TSTP Solution File: RNG111+4 by Zenon---0.7.1

%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : RNG111+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n019.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 20:48:29 EDT 2022

% Result   : Theorem 0.18s 0.54s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : RNG111+4 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_zenon %s %d
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon May 30 10:03:40 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.54  (* PROOF-FOUND *)
% 0.18/0.54  % SZS status Theorem
% 0.18/0.54  (* BEGIN-PROOF *)
% 0.18/0.54  % SZS output start Proof
% 0.18/0.54  Theorem m__ : (forall W0 : zenon_U, (((exists W1 : zenon_U, (exists W2 : zenon_U, ((aElementOf0 W1 (slsdtgt0 (xa)))/\((aElementOf0 W2 (slsdtgt0 (xb)))/\((sdtpldt0 W1 W2) = W0)))))/\((aElementOf0 W0 (xI))/\(~(W0 = (sz00)))))->((forall W1 : zenon_U, ((((exists W2 : zenon_U, (exists W3 : zenon_U, ((aElementOf0 W2 (slsdtgt0 (xa)))/\((aElementOf0 W3 (slsdtgt0 (xb)))/\((sdtpldt0 W2 W3) = W1)))))\/(aElementOf0 W1 (xI)))/\(~(W1 = (sz00))))->((iLess0 (sbrdtbr0 W1) (sbrdtbr0 W0))->(exists W2 : zenon_U, ((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (slsdtgt0 (xa)))/\((aElementOf0 W4 (slsdtgt0 (xb)))/\((sdtpldt0 W3 W4) = W2)))))/\((aElementOf0 W2 (xI))/\((~(W2 = (sz00)))/\(forall W3 : zenon_U, ((((exists W4 : zenon_U, (exists W5 : zenon_U, ((aElementOf0 W4 (slsdtgt0 (xa)))/\((aElementOf0 W5 (slsdtgt0 (xb)))/\((sdtpldt0 W4 W5) = W3)))))\/(aElementOf0 W3 (xI)))/\(~(W3 = (sz00))))->(~(iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2))))))))))))->(exists W1 : zenon_U, (((exists W2 : zenon_U, (exists W3 : zenon_U, ((aElementOf0 W2 (slsdtgt0 (xa)))/\((aElementOf0 W3 (slsdtgt0 (xb)))/\((sdtpldt0 W2 W3) = W1)))))\/(aElementOf0 W1 (xI)))/\((~(W1 = (sz00)))/\(forall W2 : zenon_U, (((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (slsdtgt0 (xa)))/\((aElementOf0 W4 (slsdtgt0 (xb)))/\((sdtpldt0 W3 W4) = W2)))))/\((aElementOf0 W2 (xI))/\(~(W2 = (sz00)))))->(~(iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))))).
% 0.18/0.54  Proof.
% 0.18/0.54  assert (zenon_L1_ : (exists W2 : zenon_U, ((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (slsdtgt0 (xa)))/\((aElementOf0 W4 (slsdtgt0 (xb)))/\((sdtpldt0 W3 W4) = W2)))))/\((aElementOf0 W2 (xI))/\((~(W2 = (sz00)))/\(forall W3 : zenon_U, ((((exists W4 : zenon_U, (exists W5 : zenon_U, ((aElementOf0 W4 (slsdtgt0 (xa)))/\((aElementOf0 W5 (slsdtgt0 (xb)))/\((sdtpldt0 W4 W5) = W3)))))\/(aElementOf0 W3 (xI)))/\(~(W3 = (sz00))))->(~(iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2))))))))) -> (~(exists W1 : zenon_U, (((exists W2 : zenon_U, (exists W3 : zenon_U, ((aElementOf0 W2 (slsdtgt0 (xa)))/\((aElementOf0 W3 (slsdtgt0 (xb)))/\((sdtpldt0 W2 W3) = W1)))))\/(aElementOf0 W1 (xI)))/\((~(W1 = (sz00)))/\(forall W2 : zenon_U, (((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (slsdtgt0 (xa)))/\((aElementOf0 W4 (slsdtgt0 (xb)))/\((sdtpldt0 W3 W4) = W2)))))/\((aElementOf0 W2 (xI))/\(~(W2 = (sz00)))))->(~(iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) -> False).
% 0.18/0.54  do 0 intro. intros zenon_H2d zenon_H2e.
% 0.18/0.54  elim zenon_H2d. zenon_intro zenon_TW2_bv. zenon_intro zenon_H30.
% 0.18/0.54  apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 0.18/0.54  apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 0.18/0.54  apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H36. zenon_intro zenon_H35.
% 0.18/0.54  apply zenon_H2e. exists zenon_TW2_bv. apply NNPP. zenon_intro zenon_H37.
% 0.18/0.54  apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ].
% 0.18/0.54  apply (zenon_notor_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 0.18/0.54  exact (zenon_H3b zenon_H32).
% 0.18/0.54  apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 0.18/0.54  exact (zenon_H3d zenon_H36).
% 0.18/0.54  apply (zenon_notallex_s (fun W2 : zenon_U => (((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (slsdtgt0 (xa)))/\((aElementOf0 W4 (slsdtgt0 (xb)))/\((sdtpldt0 W3 W4) = W2)))))/\((aElementOf0 W2 (xI))/\(~(W2 = (sz00)))))->(~(iLess0 (sbrdtbr0 W2) (sbrdtbr0 zenon_TW2_bv))))) zenon_H3c); [ zenon_intro zenon_H3e; idtac ].
% 0.18/0.54  elim zenon_H3e. zenon_intro zenon_TW2_cl. zenon_intro zenon_H40.
% 0.18/0.54  apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41.
% 0.18/0.54  apply zenon_H41. zenon_intro zenon_H43.
% 0.18/0.54  apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H45. zenon_intro zenon_H44.
% 0.18/0.54  apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H47. zenon_intro zenon_H46.
% 0.18/0.54  generalize (zenon_H35 zenon_TW2_cl). zenon_intro zenon_H48.
% 0.18/0.54  apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 0.18/0.54  apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 0.18/0.55  apply (zenon_notor_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 0.18/0.55  exact (zenon_H4e zenon_H45).
% 0.18/0.55  exact (zenon_H4b zenon_H46).
% 0.18/0.55  exact (zenon_H49 zenon_H43).
% 0.18/0.55  (* end of lemma zenon_L1_ *)
% 0.18/0.55  apply NNPP. intro zenon_G.
% 0.18/0.55  apply (zenon_notallex_s (fun W0 : zenon_U => (((exists W1 : zenon_U, (exists W2 : zenon_U, ((aElementOf0 W1 (slsdtgt0 (xa)))/\((aElementOf0 W2 (slsdtgt0 (xb)))/\((sdtpldt0 W1 W2) = W0)))))/\((aElementOf0 W0 (xI))/\(~(W0 = (sz00)))))->((forall W1 : zenon_U, ((((exists W2 : zenon_U, (exists W3 : zenon_U, ((aElementOf0 W2 (slsdtgt0 (xa)))/\((aElementOf0 W3 (slsdtgt0 (xb)))/\((sdtpldt0 W2 W3) = W1)))))\/(aElementOf0 W1 (xI)))/\(~(W1 = (sz00))))->((iLess0 (sbrdtbr0 W1) (sbrdtbr0 W0))->(exists W2 : zenon_U, ((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (slsdtgt0 (xa)))/\((aElementOf0 W4 (slsdtgt0 (xb)))/\((sdtpldt0 W3 W4) = W2)))))/\((aElementOf0 W2 (xI))/\((~(W2 = (sz00)))/\(forall W3 : zenon_U, ((((exists W4 : zenon_U, (exists W5 : zenon_U, ((aElementOf0 W4 (slsdtgt0 (xa)))/\((aElementOf0 W5 (slsdtgt0 (xb)))/\((sdtpldt0 W4 W5) = W3)))))\/(aElementOf0 W3 (xI)))/\(~(W3 = (sz00))))->(~(iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2))))))))))))->(exists W1 : zenon_U, (((exists W2 : zenon_U, (exists W3 : zenon_U, ((aElementOf0 W2 (slsdtgt0 (xa)))/\((aElementOf0 W3 (slsdtgt0 (xb)))/\((sdtpldt0 W2 W3) = W1)))))\/(aElementOf0 W1 (xI)))/\((~(W1 = (sz00)))/\(forall W2 : zenon_U, (((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (slsdtgt0 (xa)))/\((aElementOf0 W4 (slsdtgt0 (xb)))/\((sdtpldt0 W3 W4) = W2)))))/\((aElementOf0 W2 (xI))/\(~(W2 = (sz00)))))->(~(iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))))) zenon_G); [ zenon_intro zenon_H4f; idtac ].
% 0.18/0.55  elim zenon_H4f. zenon_intro zenon_TW0_dc. zenon_intro zenon_H51.
% 0.18/0.55  apply (zenon_notimply_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52.
% 0.18/0.55  apply (zenon_notimply_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H2e.
% 0.18/0.55  apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55.
% 0.18/0.55  apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57.
% 0.18/0.55  apply zenon_H2e. exists zenon_TW0_dc. apply NNPP. zenon_intro zenon_H59.
% 0.18/0.55  apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ].
% 0.18/0.55  apply (zenon_notor_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 0.18/0.55  exact (zenon_H5d zenon_H56).
% 0.18/0.55  apply (zenon_notand_s _ _ zenon_H5a); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ].
% 0.18/0.55  exact (zenon_H5f zenon_H57).
% 0.18/0.55  apply (zenon_notallex_s (fun W2 : zenon_U => (((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (slsdtgt0 (xa)))/\((aElementOf0 W4 (slsdtgt0 (xb)))/\((sdtpldt0 W3 W4) = W2)))))/\((aElementOf0 W2 (xI))/\(~(W2 = (sz00)))))->(~(iLess0 (sbrdtbr0 W2) (sbrdtbr0 zenon_TW0_dc))))) zenon_H5e); [ zenon_intro zenon_H60; idtac ].
% 0.18/0.55  elim zenon_H60. zenon_intro zenon_TW2_dt. zenon_intro zenon_H62.
% 0.18/0.55  apply (zenon_notimply_s _ _ zenon_H62). zenon_intro zenon_H64. zenon_intro zenon_H63.
% 0.18/0.55  apply zenon_H63. zenon_intro zenon_H65.
% 0.18/0.55  apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H67. zenon_intro zenon_H66.
% 0.18/0.55  apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68.
% 0.18/0.55  generalize (zenon_H54 zenon_TW2_dt). zenon_intro zenon_H6a.
% 0.18/0.55  apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ].
% 0.18/0.55  apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ].
% 0.18/0.55  apply (zenon_notor_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 0.18/0.55  exact (zenon_H70 zenon_H67).
% 0.18/0.55  exact (zenon_H6d zenon_H68).
% 0.18/0.55  apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H71 | zenon_intro zenon_H2d ].
% 0.18/0.55  exact (zenon_H71 zenon_H65).
% 0.18/0.55  apply (zenon_L1_); trivial.
% 0.18/0.55  Qed.
% 0.18/0.55  % SZS output end Proof
% 0.18/0.55  (* END-PROOF *)
% 0.18/0.55  nodes searched: 1045
% 0.18/0.55  max branch formulas: 622
% 0.18/0.55  proof nodes created: 49
% 0.18/0.55  formulas created: 9783
% 0.18/0.55  
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