# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_pos(s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,h4s_reals_pos(s(t_h4s_realaxs_real,X1))))))),file('i/f/real/REAL__POS__MONO', ch4s_reals_REALu_u_POSu_u_MONO)).
fof(2, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/real/REAL__POS__MONO', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,![X2]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X2)))),file('i/f/real/REAL__POS__MONO', ah4s_reals_REALu_u_LEu_u_REFL)).
fof(30, axiom,![X16]:![X1]:![X2]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X16)))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X16))))),file('i/f/real/REAL__POS__MONO', ah4s_reals_REALu_u_LEu_u_TRANS)).
fof(31, axiom,![X1]:![X2]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X2)))))<=>s(t_h4s_realaxs_real,X2)=s(t_h4s_realaxs_real,X1)),file('i/f/real/REAL__POS__MONO', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(32, axiom,![X2]:s(t_h4s_realaxs_real,h4s_reals_pos(s(t_h4s_realaxs_real,X2)))=s(t_h4s_realaxs_real,h4s_bools_cond(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,X2))),s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/real/REAL__POS__MONO', ah4s_reals_posu_u_def)).
fof(34, axiom,![X2]: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,h4s_reals_pos(s(t_h4s_realaxs_real,X2)))))),file('i/f/real/REAL__POS__MONO', ah4s_reals_REALu_u_POSu_u_POS)).
fof(36, axiom,![X15]:![X3]:![X4]:s(X15,h4s_bools_cond(s(t_bool,t),s(X15,X4),s(X15,X3)))=s(X15,X4),file('i/f/real/REAL__POS__MONO', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(37, axiom,![X15]:![X3]:![X4]:s(X15,h4s_bools_cond(s(t_bool,f),s(X15,X4),s(X15,X3)))=s(X15,X3),file('i/f/real/REAL__POS__MONO', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(41, axiom,p(s(t_bool,t)),file('i/f/real/REAL__POS__MONO', aHLu_TRUTH)).
fof(42, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/real/REAL__POS__MONO', aHLu_BOOLu_CASES)).
fof(44, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/real/REAL__POS__MONO', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(56, axiom,~(p(s(t_bool,f))),file('i/f/real/REAL__POS__MONO', aHLu_FALSITY)).
fof(75, axiom,![X16]:![X1]:![X2]:((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X16)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X16))))),file('i/f/real/REAL__POS__MONO', ah4s_reals_REALu_u_LTEu_u_TRANS)).
fof(80, axiom,![X2]:~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X2))))),file('i/f/real/REAL__POS__MONO', ah4s_reals_REALu_u_LTu_u_REFL)).
fof(81, axiom,![X1]:![X2]:(s(t_h4s_realaxs_real,X2)=s(t_h4s_realaxs_real,X1)|(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))|p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X2)))))),file('i/f/real/REAL__POS__MONO', ah4s_reals_REALu_u_LTu_u_TOTAL)).
# SZS output end CNFRefutation
