# 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(45, axiom,![X2]:![X1]:![X16]:s(X2,h4s_paths_first(s(t_h4s_paths_path(X2,X1),X16)))=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),X16))))),file('i/f/path/first__thm_c0', ah4s_paths_firstu_u_def)).
fof(46, 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(54, axiom,![X2]:![X1]:![X23]: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_paths_frompath(s(t_h4s_paths_path(X2,X1),X23)))))=s(t_h4s_paths_path(X2,X1),X23),file('i/f/path/first__thm_c0', ah4s_paths_pathu_u_absrepu_u_bijectionsu_c0)).
fof(57, axiom,![X1]:![X2]:![X23]:?[X17]:s(t_h4s_paths_path(X2,X1),X23)=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))),X17))),file('i/f/path/first__thm_c0', ah4s_paths_toPathu_u_onto)).
fof(60, axiom,![X2]:![X1]:![X17]:?[X23]:s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),X17)=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),X23))),file('i/f/path/first__thm_c0', ah4s_paths_fromPathu_u_onto)).
fof(91, axiom,![X1]:![X2]:![X10]:![X3]:s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X3),s(X1,X10)))))=s(X2,X3),file('i/f/path/first__thm_c0', ah4s_pairs_FST0)).
fof(92, axiom,![X2]:![X1]:![X3]:?[X15]:?[X17]:s(t_h4s_pairs_prod(X2,X1),X3)=s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X15),s(X1,X17))),file('i/f/path/first__thm_c0', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
# SZS output end CNFRefutation
