# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,X2),s(t_h4s_hreals_hreal,X1))))=>p(s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,X2))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,X1))))))),file('i/f/realax/TREAL__ISO', ch4s_realaxs_TREALu_u_ISO)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/realax/TREAL__ISO', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/realax/TREAL__ISO', aHLu_FALSITY)).
fof(6, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/realax/TREAL__ISO', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X4]:![X5]:s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X5),s(t_h4s_hreals_hreal,X4)))=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X4),s(t_h4s_hreals_hreal,X5))),file('i/f/realax/TREAL__ISO', ah4s_hreals_HREALu_u_ADDu_u_SYM)).
fof(8, axiom,![X6]:![X4]:![X5]:s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X5),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X4),s(t_h4s_hreals_hreal,X6)))))=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X5),s(t_h4s_hreals_hreal,X4))),s(t_h4s_hreals_hreal,X6))),file('i/f/realax/TREAL__ISO', ah4s_hreals_HREALu_u_ADDu_u_ASSOC)).
fof(9, axiom,![X7]:![X8]:![X9]:s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X9),s(t_h4s_hreals_hreal,X8))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X9),s(t_h4s_hreals_hreal,X7)))))=s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,X8),s(t_h4s_hreals_hreal,X7))),file('i/f/realax/TREAL__ISO', ah4s_realaxs_HREALu_u_LTu_u_LADD)).
fof(10, axiom,![X10]:![X11]:![X12]:![X13]:s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,X13),s(t_h4s_hreals_hreal,X11))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,X12),s(t_h4s_hreals_hreal,X10)))))=s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X13),s(t_h4s_hreals_hreal,X10))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X12),s(t_h4s_hreals_hreal,X11))))),file('i/f/realax/TREAL__ISO', ah4s_realaxs_trealu_u_lt0)).
fof(11, axiom,![X9]:s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,X9)))=s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X9),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),file('i/f/realax/TREAL__ISO', ah4s_realaxs_trealu_u_ofu_u_hreal0)).
fof(12, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/realax/TREAL__ISO', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
