28.
% 226.79/226.97 exact (zenon_H1c zenon_H1a).
% 226.79/226.97 exact (zenon_H22 zenon_H21).
% 226.79/226.97 exact (zenon_H19 zenon_H1b).
% 226.79/226.97 apply zenon_He. apply sym_equal. exact zenon_H13.
% 226.79/226.97 Qed.
% 226.79/226.97 % SZS output end Proof
% 226.79/226.97 (* END-PROOF *)
% 226.79/226.97 nodes searched: 6346165
% 226.79/226.97 max branch formulas: 35309
% 226.79/226.97 proof nodes created: 160050
% 226.79/226.97 formulas created: 9546198
% 226.79/226.97
%------------------------------------------------------------------------------