%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU359+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 : n021.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 14:50:32 EDT 2022 % Result : Theorem 0.19s 0.42s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SEU359+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 : n021.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 09:31:47 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.42 % SZS status Theorem % 0.19/0.42 (* PROOF-FOUND *) % 0.19/0.42 (* BEGIN-PROOF *) % 0.19/0.42 % SZS output start Proof % 0.19/0.42 1. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 0.19/0.42 2. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom % 0.19/0.42 3. (ex_sup_of_relstr_set T_0 T_2) (-. (ex_sup_of_relstr_set T_0 T_2)) ### Axiom % 0.19/0.42 4. (T_1 = (join_on_relstr T_0 T_2)) (T_1 != (join_on_relstr T_0 T_2)) ### Axiom % 0.19/0.42 5. (-. (relstr_set_smaller T_0 T_2 T_1)) (relstr_set_smaller T_0 T_2 T_1) ### Axiom % 0.19/0.42 6. ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (-. (relstr_set_smaller T_0 T_2 T_1)) ### And 5 % 0.19/0.42 7. ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (-. (relstr_set_smaller T_0 T_2 T_1)) (T_1 = (join_on_relstr T_0 T_2)) ### Equiv 4 6 % 0.19/0.42 8. ((element T_1 (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))))) (T_1 = (join_on_relstr T_0 T_2)) (-. (relstr_set_smaller T_0 T_2 T_1)) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### DisjTree 2 3 7 % 0.19/0.42 9. (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((C = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (-. (relstr_set_smaller T_0 T_2 T_1)) (T_1 = (join_on_relstr T_0 T_2)) ### All 8 % 0.19/0.42 10. (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D)))))))))) (T_1 = (join_on_relstr T_0 T_2)) (-. (relstr_set_smaller T_0 T_2 T_1)) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### All 9 % 0.19/0.42 11. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D))))))))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (-. (relstr_set_smaller T_0 T_2 T_1)) (T_1 = (join_on_relstr T_0 T_2)) (rel_str T_0) ### Imply 1 10 % 0.19/0.42 12. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (T_1 = (join_on_relstr T_0 T_2)) (-. (relstr_set_smaller T_0 T_2 T_1)) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### All 11 % 0.19/0.42 13. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 0.19/0.42 14. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom % 0.19/0.42 15. (ex_sup_of_relstr_set T_0 T_2) (-. (ex_sup_of_relstr_set T_0 T_2)) ### Axiom % 0.19/0.42 16. (T_1 = (join_on_relstr T_0 T_2)) (T_1 != (join_on_relstr T_0 T_2)) ### Axiom % 0.19/0.42 17. (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) ### Axiom % 0.19/0.42 18. ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) ### And 17 % 0.19/0.42 19. ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (T_1 = (join_on_relstr T_0 T_2)) ### Equiv 16 18 % 0.19/0.42 20. ((element T_1 (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))))) (T_1 = (join_on_relstr T_0 T_2)) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### DisjTree 14 15 19 % 0.19/0.42 21. (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((C = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (T_1 = (join_on_relstr T_0 T_2)) ### All 20 % 0.19/0.42 22. (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D)))))))))) (T_1 = (join_on_relstr T_0 T_2)) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### All 21 % 0.19/0.42 23. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D))))))))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (T_1 = (join_on_relstr T_0 T_2)) (rel_str T_0) ### Imply 13 22 % 0.19/0.42 24. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (T_1 = (join_on_relstr T_0 T_2)) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### All 23 % 0.19/0.42 25. (-. ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (T_1 = (join_on_relstr T_0 T_2)) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### NotAnd 12 24 % 0.19/0.42 26. (-. (((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2)) => ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (element T_1 (the_carrier T_0)) ### ConjTree 25 % 0.19/0.42 27. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 0.19/0.42 28. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom % 0.19/0.42 29. (antisymmetric_relstr T_0) (-. (antisymmetric_relstr T_0)) ### Axiom % 0.19/0.42 30. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 0.19/0.42 31. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom % 0.19/0.42 32. (relstr_set_smaller T_0 T_2 T_1) (-. (relstr_set_smaller T_0 T_2 T_1)) ### Axiom % 0.19/0.42 33. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) ### Axiom % 0.19/0.43 34. (-. ((element T_1 (the_carrier T_0)) /\ ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))))) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) ### DisjTree 31 32 33 % 0.19/0.43 35. (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D)))))))) (element T_1 (the_carrier T_0)) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) ### NotExists 34 % 0.19/0.43 36. (-. (ex_sup_of_relstr_set T_0 T_2)) (ex_sup_of_relstr_set T_0 T_2) ### Axiom % 0.19/0.43 37. ((ex_sup_of_relstr_set T_0 T_2) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D)))))))) (-. (ex_sup_of_relstr_set T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) ### Equiv 35 36 % 0.19/0.43 38. (All B, ((ex_sup_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (-. (ex_sup_of_relstr_set T_0 T_2)) ### All 37 % 0.19/0.43 39. (((antisymmetric_relstr T_0) /\ (rel_str T_0)) => (All B, ((ex_sup_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D)))))))))) (-. (ex_sup_of_relstr_set T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) (rel_str T_0) (antisymmetric_relstr T_0) ### DisjTree 29 30 38 % 0.19/0.43 40. (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (rel_str T_0) (element T_1 (the_carrier T_0)) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (-. (ex_sup_of_relstr_set T_0 T_2)) ### All 39 % 0.19/0.43 41. (relstr_set_smaller T_0 T_2 T_1) (-. (relstr_set_smaller T_0 T_2 T_1)) ### Axiom % 0.19/0.43 42. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) ### Axiom % 0.19/0.43 43. (-. ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) ### NotAnd 41 42 % 0.19/0.43 44. (T_1 != (join_on_relstr T_0 T_2)) (T_1 = (join_on_relstr T_0 T_2)) ### Axiom % 0.19/0.43 45. ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (T_1 != (join_on_relstr T_0 T_2)) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) ### Equiv 43 44 % 0.19/0.43 46. ((element T_1 (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))))) (T_1 != (join_on_relstr T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (rel_str T_0) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (element T_1 (the_carrier T_0)) ### DisjTree 28 40 45 % 0.19/0.43 47. (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((C = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (rel_str T_0) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (T_1 != (join_on_relstr T_0 T_2)) ### All 46 % 0.19/0.43 48. (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D)))))))))) (T_1 != (join_on_relstr T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (rel_str T_0) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (element T_1 (the_carrier T_0)) ### All 47 % 0.19/0.43 49. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D))))))))))) (element T_1 (the_carrier T_0)) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (T_1 != (join_on_relstr T_0 T_2)) (rel_str T_0) ### Imply 27 48 % 0.19/0.43 50. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (T_1 != (join_on_relstr T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (element T_1 (the_carrier T_0)) ### All 49 % 0.19/0.43 51. (-. ((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2))) (element T_1 (the_carrier T_0)) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### NotAnd 50 40 % 0.19/0.44 52. (-. (((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) => ((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2)))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (element T_1 (the_carrier T_0)) ### ConjTree 51 % 0.19/0.44 53. (-. ((((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2)) => ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) /\ (((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) => ((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (element T_1 (the_carrier T_0)) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### NotAnd 26 52 % 0.19/0.44 54. (-. (All C, ((((T_1 = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 T_1 D)))))) /\ (((relstr_set_smaller T_0 C T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 T_1 D))))) => ((T_1 = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (element T_1 (the_carrier T_0)) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) ### NotAllEx 53 % 0.19/0.44 55. (-. ((element T_1 (the_carrier T_0)) => (All C, ((((T_1 = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 T_1 D)))))) /\ (((relstr_set_smaller T_0 C T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 T_1 D))))) => ((T_1 = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C))))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### NotImply 54 % 0.19/0.44 56. (-. (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) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) ### NotAllEx 55 % 0.19/0.44 57. (-. (((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, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### ConjTree 56 % 0.19/0.44 58. (-. (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, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) ### NotAllEx 57 % 0.19/0.44 % SZS output end Proof % 0.19/0.44 (* END-PROOF *) %------------------------------------------------------------------------------