# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(~(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>p(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,h4s_integers_abs(s(t_h4s_integers_int,X1))))))),file('i/f/intExtension/INT__ABS__NOT0POS', ch4s_intExtensions_INTu_u_ABSu_u_NOT0POS)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/intExtension/INT__ABS__NOT0POS', aHLu_FALSITY)).
fof(3, axiom,![X2]:![X3]:((p(s(t_bool,X3))=>p(s(t_bool,X2)))=>((p(s(t_bool,X2))=>p(s(t_bool,X3)))=>s(t_bool,X3)=s(t_bool,X2))),file('i/f/intExtension/INT__ABS__NOT0POS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(26, axiom,![X13]:![X1]:(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,X13)|(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X13))))|p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X13),s(t_h4s_integers_int,X1)))))),file('i/f/intExtension/INT__ABS__NOT0POS', ah4s_integers_INTu_u_LTu_u_TOTAL)).
fof(27, axiom,![X1]: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,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1)))))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/intExtension/INT__ABS__NOT0POS', ah4s_integers_INTu_u_NEGu_u_GT0)).
fof(28, axiom,![X14]:s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X14)))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X14),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_neg(s(t_h4s_integers_int,X14))),s(t_h4s_integers_int,X14))),file('i/f/intExtension/INT__ABS__NOT0POS', ah4s_integers_INTu_u_ABS)).
fof(29, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/intExtension/INT__ABS__NOT0POS', aHLu_BOOLu_CASES)).
fof(30, axiom,![X12]:![X2]:![X3]:s(X12,h4s_bools_cond(s(t_bool,f),s(X12,X3),s(X12,X2)))=s(X12,X2),file('i/f/intExtension/INT__ABS__NOT0POS', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(32, axiom,![X12]:![X2]:![X3]:s(X12,h4s_bools_cond(s(t_bool,t),s(X12,X3),s(X12,X2)))=s(X12,X3),file('i/f/intExtension/INT__ABS__NOT0POS', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(35, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/intExtension/INT__ABS__NOT0POS', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
