%   ORIGINAL: h4/DeepSyntax/datatype__deep__form
% 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/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Goal: !deep__form. h4/bool/DATATYPE (deep__form h4/DeepSyntax/Conjn h4/DeepSyntax/Disjn h4/DeepSyntax/Negn h4/DeepSyntax/UnrelatedBool h4/DeepSyntax/xLT h4/DeepSyntax/LTx h4/DeepSyntax/xEQ h4/DeepSyntax/xDivided)
%   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_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Goal: !deep__form. h4/bool/DATATYPE (happ (happ (happ (happ (happ (happ (happ (happ deep__form h4/DeepSyntax/Conjn) h4/DeepSyntax/Disjn) h4/DeepSyntax/Negn) h4/DeepSyntax/UnrelatedBool) h4/DeepSyntax/xLT) h4/DeepSyntax/LTx) h4/DeepSyntax/xEQ) h4/DeepSyntax/xDivided)
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_Q349093,TV_Q349089]: ![V_f, V_g]: (![V_x]: s(TV_Q349089,happ(s(t_fun(TV_Q349093,TV_Q349089),V_f),s(TV_Q349093,V_x))) = s(TV_Q349089,happ(s(t_fun(TV_Q349093,TV_Q349089),V_g),s(TV_Q349093,V_x))) => s(t_fun(TV_Q349093,TV_Q349089),V_f) = s(t_fun(TV_Q349093,TV_Q349089),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ch4s_DeepSyntaxs_datatypeu_u_deepu_u_form, conjecture, ![V_deepu_u_form]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool),happ(s(t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool)),happ(s(t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool))),happ(s(t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool)))),happ(s(t_fun(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool))))),happ(s(t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool)))))),happ(s(t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool))))))),happ(s(t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool)))))))),V_deepu_u_form),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_conjn))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_disjn))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn))),s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool))),s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xlt))),s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_ltx))),s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xeq))),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided))))))).
