# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(8, axiom,![X8]:![X9]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X9),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8))))))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_complexu_u_scalaru_u_lmul0)).
fof(9, axiom,![X8]:![X9]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X9),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)))))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X9))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_NEG)).
fof(10, axiom,![X8]:s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)))=s(t_h4s_realaxs_real,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_RE0)).
fof(11, axiom,![X8]:s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)))=s(t_h4s_realaxs_real,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_IM0)).
fof(12, axiom,![X7]:![X10]:![X11]:![X6]:s(X10,h4s_pairs_snd(s(t_h4s_pairs_prod(X7,X10),h4s_pairs_u_2c(s(X7,X6),s(X10,X11)))))=s(X10,X11),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_pairs_SND0)).
fof(13, axiom,![X10]:![X7]:![X11]:![X6]:s(X7,h4s_pairs_fst(s(t_h4s_pairs_prod(X7,X10),h4s_pairs_u_2c(s(X7,X6),s(X10,X11)))))=s(X7,X6),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_pairs_FST0)).
fof(17, axiom,![X8]:![X13]:![X9]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X9),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X13)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X9),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X13))))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_LMULu_u_SCALARu_u_LMUL)).
fof(22, axiom,![X8]:![X13]:![X9]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X9),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X13)))))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X9),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X13))))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_RMULu_u_SCALARu_u_LMUL)).
fof(24, axiom,![X8]:![X9]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X9),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)))))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X9))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_NEGu_u_SCALARu_u_LMUL)).
fof(26, axiom,![X8]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_ZERO)).
fof(27, axiom,![X9]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X9),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_ZEROu_u_SCALARu_u_LMUL)).
fof(30, axiom,![X6]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,X6)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(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))))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_complexu_u_ofu_u_real0)).
fof(31, axiom,![X14]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,X14)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X14))))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_complexu_u_ofu_u_num0)).
fof(43, 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/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_reals_REALu_u_MULu_u_LID)).
fof(73, axiom,![X14]: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,X14)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_reals_REAL)).
fof(78, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(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_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_reals_REALu_u_MULu_u_RZERO)).
fof(91, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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,X6),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_reals_REALu_u_ADDu_u_RID)).
fof(93, axiom,![X11]:![X6]: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,X11),s(t_h4s_realaxs_real,X6))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_reals_REALu_u_MULu_u_SYM)).
fof(95, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6)))))=s(t_h4s_realaxs_real,X6),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_reals_REALu_u_NEGu_u_NEG)).
fof(98, axiom,![X11]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X11)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X11),s(t_h4s_realaxs_real,X6))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_reals_REALu_u_ADDu_u_SYM)).
fof(107, axiom,s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_NEGu_u_0)).
fof(113, axiom,![X8]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_MULu_u_RZERO)).
fof(118, axiom,![X8]:![X13]:(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X13)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X13)),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_SUBu_u_0)).
fof(119, axiom,![X8]:![X13]:(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X13)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))|s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X13)=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_complexs_COMPLEXu_u_ENTIRE)).
fof(122, axiom,![X7]:![X10]:![X17]:![X18]:(s(t_h4s_pairs_prod(X7,X10),X18)=s(t_h4s_pairs_prod(X7,X10),X17)<=>(s(X7,h4s_pairs_fst(s(t_h4s_pairs_prod(X7,X10),X18)))=s(X7,h4s_pairs_fst(s(t_h4s_pairs_prod(X7,X10),X17)))&s(X10,h4s_pairs_snd(s(t_h4s_pairs_prod(X7,X10),X18)))=s(X10,h4s_pairs_snd(s(t_h4s_pairs_prod(X7,X10),X17))))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ah4s_pairs_PAIRu_u_FSTu_u_SNDu_u_EQ)).
fof(133, conjecture,![X8]:![X9]:(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X9),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>(s(t_h4s_realaxs_real,X9)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))|s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X8)=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/complex/COMPLEX__SCALAR__LMUL__ENTIRE', ch4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_ENTIRE)).
# SZS output end CNFRefutation
