TSTP Solution File: NUM588+3 by Zenon---0.7.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : NUM588+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n026.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 : Mon Jul 18 15:57:07 EDT 2022
% Result : Theorem 0.57s 0.75s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM588+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n026.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 : Wed Jul 6 21:40:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.75 (* PROOF-FOUND *)
% 0.57/0.75 % SZS status Theorem
% 0.57/0.75 (* BEGIN-PROOF *)
% 0.57/0.75 % SZS output start Proof
% 0.57/0.75 Theorem m__ : (forall W0 : zenon_U, ((aElementOf0 W0 (szNzAzT0))->(forall W1 : zenon_U, (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0))/\((forall W1 : zenon_U, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0))->(sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))/\((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))/\((forall W1 : zenon_U, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))<->((aElement0 W1)/\((aElementOf0 W1 (sdtlpdtrp0 (xN) W0))/\(~(W1 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))/\((aSet0 W1)/\((forall W2 : zenon_U, ((aElementOf0 W2 W1)->(aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))/\((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))/\(isCountable0 W1))))))))->(forall W2 : zenon_U, (((aSet0 W2)/\((forall W3 : zenon_U, ((aElementOf0 W3 W2)->(aElementOf0 W3 W1)))/\((aSubsetOf0 W2 W1)/\(((sbrdtbr0 W2) = (xk))/\(aElementOf0 W2 (slbdtsldtrb0 W1 (xk)))))))->(((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0))/\(forall W1 : zenon_U, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0))->(sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))))->(((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))/\(forall W1 : zenon_U, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))<->((aElement0 W1)/\((aElementOf0 W1 (sdtlpdtrp0 (xN) W0))/\(~(W1 = (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))))->((forall W3 : zenon_U, ((aElementOf0 W3 W2)->(aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))\/((aSubsetOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))\/(aElementOf0 W2 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))))))))).
% 0.57/0.75 Proof.
% 0.57/0.75 apply NNPP. intro zenon_G.
% 0.57/0.75 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (szNzAzT0))->(forall W1 : zenon_U, (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0))/\((forall W1 : zenon_U, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0))->(sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1)))/\((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))/\((forall W1 : zenon_U, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))<->((aElement0 W1)/\((aElementOf0 W1 (sdtlpdtrp0 (xN) W0))/\(~(W1 = (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))))/\((aSet0 W1)/\((forall W2 : zenon_U, ((aElementOf0 W2 W1)->(aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))/\((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))/\(isCountable0 W1))))))))->(forall W2 : zenon_U, (((aSet0 W2)/\((forall W3 : zenon_U, ((aElementOf0 W3 W2)->(aElementOf0 W3 W1)))/\((aSubsetOf0 W2 W1)/\(((sbrdtbr0 W2) = (xk))/\(aElementOf0 W2 (slbdtsldtrb0 W1 (xk)))))))->(((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) (sdtlpdtrp0 (xN) W0))/\(forall W1 : zenon_U, ((aElementOf0 W1 (sdtlpdtrp0 (xN) W0))->(sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) W0)) W1))))->(((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))/\(forall W1 : zenon_U, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))<->((aElement0 W1)/\((aElementOf0 W1 (sdtlpdtrp0 (xN) W0))/\(~(W1 = (szmzizndt0 (sdtlpdtrp0 (xN) W0)))))))))->((forall W3 : zenon_U, ((aElementOf0 W3 W2)->(aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))))\/((aSubsetOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))))\/(aElementOf0 W2 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) W0) (szmzizndt0 (sdtlpdtrp0 (xN) W0))) (xk))))))))))))) zenon_G); [ zenon_intro zenon_H57; idtac ].
% 0.57/0.75 elim zenon_H57. zenon_intro zenon_TW0_dk. zenon_intro zenon_H59.
% 0.57/0.75 apply (zenon_notimply_s _ _ zenon_H59). zenon_intro zenon_H5b. zenon_intro zenon_H5a.
% 0.57/0.75 apply (zenon_notallex_s (fun W1 : zenon_U => (((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk)) (sdtlpdtrp0 (xN) zenon_TW0_dk))/\((forall W1 : zenon_U, ((aElementOf0 W1 (sdtlpdtrp0 (xN) zenon_TW0_dk))->(sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk)) W1)))/\((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))/\((forall W1 : zenon_U, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))<->((aElement0 W1)/\((aElementOf0 W1 (sdtlpdtrp0 (xN) zenon_TW0_dk))/\(~(W1 = (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))))))/\((aSet0 W1)/\((forall W2 : zenon_U, ((aElementOf0 W2 W1)->(aElementOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))))/\((aSubsetOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))/\(isCountable0 W1))))))))->(forall W2 : zenon_U, (((aSet0 W2)/\((forall W3 : zenon_U, ((aElementOf0 W3 W2)->(aElementOf0 W3 W1)))/\((aSubsetOf0 W2 W1)/\(((sbrdtbr0 W2) = (xk))/\(aElementOf0 W2 (slbdtsldtrb0 W1 (xk)))))))->(((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk)) (sdtlpdtrp0 (xN) zenon_TW0_dk))/\(forall W1 : zenon_U, ((aElementOf0 W1 (sdtlpdtrp0 (xN) zenon_TW0_dk))->(sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk)) W1))))->(((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))/\(forall W1 : zenon_U, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))<->((aElement0 W1)/\((aElementOf0 W1 (sdtlpdtrp0 (xN) zenon_TW0_dk))/\(~(W1 = (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk)))))))))->((forall W3 : zenon_U, ((aElementOf0 W3 W2)->(aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))))\/((aSubsetOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))\/(aElementOf0 W2 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))) (xk))))))))))) zenon_H5a); [ zenon_intro zenon_H5c; idtac ].
% 0.57/0.75 elim zenon_H5c. zenon_intro zenon_TW1_dp. zenon_intro zenon_H5e.
% 0.57/0.75 apply (zenon_notimply_s _ _ zenon_H5e). zenon_intro zenon_H60. zenon_intro zenon_H5f.
% 0.57/0.75 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61.
% 0.57/0.75 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63.
% 0.57/0.75 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 0.57/0.75 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67.
% 0.57/0.75 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69.
% 0.57/0.75 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b.
% 0.57/0.75 apply (zenon_notallex_s (fun W2 : zenon_U => (((aSet0 W2)/\((forall W3 : zenon_U, ((aElementOf0 W3 W2)->(aElementOf0 W3 zenon_TW1_dp)))/\((aSubsetOf0 W2 zenon_TW1_dp)/\(((sbrdtbr0 W2) = (xk))/\(aElementOf0 W2 (slbdtsldtrb0 zenon_TW1_dp (xk)))))))->(((aElementOf0 (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk)) (sdtlpdtrp0 (xN) zenon_TW0_dk))/\(forall W1 : zenon_U, ((aElementOf0 W1 (sdtlpdtrp0 (xN) zenon_TW0_dk))->(sdtlseqdt0 (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk)) W1))))->(((aSet0 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))/\(forall W1 : zenon_U, ((aElementOf0 W1 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))<->((aElement0 W1)/\((aElementOf0 W1 (sdtlpdtrp0 (xN) zenon_TW0_dk))/\(~(W1 = (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk)))))))))->((forall W3 : zenon_U, ((aElementOf0 W3 W2)->(aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))))\/((aSubsetOf0 W2 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))))\/(aElementOf0 W2 (slbdtsldtrb0 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk))) (xk))))))))) zenon_H5f); [ zenon_intro zenon_H6d; idtac ].
% 0.57/0.75 elim zenon_H6d. zenon_intro zenon_TW2_eg. zenon_intro zenon_H6f.
% 0.57/0.75 apply (zenon_notimply_s _ _ zenon_H6f). zenon_intro zenon_H71. zenon_intro zenon_H70.
% 0.57/0.75 apply (zenon_notimply_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72.
% 0.57/0.75 apply (zenon_notimply_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74.
% 0.57/0.75 apply (zenon_notor_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76.
% 0.57/0.75 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H79. zenon_intro zenon_H78.
% 0.57/0.75 apply (zenon_and_s _ _ zenon_H78). zenon_intro zenon_H7b. zenon_intro zenon_H7a.
% 0.57/0.75 apply (zenon_notallex_s (fun W3 : zenon_U => ((aElementOf0 W3 zenon_TW2_eg)->(aElementOf0 W3 (sdtmndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk) (szmzizndt0 (sdtlpdtrp0 (xN) zenon_TW0_dk)))))) zenon_H77); [ zenon_intro zenon_H7c; idtac ].
% 0.57/0.75 elim zenon_H7c. zenon_intro zenon_TW3_ev. zenon_intro zenon_H7e.
% 0.57/0.75 apply (zenon_notimply_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f.
% 0.57/0.75 generalize (zenon_H6c zenon_TW3_ev). zenon_intro zenon_H81.
% 0.57/0.75 apply (zenon_imply_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ].
% 0.57/0.75 generalize (zenon_H7b zenon_TW3_ev). zenon_intro zenon_H84.
% 0.57/0.75 apply (zenon_imply_s _ _ zenon_H84); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ].
% 0.57/0.75 exact (zenon_H86 zenon_H80).
% 0.57/0.75 exact (zenon_H83 zenon_H85).
% 0.57/0.75 exact (zenon_H7f zenon_H82).
% 0.57/0.75 Qed.
% 0.57/0.75 % SZS output end Proof
% 0.57/0.75 (* END-PROOF *)
% 0.57/0.75 nodes searched: 3611
% 0.57/0.75 max branch formulas: 2574
% 0.57/0.75 proof nodes created: 107
% 0.57/0.75 formulas created: 43751
% 0.57/0.75
%------------------------------------------------------------------------------