# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X2),s(t_h4s_rats_rat,X1))))=>~(s(t_h4s_rats_rat,X2)=s(t_h4s_rats_rat,X1))),file('i/f/rat/RAT__LES__IMP__NEQ', ch4s_rats_RATu_u_LESu_u_IMPu_u_NEQ)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/rat/RAT__LES__IMP__NEQ', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/rat/RAT__LES__IMP__NEQ', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/rat/RAT__LES__IMP__NEQ', aHLu_BOOLu_CASES)).
fof(11, axiom,![X12]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/rat/RAT__LES__IMP__NEQ', ah4s_numerals_numeralu_u_distribu_c17)).
fof(12, axiom,![X12]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/rat/RAT__LES__IMP__NEQ', ah4s_numerals_numeralu_u_equ_c1)).
fof(13, axiom,![X12]:![X13]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X13)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X12)))<=>s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,X12)),file('i/f/rat/RAT__LES__IMP__NEQ', ah4s_integers_INTu_u_INJ)).
fof(14, axiom,![X2]:(s(t_h4s_integers_int,h4s_rats_ratu_u_sgn(s(t_h4s_rats_rat,X2)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(t_h4s_rats_rat,X2)=s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/rat/RAT__LES__IMP__NEQ', ah4s_rats_RATu_u_SGNu_u_CLAUSESu_c1)).
fof(15, axiom,![X1]:![X2]:(p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X2),s(t_h4s_rats_rat,X1))))<=>s(t_h4s_integers_int,h4s_rats_ratu_u_sgn(s(t_h4s_rats_rat,h4s_rats_ratu_u_sub(s(t_h4s_rats_rat,X1),s(t_h4s_rats_rat,X2)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))),file('i/f/rat/RAT__LES__IMP__NEQ', ah4s_rats_ratu_u_lesu_u_def)).
fof(16, axiom,![X1]:![X2]:(s(t_h4s_rats_rat,h4s_rats_ratu_u_sub(s(t_h4s_rats_rat,X2),s(t_h4s_rats_rat,X1)))=s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(t_h4s_rats_rat,X2)=s(t_h4s_rats_rat,X1)),file('i/f/rat/RAT__LES__IMP__NEQ', ah4s_rats_RATu_u_EQu_u_SUB0)).
# SZS output end CNFRefutation
