# 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(2, axiom,~(p(s(t_bool,f))),file('i/f/extreal/max__comm', aHLu_FALSITY)).
fof(3, 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/extreal/max__comm', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(25, 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(26, 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(27, 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))))),file('i/f/extreal/max__comm', ah4s_extreals_leu_u_total)).
fof(31, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/extreal/max__comm', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(32, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/extreal/max__comm', aHLu_BOOLu_CASES)).
fof(33, axiom,![X7]:![X3]:![X4]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X4),s(X7,X3)))=s(X7,X3),file('i/f/extreal/max__comm', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(34, axiom,![X7]:![X3]:![X4]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X4),s(X7,X3)))=s(X7,X4),file('i/f/extreal/max__comm', ah4s_bools_CONDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
