# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,happ(s(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))))=>s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2)))=s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1)))),file('i/f/integer/TINT__LT__WELLDEFL', ch4s_integers_TINTu_u_LTu_u_WELLDEFL)).
fof(3, axiom,![X5]:![X6]:![X7]:(p(s(t_bool,happ(s(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),X7))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X6))))=>s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X7),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5)))=s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X6),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5)))),file('i/f/integer/TINT__LT__WELLDEFL', ah4s_integers_TINTu_u_LTu_u_WELLDEFR)).
fof(4, axiom,![X5]:![X3]:(p(s(t_bool,happ(s(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),X3))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5))))|(p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5))))|p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3)))))),file('i/f/integer/TINT__LT__WELLDEFL', ah4s_integers_TINTu_u_LTu_u_TOTAL)).
fof(7, axiom,![X3]:~(p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3))))),file('i/f/integer/TINT__LT__WELLDEFL', ah4s_integers_TINTu_u_LTu_u_REFL)).
fof(8, axiom,![X8]:![X5]:![X3]:((p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5))))&p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X8)))))=>p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X8))))),file('i/f/integer/TINT__LT__WELLDEFL', ah4s_integers_TINTu_u_LTu_u_TRANS)).
fof(22, axiom,![X11]:![X12]:(s(t_bool,X12)=s(t_bool,X11)<=>((p(s(t_bool,X12))&p(s(t_bool,X11)))|(~(p(s(t_bool,X12)))&~(p(s(t_bool,X11)))))),file('i/f/integer/TINT__LT__WELLDEFL', ah4s_bools_EQu_u_EXPAND)).
fof(36, axiom,![X5]:![X3]:s(t_bool,happ(s(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),X3))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X5)))=s(t_bool,happ(s(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),X5))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3))),file('i/f/integer/TINT__LT__WELLDEFL', ah4s_integers_TINTu_u_EQu_u_SYM)).
fof(39, axiom,![X16]:![X17]:(p(s(t_bool,happ(s(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),X17))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X16))))<=>s(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),X17)))=s(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),X16)))),file('i/f/integer/TINT__LT__WELLDEFL', ah4s_integers_TINTu_u_EQu_u_EQUIV)).
fof(55, axiom,~(p(s(t_bool,f))),file('i/f/integer/TINT__LT__WELLDEFL', aHLu_FALSITY)).
fof(56, axiom,![X9]:((p(s(t_bool,X9))=>p(s(t_bool,f)))<=>s(t_bool,X9)=s(t_bool,f)),file('i/f/integer/TINT__LT__WELLDEFL', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(64, axiom,![X9]:(s(t_bool,f)=s(t_bool,X9)<=>~(p(s(t_bool,X9)))),file('i/f/integer/TINT__LT__WELLDEFL', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
