# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/transc/PI2', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/transc/PI2', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/transc/PI2', aHLu_BOOLu_CASES)).
fof(8, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/transc/PI2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X8]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/transc/PI2', ah4s_numerals_numeralu_u_distribu_c17)).
fof(10, axiom,![X8]:(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/transc/PI2', ah4s_numerals_numeralu_u_equ_c3)).
fof(11, axiom,![X9]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X9)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,X6))),file('i/f/transc/PI2', ah4s_reals_REALu_u_MULu_u_SYM)).
fof(12, axiom,![X10]:![X9]:![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,X9),s(t_h4s_realaxs_real,X10)))))=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,X9))),s(t_h4s_realaxs_real,X10))),file('i/f/transc/PI2', ah4s_reals_REALu_u_MULu_u_ASSOC)).
fof(13, 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/PI2', ah4s_reals_REALu_u_MULu_u_LID)).
fof(14, 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,h4s_realaxs_inv(s(t_h4s_realaxs_real,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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))),file('i/f/transc/PI2', ah4s_reals_REALu_u_MULu_u_LINV)).
fof(15, axiom,![X9]:![X6]:s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X9)))=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,X9))))),file('i/f/transc/PI2', ah4s_reals_realu_u_div)).
fof(16, axiom,![X8]:![X11]:(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X11)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X8)))<=>s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,X8)),file('i/f/transc/PI2', ah4s_reals_REALu_u_INJ)).
fof(17, axiom,![X12]:(![X6]:(p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),X12),s(t_h4s_realaxs_real,X6))))<=>(p(s(t_bool,h4s_reals_realu_u_lte(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,X6))))&(p(s(t_bool,h4s_reals_realu_u_lte(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_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))&s(t_h4s_realaxs_real,h4s_transcs_cos(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_transcs_pi)=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_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_mins_u_40(s(t_fun(t_h4s_realaxs_real,t_bool),X12)))))),file('i/f/transc/PI2', ah4s_transcs_pi0)).
fof(18, conjecture,![X12]:(![X6]:(p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),X12),s(t_h4s_realaxs_real,X6))))<=>(p(s(t_bool,h4s_reals_realu_u_lte(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,X6))))&(p(s(t_bool,h4s_reals_realu_u_lte(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_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))&s(t_h4s_realaxs_real,h4s_transcs_cos(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_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_pi),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_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))=s(t_h4s_realaxs_real,h4s_mins_u_40(s(t_fun(t_h4s_realaxs_real,t_bool),X12)))),file('i/f/transc/PI2', ch4s_transcs_PI2)).
# SZS output end CNFRefutation
