# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(12, axiom,![X12]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12)))))),file('i/f/transc/EXP__FDIFF', ah4s_primu_u_recs_LESSu_u_0)).
fof(13, axiom,![X12]:s(t_h4s_nums_num,h4s_arithmetics_fact(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,h4s_arithmetics_fact(s(t_h4s_nums_num,X12))))),file('i/f/transc/EXP__FDIFF', ah4s_arithmetics_FACT0u_c1)).
fof(14, axiom,![X12]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_fact(s(t_h4s_nums_num,X12)))))),file('i/f/transc/EXP__FDIFF', ah4s_arithmetics_FACTu_u_LESS)).
fof(15, axiom,![X13]:![X11]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X11),s(t_h4s_realaxs_real,X13)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X11))),s(t_h4s_realaxs_real,X13))),file('i/f/transc/EXP__FDIFF', ah4s_reals_REALu_u_MULu_u_ASSOC)).
fof(16, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_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))))))),s(t_h4s_realaxs_real,X6)))=s(t_h4s_realaxs_real,X6),file('i/f/transc/EXP__FDIFF', ah4s_reals_REALu_u_MULu_u_LID)).
fof(17, axiom,![X6]:(~(s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X6)))))=s(t_h4s_realaxs_real,h4s_reals_realu_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/transc/EXP__FDIFF', ah4s_reals_REALu_u_MULu_u_RINV)).
fof(19, axiom,![X11]:![X6]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X11))))=>~(s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,X11))),file('i/f/transc/EXP__FDIFF', ah4s_reals_REALu_u_LTu_u_IMPu_u_NE)).
fof(20, axiom,![X12]:![X14]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X14))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X12)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X12))),file('i/f/transc/EXP__FDIFF', ah4s_reals_REALu_u_LT)).
fof(21, axiom,![X12]:![X14]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X14))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X12)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X12))))),file('i/f/transc/EXP__FDIFF', ah4s_reals_REALu_u_MUL)).
fof(22, axiom,![X11]:![X6]:((~(s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))&~(s(t_h4s_realaxs_real,X11)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=>s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X11)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X11)))))),file('i/f/transc/EXP__FDIFF', ah4s_reals_REALu_u_INVu_u_MUL)).
fof(23, axiom,![X15]:![X6]:s(t_h4s_realaxs_real,h4s_powsers_diffs(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X15),s(t_h4s_nums_num,X6)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6))))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X15),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6))))))),file('i/f/transc/EXP__FDIFF', ah4s_powsers_diffs0)).
fof(24, conjecture,![X16]:(![X12]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X16),s(t_h4s_nums_num,X12)))=s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_fact(s(t_h4s_nums_num,X12)))))))=>![X6]:s(t_h4s_realaxs_real,h4s_powsers_diffs(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X16),s(t_h4s_nums_num,X6)))=s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_fact(s(t_h4s_nums_num,X6)))))))),file('i/f/transc/EXP__FDIFF', ch4s_transcs_EXPu_u_FDIFF)).
# SZS output end CNFRefutation
