%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU361+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n020.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 14:50:33 EDT 2022 % Result : Theorem 9.15s 9.37s % Output : Proof 9.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU361+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n020.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 Jun 19 22:47:18 EDT 2022 % 0.12/0.34 % CPUTime : % 9.15/9.37 % SZS status Theorem % 9.15/9.37 (* PROOF-FOUND *) % 9.15/9.37 (* BEGIN-PROOF *) % 9.15/9.37 % SZS output start Proof % 9.15/9.37 1. (-. (empty_carrier T_0)) (empty_carrier T_0) ### Axiom % 9.15/9.37 2. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 9.15/9.37 3. (-. (one_sorted_str T_0)) (rel_str T_0) ### Extension/test/dt_l1_orders_2ctrp 2 % 9.15/9.37 4. (empty (the_carrier T_0)) (rel_str T_0) (-. (empty_carrier T_0)) ### Extension/test/fc1_struct_0ctrp 1 3 % 9.15/9.37 5. (antisymmetric_relstr T_0) (-. (antisymmetric_relstr T_0)) ### Axiom % 9.15/9.37 6. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 9.15/9.37 7. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 9.15/9.37 8. (-. (element (bottom_of_relstr T_0) (the_carrier T_0))) (rel_str T_0) ### Extension/test/dt_k3_yellow_0ctrp 7 % 9.15/9.37 9. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 9.15/9.37 10. ((bottom_of_relstr T_0) != (join_on_relstr T_0 (empty_set))) ((bottom_of_relstr T_0) = (join_on_relstr T_0 (empty_set))) ### Axiom % 9.15/9.37 11. ((rel_str T_0) => ((bottom_of_relstr T_0) = (join_on_relstr T_0 (empty_set)))) ((bottom_of_relstr T_0) != (join_on_relstr T_0 (empty_set))) (rel_str T_0) ### Imply 9 10 % 9.15/9.37 12. (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) (rel_str T_0) ((bottom_of_relstr T_0) != (join_on_relstr T_0 (empty_set))) ### All 11 % 9.15/9.37 13. (-. (empty_carrier T_0)) (empty_carrier T_0) ### Axiom % 9.15/9.37 14. (antisymmetric_relstr T_0) (-. (antisymmetric_relstr T_0)) ### Axiom % 9.15/9.37 15. (lower_bounded_relstr T_0) (-. (lower_bounded_relstr T_0)) ### Axiom % 9.15/9.37 16. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 9.15/9.37 17. (-. (ex_sup_of_relstr_set T_0 (empty_set))) (ex_sup_of_relstr_set T_0 (empty_set)) ### Axiom % 9.15/9.37 18. ((ex_sup_of_relstr_set T_0 (empty_set)) /\ (ex_inf_of_relstr_set T_0 (the_carrier T_0))) (-. (ex_sup_of_relstr_set T_0 (empty_set))) ### And 17 % 9.15/9.37 19. (((-. (empty_carrier T_0)) /\ ((antisymmetric_relstr T_0) /\ ((lower_bounded_relstr T_0) /\ (rel_str T_0)))) => ((ex_sup_of_relstr_set T_0 (empty_set)) /\ (ex_inf_of_relstr_set T_0 (the_carrier T_0)))) (-. (ex_sup_of_relstr_set T_0 (empty_set))) (rel_str T_0) (lower_bounded_relstr T_0) (antisymmetric_relstr T_0) (-. (empty_carrier T_0)) ### DisjTree 13 14 15 16 18 % 9.15/9.37 20. (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (-. (empty_carrier T_0)) (antisymmetric_relstr T_0) (lower_bounded_relstr T_0) (rel_str T_0) (-. (ex_sup_of_relstr_set T_0 (empty_set))) ### All 19 % 9.15/9.37 21. (in T_1 (the_carrier T_0)) (-. (in T_1 (the_carrier T_0))) ### Axiom % 9.15/9.37 22. (-. (element T_1 (the_carrier T_0))) (in T_1 (the_carrier T_0)) ### Extension/test/t1_subsetctrp 21 % 9.15/9.37 23. (-. (relstr_set_smaller T_0 (empty_set) T_1)) (relstr_set_smaller T_0 (empty_set) T_1) ### Axiom % 9.15/9.37 24. (rel_str T_0) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (in T_1 (the_carrier T_0)) ### Extension/test/t6_yellow_0_inst 22 23 % 9.15/9.37 25. (-. (related T_0 (bottom_of_relstr T_0) T_1)) (related T_0 (bottom_of_relstr T_0) T_1) ### Axiom % 9.15/9.37 26. ((element T_1 (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) T_1) => (related T_0 (bottom_of_relstr T_0) T_1))) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (rel_str T_0) (in T_1 (the_carrier T_0)) ### DisjTree 22 24 25 % 9.15/9.37 27. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) D) => (related T_0 (bottom_of_relstr T_0) D)))) (in T_1 (the_carrier T_0)) (rel_str T_0) (-. (related T_0 (bottom_of_relstr T_0) T_1)) ### All 26 % 9.15/9.37 28. ((relstr_set_smaller T_0 (empty_set) (bottom_of_relstr T_0)) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) D) => (related T_0 (bottom_of_relstr T_0) D))))) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (rel_str T_0) (in T_1 (the_carrier T_0)) ### And 27 % 9.15/9.37 29. ((((bottom_of_relstr T_0) = (join_on_relstr T_0 (empty_set))) /\ (ex_sup_of_relstr_set T_0 (empty_set))) => ((relstr_set_smaller T_0 (empty_set) (bottom_of_relstr T_0)) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) D) => (related T_0 (bottom_of_relstr T_0) D)))))) (in T_1 (the_carrier T_0)) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (lower_bounded_relstr T_0) (antisymmetric_relstr T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (rel_str T_0) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) ### DisjTree 12 20 28 % 9.15/9.37 30. (((((bottom_of_relstr T_0) = (join_on_relstr T_0 (empty_set))) /\ (ex_sup_of_relstr_set T_0 (empty_set))) => ((relstr_set_smaller T_0 (empty_set) (bottom_of_relstr T_0)) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) D) => (related T_0 (bottom_of_relstr T_0) D)))))) /\ (((relstr_set_smaller T_0 (empty_set) (bottom_of_relstr T_0)) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) D) => (related T_0 (bottom_of_relstr T_0) D))))) => (((bottom_of_relstr T_0) = (join_on_relstr T_0 (empty_set))) /\ (ex_sup_of_relstr_set T_0 (empty_set))))) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) (rel_str T_0) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (-. (empty_carrier T_0)) (antisymmetric_relstr T_0) (lower_bounded_relstr T_0) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (in T_1 (the_carrier T_0)) ### And 29 % 9.15/9.37 31. (All C, (((((bottom_of_relstr T_0) = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C (bottom_of_relstr T_0)) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 (bottom_of_relstr T_0) D)))))) /\ (((relstr_set_smaller T_0 C (bottom_of_relstr T_0)) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 (bottom_of_relstr T_0) D))))) => (((bottom_of_relstr T_0) = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C))))) (in T_1 (the_carrier T_0)) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (lower_bounded_relstr T_0) (antisymmetric_relstr T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (rel_str T_0) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) ### All 30 % 9.15/9.37 32. ((element (bottom_of_relstr T_0) (the_carrier T_0)) => (All C, (((((bottom_of_relstr T_0) = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C (bottom_of_relstr T_0)) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 (bottom_of_relstr T_0) D)))))) /\ (((relstr_set_smaller T_0 C (bottom_of_relstr T_0)) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 (bottom_of_relstr T_0) D))))) => (((bottom_of_relstr T_0) = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)))))) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (-. (empty_carrier T_0)) (antisymmetric_relstr T_0) (lower_bounded_relstr T_0) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (in T_1 (the_carrier T_0)) (rel_str T_0) ### Imply 8 31 % 9.15/9.37 33. (All B, ((element B (the_carrier T_0)) => (All C, ((((B = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C B) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 B D)))))) /\ (((relstr_set_smaller T_0 C B) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 B D))))) => ((B = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C))))))) (rel_str T_0) (in T_1 (the_carrier T_0)) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (lower_bounded_relstr T_0) (antisymmetric_relstr T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) ### All 32 % 9.21/9.38 34. (((antisymmetric_relstr T_0) /\ (rel_str T_0)) => (All B, ((element B (the_carrier T_0)) => (All C, ((((B = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C B) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 B D)))))) /\ (((relstr_set_smaller T_0 C B) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 B D))))) => ((B = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)))))))) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (-. (empty_carrier T_0)) (lower_bounded_relstr T_0) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (in T_1 (the_carrier T_0)) (rel_str T_0) (antisymmetric_relstr T_0) ### DisjTree 5 6 33 % 9.21/9.38 35. (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C)) => ((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D)))))) /\ (((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D))))) => ((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C))))))))) (antisymmetric_relstr T_0) (rel_str T_0) (in T_1 (the_carrier T_0)) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (lower_bounded_relstr T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) ### All 34 % 9.21/9.38 36. (element T_1 (the_carrier T_0)) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (lower_bounded_relstr T_0) (-. (related T_0 (bottom_of_relstr T_0) T_1)) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C)) => ((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D)))))) /\ (((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D))))) => ((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C))))))))) (-. (empty_carrier T_0)) (rel_str T_0) ### Extension/test/t2_subset 4 35 % 9.21/9.38 37. (-. ((element T_1 (the_carrier T_0)) => (related T_0 (bottom_of_relstr T_0) T_1))) (rel_str T_0) (-. (empty_carrier T_0)) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C)) => ((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D)))))) /\ (((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D))))) => ((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C))))))))) (antisymmetric_relstr T_0) (lower_bounded_relstr T_0) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) ### NotImply 36 % 9.21/9.38 38. (-. (All B, ((element B (the_carrier T_0)) => (related T_0 (bottom_of_relstr T_0) B)))) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (lower_bounded_relstr T_0) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C)) => ((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D)))))) /\ (((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D))))) => ((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C))))))))) (-. (empty_carrier T_0)) (rel_str T_0) ### NotAllEx 37 % 9.21/9.38 39. (-. (((-. (empty_carrier T_0)) /\ ((antisymmetric_relstr T_0) /\ ((lower_bounded_relstr T_0) /\ (rel_str T_0)))) => (All B, ((element B (the_carrier T_0)) => (related T_0 (bottom_of_relstr T_0) B))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C)) => ((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D)))))) /\ (((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D))))) => ((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C))))))))) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) ### ConjTree 38 % 9.21/9.38 40. (-. (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => (All B, ((element B (the_carrier A)) => (related A (bottom_of_relstr A) B)))))) (All A, ((rel_str A) => ((bottom_of_relstr A) = (join_on_relstr A (empty_set))))) (All A, (((-. (empty_carrier A)) /\ ((antisymmetric_relstr A) /\ ((lower_bounded_relstr A) /\ (rel_str A)))) => ((ex_sup_of_relstr_set A (empty_set)) /\ (ex_inf_of_relstr_set A (the_carrier A))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C)) => ((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D)))))) /\ (((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D))))) => ((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C))))))))) ### NotAllEx 39 % 9.21/9.38 % SZS output end Proof % 9.21/9.38 (* END-PROOF *) %------------------------------------------------------------------------------