%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------