%   ORIGINAL: h4/realax/TREAL__MUL__LINV
% 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/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/hreal/HREAL__ADD__SYM: !Y X. h4/hreal/hreal__add X Y = h4/hreal/hreal__add Y X
% Assm: h4/hreal/HREAL__ADD__ASSOC: !Z Y X. h4/hreal/hreal__add X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__add X Y) Z
% Assm: h4/hreal/HREAL__LDISTRIB: !Z Y X. h4/hreal/hreal__mul X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__mul X Y) (h4/hreal/hreal__mul X Z)
% Assm: h4/hreal/HREAL__MUL__LID: !X. h4/hreal/hreal__mul h4/hreal/hreal__1 X = X
% Assm: h4/hreal/HREAL__MUL__LINV: !X. h4/hreal/hreal__mul (h4/hreal/hreal__inv X) X = h4/hreal/hreal__1
% Assm: h4/hreal/HREAL__SUB__ADD: !Y X. h4/hreal/hreal__lt X Y ==> h4/hreal/hreal__add (h4/hreal/hreal__sub Y X) X = Y
% Assm: h4/hreal/HREAL__LT__TOTAL: !Y X. X = Y \/ h4/hreal/hreal__lt X Y \/ h4/hreal/hreal__lt Y X
% Assm: h4/realax/HREAL__RDISTRIB: !z y x. h4/hreal/hreal__mul (h4/hreal/hreal__add x y) z = h4/hreal/hreal__add (h4/hreal/hreal__mul x z) (h4/hreal/hreal__mul y z)
% Assm: h4/realax/HREAL__EQ__LADD: !z y x. h4/hreal/hreal__add x y = h4/hreal/hreal__add x z <=> y = z
% Assm: h4/realax/HREAL__LT__GT: !y x. h4/hreal/hreal__lt x y ==> ~h4/hreal/hreal__lt y x
% Assm: h4/realax/treal__00: h4/realax/treal__0 = h4/pair/_2C h4/hreal/hreal__1 h4/hreal/hreal__1
% Assm: h4/realax/treal__10: h4/realax/treal__1 = h4/pair/_2C (h4/hreal/hreal__add h4/hreal/hreal__1 h4/hreal/hreal__1) h4/hreal/hreal__1
% Assm: h4/realax/treal__mul0: !y2 y1 x2 x1. h4/realax/treal__mul (h4/pair/_2C x1 y1) (h4/pair/_2C x2 y2) = h4/pair/_2C (h4/hreal/hreal__add (h4/hreal/hreal__mul x1 x2) (h4/hreal/hreal__mul y1 y2)) (h4/hreal/hreal__add (h4/hreal/hreal__mul x1 y2) (h4/hreal/hreal__mul y1 x2))
% Assm: h4/realax/treal__inv0: !y x. h4/realax/treal__inv (h4/pair/_2C x y) = h4/bool/COND (x = y) h4/realax/treal__0 (h4/bool/COND (h4/hreal/hreal__lt y x) (h4/pair/_2C (h4/hreal/hreal__add (h4/hreal/hreal__inv (h4/hreal/hreal__sub x y)) h4/hreal/hreal__1) h4/hreal/hreal__1) (h4/pair/_2C h4/hreal/hreal__1 (h4/hreal/hreal__add (h4/hreal/hreal__inv (h4/hreal/hreal__sub y x)) h4/hreal/hreal__1)))
% Assm: h4/realax/treal__eq0: !y2 y1 x2 x1. h4/realax/treal__eq (h4/pair/_2C x1 y1) (h4/pair/_2C x2 y2) <=> h4/hreal/hreal__add x1 y2 = h4/hreal/hreal__add x2 y1
% Goal: !x. ~h4/realax/treal__eq x h4/realax/treal__0 ==> h4/realax/treal__eq (h4/realax/treal__mul (h4/realax/treal__inv x) x) h4/realax/treal__1
%   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_FALSITY]: !t. F ==> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_hreals_HREALu_u_ADDu_u_SYM]: !Y X. h4/hreal/hreal__add X Y = h4/hreal/hreal__add Y X
% Assm [h4s_hreals_HREALu_u_ADDu_u_ASSOC]: !Z Y X. h4/hreal/hreal__add X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__add X Y) Z
% Assm [h4s_hreals_HREALu_u_LDISTRIB]: !Z Y X. h4/hreal/hreal__mul X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__mul X Y) (h4/hreal/hreal__mul X Z)
% Assm [h4s_hreals_HREALu_u_MULu_u_LID]: !X. h4/hreal/hreal__mul h4/hreal/hreal__1 X = X
% Assm [h4s_hreals_HREALu_u_MULu_u_LINV]: !X. h4/hreal/hreal__mul (h4/hreal/hreal__inv X) X = h4/hreal/hreal__1
% Assm [h4s_hreals_HREALu_u_SUBu_u_ADD]: !Y X. h4/hreal/hreal__lt X Y ==> h4/hreal/hreal__add (h4/hreal/hreal__sub Y X) X = Y
% Assm [h4s_hreals_HREALu_u_LTu_u_TOTAL]: !Y X. X = Y \/ h4/hreal/hreal__lt X Y \/ h4/hreal/hreal__lt Y X
% Assm [h4s_realaxs_HREALu_u_RDISTRIB]: !z y x. h4/hreal/hreal__mul (h4/hreal/hreal__add x y) z = h4/hreal/hreal__add (h4/hreal/hreal__mul x z) (h4/hreal/hreal__mul y z)
% Assm [h4s_realaxs_HREALu_u_EQu_u_LADD]: !z y x. h4/hreal/hreal__add x y = h4/hreal/hreal__add x z <=> y = z
% Assm [h4s_realaxs_HREALu_u_LTu_u_GT]: !y x. h4/hreal/hreal__lt x y ==> ~h4/hreal/hreal__lt y x
% Assm [h4s_realaxs_trealu_u_00]: h4/realax/treal__0 = h4/pair/_2C h4/hreal/hreal__1 h4/hreal/hreal__1
% Assm [h4s_realaxs_trealu_u_10]: h4/realax/treal__1 = h4/pair/_2C (h4/hreal/hreal__add h4/hreal/hreal__1 h4/hreal/hreal__1) h4/hreal/hreal__1
% Assm [h4s_realaxs_trealu_u_mul0]: !y2 y1 x2 x1. h4/realax/treal__mul (h4/pair/_2C x1 y1) (h4/pair/_2C x2 y2) = h4/pair/_2C (h4/hreal/hreal__add (h4/hreal/hreal__mul x1 x2) (h4/hreal/hreal__mul y1 y2)) (h4/hreal/hreal__add (h4/hreal/hreal__mul x1 y2) (h4/hreal/hreal__mul y1 x2))
% Assm [h4s_realaxs_trealu_u_inv0]: !y x. ?v. (v <=> x = y) /\ h4/realax/treal__inv (h4/pair/_2C x y) = h4/bool/COND v h4/realax/treal__0 (h4/bool/COND (h4/hreal/hreal__lt y x) (h4/pair/_2C (h4/hreal/hreal__add (h4/hreal/hreal__inv (h4/hreal/hreal__sub x y)) h4/hreal/hreal__1) h4/hreal/hreal__1) (h4/pair/_2C h4/hreal/hreal__1 (h4/hreal/hreal__add (h4/hreal/hreal__inv (h4/hreal/hreal__sub y x)) h4/hreal/hreal__1)))
% Assm [h4s_realaxs_trealu_u_eq0]: !y2 y1 x2 x1. h4/realax/treal__eq (h4/pair/_2C x1 y1) (h4/pair/_2C x2 y2) <=> h4/hreal/hreal__add x1 y2 = h4/hreal/hreal__add x2 y1
% Goal: !x. ~h4/realax/treal__eq x h4/realax/treal__0 ==> h4/realax/treal__eq (h4/realax/treal__mul (h4/realax/treal__inv x) x) h4/realax/treal__1
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_Q328765,TV_Q328761]: ![V_f, V_g]: (![V_x]: s(TV_Q328761,happ(s(t_fun(TV_Q328765,TV_Q328761),V_f),s(TV_Q328765,V_x))) = s(TV_Q328761,happ(s(t_fun(TV_Q328765,TV_Q328761),V_g),s(TV_Q328765,V_x))) => s(t_fun(TV_Q328765,TV_Q328761),V_f) = s(t_fun(TV_Q328765,TV_Q328761),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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> 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_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
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_hreals_HREALu_u_ADDu_u_SYM, axiom, ![V_Y, V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_X)))).
fof(ah4s_hreals_HREALu_u_ADDu_u_ASSOC, axiom, ![V_Z, V_Y, V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_Z))))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y))),s(t_h4s_hreals_hreal,V_Z)))).
fof(ah4s_hreals_HREALu_u_LDISTRIB, axiom, ![V_Z, V_Y, V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_Z))))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Z)))))).
fof(ah4s_hreals_HREALu_u_MULu_u_LID, axiom, ![V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1),s(t_h4s_hreals_hreal,V_X))) = s(t_h4s_hreals_hreal,V_X)).
fof(ah4s_hreals_HREALu_u_MULu_u_LINV, axiom, ![V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_inv(s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hreals_hreal,V_X))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1)).
fof(ah4s_hreals_HREALu_u_SUBu_u_ADD, axiom, ![V_Y, V_X]: (p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y)))) => s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_sub(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hreals_hreal,V_X))) = s(t_h4s_hreals_hreal,V_Y))).
fof(ah4s_hreals_HREALu_u_LTu_u_TOTAL, axiom, ![V_Y, V_X]: (s(t_h4s_hreals_hreal,V_X) = s(t_h4s_hreals_hreal,V_Y) | (p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y)))) | p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_X))))))).
fof(ah4s_realaxs_HREALu_u_RDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))),s(t_h4s_hreals_hreal,V_z))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_z))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_y),s(t_h4s_hreals_hreal,V_z)))))).
fof(ah4s_realaxs_HREALu_u_EQu_u_LADD, axiom, ![V_z, V_y, V_x]: (s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_z))) <=> s(t_h4s_hreals_hreal,V_y) = s(t_h4s_hreals_hreal,V_z))).
fof(ah4s_realaxs_HREALu_u_LTu_u_GT, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y)))) => ~ (p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,V_y),s(t_h4s_hreals_hreal,V_x))))))).
fof(ah4s_realaxs_trealu_u_00, axiom, s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0) = s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1)))).
fof(ah4s_realaxs_trealu_u_10, axiom, s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_1) = s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1)))).
fof(ah4s_realaxs_trealu_u_mul0, axiom, ![V_y2, V_y1, V_x2, V_x1]: s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_mul(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x1),s(t_h4s_hreals_hreal,V_y1))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x2),s(t_h4s_hreals_hreal,V_y2))))) = s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_x1),s(t_h4s_hreals_hreal,V_x2))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_y1),s(t_h4s_hreals_hreal,V_y2))))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_x1),s(t_h4s_hreals_hreal,V_y2))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_y1),s(t_h4s_hreals_hreal,V_x2)))))))).
fof(ah4s_realaxs_trealu_u_inv0, axiom, ![V_y, V_x]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_hreals_hreal,V_x) = s(t_h4s_hreals_hreal,V_y)) & s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_inv(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))))) = s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_bools_cond(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,V_y),s(t_h4s_hreals_hreal,V_x))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_inv(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_sub(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_inv(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_sub(s(t_h4s_hreals_hreal,V_y),s(t_h4s_hreals_hreal,V_x))))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))))))))))).
fof(ah4s_realaxs_trealu_u_eq0, axiom, ![V_y2, V_y1, V_x2, V_x1]: (p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x1),s(t_h4s_hreals_hreal,V_y1))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x2),s(t_h4s_hreals_hreal,V_y2)))))) <=> s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x1),s(t_h4s_hreals_hreal,V_y2))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x2),s(t_h4s_hreals_hreal,V_y1))))).
fof(ch4s_realaxs_TREALu_u_MULu_u_LINV, conjecture, ![V_x]: (~ (p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0))))) => p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_mul(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_inv(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_1)))))).
