# 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_add(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_add(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__ADD__WELLDEFINED2', ch4s_hrats_TRATu_u_ADDu_u_WELLDEFINED2)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/hrat/TRAT__ADD__WELLDEFINED2', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/hrat/TRAT__ADD__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__ADD__WELLDEFINED2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(46, axiom,![X16]:![X17]:![X18]:(p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X18),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X17))))=>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_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X18),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X16))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X17),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X16))))))),file('i/f/hrat/TRAT__ADD__WELLDEFINED2', ah4s_hrats_TRATu_u_ADDu_u_WELLDEFINED)).
fof(49, axiom,![X16]:![X17]:![X18]:((p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X18),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X17))))&p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X17),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X16)))))=>p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X18),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X16))))),file('i/f/hrat/TRAT__ADD__WELLDEFINED2', ah4s_hrats_TRATu_u_EQu_u_TRANS)).
fof(54, axiom,![X20]:![X21]:s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X21),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X20)))=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X20),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X21))),file('i/f/hrat/TRAT__ADD__WELLDEFINED2', ah4s_hrats_TRATu_u_ADDu_u_SYMu_u_EQ)).
fof(77, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/hrat/TRAT__ADD__WELLDEFINED2', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
