# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X2))))))=>(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))=>s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X1)))))=s(t_bool,t))),file('i/f/int_arith/le__context__rwt1', ch4s_intu_u_ariths_leu_u_contextu_u_rwt1)).
fof(5, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1)))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X2))))),file('i/f/int_arith/le__context__rwt1', ah4s_integers_INTu_u_NOTu_u_LE)).
fof(6, axiom,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))<=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X2)))))),file('i/f/int_arith/le__context__rwt1', ah4s_integers_intu_u_le0)).
fof(16, axiom,![X4]:![X1]:![X2]:((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))&p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X4)))))=>p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X4))))),file('i/f/int_arith/le__context__rwt1', ah4s_integers_INTu_u_LEu_u_TRANS)).
fof(17, axiom,![X1]:![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X2))),file('i/f/int_arith/le__context__rwt1', ah4s_integers_INTu_u_ADDu_u_COMM)).
fof(19, axiom,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))|s(t_h4s_integers_int,X2)=s(t_h4s_integers_int,X1))),file('i/f/int_arith/le__context__rwt1', ah4s_integers_INTu_u_LEu_u_LT)).
fof(42, axiom,![X2]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X2)))),file('i/f/int_arith/le__context__rwt1', ah4s_integers_INTu_u_LEu_u_REFL)).
fof(46, axiom,p(s(t_bool,t)),file('i/f/int_arith/le__context__rwt1', aHLu_TRUTH)).
fof(47, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/int_arith/le__context__rwt1', aHLu_BOOLu_CASES)).
fof(51, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/int_arith/le__context__rwt1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(54, axiom,(~(p(s(t_bool,t)))<=>p(s(t_bool,f))),file('i/f/int_arith/le__context__rwt1', ah4s_bools_NOTu_u_CLAUSESu_c1)).
fof(70, axiom,![X4]:![X1]:![X2]:s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X4)))))=s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X4))),s(t_h4s_integers_int,X1))),file('i/f/int_arith/le__context__rwt1', ah4s_integers_INTu_u_LEu_u_SUBu_u_LADD)).
fof(76, axiom,![X4]:![X1]:![X2]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X4)))))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X4))),s(t_h4s_integers_int,X1))),file('i/f/int_arith/le__context__rwt1', ah4s_integers_INTu_u_LTu_u_SUBu_u_LADD)).
fof(79, axiom,![X4]:![X1]:![X2]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))),s(t_h4s_integers_int,X4)))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X1))))),file('i/f/int_arith/le__context__rwt1', ah4s_integers_INTu_u_LTu_u_SUBu_u_RADD)).
# SZS output end CNFRefutation
