%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : RNG093+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n020.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 20:48:26 EDT 2022 % Result : Theorem 51.77s 51.95s % Output : Proof 51.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG093+1 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n020.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 % 0.19/0.34 % CPULimit : 300 % 0.19/0.34 % WCLimit : 600 % 0.19/0.34 % DateTime : Mon May 30 19:07:08 EDT 2022 % 0.19/0.34 % CPUTime : % 51.77/51.95 (* PROOF-FOUND *) % 51.77/51.95 % SZS status Theorem % 51.77/51.95 (* BEGIN-PROOF *) % 51.77/51.95 % SZS output start Proof % 51.77/51.95 Theorem m__ : (aIdeal0 (sdtasasdt0 (xI) (xJ))). % 51.77/51.95 Proof. % 51.77/51.95 assert (zenon_L1_ : (forall W2 : zenon_U, ((W2 = (sdtasasdt0 (xI) (xJ)))<->((aSet0 W2)/\(forall W3 : zenon_U, ((aElementOf0 W3 W2)<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ)))))))) -> (~(aSet0 (sdtasasdt0 (xI) (xJ)))) -> False). % 51.77/51.95 do 0 intro. intros zenon_H1b zenon_H1c. % 51.77/51.95 generalize (zenon_H1b (sdtasasdt0 (xI) (xJ))). zenon_intro zenon_H1d. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ]. % 51.77/51.95 apply zenon_H21. apply refl_equal. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H23. zenon_intro zenon_H22. % 51.77/51.95 exact (zenon_H1c zenon_H23). % 51.77/51.95 (* end of lemma zenon_L1_ *) % 51.77/51.95 assert (zenon_L2_ : forall (zenon_TW1_bm : zenon_U), ((aElementOf0 zenon_TW1_bm (xI))/\(aElementOf0 zenon_TW1_bm (xJ))) -> (~(aElementOf0 zenon_TW1_bm (xI))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H24 zenon_H25. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H28. zenon_intro zenon_H27. % 51.77/51.95 exact (zenon_H25 zenon_H28). % 51.77/51.95 (* end of lemma zenon_L2_ *) % 51.77/51.95 assert (zenon_L3_ : forall (zenon_TW1_bm : zenon_U), (forall W3 : zenon_U, ((aElementOf0 W3 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ))))) -> (aElementOf0 zenon_TW1_bm (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 zenon_TW1_bm (xI))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H22 zenon_H29 zenon_H25. % 51.77/51.95 generalize (zenon_H22 zenon_TW1_bm). zenon_intro zenon_H2a. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H2c; zenon_intro zenon_H2b | zenon_intro zenon_H29; zenon_intro zenon_H24 ]. % 51.77/51.95 exact (zenon_H2c zenon_H29). % 51.77/51.95 apply (zenon_L2_ zenon_TW1_bm); trivial. % 51.77/51.95 (* end of lemma zenon_L3_ *) % 51.77/51.95 assert (zenon_L4_ : forall (zenon_TW2_bv : zenon_U), ((aElementOf0 zenon_TW2_bv (xI))/\(aElementOf0 zenon_TW2_bv (xJ))) -> (~(aElementOf0 zenon_TW2_bv (xI))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H2d zenon_H2e. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H31. zenon_intro zenon_H30. % 51.77/51.95 exact (zenon_H2e zenon_H31). % 51.77/51.95 (* end of lemma zenon_L4_ *) % 51.77/51.95 assert (zenon_L5_ : forall (zenon_TW2_bv : zenon_U) (zenon_TW1_bm : zenon_U), (forall W1 : zenon_U, ((aElementOf0 W1 (xI))->((forall W2 : zenon_U, ((aElementOf0 W2 (xI))->(aElementOf0 (sdtpldt0 W1 W2) (xI))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 W1) (xI))))))) -> (forall W3 : zenon_U, ((aElementOf0 W3 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ))))) -> (aElementOf0 zenon_TW1_bm (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 (sdtpldt0 zenon_TW1_bm zenon_TW2_bv) (xI))) -> (aElementOf0 zenon_TW2_bv (sdtasasdt0 (xI) (xJ))) -> False). % 51.77/51.95 do 2 intro. intros zenon_H32 zenon_H22 zenon_H29 zenon_H33 zenon_H34. % 51.77/51.95 generalize (zenon_H32 zenon_TW1_bm). zenon_intro zenon_H35. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H25 | zenon_intro zenon_H36 ]. % 51.77/51.95 apply (zenon_L3_ zenon_TW1_bm); trivial. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 51.77/51.95 generalize (zenon_H38 zenon_TW2_bv). zenon_intro zenon_H39. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H2e | zenon_intro zenon_H3a ]. % 51.77/51.95 generalize (zenon_H22 zenon_TW2_bv). zenon_intro zenon_H3b. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3d; zenon_intro zenon_H3c | zenon_intro zenon_H34; zenon_intro zenon_H2d ]. % 51.77/51.95 exact (zenon_H3d zenon_H34). % 51.77/51.95 apply (zenon_L4_ zenon_TW2_bv); trivial. % 51.77/51.95 exact (zenon_H33 zenon_H3a). % 51.77/51.95 (* end of lemma zenon_L5_ *) % 51.77/51.95 assert (zenon_L6_ : forall (zenon_TW1_bm : zenon_U), ((aElementOf0 zenon_TW1_bm (xI))/\(aElementOf0 zenon_TW1_bm (xJ))) -> (~(aElementOf0 zenon_TW1_bm (xJ))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H24 zenon_H3e. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H28. zenon_intro zenon_H27. % 51.77/51.95 exact (zenon_H3e zenon_H27). % 51.77/51.95 (* end of lemma zenon_L6_ *) % 51.77/51.95 assert (zenon_L7_ : forall (zenon_TW1_bm : zenon_U), (forall W3 : zenon_U, ((aElementOf0 W3 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ))))) -> (aElementOf0 zenon_TW1_bm (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 zenon_TW1_bm (xJ))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H22 zenon_H29 zenon_H3e. % 51.77/51.95 generalize (zenon_H22 zenon_TW1_bm). zenon_intro zenon_H2a. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H2c; zenon_intro zenon_H2b | zenon_intro zenon_H29; zenon_intro zenon_H24 ]. % 51.77/51.95 exact (zenon_H2c zenon_H29). % 51.77/51.95 apply (zenon_L6_ zenon_TW1_bm); trivial. % 51.77/51.95 (* end of lemma zenon_L7_ *) % 51.77/51.95 assert (zenon_L8_ : forall (zenon_TW2_bv : zenon_U), ((aElementOf0 zenon_TW2_bv (xI))/\(aElementOf0 zenon_TW2_bv (xJ))) -> (~(aElementOf0 zenon_TW2_bv (xJ))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H2d zenon_H3f. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H31. zenon_intro zenon_H30. % 51.77/51.95 exact (zenon_H3f zenon_H30). % 51.77/51.95 (* end of lemma zenon_L8_ *) % 51.77/51.95 assert (zenon_L9_ : forall (zenon_TW2_bv : zenon_U), (forall W3 : zenon_U, ((aElementOf0 W3 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ))))) -> (aElementOf0 zenon_TW2_bv (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 zenon_TW2_bv (xJ))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H22 zenon_H34 zenon_H3f. % 51.77/51.95 generalize (zenon_H22 zenon_TW2_bv). zenon_intro zenon_H3b. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3d; zenon_intro zenon_H3c | zenon_intro zenon_H34; zenon_intro zenon_H2d ]. % 51.77/51.95 exact (zenon_H3d zenon_H34). % 51.77/51.95 apply (zenon_L8_ zenon_TW2_bv); trivial. % 51.77/51.95 (* end of lemma zenon_L9_ *) % 51.77/51.95 assert (zenon_L10_ : forall (zenon_TW2_bv : zenon_U) (zenon_TW1_bm : zenon_U), (forall W1 : zenon_U, ((aElementOf0 W1 (xJ))->((forall W2 : zenon_U, ((aElementOf0 W2 (xJ))->(aElementOf0 (sdtpldt0 W1 W2) (xJ))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 W1) (xJ))))))) -> (forall W3 : zenon_U, ((aElementOf0 W3 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ))))) -> (aElementOf0 zenon_TW1_bm (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 (sdtpldt0 zenon_TW1_bm zenon_TW2_bv) (xJ))) -> (aElementOf0 zenon_TW2_bv (sdtasasdt0 (xI) (xJ))) -> False). % 51.77/51.95 do 2 intro. intros zenon_H40 zenon_H22 zenon_H29 zenon_H41 zenon_H34. % 51.77/51.95 generalize (zenon_H40 zenon_TW1_bm). zenon_intro zenon_H42. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H3e | zenon_intro zenon_H43 ]. % 51.77/51.95 apply (zenon_L7_ zenon_TW1_bm); trivial. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44. % 51.77/51.95 generalize (zenon_H45 zenon_TW2_bv). zenon_intro zenon_H46. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H3f | zenon_intro zenon_H47 ]. % 51.77/51.95 apply (zenon_L9_ zenon_TW2_bv); trivial. % 51.77/51.95 exact (zenon_H41 zenon_H47). % 51.77/51.95 (* end of lemma zenon_L10_ *) % 51.77/51.95 assert (zenon_L11_ : forall (zenon_TW3_cx : zenon_U), (forall W3 : zenon_U, ((aElementOf0 W3 (sdtasasdt0 (xJ) (xI)))<->((aElementOf0 W3 (xJ))/\(aElementOf0 W3 (xI))))) -> (aElementOf0 zenon_TW3_cx (sdtasasdt0 (xJ) (xI))) -> (~(aElementOf0 zenon_TW3_cx (xI))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H48 zenon_H49 zenon_H4a. % 51.77/51.95 generalize (zenon_H48 zenon_TW3_cx). zenon_intro zenon_H4c. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H49; zenon_intro zenon_H4d ]. % 51.77/51.95 exact (zenon_H4f zenon_H49). % 51.77/51.95 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H51. zenon_intro zenon_H50. % 51.77/51.95 exact (zenon_H4a zenon_H50). % 51.77/51.95 (* end of lemma zenon_L11_ *) % 51.77/51.95 assert (zenon_L12_ : forall (zenon_TW1_bm : zenon_U), (forall W2 : zenon_U, ((W2 = (sdtasasdt0 (xI) (xJ)))<->((aSet0 W2)/\(forall W3 : zenon_U, ((aElementOf0 W3 W2)<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ)))))))) -> (~(aElementOf0 zenon_TW1_bm (xJ))) -> (aElementOf0 zenon_TW1_bm (sdtasasdt0 (xI) (xJ))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H1b zenon_H3e zenon_H29. % 51.77/51.95 generalize (zenon_H1b (sdtasasdt0 (xI) (xJ))). zenon_intro zenon_H1d. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ]. % 51.77/51.95 apply zenon_H21. apply refl_equal. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H23. zenon_intro zenon_H22. % 51.77/51.95 apply (zenon_L7_ zenon_TW1_bm); trivial. % 51.77/51.95 (* end of lemma zenon_L12_ *) % 51.77/51.95 assert (zenon_L13_ : forall (zenon_TW2_dg : zenon_U) (zenon_TW1_bm : zenon_U), (forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 zenon_TW1_bm) (xJ)))) -> (aElement0 zenon_TW2_dg) -> (~(aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (xJ))) -> False). % 51.77/51.95 do 2 intro. intros zenon_H44 zenon_H52 zenon_H53. % 51.77/51.95 generalize (zenon_H44 zenon_TW2_dg). zenon_intro zenon_H55. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 51.77/51.95 exact (zenon_H57 zenon_H52). % 51.77/51.95 exact (zenon_H53 zenon_H56). % 51.77/51.95 (* end of lemma zenon_L13_ *) % 51.77/51.95 assert (zenon_L14_ : forall (zenon_TW2_dg : zenon_U) (zenon_TW1_bm : zenon_U), ((forall W2 : zenon_U, ((aElementOf0 W2 (xJ))->(aElementOf0 (sdtpldt0 zenon_TW1_bm W2) (xJ))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 zenon_TW1_bm) (xJ))))) -> (~(aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (xJ))) -> (aElement0 zenon_TW2_dg) -> False). % 51.77/51.95 do 2 intro. intros zenon_H43 zenon_H53 zenon_H52. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44. % 51.77/51.95 apply (zenon_L13_ zenon_TW2_dg zenon_TW1_bm); trivial. % 51.77/51.95 (* end of lemma zenon_L14_ *) % 51.77/51.95 assert (zenon_L15_ : forall (zenon_TW1_bm : zenon_U), (forall W2 : zenon_U, ((W2 = (sdtasasdt0 (xI) (xJ)))<->((aSet0 W2)/\(forall W3 : zenon_U, ((aElementOf0 W3 W2)<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ)))))))) -> (~(aElementOf0 zenon_TW1_bm (xI))) -> (aElementOf0 zenon_TW1_bm (sdtasasdt0 (xI) (xJ))) -> False). % 51.77/51.95 do 1 intro. intros zenon_H1b zenon_H25 zenon_H29. % 51.77/51.95 generalize (zenon_H1b (sdtasasdt0 (xI) (xJ))). zenon_intro zenon_H1d. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ]. % 51.77/51.95 apply zenon_H21. apply refl_equal. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H23. zenon_intro zenon_H22. % 51.77/51.95 apply (zenon_L3_ zenon_TW1_bm); trivial. % 51.77/51.95 (* end of lemma zenon_L15_ *) % 51.77/51.95 assert (zenon_L16_ : forall (zenon_TW2_dg : zenon_U) (zenon_TW1_bm : zenon_U), (forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 zenon_TW1_bm) (xI)))) -> (aElement0 zenon_TW2_dg) -> (~(aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (xI))) -> False). % 51.77/51.95 do 2 intro. intros zenon_H37 zenon_H52 zenon_H58. % 51.77/51.95 generalize (zenon_H37 zenon_TW2_dg). zenon_intro zenon_H59. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H57 | zenon_intro zenon_H5a ]. % 51.77/51.95 exact (zenon_H57 zenon_H52). % 51.77/51.95 exact (zenon_H58 zenon_H5a). % 51.77/51.95 (* end of lemma zenon_L16_ *) % 51.77/51.95 assert (zenon_L17_ : forall (zenon_TW2_dg : zenon_U) (zenon_TW1_bm : zenon_U), ((forall W2 : zenon_U, ((aElementOf0 W2 (xI))->(aElementOf0 (sdtpldt0 zenon_TW1_bm W2) (xI))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 zenon_TW1_bm) (xI))))) -> (~(aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (xI))) -> (aElement0 zenon_TW2_dg) -> False). % 51.77/51.95 do 2 intro. intros zenon_H36 zenon_H58 zenon_H52. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 51.77/51.95 apply (zenon_L16_ zenon_TW2_dg zenon_TW1_bm); trivial. % 51.77/51.95 (* end of lemma zenon_L17_ *) % 51.77/51.95 assert (zenon_L18_ : forall (zenon_TW2_dg : zenon_U) (zenon_TW1_bm : zenon_U), (forall W1 : zenon_U, ((aElementOf0 W1 (xI))->((forall W2 : zenon_U, ((aElementOf0 W2 (xI))->(aElementOf0 (sdtpldt0 W1 W2) (xI))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 W1) (xI))))))) -> (forall W2 : zenon_U, ((W2 = (sdtasasdt0 (xI) (xJ)))<->((aSet0 W2)/\(forall W3 : zenon_U, ((aElementOf0 W3 W2)<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ)))))))) -> (aElementOf0 zenon_TW1_bm (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (xI))) -> (aElement0 zenon_TW2_dg) -> False). % 51.77/51.95 do 2 intro. intros zenon_H32 zenon_H1b zenon_H29 zenon_H58 zenon_H52. % 51.77/51.95 generalize (zenon_H32 zenon_TW1_bm). zenon_intro zenon_H35. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H25 | zenon_intro zenon_H36 ]. % 51.77/51.95 apply (zenon_L15_ zenon_TW1_bm); trivial. % 51.77/51.95 apply (zenon_L17_ zenon_TW2_dg zenon_TW1_bm); trivial. % 51.77/51.95 (* end of lemma zenon_L18_ *) % 51.77/51.95 assert (zenon_L19_ : forall (zenon_TW1_bm : zenon_U) (zenon_TW2_dg : zenon_U), (~((aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (xJ))/\(aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (xI)))) -> (forall W1 : zenon_U, ((aElementOf0 W1 (xI))->((forall W2 : zenon_U, ((aElementOf0 W2 (xI))->(aElementOf0 (sdtpldt0 W1 W2) (xI))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 W1) (xI))))))) -> (aElement0 zenon_TW2_dg) -> (aElementOf0 zenon_TW1_bm (sdtasasdt0 (xI) (xJ))) -> (forall W2 : zenon_U, ((W2 = (sdtasasdt0 (xI) (xJ)))<->((aSet0 W2)/\(forall W3 : zenon_U, ((aElementOf0 W3 W2)<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ)))))))) -> (forall W1 : zenon_U, ((aElementOf0 W1 (xJ))->((forall W2 : zenon_U, ((aElementOf0 W2 (xJ))->(aElementOf0 (sdtpldt0 W1 W2) (xJ))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 W1) (xJ))))))) -> False). % 51.77/51.95 do 2 intro. intros zenon_H5b zenon_H32 zenon_H52 zenon_H29 zenon_H1b zenon_H40. % 51.77/51.95 apply (zenon_notand_s _ _ zenon_H5b); [ zenon_intro zenon_H53 | zenon_intro zenon_H58 ]. % 51.77/51.95 generalize (zenon_H40 zenon_TW1_bm). zenon_intro zenon_H42. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H3e | zenon_intro zenon_H43 ]. % 51.77/51.95 apply (zenon_L12_ zenon_TW1_bm); trivial. % 51.77/51.95 apply (zenon_L14_ zenon_TW2_dg zenon_TW1_bm); trivial. % 51.77/51.95 apply (zenon_L18_ zenon_TW2_dg zenon_TW1_bm); trivial. % 51.77/51.95 (* end of lemma zenon_L19_ *) % 51.77/51.95 assert (zenon_L20_ : forall (zenon_TW1_bm : zenon_U) (zenon_TW2_dg : zenon_U), (forall W3 : zenon_U, ((aElementOf0 W3 (sdtasasdt0 (xJ) (xI)))<->((aElementOf0 W3 (xJ))/\(aElementOf0 W3 (xI))))) -> (forall W1 : zenon_U, ((aElementOf0 W1 (xI))->((forall W2 : zenon_U, ((aElementOf0 W2 (xI))->(aElementOf0 (sdtpldt0 W1 W2) (xI))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 W1) (xI))))))) -> (aElement0 zenon_TW2_dg) -> (aElementOf0 zenon_TW1_bm (sdtasasdt0 (xI) (xJ))) -> (forall W2 : zenon_U, ((W2 = (sdtasasdt0 (xI) (xJ)))<->((aSet0 W2)/\(forall W3 : zenon_U, ((aElementOf0 W3 W2)<->((aElementOf0 W3 (xI))/\(aElementOf0 W3 (xJ)))))))) -> (forall W1 : zenon_U, ((aElementOf0 W1 (xJ))->((forall W2 : zenon_U, ((aElementOf0 W2 (xJ))->(aElementOf0 (sdtpldt0 W1 W2) (xJ))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 W1) (xJ))))))) -> (~(aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (sdtasasdt0 (xJ) (xI)))) -> False). % 51.77/51.95 do 2 intro. intros zenon_H48 zenon_H32 zenon_H52 zenon_H29 zenon_H1b zenon_H40 zenon_H5c. % 51.77/51.95 generalize (zenon_H48 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm)). zenon_intro zenon_H5d. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H5c; zenon_intro zenon_H5b | zenon_intro zenon_H5f; zenon_intro zenon_H5e ]. % 51.77/51.95 apply (zenon_L19_ zenon_TW1_bm zenon_TW2_dg); trivial. % 51.77/51.95 exact (zenon_H5c zenon_H5f). % 51.77/51.95 (* end of lemma zenon_L20_ *) % 51.77/51.95 assert (zenon_L21_ : forall (zenon_TW1_bm : zenon_U) (zenon_TW2_dg : zenon_U), ((aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (sdtasasdt0 (xI) (xJ)))/\(aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (xI))) -> (~(aElementOf0 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm) (sdtasasdt0 (xI) (xJ)))) -> False). % 51.77/51.95 do 2 intro. intros zenon_H60 zenon_H61. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H5a. % 51.77/51.95 exact (zenon_H61 zenon_H62). % 51.77/51.95 (* end of lemma zenon_L21_ *) % 51.77/51.95 apply NNPP. intro zenon_G. % 51.77/51.95 apply (zenon_and_s _ _ m__1150). zenon_intro zenon_H64. zenon_intro zenon_H63. % 51.77/51.95 generalize (mDefIdeal (xI)). zenon_intro zenon_H65. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H68; zenon_intro zenon_H67 | zenon_intro zenon_H64; zenon_intro zenon_H66 ]. % 51.77/51.95 exact (zenon_H68 zenon_H64). % 51.77/51.95 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H32. % 51.77/51.95 generalize (mDefIdeal (xJ)). zenon_intro zenon_H6a. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H6a); [ zenon_intro zenon_H6d; zenon_intro zenon_H6c | zenon_intro zenon_H63; zenon_intro zenon_H6b ]. % 51.77/51.95 exact (zenon_H6d zenon_H63). % 51.77/51.95 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H40. % 51.77/51.95 generalize (mDefIdeal (sdtasasdt0 (xI) (xJ))). zenon_intro zenon_H6f. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H6f); [ zenon_intro zenon_G; zenon_intro zenon_H72 | zenon_intro zenon_H71; zenon_intro zenon_H70 ]. % 51.77/51.95 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H1c | zenon_intro zenon_H73 ]. % 51.77/51.95 generalize (mDefSInt (xI)). zenon_intro zenon_H74. % 51.77/51.95 generalize (zenon_H74 (xJ)). zenon_intro zenon_H75. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H76 | zenon_intro zenon_H1b ]. % 51.77/51.95 apply (zenon_notand_s _ _ zenon_H76); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 51.77/51.95 exact (zenon_H78 zenon_H69). % 51.77/51.95 exact (zenon_H77 zenon_H6e). % 51.77/51.95 apply (zenon_L1_); trivial. % 51.77/51.95 apply (zenon_notallex_s (fun W1 : zenon_U => ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ)))->((forall W2 : zenon_U, ((aElementOf0 W2 (sdtasasdt0 (xI) (xJ)))->(aElementOf0 (sdtpldt0 W1 W2) (sdtasasdt0 (xI) (xJ)))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 W1) (sdtasasdt0 (xI) (xJ)))))))) zenon_H73); [ zenon_intro zenon_H79; idtac ]. % 51.77/51.95 elim zenon_H79. zenon_intro zenon_TW1_bm. zenon_intro zenon_H7a. % 51.77/51.95 apply (zenon_notimply_s _ _ zenon_H7a). zenon_intro zenon_H29. zenon_intro zenon_H7b. % 51.77/51.95 apply (zenon_notand_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 51.77/51.95 apply (zenon_notallex_s (fun W2 : zenon_U => ((aElementOf0 W2 (sdtasasdt0 (xI) (xJ)))->(aElementOf0 (sdtpldt0 zenon_TW1_bm W2) (sdtasasdt0 (xI) (xJ))))) zenon_H7d); [ zenon_intro zenon_H7e; idtac ]. % 51.77/51.95 elim zenon_H7e. zenon_intro zenon_TW2_bv. zenon_intro zenon_H7f. % 51.77/51.95 apply (zenon_notimply_s _ _ zenon_H7f). zenon_intro zenon_H34. zenon_intro zenon_H80. % 51.77/51.95 generalize (mDefSInt (xI)). zenon_intro zenon_H74. % 51.77/51.95 generalize (zenon_H74 (xJ)). zenon_intro zenon_H75. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H76 | zenon_intro zenon_H1b ]. % 51.77/51.95 apply (zenon_notand_s _ _ zenon_H76); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 51.77/51.95 exact (zenon_H78 zenon_H69). % 51.77/51.95 exact (zenon_H77 zenon_H6e). % 51.77/51.95 generalize (zenon_H1b (sdtasasdt0 (xI) (xJ))). zenon_intro zenon_H1d. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ]. % 51.77/51.95 apply zenon_H21. apply refl_equal. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H23. zenon_intro zenon_H22. % 51.77/51.95 generalize (zenon_H22 (sdtpldt0 zenon_TW1_bm zenon_TW2_bv)). zenon_intro zenon_H81. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H80; zenon_intro zenon_H84 | zenon_intro zenon_H83; zenon_intro zenon_H82 ]. % 51.77/51.95 apply (zenon_notand_s _ _ zenon_H84); [ zenon_intro zenon_H33 | zenon_intro zenon_H41 ]. % 51.77/51.95 apply (zenon_L5_ zenon_TW2_bv zenon_TW1_bm); trivial. % 51.77/51.95 apply (zenon_L10_ zenon_TW2_bv zenon_TW1_bm); trivial. % 51.77/51.95 exact (zenon_H80 zenon_H83). % 51.77/51.95 apply (zenon_notallex_s (fun W2 : zenon_U => ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 zenon_TW1_bm) (sdtasasdt0 (xI) (xJ))))) zenon_H7c); [ zenon_intro zenon_H85; idtac ]. % 51.77/51.95 elim zenon_H85. zenon_intro zenon_TW2_dg. zenon_intro zenon_H86. % 51.77/51.95 apply (zenon_notimply_s _ _ zenon_H86). zenon_intro zenon_H52. zenon_intro zenon_H61. % 51.77/51.95 generalize (mDefSInt (xJ)). zenon_intro zenon_H87. % 51.77/51.95 generalize (mDefSInt (xI)). zenon_intro zenon_H74. % 51.77/51.95 generalize (zenon_H87 (xI)). zenon_intro zenon_H88. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H8a | zenon_intro zenon_H89 ]. % 51.77/51.95 apply (zenon_notand_s _ _ zenon_H8a); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 51.77/51.95 exact (zenon_H77 zenon_H6e). % 51.77/51.95 exact (zenon_H78 zenon_H69). % 51.77/51.95 generalize (zenon_H74 (xJ)). zenon_intro zenon_H75. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H76 | zenon_intro zenon_H1b ]. % 51.77/51.95 apply (zenon_notand_s _ _ zenon_H76); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 51.77/51.95 exact (zenon_H78 zenon_H69). % 51.77/51.95 exact (zenon_H77 zenon_H6e). % 51.77/51.95 generalize (mDefSInt (sdtasasdt0 (xI) (xJ))). zenon_intro zenon_H8b. % 51.77/51.95 generalize (zenon_H8b (xI)). zenon_intro zenon_H8c. % 51.77/51.95 apply (zenon_imply_s _ _ zenon_H8c); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ]. % 51.77/51.95 apply (zenon_notand_s _ _ zenon_H8e); [ zenon_intro zenon_H1c | zenon_intro zenon_H78 ]. % 51.77/51.95 apply (zenon_L1_); trivial. % 51.77/51.95 exact (zenon_H78 zenon_H69). % 51.77/51.95 generalize (zenon_H1b (sdtasasdt0 (xI) (xJ))). zenon_intro zenon_H1d. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ]. % 51.77/51.95 apply zenon_H21. apply refl_equal. % 51.77/51.95 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H23. zenon_intro zenon_H22. % 51.77/51.95 generalize (zenon_H89 (sdtasasdt0 (xJ) (xI))). zenon_intro zenon_H8f. % 51.77/51.95 apply (zenon_equiv_s _ _ zenon_H8f); [ zenon_intro zenon_H93; zenon_intro zenon_H92 | zenon_intro zenon_H91; zenon_intro zenon_H90 ]. % 51.77/51.96 apply zenon_H93. apply refl_equal. % 51.77/51.96 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H94. zenon_intro zenon_H48. % 51.77/51.96 generalize (zenon_H8d (sdtasasdt0 (xJ) (xI))). zenon_intro zenon_H95. % 51.77/51.96 apply (zenon_equiv_s _ _ zenon_H95); [ zenon_intro zenon_H99; zenon_intro zenon_H98 | zenon_intro zenon_H97; zenon_intro zenon_H96 ]. % 51.77/51.96 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H9b | zenon_intro zenon_H9a ]. % 51.77/51.96 exact (zenon_H9b zenon_H94). % 51.77/51.96 apply (zenon_notallex_s (fun W3 : zenon_U => ((aElementOf0 W3 (sdtasasdt0 (xJ) (xI)))<->((aElementOf0 W3 (sdtasasdt0 (xI) (xJ)))/\(aElementOf0 W3 (xI))))) zenon_H9a); [ zenon_intro zenon_H9c; idtac ]. % 51.77/51.96 elim zenon_H9c. zenon_intro zenon_TW3_cx. zenon_intro zenon_H9d. % 51.77/51.96 apply (zenon_notequiv_s _ _ zenon_H9d); [ zenon_intro zenon_H4f; zenon_intro zenon_H9f | zenon_intro zenon_H49; zenon_intro zenon_H9e ]. % 51.77/51.96 apply (zenon_and_s _ _ zenon_H9f). zenon_intro zenon_Ha0. zenon_intro zenon_H50. % 51.77/51.96 generalize (zenon_H48 zenon_TW3_cx). zenon_intro zenon_H4c. % 51.77/51.96 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H49; zenon_intro zenon_H4d ]. % 51.77/51.96 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H4a ]. % 51.77/51.96 generalize (zenon_H22 zenon_TW3_cx). zenon_intro zenon_Ha2. % 51.77/51.96 apply (zenon_equiv_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha5; zenon_intro zenon_Ha4 | zenon_intro zenon_Ha0; zenon_intro zenon_Ha3 ]. % 51.77/51.96 exact (zenon_Ha5 zenon_Ha0). % 51.77/51.96 apply (zenon_and_s _ _ zenon_Ha3). zenon_intro zenon_H50. zenon_intro zenon_H51. % 51.77/51.96 exact (zenon_Ha1 zenon_H51). % 51.77/51.96 exact (zenon_H4a zenon_H50). % 51.77/51.96 exact (zenon_H4f zenon_H49). % 51.77/51.96 apply (zenon_notand_s _ _ zenon_H9e); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H4a ]. % 51.77/51.96 generalize (zenon_H22 zenon_TW3_cx). zenon_intro zenon_Ha2. % 51.77/51.96 apply (zenon_equiv_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha5; zenon_intro zenon_Ha4 | zenon_intro zenon_Ha0; zenon_intro zenon_Ha3 ]. % 51.77/51.96 apply (zenon_notand_s _ _ zenon_Ha4); [ zenon_intro zenon_H4a | zenon_intro zenon_Ha1 ]. % 51.77/51.96 apply (zenon_L11_ zenon_TW3_cx); trivial. % 51.77/51.96 generalize (zenon_H48 zenon_TW3_cx). zenon_intro zenon_H4c. % 51.77/51.96 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H49; zenon_intro zenon_H4d ]. % 51.77/51.96 exact (zenon_H4f zenon_H49). % 51.77/51.96 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H51. zenon_intro zenon_H50. % 51.77/51.96 exact (zenon_Ha1 zenon_H51). % 51.77/51.96 exact (zenon_Ha5 zenon_Ha0). % 51.77/51.96 apply (zenon_L11_ zenon_TW3_cx); trivial. % 51.77/51.96 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H94. zenon_intro zenon_Ha6. % 51.77/51.96 generalize (zenon_Ha6 (sdtasdt0 zenon_TW2_dg zenon_TW1_bm)). zenon_intro zenon_Ha7. % 51.77/51.96 apply (zenon_equiv_s _ _ zenon_Ha7); [ zenon_intro zenon_H5c; zenon_intro zenon_Ha8 | zenon_intro zenon_H5f; zenon_intro zenon_H60 ]. % 51.77/51.96 apply (zenon_L20_ zenon_TW1_bm zenon_TW2_dg); trivial. % 51.77/51.96 apply (zenon_L21_ zenon_TW1_bm zenon_TW2_dg); trivial. % 51.77/51.96 exact (zenon_G zenon_H71). % 51.77/51.96 Qed. % 51.77/51.96 % SZS output end Proof % 51.77/51.96 (* END-PROOF *) % 51.77/51.96 nodes searched: 1279037 % 51.77/51.96 max branch formulas: 14329 % 51.77/51.96 proof nodes created: 28126 % 51.77/51.96 formulas created: 2376396 % 51.77/51.96 %------------------------------------------------------------------------------