# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_integers_intu_u_lt(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,X3)))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X3))))&(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,X3)|(p(s(t_bool,h4s_integers_intu_u_lt(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,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))),file('i/f/int_arith/restricted__quantification__simp', ch4s_intu_u_ariths_restrictedu_u_quantificationu_u_simp)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/int_arith/restricted__quantification__simp', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/restricted__quantification__simp', aHLu_FALSITY)).
fof(5, 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/int_arith/restricted__quantification__simp', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(18, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/int_arith/restricted__quantification__simp', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(19, axiom,![X6]:(s(t_bool,X6)=s(t_bool,f)<=>~(p(s(t_bool,X6)))),file('i/f/int_arith/restricted__quantification__simp', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(39, axiom,![X14]:![X1]:(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,X14)|(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X14))))|p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X14),s(t_h4s_integers_int,X1)))))),file('i/f/int_arith/restricted__quantification__simp', ah4s_integers_INTu_u_LTu_u_TOTAL)).
fof(41, axiom,![X15]:![X14]:![X1]:((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X14))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X14),s(t_h4s_integers_int,X15)))))=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X15))))),file('i/f/int_arith/restricted__quantification__simp', ah4s_integers_INTu_u_LTu_u_TRANS)).
fof(42, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/int_arith/restricted__quantification__simp', aHLu_BOOLu_CASES)).
fof(46, axiom,![X14]:![X1]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X14))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X14))))|s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,X14))),file('i/f/int_arith/restricted__quantification__simp', ah4s_integers_INTu_u_LEu_u_LT)).
fof(47, axiom,![X15]:![X14]:![X1]:((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X14))))&p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X14),s(t_h4s_integers_int,X15)))))=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X15))))),file('i/f/int_arith/restricted__quantification__simp', ah4s_integers_INTu_u_LTEu_u_TRANS)).
fof(48, axiom,![X15]:![X14]:![X1]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X14))),s(t_h4s_integers_int,X15)))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,X14))))),file('i/f/int_arith/restricted__quantification__simp', ah4s_integers_INTu_u_LTu_u_SUBu_u_RADD)).
fof(49, axiom,![X14]:![X1]:s(t_bool,h4s_integers_intu_u_lt(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,X14)))))=s(t_bool,h4s_integers_intu_u_lt(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,X14))),file('i/f/int_arith/restricted__quantification__simp', ah4s_integers_INTu_u_LTu_u_ADDR)).
fof(50, axiom,![X16]:![X17]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X16))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X17)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17))),file('i/f/int_arith/restricted__quantification__simp', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(51, axiom,![X14]:![X1]:~((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X14))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X14),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))),file('i/f/int_arith/restricted__quantification__simp', ah4s_integers_INTu_u_DISCRETE)).
fof(52, axiom,![X16]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X16)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X16))),file('i/f/int_arith/restricted__quantification__simp', ah4s_numerals_numeralu_u_distribu_c21)).
fof(53, axiom,![X16]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X16)))))=s(t_bool,t),file('i/f/int_arith/restricted__quantification__simp', ah4s_numerals_numeralu_u_ltu_c0)).
# SZS output end CNFRefutation
