%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n028.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 16:00:52 EDT 2022 % Result : Theorem 45.20s 45.37s % Output : Proof 45.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n028.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jun 20 02:41:01 EDT 2022 % 0.13/0.34 % CPUTime : % 45.20/45.37 (* PROOF-FOUND *) % 45.20/45.37 % SZS status Theorem % 45.20/45.37 (* BEGIN-PROOF *) % 45.20/45.37 % SZS output start Proof % 45.20/45.37 Theorem s3_funct_1__e16_22__wellord2 : (forall A : zenon_U, (exists B : zenon_U, ((relation B)/\((function B)/\(((relation_dom B) = A)/\(forall C : zenon_U, ((in C A)->((apply B C) = (singleton C))))))))). % 45.20/45.37 Proof. % 45.20/45.37 assert (zenon_L1_ : forall (zenon_TA_y : zenon_U), (~(forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((in B zenon_TA_y)/\((C = (singleton B))/\(D = (singleton B))))->(C = D)))))) -> False). % 45.20/45.37 do 1 intro. intros zenon_H17. % 45.20/45.37 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((in B zenon_TA_y)/\((C = (singleton B))/\(D = (singleton B))))->(C = D))))) zenon_H17); [ zenon_intro zenon_H19; idtac ]. % 45.20/45.37 elim zenon_H19. zenon_intro zenon_TB_ba. zenon_intro zenon_H1b. % 45.20/45.37 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((in zenon_TB_ba zenon_TA_y)/\((C = (singleton zenon_TB_ba))/\(D = (singleton zenon_TB_ba))))->(C = D)))) zenon_H1b); [ zenon_intro zenon_H1c; idtac ]. % 45.20/45.37 elim zenon_H1c. zenon_intro zenon_TC_bd. zenon_intro zenon_H1e. % 45.20/45.37 apply (zenon_notallex_s (fun D : zenon_U => (((in zenon_TB_ba zenon_TA_y)/\((zenon_TC_bd = (singleton zenon_TB_ba))/\(D = (singleton zenon_TB_ba))))->(zenon_TC_bd = D))) zenon_H1e); [ zenon_intro zenon_H1f; idtac ]. % 45.20/45.37 elim zenon_H1f. zenon_intro zenon_TD_bg. zenon_intro zenon_H21. % 45.20/45.37 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H22. % 45.20/45.37 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24. % 45.20/45.37 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26. % 45.20/45.37 elim (classic (zenon_TD_bg = zenon_TD_bg)); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 45.20/45.37 cut ((zenon_TD_bg = zenon_TD_bg) = (zenon_TC_bd = zenon_TD_bg)). % 45.20/45.37 intro zenon_D_pnotp. % 45.20/45.37 apply zenon_H22. % 45.20/45.37 rewrite <- zenon_D_pnotp. % 45.20/45.37 exact zenon_H28. % 45.20/45.37 cut ((zenon_TD_bg = zenon_TD_bg)); [idtac | apply NNPP; zenon_intro zenon_H29]. % 45.20/45.37 cut ((zenon_TD_bg = zenon_TC_bd)); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 45.20/45.37 congruence. % 45.20/45.37 cut ((zenon_TD_bg = (singleton zenon_TB_ba)) = (zenon_TD_bg = zenon_TC_bd)). % 45.20/45.37 intro zenon_D_pnotp. % 45.20/45.37 apply zenon_H2a. % 45.20/45.37 rewrite <- zenon_D_pnotp. % 45.20/45.37 exact zenon_H26. % 45.20/45.37 cut (((singleton zenon_TB_ba) = zenon_TC_bd)); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 45.20/45.37 cut ((zenon_TD_bg = zenon_TD_bg)); [idtac | apply NNPP; zenon_intro zenon_H29]. % 45.20/45.37 congruence. % 45.20/45.37 apply zenon_H29. apply refl_equal. % 45.20/45.37 apply zenon_H2b. apply sym_equal. exact zenon_H27. % 45.20/45.37 apply zenon_H29. apply refl_equal. % 45.20/45.37 apply zenon_H29. apply refl_equal. % 45.20/45.37 (* end of lemma zenon_L1_ *) % 45.20/45.37 apply NNPP. intro zenon_G. % 45.20/45.37 apply (zenon_notallex_s (fun A : zenon_U => (exists B : zenon_U, ((relation B)/\((function B)/\(((relation_dom B) = A)/\(forall C : zenon_U, ((in C A)->((apply B C) = (singleton C))))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ]. % 45.20/45.37 elim zenon_H2c. zenon_intro zenon_TA_y. zenon_intro zenon_H2d. % 45.20/45.37 generalize (s2_funct_1__e16_22__wellord2__1 zenon_TA_y). zenon_intro zenon_H2e. % 45.20/45.37 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 45.20/45.37 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H17 | zenon_intro zenon_H31 ]. % 45.20/45.37 apply (zenon_L1_ zenon_TA_y); trivial. % 45.20/45.37 apply (zenon_notallex_s (fun B : zenon_U => (~((in B zenon_TA_y)/\(forall C : zenon_U, (~(C = (singleton B))))))) zenon_H31); [ zenon_intro zenon_H32; idtac ]. % 45.20/45.37 elim zenon_H32. zenon_intro zenon_TB_bz. zenon_intro zenon_H34. % 45.20/45.37 apply zenon_H34. zenon_intro zenon_H35. % 45.20/45.37 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 45.20/45.37 generalize (zenon_H36 (singleton zenon_TB_bz)). zenon_intro zenon_H38. % 45.20/45.37 apply zenon_H38. apply refl_equal. % 45.20/45.37 exact (zenon_H2d zenon_H2f). % 45.20/45.37 Qed. % 45.20/45.37 % SZS output end Proof % 45.20/45.37 (* END-PROOF *) % 45.20/45.37 nodes searched: 460070 % 45.20/45.37 max branch formulas: 13593 % 45.20/45.37 proof nodes created: 13561 % 45.20/45.37 formulas created: 440540 % 45.20/45.37 %------------------------------------------------------------------------------