# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X3))))=>(s(t_h4s_integers_int,X2)=s(t_h4s_integers_int,X1)<=>s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X2)))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X1))))),file('i/f/int_arith/eq__justify__multiplication', ch4s_intu_u_ariths_equ_u_justifyu_u_multiplication)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/int_arith/eq__justify__multiplication', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/eq__justify__multiplication', aHLu_FALSITY)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/int_arith/eq__justify__multiplication', aHLu_BOOLu_CASES)).
fof(23, axiom,![X4]:(s(t_bool,X4)=s(t_bool,f)<=>~(p(s(t_bool,X4)))),file('i/f/int_arith/eq__justify__multiplication', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(42, axiom,![X1]:![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X2))),file('i/f/int_arith/eq__justify__multiplication', ah4s_integers_INTu_u_MULu_u_COMM)).
fof(43, axiom,![X15]:![X1]:![X2]:(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X15)))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X15)))<=>(s(t_h4s_integers_int,X15)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))|s(t_h4s_integers_int,X2)=s(t_h4s_integers_int,X1))),file('i/f/int_arith/eq__justify__multiplication', ah4s_integers_INTu_u_EQu_u_RMUL)).
fof(44, axiom,![X2]:~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X2))))),file('i/f/int_arith/eq__justify__multiplication', ah4s_integers_INTu_u_LTu_u_REFL)).
# SZS output end CNFRefutation
