# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_paths_path(X1,X2),h4s_paths_pconcat(s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X3))),s(X2,X5),s(t_h4s_paths_path(X1,X2),X4)))=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X3),s(X2,X5),s(t_h4s_paths_path(X1,X2),X4))),file('i/f/path/pconcat__thm_c0', ch4s_paths_pconcatu_u_thmu_c0)).
fof(7, axiom,![X2]:![X1]:![X10]:s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_paths_frompath(s(t_h4s_paths_path(X1,X2),h4s_paths_topath(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),X10)))))=s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),X10),file('i/f/path/pconcat__thm_c0', ah4s_paths_pathu_u_repu_u_bijectionsu_u_thmu_c1)).
fof(9, axiom,![X1]:![X2]:![X3]:![X10]:![X12]:s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X3),s(X2,X10),s(t_h4s_paths_path(X1,X2),X12)))=s(t_h4s_paths_path(X1,X2),h4s_paths_topath(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_pairs_u_2c(s(X1,X3),s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_llists_lcons(s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X10),s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X12))))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_pairs_snd(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_paths_frompath(s(t_h4s_paths_path(X1,X2),X12))))))))))),file('i/f/path/pconcat__thm_c0', ah4s_paths_pconsu_u_def)).
fof(10, axiom,![X2]:![X1]:![X3]:s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X3)))=s(t_h4s_paths_path(X1,X2),h4s_paths_topath(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_pairs_u_2c(s(X1,X3),s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_llists_lnil))))),file('i/f/path/pconcat__thm_c0', ah4s_paths_stoppedu_u_atu_u_def)).
fof(11, axiom,![X2]:![X1]:![X3]:s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X3)))))=s(X1,X3),file('i/f/path/pconcat__thm_c0', ah4s_paths_firstu_u_thmu_c0)).
fof(12, axiom,![X1]:![X2]:![X4]:![X13]:![X5]:s(t_h4s_paths_path(X1,X2),h4s_paths_pconcat(s(t_h4s_paths_path(X1,X2),X13),s(X2,X5),s(t_h4s_paths_path(X1,X2),X4)))=s(t_h4s_paths_path(X1,X2),h4s_paths_topath(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_pairs_u_2c(s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X13))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_llists_lappend(s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_pairs_snd(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_paths_frompath(s(t_h4s_paths_path(X1,X2),X13))))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_llists_lcons(s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X5),s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X4))))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_pairs_snd(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_paths_frompath(s(t_h4s_paths_path(X1,X2),X4))))))))))))),file('i/f/path/pconcat__thm_c0', ah4s_paths_pconcatu_u_def)).
fof(15, axiom,![X1]:![X2]:![X7]:![X3]:s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X3),s(X2,X7)))))=s(X2,X7),file('i/f/path/pconcat__thm_c0', ah4s_pairs_SND0)).
fof(17, axiom,![X1]:![X3]:s(t_h4s_llists_llist(X1),h4s_llists_lappend(s(t_h4s_llists_llist(X1),h4s_llists_lnil),s(t_h4s_llists_llist(X1),X3)))=s(t_h4s_llists_llist(X1),X3),file('i/f/path/pconcat__thm_c0', ah4s_llists_LAPPEND0u_c0)).
# SZS output end CNFRefutation
