TSTP Solution File: SEU357+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU357+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 : n005.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 14:50:31 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU357+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n005.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 11:33:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 (* PROOF-FOUND *)
% 0.20/0.43 (* BEGIN-PROOF *)
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 1. (rel_str T_0) (-. (rel_str T_0)) ### Axiom
% 0.20/0.43 2. (antisymmetric_relstr T_0) (-. (antisymmetric_relstr T_0)) ### Axiom
% 0.20/0.43 3. (rel_str T_0) (-. (rel_str T_0)) ### Axiom
% 0.20/0.43 4. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 0.20/0.43 5. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 0.20/0.43 6. (relstr_element_smaller T_0 T_2 T_1) (-. (relstr_element_smaller T_0 T_2 T_1)) ### Axiom
% 0.20/0.43 7. (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1))))) ### Axiom
% 0.20/0.43 8. (element T_3 (the_carrier T_0)) (-. (element T_3 (the_carrier T_0))) ### Axiom
% 0.20/0.43 9. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 0.20/0.43 10. (relstr_element_smaller T_0 T_2 T_1) (-. (relstr_element_smaller T_0 T_2 T_1)) ### Axiom
% 0.20/0.43 11. (-. (related T_0 T_1 T_3)) (related T_0 T_1 T_3) ### Axiom
% 0.20/0.43 12. ((element T_1 (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 T_1) => (related T_0 T_1 T_3))) (-. (related T_0 T_1 T_3)) (relstr_element_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) ### DisjTree 9 10 11
% 0.20/0.43 13. (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E T_3)))) (element T_1 (the_carrier T_0)) (relstr_element_smaller T_0 T_2 T_1) (-. (related T_0 T_1 T_3)) ### All 12
% 0.20/0.43 14. (element T_3 (the_carrier T_0)) (-. (element T_3 (the_carrier T_0))) ### Axiom
% 0.20/0.43 15. (relstr_element_smaller T_0 T_2 T_3) (-. (relstr_element_smaller T_0 T_2 T_3)) ### Axiom
% 0.20/0.43 16. (-. (related T_0 T_3 T_1)) (related T_0 T_3 T_1) ### Axiom
% 0.20/0.43 17. ((element T_3 (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 T_3) => (related T_0 T_3 T_1))) (-. (related T_0 T_3 T_1)) (relstr_element_smaller T_0 T_2 T_3) (element T_3 (the_carrier T_0)) ### DisjTree 14 15 16
% 0.20/0.43 18. (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (element T_3 (the_carrier T_0)) (relstr_element_smaller T_0 T_2 T_3) (-. (related T_0 T_3 T_1)) ### All 17
% 0.20/0.43 19. (T_3 != T_1) (T_1 = T_3) ### Sym(=)
% 0.20/0.43 20. ((element T_3 (the_carrier T_0)) => (((related T_0 T_1 T_3) /\ (related T_0 T_3 T_1)) => (T_1 = T_3))) (T_3 != T_1) (relstr_element_smaller T_0 T_2 T_3) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (relstr_element_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E T_3)))) (element T_3 (the_carrier T_0)) ### DisjTree 8 13 18 19
% 0.20/0.43 21. (All C, ((element C (the_carrier T_0)) => (((related T_0 T_1 C) /\ (related T_0 C T_1)) => (T_1 = C)))) (element T_3 (the_carrier T_0)) (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E T_3)))) (element T_1 (the_carrier T_0)) (relstr_element_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (relstr_element_smaller T_0 T_2 T_3) (T_3 != T_1) ### All 20
% 0.20/0.43 22. (-. ((element T_3 (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 T_3) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E T_3))))) => (T_3 = T_1)))) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (relstr_element_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) (All C, ((element C (the_carrier T_0)) => (((related T_0 T_1 C) /\ (related T_0 C T_1)) => (T_1 = C)))) ### ConjTree 21
% 0.20/0.43 23. (-. (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E D))))) => (D = T_1))))) (All C, ((element C (the_carrier T_0)) => (((related T_0 T_1 C) /\ (related T_0 C T_1)) => (T_1 = C)))) (element T_1 (the_carrier T_0)) (relstr_element_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) ### NotAllEx 22
% 0.20/0.43 24. (-. ((element T_1 (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 T_1) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E D))))) => (D = T_1)))))))) (All C, ((element C (the_carrier T_0)) => (((related T_0 T_1 C) /\ (related T_0 C T_1)) => (T_1 = C)))) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (relstr_element_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) ### DisjTree 5 6 7 23
% 0.20/0.43 25. (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E D))))) => (D = C))))))))) (element T_1 (the_carrier T_0)) (relstr_element_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (All C, ((element C (the_carrier T_0)) => (((related T_0 T_1 C) /\ (related T_0 C T_1)) => (T_1 = C)))) ### NotExists 24
% 0.20/0.43 26. ((element T_1 (the_carrier T_0)) => (All C, ((element C (the_carrier T_0)) => (((related T_0 T_1 C) /\ (related T_0 C T_1)) => (T_1 = C))))) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (relstr_element_smaller T_0 T_2 T_1) (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E D))))) => (D = C))))))))) (element T_1 (the_carrier T_0)) ### Imply 4 25
% 0.20/0.43 27. (All B, ((element B (the_carrier T_0)) => (All C, ((element C (the_carrier T_0)) => (((related T_0 B C) /\ (related T_0 C B)) => (B = C)))))) (element T_1 (the_carrier T_0)) (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E D))))) => (D = C))))))))) (relstr_element_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) ### All 26
% 0.20/0.43 28. (-. (ex_inf_of_relstr_set T_0 T_2)) (ex_inf_of_relstr_set T_0 T_2) ### Axiom
% 0.20/0.43 29. ((ex_inf_of_relstr_set T_0 T_2) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E D))))) => (D = C))))))))) (-. (ex_inf_of_relstr_set T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (relstr_element_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) (All B, ((element B (the_carrier T_0)) => (All C, ((element C (the_carrier T_0)) => (((related T_0 B C) /\ (related T_0 C B)) => (B = C)))))) ### Equiv 27 28
% 0.20/0.43 30. (All B, ((ex_inf_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 B C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 B D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 B D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 B E) => (related T_0 E D))))) => (D = C)))))))))) (All B, ((element B (the_carrier T_0)) => (All C, ((element C (the_carrier T_0)) => (((related T_0 B C) /\ (related T_0 C B)) => (B = C)))))) (element T_1 (the_carrier T_0)) (relstr_element_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (-. (ex_inf_of_relstr_set T_0 T_2)) ### All 29
% 0.20/0.44 31. (((antisymmetric_relstr T_0) /\ (rel_str T_0)) => (All B, ((element B (the_carrier T_0)) => (All C, ((element C (the_carrier T_0)) => (((related T_0 B C) /\ (related T_0 C B)) => (B = C))))))) (-. (ex_inf_of_relstr_set T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (relstr_element_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) (All B, ((ex_inf_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 B C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 B D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 B D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 B E) => (related T_0 E D))))) => (D = C)))))))))) (rel_str T_0) (antisymmetric_relstr T_0) ### DisjTree 2 3 30
% 0.20/0.44 32. (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((element C (the_carrier A)) => (((related A B C) /\ (related A C B)) => (B = C)))))))) (antisymmetric_relstr T_0) (rel_str T_0) (All B, ((ex_inf_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 B C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 B D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 B D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 B E) => (related T_0 E D))))) => (D = C)))))))))) (element T_1 (the_carrier T_0)) (relstr_element_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (-. (ex_inf_of_relstr_set T_0 T_2)) ### All 31
% 0.20/0.44 33. ((rel_str T_0) => (All B, ((ex_inf_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 B C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 B D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 B D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 B E) => (related T_0 E D))))) => (D = C))))))))))) (-. (ex_inf_of_relstr_set T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (relstr_element_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((element C (the_carrier A)) => (((related A B C) /\ (related A C B)) => (B = C)))))))) (rel_str T_0) ### Imply 1 32
% 0.20/0.44 34. (All A, ((rel_str A) => (All B, ((ex_inf_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_element_smaller A B C) /\ ((All D, ((element D (the_carrier A)) => ((relstr_element_smaller A B D) => (related A D C)))) /\ (All D, ((element D (the_carrier A)) => (((relstr_element_smaller A B D) /\ (All E, ((element E (the_carrier A)) => ((relstr_element_smaller A B E) => (related A E D))))) => (D = C)))))))))))) (rel_str T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((element C (the_carrier A)) => (((related A B C) /\ (related A C B)) => (B = C)))))))) (antisymmetric_relstr T_0) (element T_1 (the_carrier T_0)) (relstr_element_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))) (-. (ex_inf_of_relstr_set T_0 T_2)) ### All 33
% 0.20/0.44 35. ((element T_1 (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_1)))))) (-. (ex_inf_of_relstr_set T_0 T_2)) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((element C (the_carrier A)) => (((related A B C) /\ (related A C B)) => (B = C)))))))) (rel_str T_0) (All A, ((rel_str A) => (All B, ((ex_inf_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_element_smaller A B C) /\ ((All D, ((element D (the_carrier A)) => ((relstr_element_smaller A B D) => (related A D C)))) /\ (All D, ((element D (the_carrier A)) => (((relstr_element_smaller A B D) /\ (All E, ((element E (the_carrier A)) => ((relstr_element_smaller A B E) => (related A E D))))) => (D = C)))))))))))) ### ConjTree 34
% 0.20/0.44 36. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C))))))) (All A, ((rel_str A) => (All B, ((ex_inf_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_element_smaller A B C) /\ ((All D, ((element D (the_carrier A)) => ((relstr_element_smaller A B D) => (related A D C)))) /\ (All D, ((element D (the_carrier A)) => (((relstr_element_smaller A B D) /\ (All E, ((element E (the_carrier A)) => ((relstr_element_smaller A B E) => (related A E D))))) => (D = C)))))))))))) (rel_str T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((element C (the_carrier A)) => (((related A B C) /\ (related A C B)) => (B = C)))))))) (antisymmetric_relstr T_0) (-. (ex_inf_of_relstr_set T_0 T_2)) ### Exists 35
% 0.20/0.44 37. (rel_str T_0) (-. (rel_str T_0)) ### Axiom
% 0.20/0.44 38. (ex_inf_of_relstr_set T_0 T_2) (-. (ex_inf_of_relstr_set T_0 T_2)) ### Axiom
% 0.20/0.44 39. (element T_4 (the_carrier T_0)) (-. (element T_4 (the_carrier T_0))) ### Axiom
% 0.20/0.44 40. (relstr_element_smaller T_0 T_2 T_4) (-. (relstr_element_smaller T_0 T_2 T_4)) ### Axiom
% 0.20/0.44 41. (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_4)))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_4))))) ### Axiom
% 0.20/0.44 42. (-. ((element T_4 (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 T_4) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_4))))))) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_4)))) (relstr_element_smaller T_0 T_2 T_4) (element T_4 (the_carrier T_0)) ### DisjTree 39 40 41
% 0.20/0.44 43. (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))))))) (element T_4 (the_carrier T_0)) (relstr_element_smaller T_0 T_2 T_4) (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_4)))) ### NotExists 42
% 0.20/0.44 44. ((element T_4 (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 T_4) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D T_4)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E D))))) => (D = T_4))))))) (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))))))) ### ConjTree 43
% 0.20/0.44 45. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E D))))) => (D = C)))))))) (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))))))) ### Exists 44
% 0.20/0.44 46. ((ex_inf_of_relstr_set T_0 T_2) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 T_2 D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 E) => (related T_0 E D))))) => (D = C))))))))) (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))))))) (ex_inf_of_relstr_set T_0 T_2) ### Equiv 38 45
% 0.20/0.44 47. (All B, ((ex_inf_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 B C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 B D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 B D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 B E) => (related T_0 E D))))) => (D = C)))))))))) (ex_inf_of_relstr_set T_0 T_2) (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))))))) ### All 46
% 0.20/0.44 48. ((rel_str T_0) => (All B, ((ex_inf_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 B C) /\ ((All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 B D) => (related T_0 D C)))) /\ (All D, ((element D (the_carrier T_0)) => (((relstr_element_smaller T_0 B D) /\ (All E, ((element E (the_carrier T_0)) => ((relstr_element_smaller T_0 B E) => (related T_0 E D))))) => (D = C))))))))))) (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))))))) (ex_inf_of_relstr_set T_0 T_2) (rel_str T_0) ### Imply 37 47
% 0.20/0.44 49. (All A, ((rel_str A) => (All B, ((ex_inf_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_element_smaller A B C) /\ ((All D, ((element D (the_carrier A)) => ((relstr_element_smaller A B D) => (related A D C)))) /\ (All D, ((element D (the_carrier A)) => (((relstr_element_smaller A B D) /\ (All E, ((element E (the_carrier A)) => ((relstr_element_smaller A B E) => (related A E D))))) => (D = C)))))))))))) (rel_str T_0) (ex_inf_of_relstr_set T_0 T_2) (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C)))))))) ### All 48
% 0.20/0.44 50. (-. ((ex_inf_of_relstr_set T_0 T_2) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 T_2 D) => (related T_0 D C))))))))) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((element C (the_carrier A)) => (((related A B C) /\ (related A C B)) => (B = C)))))))) (rel_str T_0) (All A, ((rel_str A) => (All B, ((ex_inf_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_element_smaller A B C) /\ ((All D, ((element D (the_carrier A)) => ((relstr_element_smaller A B D) => (related A D C)))) /\ (All D, ((element D (the_carrier A)) => (((relstr_element_smaller A B D) /\ (All E, ((element E (the_carrier A)) => ((relstr_element_smaller A B E) => (related A E D))))) => (D = C)))))))))))) ### NotEquiv 36 49
% 0.20/0.44 51. (-. (All B, ((ex_inf_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 B D) => (related T_0 D C)))))))))) (All A, ((rel_str A) => (All B, ((ex_inf_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_element_smaller A B C) /\ ((All D, ((element D (the_carrier A)) => ((relstr_element_smaller A B D) => (related A D C)))) /\ (All D, ((element D (the_carrier A)) => (((relstr_element_smaller A B D) /\ (All E, ((element E (the_carrier A)) => ((relstr_element_smaller A B E) => (related A E D))))) => (D = C)))))))))))) (rel_str T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((element C (the_carrier A)) => (((related A B C) /\ (related A C B)) => (B = C)))))))) (antisymmetric_relstr T_0) ### NotAllEx 50
% 0.20/0.44 52. (-. (((antisymmetric_relstr T_0) /\ (rel_str T_0)) => (All B, ((ex_inf_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_element_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_element_smaller T_0 B D) => (related T_0 D C))))))))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((element C (the_carrier A)) => (((related A B C) /\ (related A C B)) => (B = C)))))))) (All A, ((rel_str A) => (All B, ((ex_inf_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_element_smaller A B C) /\ ((All D, ((element D (the_carrier A)) => ((relstr_element_smaller A B D) => (related A D C)))) /\ (All D, ((element D (the_carrier A)) => (((relstr_element_smaller A B D) /\ (All E, ((element E (the_carrier A)) => ((relstr_element_smaller A B E) => (related A E D))))) => (D = C)))))))))))) ### ConjTree 51
% 0.20/0.44 53. (-. (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_inf_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_element_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_element_smaller A B D) => (related A D C)))))))))))) (All A, ((rel_str A) => (All B, ((ex_inf_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_element_smaller A B C) /\ ((All D, ((element D (the_carrier A)) => ((relstr_element_smaller A B D) => (related A D C)))) /\ (All D, ((element D (the_carrier A)) => (((relstr_element_smaller A B D) /\ (All E, ((element E (the_carrier A)) => ((relstr_element_smaller A B E) => (related A E D))))) => (D = C)))))))))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((element C (the_carrier A)) => (((related A B C) /\ (related A C B)) => (B = C)))))))) ### NotAllEx 52
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 (* END-PROOF *)
%------------------------------------------------------------------------------