# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X4),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3))))&p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),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),X4),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2))),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),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1))))))),file('i/f/hrat/TRAT__MUL__WELLDEFINED2', ch4s_hrats_TRATu_u_MULu_u_WELLDEFINED2)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/hrat/TRAT__MUL__WELLDEFINED2', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/hrat/TRAT__MUL__WELLDEFINED2', aHLu_FALSITY)).
fof(5, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/hrat/TRAT__MUL__WELLDEFINED2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(6, axiom,![X6]:![X7]:![X8]:((p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X7))))&p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X7),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X6)))))=>p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X6))))),file('i/f/hrat/TRAT__MUL__WELLDEFINED2', ah4s_hrats_TRATu_u_EQu_u_TRANS)).
fof(7, axiom,![X6]:![X7]:![X8]:(p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X7))))=>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),X8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X6))),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),X7),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X6))))))),file('i/f/hrat/TRAT__MUL__WELLDEFINED2', ah4s_hrats_TRATu_u_MULu_u_WELLDEFINED)).
fof(8, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/hrat/TRAT__MUL__WELLDEFINED2', aHLu_BOOLu_CASES)).
fof(9, axiom,![X9]:![X10]: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),X10),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X9)))=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),X9),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X10))),file('i/f/hrat/TRAT__MUL__WELLDEFINED2', ah4s_hrats_TRATu_u_MULu_u_SYMu_u_EQ)).
# SZS output end CNFRefutation
