# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(X2,h4s_paths_first(s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))))=s(X2,X3),file('i/f/path/first__thm_c0', ch4s_paths_firstu_u_thmu_c0)).
fof(5, axiom,![X2]:![X1]:![X4]:s(X2,h4s_paths_first(s(t_h4s_paths_path(X2,X1),X4)))=s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),h4s_paths_frompath(s(t_h4s_paths_path(X2,X1),X4))))),file('i/f/path/first__thm_c0', ah4s_paths_firstu_u_def)).
fof(6, axiom,![X1]:![X2]:![X3]:s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))=s(t_h4s_paths_path(X2,X1),h4s_paths_topath(s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),h4s_pairs_u_2c(s(X2,X3),s(t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2)),h4s_llists_lnil))))),file('i/f/path/first__thm_c0', ah4s_paths_stoppedu_u_atu_u_def)).
fof(7, axiom,![X1]:![X2]:![X5]:s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),h4s_paths_frompath(s(t_h4s_paths_path(X2,X1),h4s_paths_topath(s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),X5)))))=s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),X5),file('i/f/path/first__thm_c0', ah4s_paths_pathu_u_repu_u_bijectionsu_u_thmu_c1)).
fof(10, axiom,![X1]:![X2]:![X7]:![X3]:s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X3),s(X1,X7)))))=s(X2,X3),file('i/f/path/first__thm_c0', ah4s_pairs_FST0)).
# SZS output end CNFRefutation
