# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_absu_u_diff(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,X2)),file('i/f/arithmetic/ABS__DIFF__EQ__0', ch4s_arithmetics_ABSu_u_DIFFu_u_EQu_u_0)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/ABS__DIFF__EQ__0', 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/arithmetic/ABS__DIFF__EQ__0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(25, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X2),s(t_h4s_nums_num,X1))))|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))),file('i/f/arithmetic/ABS__DIFF__EQ__0', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(26, 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/ABS__DIFF__EQ__0', ah4s_arithmetics_LESSu_u_ANTISYM)).
fof(27, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/ABS__DIFF__EQ__0', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(28, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_absu_u_diff(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/ABS__DIFF__EQ__0', ah4s_arithmetics_ABSu_u_DIFFu_u_def)).
fof(32, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/ABS__DIFF__EQ__0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(33, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/arithmetic/ABS__DIFF__EQ__0', aHLu_BOOLu_CASES)).
fof(34, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X4),s(X6,X3)))=s(X6,X3),file('i/f/arithmetic/ABS__DIFF__EQ__0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(35, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,t),s(X6,X4),s(X6,X3)))=s(X6,X4),file('i/f/arithmetic/ABS__DIFF__EQ__0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
