%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET108+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 : Tue Jul 19 06:34:03 EDT 2022 % Result : Theorem 32.66s 32.88s % Output : Proof 32.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET108+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.12/0.13 % Command : run_zenon %s %d % 0.13/0.35 % Computer : n022.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Mon Jul 11 09:42:40 EDT 2022 % 0.13/0.35 % CPUTime : % 32.66/32.88 (* PROOF-FOUND *) % 32.66/32.88 % SZS status Theorem % 32.66/32.88 (* BEGIN-PROOF *) % 32.66/32.88 % SZS output start Proof % 32.66/32.88 Theorem existence_of_first_and_second : (forall X : zenon_U, (exists U : zenon_U, (exists V : zenon_U, (((member U (universal_class))/\((member V (universal_class))/\(X = (ordered_pair U V))))\/((~(exists Y : zenon_U, (exists Z : zenon_U, ((member Y (universal_class))/\((member Z (universal_class))/\(X = (ordered_pair Y Z)))))))/\((U = X)/\(V = X))))))). % 32.66/32.88 Proof. % 32.66/32.88 assert (zenon_L1_ : forall (zenon_TX_bu : zenon_U), (exists Y : zenon_U, (exists Z : zenon_U, ((member Y (universal_class))/\((member Z (universal_class))/\(zenon_TX_bu = (ordered_pair Y Z)))))) -> (~(exists U : zenon_U, (exists V : zenon_U, (((member U (universal_class))/\((member V (universal_class))/\(zenon_TX_bu = (ordered_pair U V))))\/((~(exists Y : zenon_U, (exists Z : zenon_U, ((member Y (universal_class))/\((member Z (universal_class))/\(zenon_TX_bu = (ordered_pair Y Z)))))))/\((U = zenon_TX_bu)/\(V = zenon_TX_bu))))))) -> False). % 32.66/32.88 do 1 intro. intros zenon_H2c zenon_H2d. % 32.66/32.88 elim zenon_H2c. zenon_intro zenon_TY_bv. zenon_intro zenon_H30. % 32.66/32.88 elim zenon_H30. zenon_intro zenon_TZ_bx. zenon_intro zenon_H32. % 32.66/32.88 apply zenon_H2d. exists zenon_TY_bv. apply NNPP. zenon_intro zenon_H33. % 32.66/32.88 apply zenon_H33. exists zenon_TZ_bx. apply NNPP. zenon_intro zenon_H34. % 32.66/32.88 apply (zenon_notor_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 32.66/32.88 exact (zenon_H36 zenon_H32). % 32.66/32.88 (* end of lemma zenon_L1_ *) % 32.66/32.88 apply NNPP. intro zenon_G. % 32.66/32.88 apply (zenon_notallex_s (fun X : zenon_U => (exists U : zenon_U, (exists V : zenon_U, (((member U (universal_class))/\((member V (universal_class))/\(X = (ordered_pair U V))))\/((~(exists Y : zenon_U, (exists Z : zenon_U, ((member Y (universal_class))/\((member Z (universal_class))/\(X = (ordered_pair Y Z)))))))/\((U = X)/\(V = X))))))) zenon_G); [ zenon_intro zenon_H37; idtac ]. % 32.66/32.88 elim zenon_H37. zenon_intro zenon_TX_bu. zenon_intro zenon_H2d. % 32.66/32.88 apply zenon_H2d. exists zenon_TX_bu. apply NNPP. zenon_intro zenon_H38. % 32.66/32.88 apply zenon_H38. exists zenon_TX_bu. apply NNPP. zenon_intro zenon_H39. % 32.66/32.88 apply (zenon_notor_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 32.66/32.88 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 32.66/32.88 apply zenon_H3d. zenon_intro zenon_H2c. % 32.66/32.88 apply (zenon_L1_ zenon_TX_bu); trivial. % 32.66/32.88 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3e ]. % 32.66/32.88 apply zenon_H3e. apply refl_equal. % 32.66/32.88 apply zenon_H3e. apply refl_equal. % 32.66/32.88 Qed. % 32.66/32.88 % SZS output end Proof % 32.66/32.88 (* END-PROOF *) % 32.66/32.88 nodes searched: 1199444 % 32.66/32.88 max branch formulas: 40952 % 32.66/32.88 proof nodes created: 39330 % 32.66/32.88 formulas created: 4029965 % 32.66/32.88 %------------------------------------------------------------------------------