# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:![X8]:(s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X4),s(X2,X6),s(t_h4s_paths_path(X1,X2),X8)))=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X3),s(X2,X5),s(t_h4s_paths_path(X1,X2),X7)))<=>(s(X1,X4)=s(X1,X3)&(s(X2,X6)=s(X2,X5)&s(t_h4s_paths_path(X1,X2),X8)=s(t_h4s_paths_path(X1,X2),X7)))),file('i/f/path/pcons__11', ch4s_paths_pconsu_u_11)).
fof(2, axiom,![X1]:![X2]:![X4]:![X6]:![X8]:s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X4),s(X2,X6),s(t_h4s_paths_path(X1,X2),X8)))=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,X4),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,X6),s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X8))))),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),X8))))))))))),file('i/f/path/pcons__11', ah4s_paths_pconsu_u_def)).
fof(3, axiom,![X2]:![X1]:![X9]:![X6]:(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))),X6)))=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))),X9)))<=>s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),X6)=s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),X9)),file('i/f/path/pcons__11', ah4s_paths_toPathu_u_11)).
fof(4, axiom,![X1]:![X2]:![X3]:![X4]:![X10]:![X11]:(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X3)))=s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X11),s(X2,X10)))<=>(s(X1,X4)=s(X1,X11)&s(X2,X3)=s(X2,X10))),file('i/f/path/pcons__11', ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ)).
fof(5, axiom,![X1]:![X12]:![X13]:![X14]:![X15]:(s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X15),s(t_h4s_llists_llist(X1),X13)))=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X14),s(t_h4s_llists_llist(X1),X12)))<=>(s(X1,X15)=s(X1,X14)&s(t_h4s_llists_llist(X1),X13)=s(t_h4s_llists_llist(X1),X12))),file('i/f/path/pcons__11', ah4s_llists_LCONSu_u_11)).
fof(6, axiom,![X1]:![X2]:![X7]:![X8]:(s(t_h4s_pairs_prod(X1,X2),X8)=s(t_h4s_pairs_prod(X1,X2),X7)<=>(s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,X2),X8)))=s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,X2),X7)))&s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),X8)))=s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),X7))))),file('i/f/path/pcons__11', ah4s_pairs_PAIRu_u_FSTu_u_SNDu_u_EQ)).
fof(7, axiom,![X1]:![X2]:![X16]:![X11]:(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),X11)))=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),X16)))<=>s(t_h4s_paths_path(X1,X2),X11)=s(t_h4s_paths_path(X1,X2),X16)),file('i/f/path/pcons__11', ah4s_paths_fromPathu_u_11)).
fof(8, axiom,![X1]:![X2]:![X8]:s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X8)))=s(X1,h4s_pairs_fst(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),X8))))),file('i/f/path/pcons__11', ah4s_paths_firstu_u_def)).
# SZS output end CNFRefutation
