# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_max(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X1)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_max(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X2))),file('i/f/extreal/max__comm', ch4s_extreals_maxu_u_comm)).
fof(4, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/extreal/max__comm', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(22, axiom,![X1]:![X2]:s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_max(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X1)))=s(t_h4s_extreals_extreal,h4s_bools_cond(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X1))),s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X2))),file('i/f/extreal/max__comm', ah4s_extreals_extrealu_u_maxu_u_def)).
fof(28, axiom,![X1]:![X2]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_max(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X1)))))),file('i/f/extreal/max__comm', ah4s_extreals_leu_u_max2)).
fof(34, axiom,![X1]:![X2]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X1))))&p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X2)))))<=>s(t_h4s_extreals_extreal,X2)=s(t_h4s_extreals_extreal,X1)),file('i/f/extreal/max__comm', ah4s_extreals_leu_u_antisym)).
fof(43, axiom,p(s(t_bool,t)),file('i/f/extreal/max__comm', aHLu_TRUTH)).
fof(44, axiom,~(p(s(t_bool,f))),file('i/f/extreal/max__comm', aHLu_FALSITY)).
fof(47, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/extreal/max__comm', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(60, axiom,![X10]:(s(t_bool,f)=s(t_bool,X10)<=>~(p(s(t_bool,X10)))),file('i/f/extreal/max__comm', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(69, axiom,![X7]:![X8]:![X9]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X9),s(X7,X8)))=s(X7,X8),file('i/f/extreal/max__comm', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(70, axiom,![X7]:![X8]:![X9]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X9),s(X7,X8)))=s(X7,X9),file('i/f/extreal/max__comm', ah4s_bools_CONDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
