%   ORIGINAL: h4/set__relation/rcomp__to__rel__conv
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/relation/O__DEF: !z x R2 R1. h4/relation/O R1 R2 x z <=> (?y. R2 x y /\ R1 y z)
% Assm: h4/pair/PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pred__set/GSPECIFICATION: !v f. h4/bool/IN v (h4/pred__set/GSPEC f) <=> (?x. h4/pair/_2C v T = f x)
% Assm: h4/set__relation/rextension: !t s. s = t <=> (!x y. h4/bool/IN (h4/pair/_2C x y) s <=> h4/bool/IN (h4/pair/_2C x y) t)
% Assm: h4/set__relation/rcomp__def: !r2 r1. h4/set__relation/rcomp r1 r2 = h4/pred__set/GSPEC (h4/pair/UNCURRY (\x y. h4/pair/_2C (h4/pair/_2C x y) (?z. h4/bool/IN (h4/pair/_2C x z) r1 /\ h4/bool/IN (h4/pair/_2C z y) r2)))
% Assm: h4/set__relation/in__rel__to__reln: !xy R. h4/bool/IN xy (h4/set__relation/rel__to__reln R) <=> R (h4/pair/FST xy) (h4/pair/SND xy)
% Assm: h4/set__relation/reln__to__rel__app: !y x r. h4/set__relation/reln__to__rel r x y <=> h4/bool/IN (h4/pair/_2C x y) r
% Goal: !r2 r1. h4/set__relation/rcomp r1 r2 = h4/set__relation/rel__to__reln (h4/relation/O (h4/set__relation/reln__to__rel r2) (h4/set__relation/reln__to__rel r1))
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_relations_Ou_u_DEF]: !z x R2 R1. happ (happ (h4/relation/O R1 R2) x) z <=> (?y. happ (happ R2 x) y /\ happ (happ R1 y) z)
% Assm [h4s_pairs_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_pairs_CLOSEDu_u_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_predu_u_sets_GSPECIFICATION]: !v f. h4/bool/IN v (h4/pred__set/GSPEC f) <=> (?x. h4/pair/_2C v T = happ f x)
% Assm [h4s_setu_u_relations_rextension]: !t s. s = t <=> (!x y. h4/bool/IN (h4/pair/_2C x y) s <=> h4/bool/IN (h4/pair/_2C x y) t)
% Assm [h4s_setu_u_relations_rcompu_u_def]: !_1. (!x r1 r2 y. ?v. (v <=> (?z. h4/bool/IN (h4/pair/_2C x z) r1 /\ h4/bool/IN (h4/pair/_2C z y) r2)) /\ happ (happ (happ (happ _1 x) r1) r2) y = h4/pair/_2C (h4/pair/_2C x y) v) ==> (!_0. (!r1 r2 x. happ (happ (happ _0 r1) r2) x = happ (happ (happ _1 x) r1) r2) ==> (!r2 r1. h4/set__relation/rcomp r1 r2 = h4/pred__set/GSPEC (h4/pair/UNCURRY (happ (happ _0 r1) r2))))
% Assm [h4s_setu_u_relations_inu_u_relu_u_tou_u_reln]: !xy R. h4/bool/IN xy (h4/set__relation/rel__to__reln R) <=> happ (happ R (h4/pair/FST xy)) (h4/pair/SND xy)
% Assm [h4s_setu_u_relations_relnu_u_tou_u_relu_u_app]: !y x r. happ (happ (h4/set__relation/reln__to__rel r) x) y <=> h4/bool/IN (h4/pair/_2C x y) r
% Goal: !r2 r1. h4/set__relation/rcomp r1 r2 = h4/set__relation/rel__to__reln (h4/relation/O (h4/set__relation/reln__to__rel r2) (h4/set__relation/reln__to__rel r1))
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_Q139422,TV_Q139418]: ![V_f, V_g]: (![V_x]: s(TV_Q139418,happ(s(t_fun(TV_Q139422,TV_Q139418),V_f),s(TV_Q139422,V_x))) = s(TV_Q139418,happ(s(t_fun(TV_Q139422,TV_Q139418),V_g),s(TV_Q139422,V_x))) => s(t_fun(TV_Q139422,TV_Q139418),V_f) = s(t_fun(TV_Q139422,TV_Q139418),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
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_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_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_relations_Ou_u_DEF, axiom, ![TV_u_27g,TV_u_27h,TV_u_27k]: ![V_z, V_x, V_R2, V_R1]: (p(s(t_bool,happ(s(t_fun(TV_u_27k,t_bool),happ(s(t_fun(TV_u_27g,t_fun(TV_u_27k,t_bool)),h4s_relations_o(s(t_fun(TV_u_27h,t_fun(TV_u_27k,t_bool)),V_R1),s(t_fun(TV_u_27g,t_fun(TV_u_27h,t_bool)),V_R2))),s(TV_u_27g,V_x))),s(TV_u_27k,V_z)))) <=> ?[V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27h,t_bool),happ(s(t_fun(TV_u_27g,t_fun(TV_u_27h,t_bool)),V_R2),s(TV_u_27g,V_x))),s(TV_u_27h,V_y)))) & p(s(t_bool,happ(s(t_fun(TV_u_27k,t_bool),happ(s(t_fun(TV_u_27h,t_fun(TV_u_27k,t_bool)),V_R1),s(TV_u_27h,V_y))),s(TV_u_27k,V_z))))))).
fof(ah4s_pairs_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_predu_u_sets_GSPECIFICATION, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_v),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_f)))))) <=> ?[V_x]: s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_v),s(t_bool,t))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_f),s(TV_u_27b,V_x))))).
fof(ah4s_setu_u_relations_rextension, axiom, ![TV_u_27a,TV_u_27b]: ![V_t, V_s]: (s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_s) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_t) <=> ![V_x, V_y]: s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_s))) = s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_t))))).
fof(ah4s_setu_u_relations_rcompu_u_def, axiom, ![TV_u_27a,TV_u_27c,TV_u_27b]: ![V_uu_1]: (![V_x, V_r1, V_r2, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> ?[V_z]: (p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27c,V_z))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1)))) & p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27c,V_z),s(TV_u_27b,V_y))),s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2)))))) & s(t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool)))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool))))),V_uu_1),s(TV_u_27a,V_x))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1))),s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_pairs_u_2c(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_bool,V_v)))) => ![V_uu_0]: (![V_r1, V_r2, V_x]: s(t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool))))),V_uu_0),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1))),s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool)))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool))))),V_uu_1),s(TV_u_27a,V_x))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1))),s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))) => ![V_r2, V_r1]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_setu_u_relations_rcomp(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1),s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_predu_u_sets_gspec(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool)),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),t_fun(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool))))),V_uu_0),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1))),s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2)))))))))).
fof(ah4s_setu_u_relations_inu_u_relu_u_tou_u_reln, axiom, ![TV_u_27a,TV_u_27b]: ![V_xy, V_R]: s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_xy),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_setu_u_relations_relu_u_tou_u_reln(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_xy))))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_xy)))))).
fof(ah4s_setu_u_relations_relnu_u_tou_u_relu_u_app, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_r]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r))),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r)))).
fof(ch4s_setu_u_relations_rcompu_u_tou_u_relu_u_conv, conjecture, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_r2, V_r1]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_setu_u_relations_rcomp(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1),s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_setu_u_relations_relu_u_tou_u_reln(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_relations_o(s(t_fun(TV_u_27c,t_fun(TV_u_27b,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))),s(t_fun(TV_u_27a,t_fun(TV_u_27c,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1)))))))).
