# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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/integer/INT__LE__CALCULATE', ch4s_integers_INTu_u_LEu_u_CALCULATE)).
fof(2, 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/integer/INT__LE__CALCULATE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(5, axiom,![X1]:![X2]:(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_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X2)))))),file('i/f/integer/INT__LE__CALCULATE', ah4s_integers_INTu_u_LTu_u_GT)).
fof(6, axiom,![X7]:![X8]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X7)))=s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_integers_intu_u_rep),s(t_h4s_integers_int,X8))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_integers_intu_u_rep),s(t_h4s_integers_int,X7))))),file('i/f/integer/INT__LE__CALCULATE', ah4s_integers_intu_u_lt0)).
fof(7, 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/integer/INT__LE__CALCULATE', ah4s_integers_intu_u_le0)).
fof(8, axiom,![X1]:![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_integers_tintu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1))))|(p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1))))|p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2)))))),file('i/f/integer/INT__LE__CALCULATE', ah4s_integers_TINTu_u_LTu_u_TOTAL)).
fof(9, axiom,![X2]:~(p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2))))),file('i/f/integer/INT__LE__CALCULATE', ah4s_integers_TINTu_u_LTu_u_REFL)).
fof(12, axiom,![X5]:![X17]:![X18]:![X19]:![X20]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X5,t_fun(X5,t_bool)),X20),s(t_fun(X5,X17),X19),s(t_fun(X17,X5),X18))))=>![X2]:![X1]:(s(X17,X2)=s(X17,X1)<=>p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X20),s(X5,happ(s(t_fun(X17,X5),X18),s(X17,X2))))),s(X5,happ(s(t_fun(X17,X5),X18),s(X17,X1)))))))),file('i/f/integer/INT__LE__CALCULATE', ah4s_quotients_EQUALSu_u_PRS)).
fof(15, axiom,p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_integers_tintu_u_eq),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_integers_int),h4s_integers_intu_u_abs),s(t_fun(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_integers_intu_u_rep)))),file('i/f/integer/INT__LE__CALCULATE', ah4s_integers_intu_u_QUOTIENT)).
# SZS output end CNFRefutation
