%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU413+1 : TPTP v8.1.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n011.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 14:51:01 EDT 2022 % Result : Theorem 13.79s 13.99s % Output : Proof 13.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU413+1 : TPTP v8.1.0. Released v3.4.0. % 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n011.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 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 19 20:53:09 EDT 2022 % 0.12/0.34 % CPUTime : % 13.79/13.99 % SZS status Theorem % 13.79/13.99 (* PROOF-FOUND *) % 13.79/13.99 (* BEGIN-PROOF *) % 13.79/13.99 % SZS output start Proof % 13.79/13.99 1. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom % 13.79/13.99 2. (l1_orders_2 T_1) (-. (l1_orders_2 T_1)) ### Axiom % 13.79/13.99 3. (v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) (-. (v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1)) ### Axiom % 13.79/13.99 4. (m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) (-. (m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1)))) ### Axiom % 13.79/13.99 5. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom % 13.79/13.99 6. (l1_orders_2 T_1) (-. (l1_orders_2 T_1)) ### Axiom % 13.79/13.99 7. (-. (l1_orders_2 (k1_latsum_1 T_0 T_1))) (l1_orders_2 (k1_latsum_1 T_0 T_1)) ### Axiom % 13.79/13.99 8. ((v1_orders_2 (k1_latsum_1 T_0 T_1)) /\ (l1_orders_2 (k1_latsum_1 T_0 T_1))) (-. (l1_orders_2 (k1_latsum_1 T_0 T_1))) ### And 7 % 13.79/13.99 9. (((l1_orders_2 T_0) /\ (l1_orders_2 T_1)) => ((v1_orders_2 (k1_latsum_1 T_0 T_1)) /\ (l1_orders_2 (k1_latsum_1 T_0 T_1)))) (-. (l1_orders_2 (k1_latsum_1 T_0 T_1))) (l1_orders_2 T_1) (l1_orders_2 T_0) ### DisjTree 5 6 8 % 13.79/13.99 10. (All B, (((l1_orders_2 T_0) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 T_0 B)) /\ (l1_orders_2 (k1_latsum_1 T_0 B))))) (l1_orders_2 T_0) (l1_orders_2 T_1) (-. (l1_orders_2 (k1_latsum_1 T_0 T_1))) ### All 9 % 13.79/13.99 11. (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (-. (l1_orders_2 (k1_latsum_1 T_0 T_1))) (l1_orders_2 T_1) (l1_orders_2 T_0) ### All 10 % 13.79/13.99 12. (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (-. (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1)))) ### Axiom % 13.79/13.99 13. (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (-. (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1)))) ### Axiom % 13.79/13.99 14. (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (-. (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3)) ### Axiom % 13.79/13.99 15. (-. (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1)))) (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1))) ### Axiom % 13.79/13.99 16. ((r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) <=> (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1)))) (-. (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1)))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) ### Equiv 14 15 % 13.79/13.99 17. ((m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) => ((r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) <=> (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1))))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (-. (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1)))) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) ### Imply 13 16 % 13.79/13.99 18. (All C, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 T_0 T_1))) => ((r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 C) <=> (r2_hidden (k4_tarski T_2 C) (u1_orders_2 (k1_latsum_1 T_0 T_1)))))) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (-. (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1)))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) ### All 17 % 13.79/13.99 19. ((m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (All C, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 T_0 T_1))) => ((r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 C) <=> (r2_hidden (k4_tarski T_2 C) (u1_orders_2 (k1_latsum_1 T_0 T_1))))))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (-. (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1)))) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) ### Imply 12 18 % 13.79/13.99 20. (All B, ((m1_subset_1 B (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (All C, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 T_0 T_1))) => ((r1_orders_2 (k1_latsum_1 T_0 T_1) B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 (k1_latsum_1 T_0 T_1)))))))) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (-. (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1)))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) ### All 19 % 13.79/13.99 21. ((l1_orders_2 (k1_latsum_1 T_0 T_1)) => (All B, ((m1_subset_1 B (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (All C, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 T_0 T_1))) => ((r1_orders_2 (k1_latsum_1 T_0 T_1) B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 (k1_latsum_1 T_0 T_1))))))))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (-. (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1)))) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (l1_orders_2 T_0) (l1_orders_2 T_1) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) ### Imply 11 20 % 13.79/13.99 22. (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (l1_orders_2 T_1) (l1_orders_2 T_0) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (-. (r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1)))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) ### All 21 % 13.79/13.99 23. (r2_hidden T_3 (u1_struct_0 T_0)) (-. (r2_hidden T_3 (u1_struct_0 T_0))) ### Axiom % 13.79/13.99 24. (-. (r2_hidden T_2 (u1_struct_0 T_0))) (r2_hidden T_2 (u1_struct_0 T_0)) ### Axiom % 13.79/13.99 25. (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) /\ ((r2_hidden (k4_tarski T_2 T_3) (u1_orders_2 (k1_latsum_1 T_0 T_1))) /\ (r2_hidden T_3 (u1_struct_0 T_0))))) => (r2_hidden T_2 (u1_struct_0 T_0))) (-. (r2_hidden T_2 (u1_struct_0 T_0))) (r2_hidden T_3 (u1_struct_0 T_0)) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (l1_orders_2 T_0) (l1_orders_2 T_1) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) (v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) ### DisjTree 3 4 22 23 24 % 13.79/13.99 26. (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) /\ ((r2_hidden (k4_tarski T_2 D) (u1_orders_2 (k1_latsum_1 T_0 T_1))) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden T_2 (u1_struct_0 T_0)))) (v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) (m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (l1_orders_2 T_1) (l1_orders_2 T_0) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (r2_hidden T_3 (u1_struct_0 T_0)) (-. (r2_hidden T_2 (u1_struct_0 T_0))) ### All 25 % 13.79/13.99 27. (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 T_0 T_1))) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden C (u1_struct_0 T_0))))) (-. (r2_hidden T_2 (u1_struct_0 T_0))) (r2_hidden T_3 (u1_struct_0 T_0)) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (l1_orders_2 T_0) (l1_orders_2 T_1) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) (v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) ### All 26 % 13.90/14.10 28. ((l1_orders_2 T_1) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 T_0 T_1))) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden C (u1_struct_0 T_0)))))) (v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) (m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (l1_orders_2 T_0) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (r2_hidden T_3 (u1_struct_0 T_0)) (-. (r2_hidden T_2 (u1_struct_0 T_0))) (l1_orders_2 T_1) ### Imply 2 27 % 13.90/14.10 29. (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 T_0 B))) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden C (u1_struct_0 T_0))))))) (l1_orders_2 T_1) (-. (r2_hidden T_2 (u1_struct_0 T_0))) (r2_hidden T_3 (u1_struct_0 T_0)) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (l1_orders_2 T_0) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) (v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) ### All 28 % 13.90/14.10 30. ((l1_orders_2 T_0) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 T_0 B))) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden C (u1_struct_0 T_0)))))))) (v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) (m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (r2_hidden T_3 (u1_struct_0 T_0)) (-. (r2_hidden T_2 (u1_struct_0 T_0))) (l1_orders_2 T_1) (l1_orders_2 T_0) ### Imply 1 29 % 13.90/14.10 31. (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A))))))))) (l1_orders_2 T_0) (l1_orders_2 T_1) (-. (r2_hidden T_2 (u1_struct_0 T_0))) (r2_hidden T_3 (u1_struct_0 T_0)) (r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) (m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) (v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) ### All 30 % 13.90/14.10 32. (-. ((m1_subset_1 T_3 (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) /\ ((r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 T_3) /\ (r2_hidden T_3 (u1_struct_0 T_0))))) => (r2_hidden T_2 (u1_struct_0 T_0))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (l1_orders_2 T_1) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A))))))))) ### ConjTree 31 % 13.90/14.10 33. (-. (All D, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) /\ ((r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 D) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden T_2 (u1_struct_0 T_0)))))) (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A))))))))) (l1_orders_2 T_0) (l1_orders_2 T_1) (m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) ### NotAllEx 32 % 13.90/14.10 34. (-. ((m1_subset_1 T_2 (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (All D, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) /\ ((r1_orders_2 (k1_latsum_1 T_0 T_1) T_2 D) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden T_2 (u1_struct_0 T_0))))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (l1_orders_2 T_1) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A))))))))) ### NotImply 33 % 13.90/14.10 35. (-. (All C, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (All D, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) /\ ((r1_orders_2 (k1_latsum_1 T_0 T_1) C D) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden C (u1_struct_0 T_0)))))))) (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A))))))))) (l1_orders_2 T_0) (l1_orders_2 T_1) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) ### NotAllEx 34 % 13.90/14.10 36. (-. ((l1_orders_2 T_1) => (All C, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (All D, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 T_0 T_1))) => (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) T_1) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 T_1)) (k1_zfmisc_1 (u1_struct_0 T_1))) /\ ((r1_orders_2 (k1_latsum_1 T_0 T_1) C D) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden C (u1_struct_0 T_0))))))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A))))))))) ### NotImply 35 % 13.90/14.10 37. (-. (All B, ((l1_orders_2 B) => (All C, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 T_0 B))) => (All D, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 T_0 B))) => (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r1_orders_2 (k1_latsum_1 T_0 B) C D) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden C (u1_struct_0 T_0)))))))))) (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A))))))))) (l1_orders_2 T_0) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) ### NotAllEx 36 % 13.90/14.10 38. (-. ((l1_orders_2 T_0) => (All B, ((l1_orders_2 B) => (All C, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 T_0 B))) => (All D, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 T_0 B))) => (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 T_0) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r1_orders_2 (k1_latsum_1 T_0 B) C D) /\ (r2_hidden D (u1_struct_0 T_0))))) => (r2_hidden C (u1_struct_0 T_0))))))))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A))))))))) ### NotImply 37 % 13.90/14.10 39. (-. (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 A B))) => (All D, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 A B))) => (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r1_orders_2 (k1_latsum_1 A B) C D) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A)))))))))))) (All A, ((l1_orders_2 A) => (All B, ((l1_orders_2 B) => (All C, (All D, (((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) /\ ((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))) /\ ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) /\ (r2_hidden D (u1_struct_0 A))))) => (r2_hidden C (u1_struct_0 A))))))))) (All A, (All B, (((l1_orders_2 A) /\ (l1_orders_2 B)) => ((v1_orders_2 (k1_latsum_1 A B)) /\ (l1_orders_2 (k1_latsum_1 A B)))))) (All A, ((l1_orders_2 A) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))))))))) ### NotAllEx 38 % 13.90/14.10 % SZS output end Proof % 13.90/14.10 (* END-PROOF *) %------------------------------------------------------------------------------