%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n014.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 06:37:25 EDT 2022 % Result : Theorem 0.46s 0.64s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n014.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 : Sun Jul 10 06:45:05 EDT 2022 % 0.12/0.33 % CPUTime : % 0.46/0.64 (* PROOF-FOUND *) % 0.46/0.64 % SZS status Theorem % 0.46/0.64 (* BEGIN-PROOF *) % 0.46/0.64 % SZS output start Proof % 0.46/0.64 Theorem prove_th93 : (forall B : zenon_U, ((symmetric_difference B B) = (empty_set))). % 0.46/0.64 Proof. % 0.46/0.64 assert (zenon_L1_ : forall (zenon_TB_n : zenon_U), (~((difference zenon_TB_n zenon_TB_n) = (empty_set))) -> False). % 0.46/0.64 do 1 intro. intros zenon_Hc. % 0.46/0.64 generalize (self_difference_is_empty_set zenon_TB_n). zenon_intro zenon_He. % 0.46/0.64 exact (zenon_Hc zenon_He). % 0.46/0.64 (* end of lemma zenon_L1_ *) % 0.46/0.64 assert (zenon_L2_ : (~((empty_set) = (empty_set))) -> False). % 0.46/0.64 do 0 intro. intros zenon_Hf. % 0.46/0.64 apply zenon_Hf. apply refl_equal. % 0.46/0.64 (* end of lemma zenon_L2_ *) % 0.46/0.64 apply NNPP. intro zenon_G. % 0.46/0.64 apply (zenon_notallex_s (fun B : zenon_U => ((symmetric_difference B B) = (empty_set))) zenon_G); [ zenon_intro zenon_H10; idtac ]. % 0.46/0.64 elim zenon_H10. zenon_intro zenon_TB_n. zenon_intro zenon_H11. % 0.46/0.64 generalize (symmetric_difference_defn zenon_TB_n). zenon_intro zenon_H12. % 0.46/0.64 generalize (zenon_H12 zenon_TB_n). zenon_intro zenon_H13. % 0.46/0.64 apply (zenon_congruence_lr_s _ (fun zenon_Vg : _ => (~(zenon_Vg = (empty_set)))) _ _ zenon_H11 zenon_H13). zenon_intro zenon_H14. % 0.46/0.64 generalize (self_difference_is_empty_set zenon_E). zenon_intro zenon_H15. % 0.46/0.64 cut (((difference zenon_E zenon_E) = (empty_set)) = ((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (empty_set))). % 0.46/0.64 intro zenon_D_pnotp. % 0.46/0.64 apply zenon_H14. % 0.46/0.64 rewrite <- zenon_D_pnotp. % 0.46/0.64 exact zenon_H15. % 0.46/0.64 cut (((empty_set) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 0.46/0.64 cut (((difference zenon_E zenon_E) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 0.46/0.64 congruence. % 0.46/0.64 elim (classic ((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [ zenon_intro zenon_H17 | zenon_intro zenon_H18 ]. % 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n))) = ((difference zenon_E zenon_E) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))). % 0.46/0.64 intro zenon_D_pnotp. % 0.46/0.64 apply zenon_H16. % 0.46/0.64 rewrite <- zenon_D_pnotp. % 0.46/0.64 exact zenon_H17. % 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (difference zenon_E zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 0.46/0.64 congruence. % 0.46/0.64 generalize (idempotency_of_union (empty_set)). zenon_intro zenon_H1a. % 0.46/0.64 cut (((union (empty_set) (empty_set)) = (empty_set)) = ((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (difference zenon_E zenon_E))). % 0.46/0.64 intro zenon_D_pnotp. % 0.46/0.64 apply zenon_H19. % 0.46/0.64 rewrite <- zenon_D_pnotp. % 0.46/0.64 exact zenon_H1a. % 0.46/0.64 cut (((empty_set) = (difference zenon_E zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 0.46/0.64 cut (((union (empty_set) (empty_set)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 0.46/0.64 congruence. % 0.46/0.64 elim (classic ((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [ zenon_intro zenon_H17 | zenon_intro zenon_H18 ]. % 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n))) = ((union (empty_set) (empty_set)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))). % 0.46/0.64 intro zenon_D_pnotp. % 0.46/0.64 apply zenon_H1c. % 0.46/0.64 rewrite <- zenon_D_pnotp. % 0.46/0.64 exact zenon_H17. % 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (empty_set) (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 0.46/0.64 congruence. % 0.46/0.64 cut (((difference zenon_TB_n zenon_TB_n) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 0.46/0.64 cut (((difference zenon_TB_n zenon_TB_n) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 0.46/0.64 congruence. % 0.46/0.64 apply (zenon_L1_ zenon_TB_n); trivial. % 0.46/0.64 apply (zenon_L1_ zenon_TB_n); trivial. % 0.46/0.64 apply zenon_H18. apply refl_equal. % 0.46/0.64 apply zenon_H18. apply refl_equal. % 0.46/0.64 apply zenon_H1b. apply sym_equal. exact zenon_H15. % 0.46/0.64 apply zenon_H18. apply refl_equal. % 0.46/0.64 apply zenon_H18. apply refl_equal. % 0.46/0.64 apply zenon_Hf. apply refl_equal. % 0.46/0.64 Qed. % 0.46/0.64 % SZS output end Proof % 0.46/0.64 (* END-PROOF *) % 0.46/0.64 nodes searched: 3123 % 0.46/0.64 max branch formulas: 408 % 0.46/0.64 proof nodes created: 252 % 0.46/0.64 formulas created: 10132 % 0.46/0.64 %------------------------------------------------------------------------------