%   ORIGINAL: h4/operator/MONOID__DISJ__F
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/operator/ASSOC__DEF: !f. h4/operator/ASSOC f <=> (!x y z. f x (f y z) = f (f x y) z)
% Assm: h4/operator/RIGHT__ID__DEF: !f e. h4/operator/RIGHT__ID f e <=> (!x. f x e = x)
% Assm: h4/operator/LEFT__ID__DEF: !f e. h4/operator/LEFT__ID f e <=> (!x. f e x = x)
% Assm: h4/operator/MONOID__DEF: !f e. h4/operator/MONOID f e <=> h4/operator/ASSOC f /\ h4/operator/RIGHT__ID f e /\ h4/operator/LEFT__ID f e
% Goal: h4/operator/MONOID $or F
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_operators_ASSOCu_u_DEF]: !f. h4/operator/ASSOC f <=> (!x y z. happ (happ f x) (happ (happ f y) z) = happ (happ f (happ (happ f x) y)) z)
% Assm [h4s_operators_RIGHTu_u_IDu_u_DEF]: !f e. h4/operator/RIGHT__ID f e <=> (!x. happ (happ f x) e = x)
% Assm [h4s_operators_LEFTu_u_IDu_u_DEF]: !f e. h4/operator/LEFT__ID f e <=> (!x. happ (happ f e) x = x)
% Assm [h4s_operators_MONOIDu_u_DEF]: !f e. h4/operator/MONOID f e <=> h4/operator/ASSOC f /\ h4/operator/RIGHT__ID f e /\ h4/operator/LEFT__ID f e
% Goal: h4/operator/MONOID $or F
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_Q203573,TV_Q203569]: ![V_f, V_g]: (![V_x]: s(TV_Q203569,happ(s(t_fun(TV_Q203573,TV_Q203569),V_f),s(TV_Q203573,V_x))) = s(TV_Q203569,happ(s(t_fun(TV_Q203573,TV_Q203569),V_g),s(TV_Q203573,V_x))) => s(t_fun(TV_Q203573,TV_Q203569),V_f) = s(t_fun(TV_Q203573,TV_Q203569),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_operators_ASSOCu_u_DEF, axiom, ![TV_u_27a]: ![V_f]: (p(s(t_bool,h4s_operators_assoc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f)))) <=> ![V_x, V_y, V_z]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27a,V_z))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))))),s(TV_u_27a,V_z))))).
fof(ah4s_operators_RIGHTu_u_IDu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_e]: (p(s(t_bool,h4s_operators_rightu_u_id(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27b,V_e)))) <=> ![V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_e))) = s(TV_u_27a,V_x))).
fof(ah4s_operators_LEFTu_u_IDu_u_DEF, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_e]: (p(s(t_bool,h4s_operators_leftu_u_id(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_e)))) <=> ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_e))),s(TV_u_27b,V_x))) = s(TV_u_27b,V_x))).
fof(ah4s_operators_MONOIDu_u_DEF, axiom, ![TV_u_27a]: ![V_f, V_e]: (p(s(t_bool,h4s_operators_monoid(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_e)))) <=> (p(s(t_bool,h4s_operators_assoc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f)))) & (p(s(t_bool,h4s_operators_rightu_u_id(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_e)))) & p(s(t_bool,h4s_operators_leftu_u_id(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_e)))))))).
fof(ch4s_operators_MONOIDu_u_DISJu_u_F, conjecture, p(s(t_bool,h4s_operators_monoid(s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_or),s(t_bool,f))))).
