# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/MIN__COMM', ch4s_arithmetics_MINu_u_COMM)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MIN__COMM', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/MIN__COMM', aHLu_BOOLu_CASES)).
fof(6, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/arithmetic/MIN__COMM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(11, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),file('i/f/arithmetic/MIN__COMM', ah4s_arithmetics_MINu_u_DEF)).
fof(12, axiom,![X1]:![X2]:~((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/MIN__COMM', ah4s_arithmetics_LESSu_u_ANTISYM)).
fof(13, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MIN__COMM', ah4s_arithmetics_NOTu_u_LESS)).
fof(14, axiom,![X1]:![X2]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,X2)),file('i/f/arithmetic/MIN__COMM', ah4s_arithmetics_LESSu_u_EQUALu_u_ANTISYM)).
fof(15, axiom,![X6]:![X4]:![X5]:s(X6,h4s_bools_cond(s(t_bool,t),s(X6,X5),s(X6,X4)))=s(X6,X5),file('i/f/arithmetic/MIN__COMM', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(16, axiom,![X6]:![X4]:![X5]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X5),s(X6,X4)))=s(X6,X4),file('i/f/arithmetic/MIN__COMM', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
