%   ORIGINAL: h4/quantHeuristics/LIST__LENGTH__COMPARE__SUC_c2
% 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/AND__CLAUSES_c0: !t. T /\ 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/arithmetic/ADD1: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c8: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c9: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c12: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Goal: !x l. h4/list/LENGTH l = h4/num/SUC x <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
%   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_ANDu_u_CLAUSESu_c0]: !t. T /\ 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_arithmetics_ADD1]: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c8]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c9]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c12]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Goal: !x l. h4/list/LENGTH l = h4/num/SUC x <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
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_Q58020,TV_Q58016]: ![V_f, V_g]: (![V_x]: s(TV_Q58016,happ(s(t_fun(TV_Q58020,TV_Q58016),V_f),s(TV_Q58020,V_x))) = s(TV_Q58016,happ(s(t_fun(TV_Q58020,TV_Q58016),V_g),s(TV_Q58020,V_x))) => s(t_fun(TV_Q58020,TV_Q58016),V_f) = s(t_fun(TV_Q58020,TV_Q58016),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_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_arithmetics_ADD1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c8, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c9, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c12, axiom, ![TV_u_27a]: ![V_x, V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) <=> ?[V_lu_27, V_e1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ch4s_quantHeuristicss_LISTu_u_LENGTHu_u_COMPAREu_u_SUCu_c2, conjecture, ![TV_u_27a]: ![V_x, V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_x))) <=> ?[V_lu_27, V_e1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
