TSTP Solution File: SET056+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET056+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 06:33:11 EDT 2022
% Result : Theorem 0.46s 0.70s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET056+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 22:41:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.46/0.70 (* PROOF-FOUND *)
% 0.46/0.70 % SZS status Theorem
% 0.46/0.70 (* BEGIN-PROOF *)
% 0.46/0.70 % SZS output start Proof
% 0.46/0.70 Theorem equality1 : (forall X : zenon_U, (forall Y : zenon_U, ((X = Y)\/((exists U : zenon_U, ((member U X)/\(~(member U Y))))\/(exists W : zenon_U, ((member W Y)/\(~(member W X)))))))).
% 0.46/0.70 Proof.
% 0.46/0.70 apply NNPP. intro zenon_G.
% 0.46/0.70 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, ((X = Y)\/((exists U : zenon_U, ((member U X)/\(~(member U Y))))\/(exists W : zenon_U, ((member W Y)/\(~(member W X)))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ].
% 0.46/0.70 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e.
% 0.46/0.70 apply (zenon_notallex_s (fun Y : zenon_U => ((zenon_TX_bt = Y)\/((exists U : zenon_U, ((member U zenon_TX_bt)/\(~(member U Y))))\/(exists W : zenon_U, ((member W Y)/\(~(member W zenon_TX_bt))))))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ].
% 0.46/0.70 elim zenon_H2f. zenon_intro zenon_TY_bw. zenon_intro zenon_H31.
% 0.46/0.70 apply (zenon_notor_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32.
% 0.46/0.70 apply (zenon_notor_s _ _ zenon_H32). zenon_intro zenon_H35. zenon_intro zenon_H34.
% 0.46/0.70 generalize (extensionality zenon_TY_bw). zenon_intro zenon_H36.
% 0.46/0.70 generalize (zenon_H36 zenon_TX_bt). zenon_intro zenon_H37.
% 0.46/0.70 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3b; zenon_intro zenon_H3a | zenon_intro zenon_H39; zenon_intro zenon_H38 ].
% 0.46/0.70 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 0.46/0.70 generalize (subclass_defn zenon_TY_bw). zenon_intro zenon_H3e.
% 0.46/0.70 generalize (zenon_H3e zenon_TX_bt). zenon_intro zenon_H3f.
% 0.46/0.70 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H3d; zenon_intro zenon_H42 | zenon_intro zenon_H41; zenon_intro zenon_H40 ].
% 0.46/0.70 apply (zenon_notallex_s (fun U : zenon_U => ((member U zenon_TY_bw)->(member U zenon_TX_bt))) zenon_H42); [ zenon_intro zenon_H43; idtac ].
% 0.46/0.70 elim zenon_H43. zenon_intro zenon_TU_cq. zenon_intro zenon_H45.
% 0.46/0.70 apply (zenon_notimply_s _ _ zenon_H45). zenon_intro zenon_H47. zenon_intro zenon_H46.
% 0.46/0.70 apply zenon_H34. exists zenon_TU_cq. apply NNPP. zenon_intro zenon_H48.
% 0.46/0.70 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 0.46/0.70 exact (zenon_H4a zenon_H47).
% 0.46/0.70 exact (zenon_H49 zenon_H46).
% 0.46/0.70 exact (zenon_H3d zenon_H41).
% 0.46/0.70 generalize (subclass_defn zenon_TX_bt). zenon_intro zenon_H4b.
% 0.46/0.70 generalize (zenon_H4b zenon_TY_bw). zenon_intro zenon_H4c.
% 0.46/0.70 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H3c; zenon_intro zenon_H4f | zenon_intro zenon_H4e; zenon_intro zenon_H4d ].
% 0.46/0.70 apply (zenon_notallex_s (fun U : zenon_U => ((member U zenon_TX_bt)->(member U zenon_TY_bw))) zenon_H4f); [ zenon_intro zenon_H50; idtac ].
% 0.46/0.70 elim zenon_H50. zenon_intro zenon_TU_dd. zenon_intro zenon_H52.
% 0.46/0.70 apply (zenon_notimply_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 0.46/0.70 apply zenon_H35. exists zenon_TU_dd. apply NNPP. zenon_intro zenon_H55.
% 0.46/0.70 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 0.46/0.70 exact (zenon_H57 zenon_H54).
% 0.46/0.70 exact (zenon_H56 zenon_H53).
% 0.46/0.70 exact (zenon_H3c zenon_H4e).
% 0.46/0.70 apply zenon_H33. apply sym_equal. exact zenon_H39.
% 0.46/0.70 Qed.
% 0.46/0.70 % SZS output end Proof
% 0.46/0.70 (* END-PROOF *)
% 0.46/0.70 nodes searched: 6097
% 0.46/0.70 max branch formulas: 1977
% 0.46/0.70 proof nodes created: 729
% 0.46/0.70 formulas created: 34690
% 0.46/0.70
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