%   ORIGINAL: h4/integerRing/int__calculate_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/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/integer/INT__ADD__CALCULATE_c2: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/_2B n m)
% Assm: h4/integer/INT__ADD__CALCULATE_c3: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/_2D n m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D m n)))
% Assm: h4/integer/INT__ADD__CALCULATE_c4: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__of__num m) = h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/integer/int__of__num (h4/arithmetic/_2D m n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D n m)))
% Assm: h4/integer/INT__ADD__CALCULATE_c5: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2B n m))
% Assm: h4/integer/INT__MUL__CALCULATE_c0: !n m. h4/integer/int__mul (h4/integer/int__of__num m) (h4/integer/int__of__num n) = h4/integer/int__of__num (h4/arithmetic/_2A m n)
% Assm: h4/integer/INT__MUL__CALCULATE_c1: !y x. h4/integer/int__mul (h4/integer/int__neg x) y = h4/integer/int__neg (h4/integer/int__mul x y)
% Assm: h4/integer/INT__MUL__CALCULATE_c2: !y x. h4/integer/int__mul x (h4/integer/int__neg y) = h4/integer/int__neg (h4/integer/int__mul x y)
% Assm: h4/integer/INT__MUL__CALCULATE_c3: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm: h4/integer/INT__EQ__CALCULATE_c0: !n m. h4/integer/int__of__num m = h4/integer/int__of__num n <=> m = n
% Assm: h4/integer/INT__EQ__CALCULATE_c1: !y x. h4/integer/int__neg x = h4/integer/int__neg y <=> x = y
% Assm: h4/integer/INT__EQ__CALCULATE_c2: !n m. h4/integer/int__of__num n = h4/integer/int__neg (h4/integer/int__of__num m) <=> n = h4/num/0 /\ m = h4/num/0
% Assm: h4/integer/INT__EQ__CALCULATE_c3: !n m. h4/integer/int__neg (h4/integer/int__of__num n) = h4/integer/int__of__num m <=> n = h4/num/0 /\ m = h4/num/0
% Goal: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/_2D n m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D m n)))
%   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_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_integers_INTu_u_ADDu_u_CALCULATEu_c2]: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/_2B n m)
% Assm [h4s_integers_INTu_u_ADDu_u_CALCULATEu_c3]: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/_2D n m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D m n)))
% Assm [h4s_integers_INTu_u_ADDu_u_CALCULATEu_c4]: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__of__num m) = h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/integer/int__of__num (h4/arithmetic/_2D m n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D n m)))
% Assm [h4s_integers_INTu_u_ADDu_u_CALCULATEu_c5]: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2B n m))
% Assm [h4s_integers_INTu_u_MULu_u_CALCULATEu_c0]: !n m. h4/integer/int__mul (h4/integer/int__of__num m) (h4/integer/int__of__num n) = h4/integer/int__of__num (h4/arithmetic/_2A m n)
% Assm [h4s_integers_INTu_u_MULu_u_CALCULATEu_c1]: !y x. h4/integer/int__mul (h4/integer/int__neg x) y = h4/integer/int__neg (h4/integer/int__mul x y)
% Assm [h4s_integers_INTu_u_MULu_u_CALCULATEu_c2]: !y x. h4/integer/int__mul x (h4/integer/int__neg y) = h4/integer/int__neg (h4/integer/int__mul x y)
% Assm [h4s_integers_INTu_u_MULu_u_CALCULATEu_c3]: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm [h4s_integers_INTu_u_EQu_u_CALCULATEu_c0]: !n m. h4/integer/int__of__num m = h4/integer/int__of__num n <=> m = n
% Assm [h4s_integers_INTu_u_EQu_u_CALCULATEu_c1]: !y x. h4/integer/int__neg x = h4/integer/int__neg y <=> x = y
% Assm [h4s_integers_INTu_u_EQu_u_CALCULATEu_c2]: !n m. h4/integer/int__of__num n = h4/integer/int__neg (h4/integer/int__of__num m) <=> n = h4/num/0 /\ m = h4/num/0
% Assm [h4s_integers_INTu_u_EQu_u_CALCULATEu_c3]: !n m. h4/integer/int__neg (h4/integer/int__of__num n) = h4/integer/int__of__num m <=> n = h4/num/0 /\ m = h4/num/0
% Goal: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/_2D n m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D m n)))
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_Q167281,TV_Q167277]: ![V_f, V_g]: (![V_x]: s(TV_Q167277,happ(s(t_fun(TV_Q167281,TV_Q167277),V_f),s(TV_Q167281,V_x))) = s(TV_Q167277,happ(s(t_fun(TV_Q167281,TV_Q167277),V_g),s(TV_Q167281,V_x))) => s(t_fun(TV_Q167281,TV_Q167277),V_f) = s(t_fun(TV_Q167281,TV_Q167277),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_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_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_integers_INTu_u_ADDu_u_CALCULATEu_c2, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_integers_INTu_u_ADDu_u_CALCULATEu_c3, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_integers_INTu_u_ADDu_u_CALCULATEu_c4, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))))).
fof(ah4s_integers_INTu_u_ADDu_u_CALCULATEu_c5, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_integers_INTu_u_MULu_u_CALCULATEu_c0, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_integers_INTu_u_MULu_u_CALCULATEu_c1, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_MULu_u_CALCULATEu_c2, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_MULu_u_CALCULATEu_c3, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_EQu_u_CALCULATEu_c0, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_integers_INTu_u_EQu_u_CALCULATEu_c1, axiom, ![V_y, V_x]: (s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y))) <=> s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y))).
fof(ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) <=> (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0) & s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integers_INTu_u_EQu_u_CALCULATEu_c3, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))) <=> (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0) & s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0)))).
fof(ch4s_integerRings_intu_u_calculateu_c2, conjecture, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))))).
