# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/ABS__DIFF__COMM', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/ABS__DIFF__COMM', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/arithmetic/ABS__DIFF__COMM', aHLu_BOOLu_CASES)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/arithmetic/ABS__DIFF__COMM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(13, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/ABS__DIFF__COMM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(14, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X8),s(X9,X7)))=s(X9,X8),file('i/f/arithmetic/ABS__DIFF__COMM', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(15, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/arithmetic/ABS__DIFF__COMM', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(32, axiom,![X16]:![X17]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))|s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X16))),file('i/f/arithmetic/ABS__DIFF__COMM', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(33, axiom,![X16]:![X17]:~((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17)))))),file('i/f/arithmetic/ABS__DIFF__COMM', ah4s_arithmetics_LESSu_u_ANTISYM)).
fof(34, axiom,![X16]:![X17]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17))))),file('i/f/arithmetic/ABS__DIFF__COMM', ah4s_arithmetics_NOTu_u_LESS)).
fof(35, axiom,![X16]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_absu_u_diff(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17))))),file('i/f/arithmetic/ABS__DIFF__COMM', ah4s_arithmetics_ABSu_u_DIFFu_u_def)).
fof(36, conjecture,![X16]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_absu_u_diff(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_arithmetics_absu_u_diff(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))),file('i/f/arithmetic/ABS__DIFF__COMM', ch4s_arithmetics_ABSu_u_DIFFu_u_COMM)).
# SZS output end CNFRefutation
