%   ORIGINAL: h4/operator/ASSOC__CONJ
% 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/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/operator/ASSOC__DEF: !f. h4/operator/ASSOC f <=> (!x y z. f x (f y z) = f (f x y) z)
% Goal: h4/operator/ASSOC $and
%   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_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% 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)
% Goal: h4/operator/ASSOC $and
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_Q203448,TV_Q203444]: ![V_f, V_g]: (![V_x]: s(TV_Q203444,happ(s(t_fun(TV_Q203448,TV_Q203444),V_f),s(TV_Q203448,V_x))) = s(TV_Q203444,happ(s(t_fun(TV_Q203448,TV_Q203444),V_g),s(TV_Q203448,V_x))) => s(t_fun(TV_Q203448,TV_Q203444),V_f) = s(t_fun(TV_Q203448,TV_Q203444),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_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
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_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(ch4s_operators_ASSOCu_u_CONJ, conjecture, p(s(t_bool,h4s_operators_assoc(s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_and))))).
