# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,h4s_extreals_neginf)))=s(t_h4s_extreals_extreal,h4s_extreals_neginf),file('i/f/extreal/min__infty_c3', ch4s_extreals_minu_u_inftyu_c3)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/extreal/min__infty_c3', aHLu_TRUTH)).
fof(6, axiom,![X2]:![X4]:![X5]:s(X2,h4s_bools_cond(s(t_bool,X5),s(X2,X4),s(X2,X4)))=s(X2,X4),file('i/f/extreal/min__infty_c3', ah4s_bools_CONDu_u_ID)).
fof(8, axiom,![X2]:![X9]:![X3]:![X10]:![X1]:![X11]:![X12]:((s(t_bool,X12)=s(t_bool,X11)&((p(s(t_bool,X11))=>s(X2,X1)=s(X2,X10))&(~(p(s(t_bool,X11)))=>s(X2,X3)=s(X2,X9))))=>s(X2,h4s_bools_cond(s(t_bool,X12),s(X2,X1),s(X2,X3)))=s(X2,h4s_bools_cond(s(t_bool,X11),s(X2,X10),s(X2,X9)))),file('i/f/extreal/min__infty_c3', ah4s_bools_CONDu_u_CONG)).
fof(9, axiom,![X1]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,h4s_extreals_neginf))))<=>s(t_h4s_extreals_extreal,X1)=s(t_h4s_extreals_extreal,h4s_extreals_neginf)),file('i/f/extreal/min__infty_c3', ah4s_extreals_leu_u_inftyu_c2)).
fof(10, axiom,![X3]:![X1]:s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X3)))=s(t_h4s_extreals_extreal,h4s_bools_cond(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X3))),s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X3))),file('i/f/extreal/min__infty_c3', ah4s_extreals_extrealu_u_minu_u_def)).
fof(11, axiom,~(p(s(t_bool,f))),file('i/f/extreal/min__infty_c3', aHLu_FALSITY)).
fof(12, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/extreal/min__infty_c3', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
