%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : RNG111+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 0.19s 0.56s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : RNG111+1 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n017.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon May 30 20:59:10 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.56 (* PROOF-FOUND *) % 0.19/0.56 % SZS status Theorem % 0.19/0.56 (* BEGIN-PROOF *) % 0.19/0.56 % SZS output start Proof % 0.19/0.56 Theorem m__ : (forall W0 : zenon_U, (((aElementOf0 W0 (xI))/\(~(W0 = (sz00))))->((forall W1 : zenon_U, (((aElementOf0 W1 (xI))/\(~(W1 = (sz00))))->((iLess0 (sbrdtbr0 W1) (sbrdtbr0 W0))->(exists W2 : zenon_U, ((aElementOf0 W2 (xI))/\((~(W2 = (sz00)))/\(forall W3 : zenon_U, (((aElementOf0 W3 (xI))/\(~(W3 = (sz00))))->(~(iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2)))))))))))->(exists W2 : zenon_U, ((aElementOf0 W2 (xI))/\((~(W2 = (sz00)))/\(forall W3 : zenon_U, (((aElementOf0 W3 (xI))/\(~(W3 = (sz00))))->(~(iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2))))))))))). % 0.19/0.56 Proof. % 0.19/0.56 apply NNPP. intro zenon_G. % 0.19/0.56 apply (zenon_notallex_s (fun W0 : zenon_U => (((aElementOf0 W0 (xI))/\(~(W0 = (sz00))))->((forall W1 : zenon_U, (((aElementOf0 W1 (xI))/\(~(W1 = (sz00))))->((iLess0 (sbrdtbr0 W1) (sbrdtbr0 W0))->(exists W2 : zenon_U, ((aElementOf0 W2 (xI))/\((~(W2 = (sz00)))/\(forall W3 : zenon_U, (((aElementOf0 W3 (xI))/\(~(W3 = (sz00))))->(~(iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2)))))))))))->(exists W2 : zenon_U, ((aElementOf0 W2 (xI))/\((~(W2 = (sz00)))/\(forall W3 : zenon_U, (((aElementOf0 W3 (xI))/\(~(W3 = (sz00))))->(~(iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2))))))))))) zenon_G); [ zenon_intro zenon_H2d; idtac ]. % 0.19/0.56 elim zenon_H2d. zenon_intro zenon_TW0_bu. zenon_intro zenon_H2f. % 0.19/0.56 apply (zenon_notimply_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 0.19/0.56 apply (zenon_notimply_s _ _ zenon_H30). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.19/0.56 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H35. zenon_intro zenon_H34. % 0.19/0.56 apply zenon_H32. exists zenon_TW0_bu. apply NNPP. zenon_intro zenon_H36. % 0.19/0.56 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.19/0.56 exact (zenon_H38 zenon_H35). % 0.19/0.56 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.19/0.56 exact (zenon_H3a zenon_H34). % 0.19/0.56 apply (zenon_notallex_s (fun W3 : zenon_U => (((aElementOf0 W3 (xI))/\(~(W3 = (sz00))))->(~(iLess0 (sbrdtbr0 W3) (sbrdtbr0 zenon_TW0_bu))))) zenon_H39); [ zenon_intro zenon_H3b; idtac ]. % 0.19/0.56 elim zenon_H3b. zenon_intro zenon_TW3_ci. zenon_intro zenon_H3d. % 0.19/0.56 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.19/0.56 apply zenon_H3e. zenon_intro zenon_H40. % 0.19/0.56 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.19/0.56 generalize (zenon_H33 zenon_TW3_ci). zenon_intro zenon_H43. % 0.19/0.56 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.19/0.56 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.19/0.56 exact (zenon_H47 zenon_H42). % 0.19/0.56 exact (zenon_H46 zenon_H41). % 0.19/0.56 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.19/0.56 exact (zenon_H49 zenon_H40). % 0.19/0.56 exact (zenon_H32 zenon_H48). % 0.19/0.56 Qed. % 0.19/0.56 % SZS output end Proof % 0.19/0.56 (* END-PROOF *) % 0.19/0.56 nodes searched: 919 % 0.19/0.56 max branch formulas: 643 % 0.19/0.56 proof nodes created: 31 % 0.19/0.56 formulas created: 9697 % 0.19/0.56 %------------------------------------------------------------------------------