# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_1),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1)))),file('i/f/hrat/TRAT__MUL__LID', ch4s_hrats_TRATu_u_MULu_u_LID)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/hrat/TRAT__MUL__LID', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/hrat/TRAT__MUL__LID', aHLu_FALSITY)).
fof(6, axiom,![X4]:![X5]:(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5)=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X4)=>p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X4))))),file('i/f/hrat/TRAT__MUL__LID', ah4s_hrats_TRATu_u_EQu_u_AP)).
fof(7, axiom,![X2]:![X6]:![X3]:s(t_h4s_pairs_prod(X2,X6),h4s_pairs_u_2c(s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X6),X3))),s(X6,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,X6),X3)))))=s(t_h4s_pairs_prod(X2,X6),X3),file('i/f/hrat/TRAT__MUL__LID', ah4s_pairs_PAIR)).
fof(8, axiom,s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_1)=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_0))),file('i/f/hrat/TRAT__MUL__LID', ah4s_hrats_tratu_u_10)).
fof(9, axiom,![X7]:![X8]:![X9]:![X3]:s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X8))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7)))))=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))))))),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))))))))),file('i/f/hrat/TRAT__MUL__LID', ah4s_hrats_tratu_u_mul0)).
fof(10, axiom,![X10]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))))=s(t_h4s_nums_num,X10),file('i/f/hrat/TRAT__MUL__LID', ah4s_primu_u_recs_PRE0u_c1)).
fof(11, axiom,![X10]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,X10),file('i/f/hrat/TRAT__MUL__LID', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(13, axiom,![X10]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/hrat/TRAT__MUL__LID', ah4s_arithmetics_MULTu_u_CLAUSESu_c0)).
fof(14, axiom,![X11]:![X10]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X11))),file('i/f/hrat/TRAT__MUL__LID', ah4s_arithmetics_MULTu_u_CLAUSESu_c4)).
fof(15, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)|s(t_bool,X12)=s(t_bool,f)),file('i/f/hrat/TRAT__MUL__LID', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
