%   ORIGINAL: h4/binary__ieee/some__nan__properties_c1
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/binary__ieee/float__value__case__def_c2: !v1 v f. h4/binary__ieee/float__value__CASE h4/binary__ieee/NaN f v v1 = v1
% Assm: h4/binary__ieee/float__is__finite__def: !x. h4/binary__ieee/float__is__finite x <=> h4/binary__ieee/float__value__CASE (h4/binary__ieee/float__value0 x) (\v1. T) F F
% Assm: h4/binary__ieee/float__values_c2: h4/binary__ieee/float__value0 (h4/binary__ieee/float__some__nan h4/bool/the__value) = h4/binary__ieee/NaN
% Goal: ~h4/binary__ieee/float__is__finite (h4/binary__ieee/float__some__nan h4/bool/the__value)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_binaryu_u_ieees_floatu_u_valueu_u_caseu_u_defu_c2]: !v1 v f. h4/binary__ieee/float__value__CASE h4/binary__ieee/NaN f v v1 = v1
% Assm [h4s_binaryu_u_ieees_floatu_u_isu_u_finiteu_u_def]: !_0. (!v1. happ _0 v1 <=> T) ==> (!x. h4/binary__ieee/float__is__finite x <=> h4/binary__ieee/float__value__CASE (h4/binary__ieee/float__value0 x) _0 F F)
% Assm [h4s_binaryu_u_ieees_floatu_u_valuesu_c2]: h4/binary__ieee/float__value0 (h4/binary__ieee/float__some__nan h4/bool/the__value) = h4/binary__ieee/NaN
% Goal: ~h4/binary__ieee/float__is__finite (h4/binary__ieee/float__some__nan h4/bool/the__value)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q106253,TV_Q106249]: ![V_f, V_g]: (![V_x]: s(TV_Q106249,happ(s(t_fun(TV_Q106253,TV_Q106249),V_f),s(TV_Q106253,V_x))) = s(TV_Q106249,happ(s(t_fun(TV_Q106253,TV_Q106249),V_g),s(TV_Q106253,V_x))) => s(t_fun(TV_Q106253,TV_Q106249),V_f) = s(t_fun(TV_Q106253,TV_Q106249),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_binaryu_u_ieees_floatu_u_valueu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v1, V_v, V_f]: s(TV_u_27a,h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_nan),s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f),s(TV_u_27a,V_v),s(TV_u_27a,V_v1))) = s(TV_u_27a,V_v1)).
fof(ah4s_binaryu_u_ieees_floatu_u_isu_u_finiteu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_uu_0]: (![V_v1]: s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_uu_0),s(t_h4s_realaxs_real,V_v1))) = s(t_bool,t) => ![V_x]: s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_finite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_bool,h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_floatu_u_value0(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_fun(t_h4s_realaxs_real,t_bool),V_uu_0),s(t_bool,f),s(t_bool,f))))).
fof(ah4s_binaryu_u_ieees_floatu_u_valuesu_c2, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_floatu_u_value0(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_nan)).
fof(ch4s_binaryu_u_ieees_someu_u_nanu_u_propertiesu_c1, conjecture, ![TV_u_27t,TV_u_27w]: ~ (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_finite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value)))))))).
