TSTP Solution File: ITP193^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP193^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:19:03 EDT 2023
% Result : Theorem 62.91s 63.20s
% Output : Proof 62.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.16 % Problem : ITP193^1 : TPTP v8.1.2. Released v7.5.0.
% 0.17/0.17 % Command : do_cvc5 %s %d
% 0.18/0.38 % Computer : n021.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Sun Aug 27 15:20:27 EDT 2023
% 0.18/0.38 % CPUTime :
% 0.25/0.55 %----Proving TH0
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 % File : ITP193^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.56 % Domain : Interactive Theorem Proving
% 0.25/0.56 % Problem : Sledgehammer Sturm_Tarski problem prob_1192__5884460_1
% 0.25/0.56 % Version : Especial.
% 0.25/0.56 % English :
% 0.25/0.56
% 0.25/0.56 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.56 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.56 % Source : [Des21]
% 0.25/0.56 % Names : Sturm_Tarski/prob_1192__5884460_1 [Des21]
% 0.25/0.56
% 0.25/0.56 % Status : Theorem
% 0.25/0.56 % Rating : 0.31 v8.1.0, 0.36 v7.5.0
% 0.25/0.56 % Syntax : Number of formulae : 426 ( 113 unt; 75 typ; 0 def)
% 0.25/0.56 % Number of atoms : 1144 ( 273 equ; 0 cnn)
% 0.25/0.56 % Maximal formula atoms : 12 ( 3 avg)
% 0.25/0.56 % Number of connectives : 3014 ( 146 ~; 43 |; 87 &;2157 @)
% 0.25/0.56 % ( 0 <=>; 581 =>; 0 <=; 0 <~>)
% 0.25/0.56 % Maximal formula depth : 18 ( 7 avg)
% 0.25/0.56 % Number of types : 16 ( 15 usr)
% 0.25/0.56 % Number of type conns : 215 ( 215 >; 0 *; 0 +; 0 <<)
% 0.25/0.56 % Number of symbols : 61 ( 60 usr; 14 con; 0-4 aty)
% 0.25/0.56 % Number of variables : 1091 ( 95 ^; 927 !; 69 ?;1091 :)
% 0.25/0.56 % SPC : TH0_THM_EQU_NAR
% 0.25/0.56
% 0.25/0.56 % Comments : This file was generated by Sledgehammer 2021-02-23 15:44:34.506
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 % Could-be-implicit typings (15)
% 0.25/0.56 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.25/0.56 poly_poly_poly_real: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.25/0.56 set_poly_poly_real: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.25/0.56 poly_poly_real: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Int__Oint_J_J,type,
% 0.25/0.56 poly_poly_int: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.25/0.56 set_poly_real: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Int__Oint_J_J,type,
% 0.25/0.56 set_poly_int: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Real__Oreal_J_J,type,
% 0.25/0.56 set_set_real: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 0.25/0.56 set_set_int: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 poly_real: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.25/0.56 poly_int: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.25/0.56 set_real: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 0.25/0.56 set_int: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Real__Oreal,type,
% 0.25/0.56 real: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Nat__Onat,type,
% 0.25/0.56 nat: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Int__Oint,type,
% 0.25/0.56 int: $tType ).
% 0.25/0.56
% 0.25/0.56 % Explicit typings (60)
% 0.25/0.56 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 0.25/0.56 finite_finite_int: set_int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.25/0.56 finite385822667ly_int: set_poly_int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.25/0.56 finite1328464339y_real: set_poly_poly_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 finite1810960971y_real: set_poly_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 0.25/0.56 finite_finite_real: set_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 0.25/0.56 finite26677625et_int: set_set_int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.25/0.56 finite475462905t_real: set_set_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 0.25/0.56 one_one_int: int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 one_one_poly_real: poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 0.25/0.56 zero_zero_int: int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.25/0.56 zero_zero_poly_int: poly_int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Int__Oint_J_J,type,
% 0.25/0.56 zero_z1549157189ly_int: poly_poly_int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.25/0.56 zero_z935034829y_real: poly_poly_poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.25/0.56 zero_z1423781445y_real: poly_poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 zero_zero_poly_real: poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.25/0.56 zero_zero_real: real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Int__Oint,type,
% 0.25/0.56 groups2051521940al_int: ( real > int ) > set_real > int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.25/0.56 ord_less_int: int > int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.25/0.56 ord_less_poly_int: poly_int > poly_int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.25/0.56 ord_le38482960y_real: poly_poly_real > poly_poly_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 ord_less_poly_real: poly_real > poly_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 0.25/0.56 ord_less_real: real > real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
% 0.25/0.56 ord_less_set_int: set_int > set_int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.25/0.56 ord_less_set_real: set_real > set_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Real__Oreal_M_Eo_J,type,
% 0.25/0.56 ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 0.25/0.56 ord_less_eq_int: int > int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.25/0.56 ord_less_eq_poly_int: poly_int > poly_int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.25/0.56 ord_le893774876y_real: poly_poly_real > poly_poly_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 ord_le1180086932y_real: poly_real > poly_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.25/0.56 ord_less_eq_real: real > real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
% 0.25/0.56 ord_less_eq_set_int: set_int > set_int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.25/0.56 ord_less_eq_set_real: set_real > set_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Ois__zero_001t__Int__Oint,type,
% 0.25/0.56 is_zero_int: poly_int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 is_zero_poly_real: poly_poly_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Ois__zero_001t__Real__Oreal,type,
% 0.25/0.56 is_zero_real: poly_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Opoly_001t__Int__Oint,type,
% 0.25/0.56 poly_int2: poly_int > int > int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.25/0.56 poly_poly_int2: poly_poly_int > poly_int > poly_int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.25/0.56 poly_poly_poly_real2: poly_poly_poly_real > poly_poly_real > poly_poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 poly_poly_real2: poly_poly_real > poly_real > poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Opoly_001t__Real__Oreal,type,
% 0.25/0.56 poly_real2: poly_real > real > real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Opoly__cutoff_001t__Int__Oint,type,
% 0.25/0.56 poly_cutoff_int: nat > poly_int > poly_int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 poly_c1404107022y_real: nat > poly_poly_real > poly_poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Polynomial_Opoly__cutoff_001t__Real__Oreal,type,
% 0.25/0.56 poly_cutoff_real: nat > poly_real > poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 0.25/0.56 collect_int: ( int > $o ) > set_int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.25/0.56 collect_poly_int: ( poly_int > $o ) > set_poly_int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.25/0.56 collec927113489y_real: ( poly_poly_real > $o ) > set_poly_poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.25/0.56 collect_poly_real: ( poly_real > $o ) > set_poly_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 0.25/0.56 collect_real: ( real > $o ) > set_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
% 0.25/0.56 collect_set_int: ( set_int > $o ) > set_set_int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.25/0.56 collect_set_real: ( set_real > $o ) > set_set_real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Ocindex__poly,type,
% 0.25/0.56 sturm_308542325x_poly: real > real > poly_real > poly_real > int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Ocross,type,
% 0.25/0.56 sturm_1953858694_cross: poly_real > real > real > int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Ojump__poly,type,
% 0.25/0.56 sturm_276991412p_poly: poly_real > poly_real > real > int ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_member_001t__Int__Oint,type,
% 0.25/0.56 member_int: int > set_int > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_member_001t__Real__Oreal,type,
% 0.25/0.56 member_real: real > set_real > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_a,type,
% 0.25/0.56 a: real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_a_H,type,
% 0.25/0.56 a2: real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_b,type,
% 0.25/0.56 b: real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_b_H,type,
% 0.25/0.56 b2: real ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_p,type,
% 0.25/0.56 p: poly_real ).
% 0.25/0.56
% 0.25/0.56 % Relevant facts (350)
% 0.25/0.56 thf(fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062,axiom,
% 0.25/0.56 ( finite_finite_real
% 0.25/0.56 @ ( collect_real
% 0.25/0.56 @ ^ [X: real] :
% 0.25/0.56 ( ( poly_real2 @ p @ X )
% 0.25/0.56 = zero_zero_real ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % \<open>finite {x. poly p x = 0}\<close>
% 0.25/0.56 thf(fact_1_assms_I2_J,axiom,
% 0.25/0.56 ord_less_real @ a2 @ b2 ).
% 0.25/0.56
% 0.25/0.56 % assms(2)
% 0.25/0.56 thf(fact_2_assms_I3_J,axiom,
% 0.25/0.56 ord_less_real @ b2 @ b ).
% 0.25/0.56
% 0.25/0.56 % assms(3)
% 0.25/0.56 thf(fact_3_assms_I1_J,axiom,
% 0.25/0.56 ord_less_real @ a @ a2 ).
% 0.25/0.56
% 0.25/0.56 % assms(1)
% 0.25/0.56 thf(fact_4_False,axiom,
% 0.25/0.56 p != zero_zero_poly_real ).
% 0.25/0.56
% 0.25/0.56 % False
% 0.25/0.56 thf(fact_5_poly__0,axiom,
% 0.25/0.56 ! [X2: poly_int] :
% 0.25/0.56 ( ( poly_poly_int2 @ zero_z1549157189ly_int @ X2 )
% 0.25/0.56 = zero_zero_poly_int ) ).
% 0.25/0.56
% 0.25/0.56 % poly_0
% 0.25/0.56 thf(fact_6_poly__0,axiom,
% 0.25/0.56 ! [X2: poly_poly_real] :
% 0.25/0.56 ( ( poly_poly_poly_real2 @ zero_z935034829y_real @ X2 )
% 0.25/0.56 = zero_z1423781445y_real ) ).
% 0.25/0.56
% 0.25/0.56 % poly_0
% 0.25/0.56 thf(fact_7_poly__0,axiom,
% 0.25/0.56 ! [X2: poly_real] :
% 0.25/0.56 ( ( poly_poly_real2 @ zero_z1423781445y_real @ X2 )
% 0.25/0.56 = zero_zero_poly_real ) ).
% 0.25/0.56
% 0.25/0.56 % poly_0
% 0.25/0.56 thf(fact_8_poly__0,axiom,
% 0.25/0.56 ! [X2: int] :
% 0.25/0.56 ( ( poly_int2 @ zero_zero_poly_int @ X2 )
% 0.25/0.56 = zero_zero_int ) ).
% 0.25/0.56
% 0.25/0.56 % poly_0
% 0.25/0.56 thf(fact_9_poly__0,axiom,
% 0.25/0.56 ! [X2: real] :
% 0.25/0.56 ( ( poly_real2 @ zero_zero_poly_real @ X2 )
% 0.25/0.56 = zero_zero_real ) ).
% 0.25/0.56
% 0.25/0.56 % poly_0
% 0.25/0.56 thf(fact_10_assms_I4_J,axiom,
% 0.25/0.56 ! [X3: real] :
% 0.25/0.56 ( ( ( ( ord_less_real @ a @ X3 )
% 0.25/0.56 & ( ord_less_eq_real @ X3 @ a2 ) )
% 0.25/0.56 | ( ( ord_less_eq_real @ b2 @ X3 )
% 0.25/0.56 & ( ord_less_real @ X3 @ b ) ) )
% 0.25/0.56 => ( ( poly_real2 @ p @ X3 )
% 0.25/0.56 != zero_zero_real ) ) ).
% 0.25/0.56
% 0.25/0.56 % assms(4)
% 0.25/0.56 thf(fact_11_finite__Collect__conjI,axiom,
% 0.25/0.56 ! [P: real > $o,Q: real > $o] :
% 0.25/0.56 ( ( ( finite_finite_real @ ( collect_real @ P ) )
% 0.25/0.56 | ( finite_finite_real @ ( collect_real @ Q ) ) )
% 0.25/0.56 => ( finite_finite_real
% 0.25/0.56 @ ( collect_real
% 0.25/0.56 @ ^ [X: real] :
% 0.25/0.56 ( ( P @ X )
% 0.25/0.56 & ( Q @ X ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_Collect_conjI
% 0.25/0.56 thf(fact_12_finite__Collect__conjI,axiom,
% 0.25/0.56 ! [P: int > $o,Q: int > $o] :
% 0.25/0.56 ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 0.25/0.56 | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 0.25/0.56 => ( finite_finite_int
% 0.25/0.56 @ ( collect_int
% 0.25/0.56 @ ^ [X: int] :
% 0.25/0.56 ( ( P @ X )
% 0.25/0.56 & ( Q @ X ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_Collect_conjI
% 0.25/0.56 thf(fact_13_finite__Collect__disjI,axiom,
% 0.25/0.56 ! [P: real > $o,Q: real > $o] :
% 0.25/0.56 ( ( finite_finite_real
% 0.25/0.56 @ ( collect_real
% 0.25/0.56 @ ^ [X: real] :
% 0.25/0.56 ( ( P @ X )
% 0.25/0.56 | ( Q @ X ) ) ) )
% 0.25/0.56 = ( ( finite_finite_real @ ( collect_real @ P ) )
% 0.25/0.56 & ( finite_finite_real @ ( collect_real @ Q ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_Collect_disjI
% 0.25/0.56 thf(fact_14_finite__Collect__disjI,axiom,
% 0.25/0.56 ! [P: int > $o,Q: int > $o] :
% 0.25/0.56 ( ( finite_finite_int
% 0.25/0.56 @ ( collect_int
% 0.25/0.56 @ ^ [X: int] :
% 0.25/0.56 ( ( P @ X )
% 0.25/0.56 | ( Q @ X ) ) ) )
% 0.25/0.56 = ( ( finite_finite_int @ ( collect_int @ P ) )
% 0.25/0.56 & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_Collect_disjI
% 0.25/0.56 thf(fact_15_poly__roots__finite,axiom,
% 0.25/0.56 ! [P2: poly_poly_int] :
% 0.25/0.56 ( ( P2 != zero_z1549157189ly_int )
% 0.25/0.56 => ( finite385822667ly_int
% 0.25/0.56 @ ( collect_poly_int
% 0.25/0.56 @ ^ [X: poly_int] :
% 0.25/0.56 ( ( poly_poly_int2 @ P2 @ X )
% 0.25/0.56 = zero_zero_poly_int ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_roots_finite
% 0.25/0.56 thf(fact_16_poly__roots__finite,axiom,
% 0.25/0.56 ! [P2: poly_poly_poly_real] :
% 0.25/0.56 ( ( P2 != zero_z935034829y_real )
% 0.25/0.56 => ( finite1328464339y_real
% 0.25/0.56 @ ( collec927113489y_real
% 0.25/0.56 @ ^ [X: poly_poly_real] :
% 0.25/0.56 ( ( poly_poly_poly_real2 @ P2 @ X )
% 0.25/0.56 = zero_z1423781445y_real ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_roots_finite
% 0.25/0.56 thf(fact_17_poly__roots__finite,axiom,
% 0.25/0.56 ! [P2: poly_real] :
% 0.25/0.56 ( ( P2 != zero_zero_poly_real )
% 0.25/0.56 => ( finite_finite_real
% 0.25/0.56 @ ( collect_real
% 0.25/0.56 @ ^ [X: real] :
% 0.25/0.56 ( ( poly_real2 @ P2 @ X )
% 0.25/0.56 = zero_zero_real ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_roots_finite
% 0.25/0.56 thf(fact_18_poly__roots__finite,axiom,
% 0.25/0.56 ! [P2: poly_int] :
% 0.25/0.56 ( ( P2 != zero_zero_poly_int )
% 0.25/0.56 => ( finite_finite_int
% 0.25/0.56 @ ( collect_int
% 0.25/0.56 @ ^ [X: int] :
% 0.25/0.56 ( ( poly_int2 @ P2 @ X )
% 0.25/0.56 = zero_zero_int ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_roots_finite
% 0.25/0.56 thf(fact_19_poly__roots__finite,axiom,
% 0.25/0.56 ! [P2: poly_poly_real] :
% 0.25/0.56 ( ( P2 != zero_z1423781445y_real )
% 0.25/0.56 => ( finite1810960971y_real
% 0.25/0.56 @ ( collect_poly_real
% 0.25/0.56 @ ^ [X: poly_real] :
% 0.25/0.56 ( ( poly_poly_real2 @ P2 @ X )
% 0.25/0.56 = zero_zero_poly_real ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_roots_finite
% 0.25/0.56 thf(fact_20_poly__IVT__neg,axiom,
% 0.25/0.56 ! [A: real,B: real,P2: poly_real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ A ) )
% 0.25/0.56 => ( ( ord_less_real @ ( poly_real2 @ P2 @ B ) @ zero_zero_real )
% 0.25/0.56 => ? [X4: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ X4 )
% 0.25/0.56 & ( ord_less_real @ X4 @ B )
% 0.25/0.56 & ( ( poly_real2 @ P2 @ X4 )
% 0.25/0.56 = zero_zero_real ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_IVT_neg
% 0.25/0.56 thf(fact_21_poly__IVT__pos,axiom,
% 0.25/0.56 ! [A: real,B: real,P2: poly_real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ( ord_less_real @ ( poly_real2 @ P2 @ A ) @ zero_zero_real )
% 0.25/0.56 => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ B ) )
% 0.25/0.56 => ? [X4: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ X4 )
% 0.25/0.56 & ( ord_less_real @ X4 @ B )
% 0.25/0.56 & ( ( poly_real2 @ P2 @ X4 )
% 0.25/0.56 = zero_zero_real ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_IVT_pos
% 0.25/0.56 thf(fact_22_poly__all__0__iff__0,axiom,
% 0.25/0.56 ! [P2: poly_real] :
% 0.25/0.56 ( ( ! [X: real] :
% 0.25/0.56 ( ( poly_real2 @ P2 @ X )
% 0.25/0.56 = zero_zero_real ) )
% 0.25/0.56 = ( P2 = zero_zero_poly_real ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_all_0_iff_0
% 0.25/0.56 thf(fact_23_poly__all__0__iff__0,axiom,
% 0.25/0.56 ! [P2: poly_poly_real] :
% 0.25/0.56 ( ( ! [X: poly_real] :
% 0.25/0.56 ( ( poly_poly_real2 @ P2 @ X )
% 0.25/0.56 = zero_zero_poly_real ) )
% 0.25/0.56 = ( P2 = zero_z1423781445y_real ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_all_0_iff_0
% 0.25/0.56 thf(fact_24_poly__all__0__iff__0,axiom,
% 0.25/0.56 ! [P2: poly_int] :
% 0.25/0.56 ( ( ! [X: int] :
% 0.25/0.56 ( ( poly_int2 @ P2 @ X )
% 0.25/0.56 = zero_zero_int ) )
% 0.25/0.56 = ( P2 = zero_zero_poly_int ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_all_0_iff_0
% 0.25/0.56 thf(fact_25_poly__all__0__iff__0,axiom,
% 0.25/0.56 ! [P2: poly_poly_int] :
% 0.25/0.56 ( ( ! [X: poly_int] :
% 0.25/0.56 ( ( poly_poly_int2 @ P2 @ X )
% 0.25/0.56 = zero_zero_poly_int ) )
% 0.25/0.56 = ( P2 = zero_z1549157189ly_int ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_all_0_iff_0
% 0.25/0.56 thf(fact_26_poly__all__0__iff__0,axiom,
% 0.25/0.56 ! [P2: poly_poly_poly_real] :
% 0.25/0.56 ( ( ! [X: poly_poly_real] :
% 0.25/0.56 ( ( poly_poly_poly_real2 @ P2 @ X )
% 0.25/0.56 = zero_z1423781445y_real ) )
% 0.25/0.56 = ( P2 = zero_z935034829y_real ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_all_0_iff_0
% 0.25/0.56 thf(fact_27_less__numeral__extra_I3_J,axiom,
% 0.25/0.56 ~ ( ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(3)
% 0.25/0.56 thf(fact_28_less__numeral__extra_I3_J,axiom,
% 0.25/0.56 ~ ( ord_less_poly_int @ zero_zero_poly_int @ zero_zero_poly_int ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(3)
% 0.25/0.56 thf(fact_29_less__numeral__extra_I3_J,axiom,
% 0.25/0.56 ~ ( ord_le38482960y_real @ zero_z1423781445y_real @ zero_z1423781445y_real ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(3)
% 0.25/0.56 thf(fact_30_less__numeral__extra_I3_J,axiom,
% 0.25/0.56 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(3)
% 0.25/0.56 thf(fact_31_less__numeral__extra_I3_J,axiom,
% 0.25/0.56 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(3)
% 0.25/0.56 thf(fact_32_le__numeral__extra_I3_J,axiom,
% 0.25/0.56 ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real ).
% 0.25/0.56
% 0.25/0.56 % le_numeral_extra(3)
% 0.25/0.56 thf(fact_33_le__numeral__extra_I3_J,axiom,
% 0.25/0.56 ord_less_eq_poly_int @ zero_zero_poly_int @ zero_zero_poly_int ).
% 0.25/0.56
% 0.25/0.56 % le_numeral_extra(3)
% 0.25/0.56 thf(fact_34_le__numeral__extra_I3_J,axiom,
% 0.25/0.56 ord_le893774876y_real @ zero_z1423781445y_real @ zero_z1423781445y_real ).
% 0.25/0.56
% 0.25/0.56 % le_numeral_extra(3)
% 0.25/0.56 thf(fact_35_le__numeral__extra_I3_J,axiom,
% 0.25/0.56 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.25/0.56
% 0.25/0.56 % le_numeral_extra(3)
% 0.25/0.56 thf(fact_36_le__numeral__extra_I3_J,axiom,
% 0.25/0.56 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.25/0.56
% 0.25/0.56 % le_numeral_extra(3)
% 0.25/0.56 thf(fact_37_finite__psubset__induct,axiom,
% 0.25/0.56 ! [A2: set_real,P: set_real > $o] :
% 0.25/0.56 ( ( finite_finite_real @ A2 )
% 0.25/0.56 => ( ! [A3: set_real] :
% 0.25/0.56 ( ( finite_finite_real @ A3 )
% 0.25/0.56 => ( ! [B2: set_real] :
% 0.25/0.56 ( ( ord_less_set_real @ B2 @ A3 )
% 0.25/0.56 => ( P @ B2 ) )
% 0.25/0.56 => ( P @ A3 ) ) )
% 0.25/0.56 => ( P @ A2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_psubset_induct
% 0.25/0.56 thf(fact_38_finite__psubset__induct,axiom,
% 0.25/0.56 ! [A2: set_int,P: set_int > $o] :
% 0.25/0.56 ( ( finite_finite_int @ A2 )
% 0.25/0.56 => ( ! [A3: set_int] :
% 0.25/0.56 ( ( finite_finite_int @ A3 )
% 0.25/0.56 => ( ! [B2: set_int] :
% 0.25/0.56 ( ( ord_less_set_int @ B2 @ A3 )
% 0.25/0.56 => ( P @ B2 ) )
% 0.25/0.56 => ( P @ A3 ) ) )
% 0.25/0.56 => ( P @ A2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_psubset_induct
% 0.25/0.56 thf(fact_39_finite__has__minimal2,axiom,
% 0.25/0.56 ! [A2: set_real,A: real] :
% 0.25/0.56 ( ( finite_finite_real @ A2 )
% 0.25/0.56 => ( ( member_real @ A @ A2 )
% 0.25/0.56 => ? [X4: real] :
% 0.25/0.56 ( ( member_real @ X4 @ A2 )
% 0.25/0.56 & ( ord_less_eq_real @ X4 @ A )
% 0.25/0.56 & ! [Xa: real] :
% 0.25/0.56 ( ( member_real @ Xa @ A2 )
% 0.25/0.56 => ( ( ord_less_eq_real @ Xa @ X4 )
% 0.25/0.56 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_has_minimal2
% 0.25/0.56 thf(fact_40_finite__has__minimal2,axiom,
% 0.25/0.56 ! [A2: set_int,A: int] :
% 0.25/0.56 ( ( finite_finite_int @ A2 )
% 0.25/0.56 => ( ( member_int @ A @ A2 )
% 0.25/0.56 => ? [X4: int] :
% 0.25/0.56 ( ( member_int @ X4 @ A2 )
% 0.25/0.56 & ( ord_less_eq_int @ X4 @ A )
% 0.25/0.56 & ! [Xa: int] :
% 0.25/0.56 ( ( member_int @ Xa @ A2 )
% 0.25/0.56 => ( ( ord_less_eq_int @ Xa @ X4 )
% 0.25/0.56 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_has_minimal2
% 0.25/0.56 thf(fact_41_finite__has__maximal2,axiom,
% 0.25/0.56 ! [A2: set_real,A: real] :
% 0.25/0.56 ( ( finite_finite_real @ A2 )
% 0.25/0.56 => ( ( member_real @ A @ A2 )
% 0.25/0.56 => ? [X4: real] :
% 0.25/0.56 ( ( member_real @ X4 @ A2 )
% 0.25/0.56 & ( ord_less_eq_real @ A @ X4 )
% 0.25/0.56 & ! [Xa: real] :
% 0.25/0.56 ( ( member_real @ Xa @ A2 )
% 0.25/0.56 => ( ( ord_less_eq_real @ X4 @ Xa )
% 0.25/0.56 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_has_maximal2
% 0.25/0.56 thf(fact_42_finite__has__maximal2,axiom,
% 0.25/0.56 ! [A2: set_int,A: int] :
% 0.25/0.56 ( ( finite_finite_int @ A2 )
% 0.25/0.56 => ( ( member_int @ A @ A2 )
% 0.25/0.56 => ? [X4: int] :
% 0.25/0.56 ( ( member_int @ X4 @ A2 )
% 0.25/0.56 & ( ord_less_eq_int @ A @ X4 )
% 0.25/0.56 & ! [Xa: int] :
% 0.25/0.56 ( ( member_int @ Xa @ A2 )
% 0.25/0.56 => ( ( ord_less_eq_int @ X4 @ Xa )
% 0.25/0.56 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_has_maximal2
% 0.25/0.56 thf(fact_43_next__non__root__interval,axiom,
% 0.25/0.56 ! [P2: poly_real,Lb: real] :
% 0.25/0.56 ( ( P2 != zero_zero_poly_real )
% 0.25/0.56 => ~ ! [Ub: real] :
% 0.25/0.56 ( ( ord_less_real @ Lb @ Ub )
% 0.25/0.56 => ~ ! [Z: real] :
% 0.25/0.56 ( ( ( ord_less_real @ Lb @ Z )
% 0.25/0.56 & ( ord_less_eq_real @ Z @ Ub ) )
% 0.25/0.56 => ( ( poly_real2 @ P2 @ Z )
% 0.25/0.56 != zero_zero_real ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % next_non_root_interval
% 0.25/0.56 thf(fact_44_last__non__root__interval,axiom,
% 0.25/0.56 ! [P2: poly_real,Ub2: real] :
% 0.25/0.56 ( ( P2 != zero_zero_poly_real )
% 0.25/0.56 => ~ ! [Lb2: real] :
% 0.25/0.56 ( ( ord_less_real @ Lb2 @ Ub2 )
% 0.25/0.56 => ~ ! [Z: real] :
% 0.25/0.56 ( ( ( ord_less_eq_real @ Lb2 @ Z )
% 0.25/0.56 & ( ord_less_real @ Z @ Ub2 ) )
% 0.25/0.56 => ( ( poly_real2 @ P2 @ Z )
% 0.25/0.56 != zero_zero_real ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % last_non_root_interval
% 0.25/0.56 thf(fact_45_zero__reorient,axiom,
% 0.25/0.56 ! [X2: real] :
% 0.25/0.56 ( ( zero_zero_real = X2 )
% 0.25/0.56 = ( X2 = zero_zero_real ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_reorient
% 0.25/0.56 thf(fact_46_zero__reorient,axiom,
% 0.25/0.56 ! [X2: poly_real] :
% 0.25/0.56 ( ( zero_zero_poly_real = X2 )
% 0.25/0.56 = ( X2 = zero_zero_poly_real ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_reorient
% 0.25/0.56 thf(fact_47_zero__reorient,axiom,
% 0.25/0.56 ! [X2: int] :
% 0.25/0.56 ( ( zero_zero_int = X2 )
% 0.25/0.56 = ( X2 = zero_zero_int ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_reorient
% 0.25/0.56 thf(fact_48_zero__reorient,axiom,
% 0.25/0.56 ! [X2: poly_int] :
% 0.25/0.56 ( ( zero_zero_poly_int = X2 )
% 0.25/0.56 = ( X2 = zero_zero_poly_int ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_reorient
% 0.25/0.56 thf(fact_49_zero__reorient,axiom,
% 0.25/0.56 ! [X2: poly_poly_real] :
% 0.25/0.56 ( ( zero_z1423781445y_real = X2 )
% 0.25/0.56 = ( X2 = zero_z1423781445y_real ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_reorient
% 0.25/0.56 thf(fact_50_not__eq__pos__or__neg__iff__2,axiom,
% 0.25/0.56 ! [Lb: real,Ub2: real,P2: poly_real] :
% 0.25/0.56 ( ( ! [Z2: real] :
% 0.25/0.56 ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 0.25/0.56 & ( ord_less_real @ Z2 @ Ub2 ) )
% 0.25/0.56 => ( ( poly_real2 @ P2 @ Z2 )
% 0.25/0.56 != zero_zero_real ) ) )
% 0.25/0.56 = ( ! [Z2: real] :
% 0.25/0.56 ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 0.25/0.56 & ( ord_less_real @ Z2 @ Ub2 ) )
% 0.25/0.56 => ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ Z2 ) ) )
% 0.25/0.56 | ! [Z2: real] :
% 0.25/0.56 ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 0.25/0.56 & ( ord_less_real @ Z2 @ Ub2 ) )
% 0.25/0.56 => ( ord_less_real @ ( poly_real2 @ P2 @ Z2 ) @ zero_zero_real ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_eq_pos_or_neg_iff_2
% 0.25/0.56 thf(fact_51_not__eq__pos__or__neg__iff__1,axiom,
% 0.25/0.56 ! [Lb: real,Ub2: real,P2: poly_real] :
% 0.25/0.56 ( ( ! [Z2: real] :
% 0.25/0.56 ( ( ( ord_less_real @ Lb @ Z2 )
% 0.25/0.56 & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 0.25/0.56 => ( ( poly_real2 @ P2 @ Z2 )
% 0.25/0.56 != zero_zero_real ) ) )
% 0.25/0.56 = ( ! [Z2: real] :
% 0.25/0.56 ( ( ( ord_less_real @ Lb @ Z2 )
% 0.25/0.56 & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 0.25/0.56 => ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ Z2 ) ) )
% 0.25/0.56 | ! [Z2: real] :
% 0.25/0.56 ( ( ( ord_less_real @ Lb @ Z2 )
% 0.25/0.56 & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 0.25/0.56 => ( ord_less_real @ ( poly_real2 @ P2 @ Z2 ) @ zero_zero_real ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_eq_pos_or_neg_iff_1
% 0.25/0.56 thf(fact_52_poly__eq__poly__eq__iff,axiom,
% 0.25/0.56 ! [P2: poly_real,Q2: poly_real] :
% 0.25/0.56 ( ( ( poly_real2 @ P2 )
% 0.25/0.56 = ( poly_real2 @ Q2 ) )
% 0.25/0.56 = ( P2 = Q2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_eq_poly_eq_iff
% 0.25/0.56 thf(fact_53_poly__eq__poly__eq__iff,axiom,
% 0.25/0.56 ! [P2: poly_int,Q2: poly_int] :
% 0.25/0.56 ( ( ( poly_int2 @ P2 )
% 0.25/0.56 = ( poly_int2 @ Q2 ) )
% 0.25/0.56 = ( P2 = Q2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_eq_poly_eq_iff
% 0.25/0.56 thf(fact_54_poly__eq__poly__eq__iff,axiom,
% 0.25/0.56 ! [P2: poly_poly_real,Q2: poly_poly_real] :
% 0.25/0.56 ( ( ( poly_poly_real2 @ P2 )
% 0.25/0.56 = ( poly_poly_real2 @ Q2 ) )
% 0.25/0.56 = ( P2 = Q2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_eq_poly_eq_iff
% 0.25/0.56 thf(fact_55_pigeonhole__infinite__rel,axiom,
% 0.25/0.56 ! [A2: set_real,B3: set_real,R: real > real > $o] :
% 0.25/0.56 ( ~ ( finite_finite_real @ A2 )
% 0.25/0.56 => ( ( finite_finite_real @ B3 )
% 0.25/0.56 => ( ! [X4: real] :
% 0.25/0.56 ( ( member_real @ X4 @ A2 )
% 0.25/0.56 => ? [Xa: real] :
% 0.25/0.56 ( ( member_real @ Xa @ B3 )
% 0.25/0.56 & ( R @ X4 @ Xa ) ) )
% 0.25/0.56 => ? [X4: real] :
% 0.25/0.56 ( ( member_real @ X4 @ B3 )
% 0.25/0.56 & ~ ( finite_finite_real
% 0.25/0.56 @ ( collect_real
% 0.25/0.56 @ ^ [A4: real] :
% 0.25/0.56 ( ( member_real @ A4 @ A2 )
% 0.25/0.56 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % pigeonhole_infinite_rel
% 0.25/0.56 thf(fact_56_pigeonhole__infinite__rel,axiom,
% 0.25/0.56 ! [A2: set_real,B3: set_int,R: real > int > $o] :
% 0.25/0.56 ( ~ ( finite_finite_real @ A2 )
% 0.25/0.56 => ( ( finite_finite_int @ B3 )
% 0.25/0.56 => ( ! [X4: real] :
% 0.25/0.56 ( ( member_real @ X4 @ A2 )
% 0.25/0.56 => ? [Xa: int] :
% 0.25/0.56 ( ( member_int @ Xa @ B3 )
% 0.25/0.56 & ( R @ X4 @ Xa ) ) )
% 0.25/0.56 => ? [X4: int] :
% 0.25/0.56 ( ( member_int @ X4 @ B3 )
% 0.25/0.56 & ~ ( finite_finite_real
% 0.25/0.56 @ ( collect_real
% 0.25/0.56 @ ^ [A4: real] :
% 0.25/0.56 ( ( member_real @ A4 @ A2 )
% 0.25/0.56 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % pigeonhole_infinite_rel
% 0.25/0.56 thf(fact_57_pigeonhole__infinite__rel,axiom,
% 0.25/0.56 ! [A2: set_int,B3: set_real,R: int > real > $o] :
% 0.25/0.56 ( ~ ( finite_finite_int @ A2 )
% 0.25/0.56 => ( ( finite_finite_real @ B3 )
% 0.25/0.56 => ( ! [X4: int] :
% 0.25/0.56 ( ( member_int @ X4 @ A2 )
% 0.25/0.56 => ? [Xa: real] :
% 0.25/0.56 ( ( member_real @ Xa @ B3 )
% 0.25/0.56 & ( R @ X4 @ Xa ) ) )
% 0.25/0.56 => ? [X4: real] :
% 0.25/0.56 ( ( member_real @ X4 @ B3 )
% 0.25/0.56 & ~ ( finite_finite_int
% 0.25/0.56 @ ( collect_int
% 0.25/0.56 @ ^ [A4: int] :
% 0.25/0.56 ( ( member_int @ A4 @ A2 )
% 0.25/0.56 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % pigeonhole_infinite_rel
% 0.25/0.56 thf(fact_58_pigeonhole__infinite__rel,axiom,
% 0.25/0.56 ! [A2: set_int,B3: set_int,R: int > int > $o] :
% 0.25/0.56 ( ~ ( finite_finite_int @ A2 )
% 0.25/0.56 => ( ( finite_finite_int @ B3 )
% 0.25/0.56 => ( ! [X4: int] :
% 0.25/0.56 ( ( member_int @ X4 @ A2 )
% 0.25/0.56 => ? [Xa: int] :
% 0.25/0.56 ( ( member_int @ Xa @ B3 )
% 0.25/0.56 & ( R @ X4 @ Xa ) ) )
% 0.25/0.56 => ? [X4: int] :
% 0.25/0.56 ( ( member_int @ X4 @ B3 )
% 0.25/0.56 & ~ ( finite_finite_int
% 0.25/0.56 @ ( collect_int
% 0.25/0.56 @ ^ [A4: int] :
% 0.25/0.56 ( ( member_int @ A4 @ A2 )
% 0.25/0.56 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % pigeonhole_infinite_rel
% 0.25/0.56 thf(fact_59_not__finite__existsD,axiom,
% 0.25/0.56 ! [P: real > $o] :
% 0.25/0.56 ( ~ ( finite_finite_real @ ( collect_real @ P ) )
% 0.25/0.56 => ? [X_1: real] : ( P @ X_1 ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_finite_existsD
% 0.25/0.56 thf(fact_60_not__finite__existsD,axiom,
% 0.25/0.56 ! [P: int > $o] :
% 0.25/0.56 ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 0.25/0.56 => ? [X_1: int] : ( P @ X_1 ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_finite_existsD
% 0.25/0.56 thf(fact_61_order__refl,axiom,
% 0.25/0.56 ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 0.25/0.56
% 0.25/0.56 % order_refl
% 0.25/0.56 thf(fact_62_order__refl,axiom,
% 0.25/0.56 ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 0.25/0.56
% 0.25/0.56 % order_refl
% 0.25/0.56 thf(fact_63_cross__no__root,axiom,
% 0.25/0.56 ! [A: real,B: real,P2: poly_real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ! [X4: real] :
% 0.25/0.56 ( ( ( ord_less_real @ A @ X4 )
% 0.25/0.56 & ( ord_less_real @ X4 @ B ) )
% 0.25/0.56 => ( ( poly_real2 @ P2 @ X4 )
% 0.25/0.56 != zero_zero_real ) )
% 0.25/0.56 => ( ( sturm_1953858694_cross @ P2 @ A @ B )
% 0.25/0.56 = zero_zero_int ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % cross_no_root
% 0.25/0.56 thf(fact_64_less__eq__real__def,axiom,
% 0.25/0.56 ( ord_less_eq_real
% 0.25/0.56 = ( ^ [X: real,Y: real] :
% 0.25/0.56 ( ( ord_less_real @ X @ Y )
% 0.25/0.56 | ( X = Y ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_eq_real_def
% 0.25/0.56 thf(fact_65_complete__interval,axiom,
% 0.25/0.56 ! [A: real,B: real,P: real > $o] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ( P @ A )
% 0.25/0.56 => ( ~ ( P @ B )
% 0.25/0.56 => ? [C: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ C )
% 0.25/0.56 & ( ord_less_eq_real @ C @ B )
% 0.25/0.56 & ! [X3: real] :
% 0.25/0.56 ( ( ( ord_less_eq_real @ A @ X3 )
% 0.25/0.56 & ( ord_less_real @ X3 @ C ) )
% 0.25/0.56 => ( P @ X3 ) )
% 0.25/0.56 & ! [D: real] :
% 0.25/0.56 ( ! [X4: real] :
% 0.25/0.56 ( ( ( ord_less_eq_real @ A @ X4 )
% 0.25/0.56 & ( ord_less_real @ X4 @ D ) )
% 0.25/0.56 => ( P @ X4 ) )
% 0.25/0.56 => ( ord_less_eq_real @ D @ C ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % complete_interval
% 0.25/0.56 thf(fact_66_complete__interval,axiom,
% 0.25/0.56 ! [A: int,B: int,P: int > $o] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ( ( P @ A )
% 0.25/0.56 => ( ~ ( P @ B )
% 0.25/0.56 => ? [C: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ C )
% 0.25/0.56 & ( ord_less_eq_int @ C @ B )
% 0.25/0.56 & ! [X3: int] :
% 0.25/0.56 ( ( ( ord_less_eq_int @ A @ X3 )
% 0.25/0.56 & ( ord_less_int @ X3 @ C ) )
% 0.25/0.56 => ( P @ X3 ) )
% 0.25/0.56 & ! [D: int] :
% 0.25/0.56 ( ! [X4: int] :
% 0.25/0.56 ( ( ( ord_less_eq_int @ A @ X4 )
% 0.25/0.56 & ( ord_less_int @ X4 @ D ) )
% 0.25/0.56 => ( P @ X4 ) )
% 0.25/0.56 => ( ord_less_eq_int @ D @ C ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % complete_interval
% 0.25/0.56 thf(fact_67_order_Onot__eq__order__implies__strict,axiom,
% 0.25/0.56 ! [A: real,B: real] :
% 0.25/0.56 ( ( A != B )
% 0.25/0.56 => ( ( ord_less_eq_real @ A @ B )
% 0.25/0.56 => ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.not_eq_order_implies_strict
% 0.25/0.56 thf(fact_68_order_Onot__eq__order__implies__strict,axiom,
% 0.25/0.56 ! [A: int,B: int] :
% 0.25/0.56 ( ( A != B )
% 0.25/0.56 => ( ( ord_less_eq_int @ A @ B )
% 0.25/0.56 => ( ord_less_int @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.not_eq_order_implies_strict
% 0.25/0.56 thf(fact_69_dual__order_Ostrict__implies__order,axiom,
% 0.25/0.56 ! [B: real,A: real] :
% 0.25/0.56 ( ( ord_less_real @ B @ A )
% 0.25/0.56 => ( ord_less_eq_real @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_implies_order
% 0.25/0.56 thf(fact_70_dual__order_Ostrict__implies__order,axiom,
% 0.25/0.56 ! [B: int,A: int] :
% 0.25/0.56 ( ( ord_less_int @ B @ A )
% 0.25/0.56 => ( ord_less_eq_int @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_implies_order
% 0.25/0.56 thf(fact_71_dual__order_Ostrict__iff__order,axiom,
% 0.25/0.56 ( ord_less_real
% 0.25/0.56 = ( ^ [B4: real,A4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ B4 @ A4 )
% 0.25/0.56 & ( A4 != B4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_iff_order
% 0.25/0.56 thf(fact_72_dual__order_Ostrict__iff__order,axiom,
% 0.25/0.56 ( ord_less_int
% 0.25/0.56 = ( ^ [B4: int,A4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ B4 @ A4 )
% 0.25/0.56 & ( A4 != B4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_iff_order
% 0.25/0.56 thf(fact_73_dual__order_Oorder__iff__strict,axiom,
% 0.25/0.56 ( ord_less_eq_real
% 0.25/0.56 = ( ^ [B4: real,A4: real] :
% 0.25/0.56 ( ( ord_less_real @ B4 @ A4 )
% 0.25/0.56 | ( A4 = B4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.order_iff_strict
% 0.25/0.56 thf(fact_74_dual__order_Oorder__iff__strict,axiom,
% 0.25/0.56 ( ord_less_eq_int
% 0.25/0.56 = ( ^ [B4: int,A4: int] :
% 0.25/0.56 ( ( ord_less_int @ B4 @ A4 )
% 0.25/0.56 | ( A4 = B4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.order_iff_strict
% 0.25/0.56 thf(fact_75_mem__Collect__eq,axiom,
% 0.25/0.56 ! [A: real,P: real > $o] :
% 0.25/0.56 ( ( member_real @ A @ ( collect_real @ P ) )
% 0.25/0.56 = ( P @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % mem_Collect_eq
% 0.25/0.56 thf(fact_76_mem__Collect__eq,axiom,
% 0.25/0.56 ! [A: int,P: int > $o] :
% 0.25/0.56 ( ( member_int @ A @ ( collect_int @ P ) )
% 0.25/0.56 = ( P @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % mem_Collect_eq
% 0.25/0.56 thf(fact_77_Collect__mem__eq,axiom,
% 0.25/0.56 ! [A2: set_real] :
% 0.25/0.56 ( ( collect_real
% 0.25/0.56 @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 0.25/0.56 = A2 ) ).
% 0.25/0.56
% 0.25/0.56 % Collect_mem_eq
% 0.25/0.56 thf(fact_78_Collect__mem__eq,axiom,
% 0.25/0.56 ! [A2: set_int] :
% 0.25/0.56 ( ( collect_int
% 0.25/0.56 @ ^ [X: int] : ( member_int @ X @ A2 ) )
% 0.25/0.56 = A2 ) ).
% 0.25/0.56
% 0.25/0.56 % Collect_mem_eq
% 0.25/0.56 thf(fact_79_Collect__cong,axiom,
% 0.25/0.56 ! [P: real > $o,Q: real > $o] :
% 0.25/0.56 ( ! [X4: real] :
% 0.25/0.56 ( ( P @ X4 )
% 0.25/0.56 = ( Q @ X4 ) )
% 0.25/0.56 => ( ( collect_real @ P )
% 0.25/0.56 = ( collect_real @ Q ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Collect_cong
% 0.25/0.56 thf(fact_80_Collect__cong,axiom,
% 0.25/0.56 ! [P: int > $o,Q: int > $o] :
% 0.25/0.56 ( ! [X4: int] :
% 0.25/0.56 ( ( P @ X4 )
% 0.25/0.56 = ( Q @ X4 ) )
% 0.25/0.56 => ( ( collect_int @ P )
% 0.25/0.56 = ( collect_int @ Q ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Collect_cong
% 0.25/0.56 thf(fact_81_order_Ostrict__implies__order,axiom,
% 0.25/0.56 ! [A: real,B: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_implies_order
% 0.25/0.56 thf(fact_82_order_Ostrict__implies__order,axiom,
% 0.25/0.56 ! [A: int,B: int] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_implies_order
% 0.25/0.56 thf(fact_83_dense__le__bounded,axiom,
% 0.25/0.56 ! [X2: real,Y2: real,Z3: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ( ! [W: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ W )
% 0.25/0.56 => ( ( ord_less_real @ W @ Y2 )
% 0.25/0.56 => ( ord_less_eq_real @ W @ Z3 ) ) )
% 0.25/0.56 => ( ord_less_eq_real @ Y2 @ Z3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dense_le_bounded
% 0.25/0.56 thf(fact_84_finite__Collect__subsets,axiom,
% 0.25/0.56 ! [A2: set_real] :
% 0.25/0.56 ( ( finite_finite_real @ A2 )
% 0.25/0.56 => ( finite475462905t_real
% 0.25/0.56 @ ( collect_set_real
% 0.25/0.56 @ ^ [B5: set_real] : ( ord_less_eq_set_real @ B5 @ A2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_Collect_subsets
% 0.25/0.56 thf(fact_85_finite__Collect__subsets,axiom,
% 0.25/0.56 ! [A2: set_int] :
% 0.25/0.56 ( ( finite_finite_int @ A2 )
% 0.25/0.56 => ( finite26677625et_int
% 0.25/0.56 @ ( collect_set_int
% 0.25/0.56 @ ^ [B5: set_int] : ( ord_less_eq_set_int @ B5 @ A2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_Collect_subsets
% 0.25/0.56 thf(fact_86_cross__0,axiom,
% 0.25/0.56 ! [A: real,B: real] :
% 0.25/0.56 ( ( sturm_1953858694_cross @ zero_zero_poly_real @ A @ B )
% 0.25/0.56 = zero_zero_int ) ).
% 0.25/0.56
% 0.25/0.56 % cross_0
% 0.25/0.56 thf(fact_87_finite__subset,axiom,
% 0.25/0.56 ! [A2: set_real,B3: set_real] :
% 0.25/0.56 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.25/0.56 => ( ( finite_finite_real @ B3 )
% 0.25/0.56 => ( finite_finite_real @ A2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_subset
% 0.25/0.56 thf(fact_88_finite__subset,axiom,
% 0.25/0.56 ! [A2: set_int,B3: set_int] :
% 0.25/0.56 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.25/0.56 => ( ( finite_finite_int @ B3 )
% 0.25/0.56 => ( finite_finite_int @ A2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % finite_subset
% 0.25/0.56 thf(fact_89_infinite__super,axiom,
% 0.25/0.56 ! [S: set_real,T: set_real] :
% 0.25/0.56 ( ( ord_less_eq_set_real @ S @ T )
% 0.25/0.56 => ( ~ ( finite_finite_real @ S )
% 0.25/0.56 => ~ ( finite_finite_real @ T ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % infinite_super
% 0.25/0.56 thf(fact_90_infinite__super,axiom,
% 0.25/0.56 ! [S: set_int,T: set_int] :
% 0.25/0.56 ( ( ord_less_eq_set_int @ S @ T )
% 0.25/0.56 => ( ~ ( finite_finite_int @ S )
% 0.25/0.56 => ~ ( finite_finite_int @ T ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % infinite_super
% 0.25/0.56 thf(fact_91_rev__finite__subset,axiom,
% 0.25/0.56 ! [B3: set_real,A2: set_real] :
% 0.25/0.56 ( ( finite_finite_real @ B3 )
% 0.25/0.56 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.25/0.56 => ( finite_finite_real @ A2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % rev_finite_subset
% 0.25/0.56 thf(fact_92_rev__finite__subset,axiom,
% 0.25/0.56 ! [B3: set_int,A2: set_int] :
% 0.25/0.56 ( ( finite_finite_int @ B3 )
% 0.25/0.56 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.25/0.56 => ( finite_finite_int @ A2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % rev_finite_subset
% 0.25/0.56 thf(fact_93_dual__order_Oantisym,axiom,
% 0.25/0.56 ! [B: real,A: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ B @ A )
% 0.25/0.56 => ( ( ord_less_eq_real @ A @ B )
% 0.25/0.56 => ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.antisym
% 0.25/0.56 thf(fact_94_dual__order_Oantisym,axiom,
% 0.25/0.56 ! [B: int,A: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ B @ A )
% 0.25/0.56 => ( ( ord_less_eq_int @ A @ B )
% 0.25/0.56 => ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.antisym
% 0.25/0.56 thf(fact_95_dual__order_Oeq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: real,Z4: real] : ( Y3 = Z4 ) )
% 0.25/0.56 = ( ^ [A4: real,B4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ B4 @ A4 )
% 0.25/0.56 & ( ord_less_eq_real @ A4 @ B4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.eq_iff
% 0.25/0.56 thf(fact_96_dual__order_Oeq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: int,Z4: int] : ( Y3 = Z4 ) )
% 0.25/0.56 = ( ^ [A4: int,B4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ B4 @ A4 )
% 0.25/0.56 & ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.eq_iff
% 0.25/0.56 thf(fact_97_dual__order_Otrans,axiom,
% 0.25/0.56 ! [B: real,A: real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ B @ A )
% 0.25/0.56 => ( ( ord_less_eq_real @ C2 @ B )
% 0.25/0.56 => ( ord_less_eq_real @ C2 @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.trans
% 0.25/0.56 thf(fact_98_dual__order_Otrans,axiom,
% 0.25/0.56 ! [B: int,A: int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ B @ A )
% 0.25/0.56 => ( ( ord_less_eq_int @ C2 @ B )
% 0.25/0.56 => ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.trans
% 0.25/0.56 thf(fact_99_linorder__wlog,axiom,
% 0.25/0.56 ! [P: real > real > $o,A: real,B: real] :
% 0.25/0.56 ( ! [A5: real,B6: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A5 @ B6 )
% 0.25/0.56 => ( P @ A5 @ B6 ) )
% 0.25/0.56 => ( ! [A5: real,B6: real] :
% 0.25/0.56 ( ( P @ B6 @ A5 )
% 0.25/0.56 => ( P @ A5 @ B6 ) )
% 0.25/0.56 => ( P @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_wlog
% 0.25/0.56 thf(fact_100_linorder__wlog,axiom,
% 0.25/0.56 ! [P: int > int > $o,A: int,B: int] :
% 0.25/0.56 ( ! [A5: int,B6: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A5 @ B6 )
% 0.25/0.56 => ( P @ A5 @ B6 ) )
% 0.25/0.56 => ( ! [A5: int,B6: int] :
% 0.25/0.56 ( ( P @ B6 @ A5 )
% 0.25/0.56 => ( P @ A5 @ B6 ) )
% 0.25/0.56 => ( P @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_wlog
% 0.25/0.56 thf(fact_101_dual__order_Orefl,axiom,
% 0.25/0.56 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.refl
% 0.25/0.56 thf(fact_102_dual__order_Orefl,axiom,
% 0.25/0.56 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.refl
% 0.25/0.56 thf(fact_103_order__trans,axiom,
% 0.25/0.56 ! [X2: real,Y2: real,Z3: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.56 => ( ( ord_less_eq_real @ Y2 @ Z3 )
% 0.25/0.56 => ( ord_less_eq_real @ X2 @ Z3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_trans
% 0.25/0.56 thf(fact_104_order__trans,axiom,
% 0.25/0.56 ! [X2: int,Y2: int,Z3: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.56 => ( ( ord_less_eq_int @ Y2 @ Z3 )
% 0.25/0.56 => ( ord_less_eq_int @ X2 @ Z3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_trans
% 0.25/0.56 thf(fact_105_order__class_Oorder_Oantisym,axiom,
% 0.25/0.56 ! [A: real,B: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_real @ B @ A )
% 0.25/0.56 => ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_class.order.antisym
% 0.25/0.56 thf(fact_106_order__class_Oorder_Oantisym,axiom,
% 0.25/0.56 ! [A: int,B: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_int @ B @ A )
% 0.25/0.56 => ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_class.order.antisym
% 0.25/0.56 thf(fact_107_ord__le__eq__trans,axiom,
% 0.25/0.56 ! [A: real,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.56 => ( ( B = C2 )
% 0.25/0.56 => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_trans
% 0.25/0.56 thf(fact_108_ord__le__eq__trans,axiom,
% 0.25/0.56 ! [A: int,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.56 => ( ( B = C2 )
% 0.25/0.56 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_trans
% 0.25/0.56 thf(fact_109_ord__eq__le__trans,axiom,
% 0.25/0.56 ! [A: real,B: real,C2: real] :
% 0.25/0.56 ( ( A = B )
% 0.25/0.56 => ( ( ord_less_eq_real @ B @ C2 )
% 0.25/0.56 => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_trans
% 0.25/0.56 thf(fact_110_ord__eq__le__trans,axiom,
% 0.25/0.56 ! [A: int,B: int,C2: int] :
% 0.25/0.56 ( ( A = B )
% 0.25/0.56 => ( ( ord_less_eq_int @ B @ C2 )
% 0.25/0.56 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_trans
% 0.25/0.56 thf(fact_111_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: real,Z4: real] : ( Y3 = Z4 ) )
% 0.25/0.56 = ( ^ [A4: real,B4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A4 @ B4 )
% 0.25/0.56 & ( ord_less_eq_real @ B4 @ A4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_class.order.eq_iff
% 0.25/0.56 thf(fact_112_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: int,Z4: int] : ( Y3 = Z4 ) )
% 0.25/0.56 = ( ^ [A4: int,B4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A4 @ B4 )
% 0.25/0.56 & ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_class.order.eq_iff
% 0.25/0.56 thf(fact_113_antisym__conv,axiom,
% 0.25/0.56 ! [Y2: real,X2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.25/0.56 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.56 = ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv
% 0.25/0.56 thf(fact_114_antisym__conv,axiom,
% 0.25/0.56 ! [Y2: int,X2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ Y2 @ X2 )
% 0.25/0.56 => ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.56 = ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv
% 0.25/0.56 thf(fact_115_le__cases3,axiom,
% 0.25/0.56 ! [X2: real,Y2: real,Z3: real] :
% 0.25/0.56 ( ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_eq_real @ Y2 @ Z3 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.25/0.56 => ~ ( ord_less_eq_real @ X2 @ Z3 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_real @ X2 @ Z3 )
% 0.25/0.56 => ~ ( ord_less_eq_real @ Z3 @ Y2 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_real @ Z3 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_eq_real @ Y2 @ X2 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_real @ Y2 @ Z3 )
% 0.25/0.56 => ~ ( ord_less_eq_real @ Z3 @ X2 ) )
% 0.25/0.56 => ~ ( ( ord_less_eq_real @ Z3 @ X2 )
% 0.25/0.56 => ~ ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_cases3
% 0.25/0.56 thf(fact_116_le__cases3,axiom,
% 0.25/0.56 ! [X2: int,Y2: int,Z3: int] :
% 0.25/0.56 ( ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_eq_int @ Y2 @ Z3 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_int @ Y2 @ X2 )
% 0.25/0.56 => ~ ( ord_less_eq_int @ X2 @ Z3 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_int @ X2 @ Z3 )
% 0.25/0.56 => ~ ( ord_less_eq_int @ Z3 @ Y2 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_int @ Z3 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_eq_int @ Y2 @ X2 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_int @ Y2 @ Z3 )
% 0.25/0.56 => ~ ( ord_less_eq_int @ Z3 @ X2 ) )
% 0.25/0.56 => ~ ( ( ord_less_eq_int @ Z3 @ X2 )
% 0.25/0.56 => ~ ( ord_less_eq_int @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_cases3
% 0.25/0.56 thf(fact_117_order_Otrans,axiom,
% 0.25/0.56 ! [A: real,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_real @ B @ C2 )
% 0.25/0.56 => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.trans
% 0.25/0.56 thf(fact_118_order_Otrans,axiom,
% 0.25/0.56 ! [A: int,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_int @ B @ C2 )
% 0.25/0.56 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.trans
% 0.25/0.56 thf(fact_119_le__cases,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ~ ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_cases
% 0.25/0.56 thf(fact_120_le__cases,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ~ ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_cases
% 0.25/0.56 thf(fact_121_eq__refl,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( X2 = Y2 )
% 0.25/0.56 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_refl
% 0.25/0.56 thf(fact_122_eq__refl,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( X2 = Y2 )
% 0.25/0.56 => ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_refl
% 0.25/0.56 thf(fact_123_linear,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.56 | ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % linear
% 0.25/0.56 thf(fact_124_linear,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.56 | ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % linear
% 0.25/0.56 thf(fact_125_antisym,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.56 => ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.25/0.56 => ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym
% 0.25/0.56 thf(fact_126_antisym,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.56 => ( ( ord_less_eq_int @ Y2 @ X2 )
% 0.25/0.56 => ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym
% 0.25/0.56 thf(fact_127_eq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: real,Z4: real] : ( Y3 = Z4 ) )
% 0.25/0.56 = ( ^ [X: real,Y: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X @ Y )
% 0.25/0.56 & ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_iff
% 0.25/0.56 thf(fact_128_eq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: int,Z4: int] : ( Y3 = Z4 ) )
% 0.25/0.56 = ( ^ [X: int,Y: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X @ Y )
% 0.25/0.56 & ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_iff
% 0.25/0.56 thf(fact_129_ord__le__eq__subst,axiom,
% 0.25/0.56 ! [A: real,B: real,F: real > real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_subst
% 0.25/0.56 thf(fact_130_ord__le__eq__subst,axiom,
% 0.25/0.56 ! [A: real,B: real,F: real > int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_subst
% 0.25/0.56 thf(fact_131_ord__le__eq__subst,axiom,
% 0.25/0.56 ! [A: int,B: int,F: int > real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_subst
% 0.25/0.56 thf(fact_132_ord__le__eq__subst,axiom,
% 0.25/0.56 ! [A: int,B: int,F: int > int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_subst
% 0.25/0.56 thf(fact_133_ord__eq__le__subst,axiom,
% 0.25/0.56 ! [A: real,F: real > real,B: real,C2: real] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_subst
% 0.25/0.56 thf(fact_134_ord__eq__le__subst,axiom,
% 0.25/0.56 ! [A: int,F: real > int,B: real,C2: real] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_subst
% 0.25/0.56 thf(fact_135_ord__eq__le__subst,axiom,
% 0.25/0.56 ! [A: real,F: int > real,B: int,C2: int] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_subst
% 0.25/0.56 thf(fact_136_ord__eq__le__subst,axiom,
% 0.25/0.56 ! [A: int,F: int > int,B: int,C2: int] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_subst
% 0.25/0.56 thf(fact_137_order__subst2,axiom,
% 0.25/0.56 ! [A: real,B: real,F: real > real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_138_order__subst2,axiom,
% 0.25/0.56 ! [A: real,B: real,F: real > int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_139_order__subst2,axiom,
% 0.25/0.56 ! [A: int,B: int,F: int > real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_140_order__subst2,axiom,
% 0.25/0.56 ! [A: int,B: int,F: int > int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_141_order__subst1,axiom,
% 0.25/0.56 ! [A: real,F: real > real,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_142_order__subst1,axiom,
% 0.25/0.56 ! [A: real,F: int > real,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_143_order__subst1,axiom,
% 0.25/0.56 ! [A: int,F: real > int,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_144_order__subst1,axiom,
% 0.25/0.56 ! [A: int,F: int > int,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_145_ord__eq__less__subst,axiom,
% 0.25/0.56 ! [A: real,F: real > real,B: real,C2: real] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_less_subst
% 0.25/0.56 thf(fact_146_ord__eq__less__subst,axiom,
% 0.25/0.56 ! [A: int,F: real > int,B: real,C2: real] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_less_subst
% 0.25/0.56 thf(fact_147_ord__eq__less__subst,axiom,
% 0.25/0.56 ! [A: real,F: int > real,B: int,C2: int] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_less_subst
% 0.25/0.56 thf(fact_148_ord__eq__less__subst,axiom,
% 0.25/0.56 ! [A: int,F: int > int,B: int,C2: int] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_less_subst
% 0.25/0.56 thf(fact_149_ord__less__eq__subst,axiom,
% 0.25/0.56 ! [A: real,B: real,F: real > real,C2: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_less_eq_subst
% 0.25/0.56 thf(fact_150_ord__less__eq__subst,axiom,
% 0.25/0.56 ! [A: real,B: real,F: real > int,C2: int] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_less_eq_subst
% 0.25/0.56 thf(fact_151_ord__less__eq__subst,axiom,
% 0.25/0.56 ! [A: int,B: int,F: int > real,C2: real] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_less_eq_subst
% 0.25/0.56 thf(fact_152_ord__less__eq__subst,axiom,
% 0.25/0.56 ! [A: int,B: int,F: int > int,C2: int] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_less_eq_subst
% 0.25/0.56 thf(fact_153_order__less__subst1,axiom,
% 0.25/0.56 ! [A: real,F: real > real,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst1
% 0.25/0.56 thf(fact_154_order__less__subst1,axiom,
% 0.25/0.56 ! [A: real,F: int > real,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst1
% 0.25/0.56 thf(fact_155_order__less__subst1,axiom,
% 0.25/0.56 ! [A: int,F: real > int,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_int @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst1
% 0.25/0.56 thf(fact_156_order__less__subst1,axiom,
% 0.25/0.56 ! [A: int,F: int > int,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_int @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst1
% 0.25/0.56 thf(fact_157_order__less__subst2,axiom,
% 0.25/0.56 ! [A: real,B: real,F: real > real,C2: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst2
% 0.25/0.56 thf(fact_158_order__less__subst2,axiom,
% 0.25/0.56 ! [A: real,B: real,F: real > int,C2: int] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst2
% 0.25/0.56 thf(fact_159_order__less__subst2,axiom,
% 0.25/0.56 ! [A: int,B: int,F: int > real,C2: real] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst2
% 0.25/0.56 thf(fact_160_order__less__subst2,axiom,
% 0.25/0.56 ! [A: int,B: int,F: int > int,C2: int] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst2
% 0.25/0.56 thf(fact_161_lt__ex,axiom,
% 0.25/0.56 ! [X2: real] :
% 0.25/0.56 ? [Y4: real] : ( ord_less_real @ Y4 @ X2 ) ).
% 0.25/0.56
% 0.25/0.56 % lt_ex
% 0.25/0.56 thf(fact_162_lt__ex,axiom,
% 0.25/0.56 ! [X2: int] :
% 0.25/0.56 ? [Y4: int] : ( ord_less_int @ Y4 @ X2 ) ).
% 0.25/0.56
% 0.25/0.56 % lt_ex
% 0.25/0.56 thf(fact_163_gt__ex,axiom,
% 0.25/0.56 ! [X2: real] :
% 0.25/0.56 ? [X_1: real] : ( ord_less_real @ X2 @ X_1 ) ).
% 0.25/0.56
% 0.25/0.56 % gt_ex
% 0.25/0.56 thf(fact_164_gt__ex,axiom,
% 0.25/0.56 ! [X2: int] :
% 0.25/0.56 ? [X_1: int] : ( ord_less_int @ X2 @ X_1 ) ).
% 0.25/0.56
% 0.25/0.56 % gt_ex
% 0.25/0.56 thf(fact_165_neqE,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( X2 != Y2 )
% 0.25/0.56 => ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % neqE
% 0.25/0.56 thf(fact_166_neqE,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( X2 != Y2 )
% 0.25/0.56 => ( ~ ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % neqE
% 0.25/0.56 thf(fact_167_neq__iff,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( X2 != Y2 )
% 0.25/0.56 = ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 | ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % neq_iff
% 0.25/0.56 thf(fact_168_neq__iff,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( X2 != Y2 )
% 0.25/0.56 = ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 | ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % neq_iff
% 0.25/0.56 thf(fact_169_order_Oasym,axiom,
% 0.25/0.56 ! [A: real,B: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ~ ( ord_less_real @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.asym
% 0.25/0.56 thf(fact_170_order_Oasym,axiom,
% 0.25/0.56 ! [A: int,B: int] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ~ ( ord_less_int @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.asym
% 0.25/0.56 thf(fact_171_dense,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ? [Z5: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Z5 )
% 0.25/0.56 & ( ord_less_real @ Z5 @ Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dense
% 0.25/0.56 thf(fact_172_less__imp__neq,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ( X2 != Y2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_neq
% 0.25/0.56 thf(fact_173_less__imp__neq,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ( X2 != Y2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_neq
% 0.25/0.56 thf(fact_174_less__asym,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_asym
% 0.25/0.56 thf(fact_175_less__asym,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_asym
% 0.25/0.56 thf(fact_176_less__asym_H,axiom,
% 0.25/0.56 ! [A: real,B: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ~ ( ord_less_real @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_asym'
% 0.25/0.56 thf(fact_177_less__asym_H,axiom,
% 0.25/0.56 ! [A: int,B: int] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ~ ( ord_less_int @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_asym'
% 0.25/0.56 thf(fact_178_less__trans,axiom,
% 0.25/0.56 ! [X2: real,Y2: real,Z3: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ( ( ord_less_real @ Y2 @ Z3 )
% 0.25/0.56 => ( ord_less_real @ X2 @ Z3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_trans
% 0.25/0.56 thf(fact_179_less__trans,axiom,
% 0.25/0.56 ! [X2: int,Y2: int,Z3: int] :
% 0.25/0.56 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ( ( ord_less_int @ Y2 @ Z3 )
% 0.25/0.56 => ( ord_less_int @ X2 @ Z3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_trans
% 0.25/0.56 thf(fact_180_less__linear,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 | ( X2 = Y2 )
% 0.25/0.56 | ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_linear
% 0.25/0.56 thf(fact_181_less__linear,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 | ( X2 = Y2 )
% 0.25/0.56 | ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_linear
% 0.25/0.56 thf(fact_182_less__irrefl,axiom,
% 0.25/0.56 ! [X2: real] :
% 0.25/0.56 ~ ( ord_less_real @ X2 @ X2 ) ).
% 0.25/0.56
% 0.25/0.56 % less_irrefl
% 0.25/0.56 thf(fact_183_less__irrefl,axiom,
% 0.25/0.56 ! [X2: int] :
% 0.25/0.56 ~ ( ord_less_int @ X2 @ X2 ) ).
% 0.25/0.56
% 0.25/0.56 % less_irrefl
% 0.25/0.56 thf(fact_184_ord__eq__less__trans,axiom,
% 0.25/0.56 ! [A: real,B: real,C2: real] :
% 0.25/0.56 ( ( A = B )
% 0.25/0.56 => ( ( ord_less_real @ B @ C2 )
% 0.25/0.56 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_less_trans
% 0.25/0.56 thf(fact_185_ord__eq__less__trans,axiom,
% 0.25/0.56 ! [A: int,B: int,C2: int] :
% 0.25/0.56 ( ( A = B )
% 0.25/0.56 => ( ( ord_less_int @ B @ C2 )
% 0.25/0.56 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_less_trans
% 0.25/0.56 thf(fact_186_ord__less__eq__trans,axiom,
% 0.25/0.56 ! [A: real,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ( B = C2 )
% 0.25/0.56 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_less_eq_trans
% 0.25/0.56 thf(fact_187_ord__less__eq__trans,axiom,
% 0.25/0.56 ! [A: int,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ( ( B = C2 )
% 0.25/0.56 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_less_eq_trans
% 0.25/0.56 thf(fact_188_dual__order_Oasym,axiom,
% 0.25/0.56 ! [B: real,A: real] :
% 0.25/0.56 ( ( ord_less_real @ B @ A )
% 0.25/0.56 => ~ ( ord_less_real @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.asym
% 0.25/0.56 thf(fact_189_dual__order_Oasym,axiom,
% 0.25/0.56 ! [B: int,A: int] :
% 0.25/0.56 ( ( ord_less_int @ B @ A )
% 0.25/0.56 => ~ ( ord_less_int @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.asym
% 0.25/0.56 thf(fact_190_less__imp__not__eq,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ( X2 != Y2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_not_eq
% 0.25/0.56 thf(fact_191_less__imp__not__eq,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ( X2 != Y2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_not_eq
% 0.25/0.56 thf(fact_192_less__not__sym,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_not_sym
% 0.25/0.56 thf(fact_193_less__not__sym,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_not_sym
% 0.25/0.56 thf(fact_194_antisym__conv3,axiom,
% 0.25/0.56 ! [Y2: real,X2: real] :
% 0.25/0.56 ( ~ ( ord_less_real @ Y2 @ X2 )
% 0.25/0.56 => ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 0.25/0.56 = ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv3
% 0.25/0.56 thf(fact_195_antisym__conv3,axiom,
% 0.25/0.56 ! [Y2: int,X2: int] :
% 0.25/0.56 ( ~ ( ord_less_int @ Y2 @ X2 )
% 0.25/0.56 => ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 0.25/0.56 = ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv3
% 0.25/0.56 thf(fact_196_less__imp__not__eq2,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ( Y2 != X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_not_eq2
% 0.25/0.56 thf(fact_197_less__imp__not__eq2,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ( Y2 != X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_not_eq2
% 0.25/0.56 thf(fact_198_less__imp__triv,axiom,
% 0.25/0.56 ! [X2: real,Y2: real,P: $o] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ( ( ord_less_real @ Y2 @ X2 )
% 0.25/0.56 => P ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_triv
% 0.25/0.56 thf(fact_199_less__imp__triv,axiom,
% 0.25/0.56 ! [X2: int,Y2: int,P: $o] :
% 0.25/0.56 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ( ( ord_less_int @ Y2 @ X2 )
% 0.25/0.56 => P ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_triv
% 0.25/0.56 thf(fact_200_linorder__cases,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ( ( X2 != Y2 )
% 0.25/0.56 => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_cases
% 0.25/0.56 thf(fact_201_linorder__cases,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ~ ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ( ( X2 != Y2 )
% 0.25/0.56 => ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_cases
% 0.25/0.56 thf(fact_202_dual__order_Oirrefl,axiom,
% 0.25/0.56 ! [A: real] :
% 0.25/0.56 ~ ( ord_less_real @ A @ A ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.irrefl
% 0.25/0.56 thf(fact_203_dual__order_Oirrefl,axiom,
% 0.25/0.56 ! [A: int] :
% 0.25/0.56 ~ ( ord_less_int @ A @ A ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.irrefl
% 0.25/0.56 thf(fact_204_order_Ostrict__trans,axiom,
% 0.25/0.56 ! [A: real,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( ( ord_less_real @ B @ C2 )
% 0.25/0.56 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_trans
% 0.25/0.56 thf(fact_205_order_Ostrict__trans,axiom,
% 0.25/0.56 ! [A: int,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ( ( ord_less_int @ B @ C2 )
% 0.25/0.56 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_trans
% 0.25/0.56 thf(fact_206_less__imp__not__less,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_not_less
% 0.25/0.56 thf(fact_207_less__imp__not__less,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ~ ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_not_less
% 0.25/0.56 thf(fact_208_linorder__less__wlog,axiom,
% 0.25/0.56 ! [P: real > real > $o,A: real,B: real] :
% 0.25/0.56 ( ! [A5: real,B6: real] :
% 0.25/0.56 ( ( ord_less_real @ A5 @ B6 )
% 0.25/0.56 => ( P @ A5 @ B6 ) )
% 0.25/0.56 => ( ! [A5: real] : ( P @ A5 @ A5 )
% 0.25/0.56 => ( ! [A5: real,B6: real] :
% 0.25/0.56 ( ( P @ B6 @ A5 )
% 0.25/0.56 => ( P @ A5 @ B6 ) )
% 0.25/0.56 => ( P @ A @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_less_wlog
% 0.25/0.56 thf(fact_209_linorder__less__wlog,axiom,
% 0.25/0.56 ! [P: int > int > $o,A: int,B: int] :
% 0.25/0.56 ( ! [A5: int,B6: int] :
% 0.25/0.56 ( ( ord_less_int @ A5 @ B6 )
% 0.25/0.56 => ( P @ A5 @ B6 ) )
% 0.25/0.56 => ( ! [A5: int] : ( P @ A5 @ A5 )
% 0.25/0.56 => ( ! [A5: int,B6: int] :
% 0.25/0.56 ( ( P @ B6 @ A5 )
% 0.25/0.56 => ( P @ A5 @ B6 ) )
% 0.25/0.56 => ( P @ A @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_less_wlog
% 0.25/0.56 thf(fact_210_dual__order_Ostrict__trans,axiom,
% 0.25/0.56 ! [B: real,A: real,C2: real] :
% 0.25/0.56 ( ( ord_less_real @ B @ A )
% 0.25/0.56 => ( ( ord_less_real @ C2 @ B )
% 0.25/0.56 => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_trans
% 0.25/0.56 thf(fact_211_dual__order_Ostrict__trans,axiom,
% 0.25/0.56 ! [B: int,A: int,C2: int] :
% 0.25/0.56 ( ( ord_less_int @ B @ A )
% 0.25/0.56 => ( ( ord_less_int @ C2 @ B )
% 0.25/0.56 => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_trans
% 0.25/0.56 thf(fact_212_not__less__iff__gr__or__eq,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 0.25/0.56 = ( ( ord_less_real @ Y2 @ X2 )
% 0.25/0.56 | ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_less_iff_gr_or_eq
% 0.25/0.56 thf(fact_213_not__less__iff__gr__or__eq,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 0.25/0.56 = ( ( ord_less_int @ Y2 @ X2 )
% 0.25/0.56 | ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_less_iff_gr_or_eq
% 0.25/0.56 thf(fact_214_order_Ostrict__implies__not__eq,axiom,
% 0.25/0.56 ! [A: real,B: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B )
% 0.25/0.56 => ( A != B ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_implies_not_eq
% 0.25/0.56 thf(fact_215_order_Ostrict__implies__not__eq,axiom,
% 0.25/0.56 ! [A: int,B: int] :
% 0.25/0.56 ( ( ord_less_int @ A @ B )
% 0.25/0.56 => ( A != B ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_implies_not_eq
% 0.25/0.56 thf(fact_216_dual__order_Ostrict__implies__not__eq,axiom,
% 0.25/0.56 ! [B: real,A: real] :
% 0.25/0.56 ( ( ord_less_real @ B @ A )
% 0.25/0.56 => ( A != B ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_implies_not_eq
% 0.25/0.56 thf(fact_217_dual__order_Ostrict__implies__not__eq,axiom,
% 0.25/0.56 ! [B: int,A: int] :
% 0.25/0.56 ( ( ord_less_int @ B @ A )
% 0.25/0.56 => ( A != B ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_implies_not_eq
% 0.25/0.56 thf(fact_218_ex__gt__or__lt,axiom,
% 0.25/0.56 ! [A: real] :
% 0.25/0.56 ? [B6: real] :
% 0.25/0.56 ( ( ord_less_real @ A @ B6 )
% 0.25/0.56 | ( ord_less_real @ B6 @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % ex_gt_or_lt
% 0.25/0.56 thf(fact_219_complete__real,axiom,
% 0.25/0.56 ! [S: set_real] :
% 0.25/0.56 ( ? [X3: real] : ( member_real @ X3 @ S )
% 0.25/0.56 => ( ? [Z: real] :
% 0.25/0.56 ! [X4: real] :
% 0.25/0.56 ( ( member_real @ X4 @ S )
% 0.25/0.56 => ( ord_less_eq_real @ X4 @ Z ) )
% 0.25/0.56 => ? [Y4: real] :
% 0.25/0.56 ( ! [X3: real] :
% 0.25/0.56 ( ( member_real @ X3 @ S )
% 0.25/0.56 => ( ord_less_eq_real @ X3 @ Y4 ) )
% 0.25/0.56 & ! [Z: real] :
% 0.25/0.56 ( ! [X4: real] :
% 0.25/0.56 ( ( member_real @ X4 @ S )
% 0.25/0.56 => ( ord_less_eq_real @ X4 @ Z ) )
% 0.25/0.56 => ( ord_less_eq_real @ Y4 @ Z ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % complete_real
% 0.25/0.56 thf(fact_220_field__lbound__gt__zero,axiom,
% 0.25/0.56 ! [D1: real,D2: real] :
% 0.25/0.56 ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.25/0.56 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.25/0.56 => ? [E: real] :
% 0.25/0.56 ( ( ord_less_real @ zero_zero_real @ E )
% 0.25/0.56 & ( ord_less_real @ E @ D1 )
% 0.25/0.56 & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % field_lbound_gt_zero
% 0.25/0.56 thf(fact_221_leD,axiom,
% 0.25/0.56 ! [Y2: real,X2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.25/0.56 => ~ ( ord_less_real @ X2 @ Y2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % leD
% 0.25/0.56 thf(fact_222_leD,axiom,
% 0.25/0.56 ! [Y2: int,X2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ Y2 @ X2 )
% 0.25/0.56 => ~ ( ord_less_int @ X2 @ Y2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % leD
% 0.25/0.56 thf(fact_223_leI,axiom,
% 0.25/0.56 ! [X2: real,Y2: real] :
% 0.25/0.56 ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % leI
% 0.25/0.56 thf(fact_224_leI,axiom,
% 0.25/0.56 ! [X2: int,Y2: int] :
% 0.25/0.56 ( ~ ( ord_less_int @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % leI
% 0.25/0.56 thf(fact_225_le__less,axiom,
% 0.25/0.56 ( ord_less_eq_real
% 0.25/0.56 = ( ^ [X: real,Y: real] :
% 0.25/0.56 ( ( ord_less_real @ X @ Y )
% 0.25/0.56 | ( X = Y ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_less
% 0.25/0.56 thf(fact_226_le__less,axiom,
% 0.25/0.56 ( ord_less_eq_int
% 0.25/0.56 = ( ^ [X: int,Y: int] :
% 0.25/0.56 ( ( ord_less_int @ X @ Y )
% 0.25/0.56 | ( X = Y ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_less
% 0.25/0.56 thf(fact_227_less__le,axiom,
% 0.25/0.56 ( ord_less_real
% 0.25/0.56 = ( ^ [X: real,Y: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ X @ Y )
% 0.25/0.56 & ( X != Y ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_le
% 0.25/0.56 thf(fact_228_less__le,axiom,
% 0.25/0.56 ( ord_less_int
% 0.25/0.56 = ( ^ [X: int,Y: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ X @ Y )
% 0.25/0.56 & ( X != Y ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_le
% 0.25/0.56 thf(fact_229_order__le__less__subst1,axiom,
% 0.25/0.56 ! [A: real,F: real > real,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst1
% 0.25/0.56 thf(fact_230_order__le__less__subst1,axiom,
% 0.25/0.56 ! [A: real,F: int > real,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst1
% 0.25/0.56 thf(fact_231_order__le__less__subst1,axiom,
% 0.25/0.56 ! [A: int,F: real > int,B: real,C2: real] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_real @ B @ C2 )
% 0.25/0.56 => ( ! [X4: real,Y4: real] :
% 0.25/0.56 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst1
% 0.25/0.56 thf(fact_232_order__le__less__subst1,axiom,
% 0.25/0.56 ! [A: int,F: int > int,B: int,C2: int] :
% 0.25/0.56 ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_int @ B @ C2 )
% 0.25/0.56 => ( ! [X4: int,Y4: int] :
% 0.25/0.56 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.56 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.56 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst1
% 0.25/0.56 thf(fact_233_order__le__less__subst2,axiom,
% 0.25/0.56 ! [A: real,B: real,F: real > real,C2: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.57 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.25/0.57 => ( ! [X4: real,Y4: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_le_less_subst2
% 0.25/0.57 thf(fact_234_order__le__less__subst2,axiom,
% 0.25/0.57 ! [A: real,B: real,F: real > int,C2: int] :
% 0.25/0.57 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.57 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.25/0.57 => ( ! [X4: real,Y4: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_le_less_subst2
% 0.25/0.57 thf(fact_235_order__le__less__subst2,axiom,
% 0.25/0.57 ! [A: int,B: int,F: int > real,C2: real] :
% 0.25/0.57 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.57 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.25/0.57 => ( ! [X4: int,Y4: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_le_less_subst2
% 0.25/0.57 thf(fact_236_order__le__less__subst2,axiom,
% 0.25/0.57 ! [A: int,B: int,F: int > int,C2: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.57 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.25/0.57 => ( ! [X4: int,Y4: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_le_less_subst2
% 0.25/0.57 thf(fact_237_order__less__le__subst1,axiom,
% 0.25/0.57 ! [A: real,F: real > real,B: real,C2: real] :
% 0.25/0.57 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.25/0.57 => ( ( ord_less_eq_real @ B @ C2 )
% 0.25/0.57 => ( ! [X4: real,Y4: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_less_le_subst1
% 0.25/0.57 thf(fact_238_order__less__le__subst1,axiom,
% 0.25/0.57 ! [A: int,F: real > int,B: real,C2: real] :
% 0.25/0.57 ( ( ord_less_int @ A @ ( F @ B ) )
% 0.25/0.57 => ( ( ord_less_eq_real @ B @ C2 )
% 0.25/0.57 => ( ! [X4: real,Y4: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_less_le_subst1
% 0.25/0.57 thf(fact_239_order__less__le__subst1,axiom,
% 0.25/0.57 ! [A: real,F: int > real,B: int,C2: int] :
% 0.25/0.57 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.25/0.57 => ( ( ord_less_eq_int @ B @ C2 )
% 0.25/0.57 => ( ! [X4: int,Y4: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_less_le_subst1
% 0.25/0.57 thf(fact_240_order__less__le__subst1,axiom,
% 0.25/0.57 ! [A: int,F: int > int,B: int,C2: int] :
% 0.25/0.57 ( ( ord_less_int @ A @ ( F @ B ) )
% 0.25/0.57 => ( ( ord_less_eq_int @ B @ C2 )
% 0.25/0.57 => ( ! [X4: int,Y4: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_less_le_subst1
% 0.25/0.57 thf(fact_241_order__less__le__subst2,axiom,
% 0.25/0.57 ! [A: real,B: real,F: real > real,C2: real] :
% 0.25/0.57 ( ( ord_less_real @ A @ B )
% 0.25/0.57 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.25/0.57 => ( ! [X4: real,Y4: real] :
% 0.25/0.57 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_less_le_subst2
% 0.25/0.57 thf(fact_242_order__less__le__subst2,axiom,
% 0.25/0.57 ! [A: int,B: int,F: int > real,C2: real] :
% 0.25/0.57 ( ( ord_less_int @ A @ B )
% 0.25/0.57 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.25/0.57 => ( ! [X4: int,Y4: int] :
% 0.25/0.57 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_less_le_subst2
% 0.25/0.57 thf(fact_243_order__less__le__subst2,axiom,
% 0.25/0.57 ! [A: real,B: real,F: real > int,C2: int] :
% 0.25/0.57 ( ( ord_less_real @ A @ B )
% 0.25/0.57 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.25/0.57 => ( ! [X4: real,Y4: real] :
% 0.25/0.57 ( ( ord_less_real @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_less_le_subst2
% 0.25/0.57 thf(fact_244_order__less__le__subst2,axiom,
% 0.25/0.57 ! [A: int,B: int,F: int > int,C2: int] :
% 0.25/0.57 ( ( ord_less_int @ A @ B )
% 0.25/0.57 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.25/0.57 => ( ! [X4: int,Y4: int] :
% 0.25/0.57 ( ( ord_less_int @ X4 @ Y4 )
% 0.25/0.57 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.25/0.57 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order_less_le_subst2
% 0.25/0.57 thf(fact_245_not__le,axiom,
% 0.25/0.57 ! [X2: real,Y2: real] :
% 0.25/0.57 ( ( ~ ( ord_less_eq_real @ X2 @ Y2 ) )
% 0.25/0.57 = ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_le
% 0.25/0.57 thf(fact_246_not__le,axiom,
% 0.25/0.57 ! [X2: int,Y2: int] :
% 0.25/0.57 ( ( ~ ( ord_less_eq_int @ X2 @ Y2 ) )
% 0.25/0.57 = ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_le
% 0.25/0.57 thf(fact_247_not__less,axiom,
% 0.25/0.57 ! [X2: real,Y2: real] :
% 0.25/0.57 ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 0.25/0.57 = ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_less
% 0.25/0.57 thf(fact_248_not__less,axiom,
% 0.25/0.57 ! [X2: int,Y2: int] :
% 0.25/0.57 ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 0.25/0.57 = ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_less
% 0.25/0.57 thf(fact_249_le__neq__trans,axiom,
% 0.25/0.57 ! [A: real,B: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.57 => ( ( A != B )
% 0.25/0.57 => ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % le_neq_trans
% 0.25/0.57 thf(fact_250_le__neq__trans,axiom,
% 0.25/0.57 ! [A: int,B: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.57 => ( ( A != B )
% 0.25/0.57 => ( ord_less_int @ A @ B ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % le_neq_trans
% 0.25/0.57 thf(fact_251_antisym__conv1,axiom,
% 0.25/0.57 ! [X2: real,Y2: real] :
% 0.25/0.57 ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.25/0.57 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.57 = ( X2 = Y2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % antisym_conv1
% 0.25/0.57 thf(fact_252_antisym__conv1,axiom,
% 0.25/0.57 ! [X2: int,Y2: int] :
% 0.25/0.57 ( ~ ( ord_less_int @ X2 @ Y2 )
% 0.25/0.57 => ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.57 = ( X2 = Y2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % antisym_conv1
% 0.25/0.57 thf(fact_253_antisym__conv2,axiom,
% 0.25/0.57 ! [X2: real,Y2: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.57 => ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 0.25/0.57 = ( X2 = Y2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % antisym_conv2
% 0.25/0.57 thf(fact_254_antisym__conv2,axiom,
% 0.25/0.57 ! [X2: int,Y2: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.57 => ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 0.25/0.57 = ( X2 = Y2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % antisym_conv2
% 0.25/0.57 thf(fact_255_less__imp__le,axiom,
% 0.25/0.57 ! [X2: real,Y2: real] :
% 0.25/0.57 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.57 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_imp_le
% 0.25/0.57 thf(fact_256_less__imp__le,axiom,
% 0.25/0.57 ! [X2: int,Y2: int] :
% 0.25/0.57 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.57 => ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_imp_le
% 0.25/0.57 thf(fact_257_le__less__trans,axiom,
% 0.25/0.57 ! [X2: real,Y2: real,Z3: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.57 => ( ( ord_less_real @ Y2 @ Z3 )
% 0.25/0.57 => ( ord_less_real @ X2 @ Z3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % le_less_trans
% 0.25/0.57 thf(fact_258_le__less__trans,axiom,
% 0.25/0.57 ! [X2: int,Y2: int,Z3: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.57 => ( ( ord_less_int @ Y2 @ Z3 )
% 0.25/0.57 => ( ord_less_int @ X2 @ Z3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % le_less_trans
% 0.25/0.57 thf(fact_259_less__le__trans,axiom,
% 0.25/0.57 ! [X2: real,Y2: real,Z3: real] :
% 0.25/0.57 ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.57 => ( ( ord_less_eq_real @ Y2 @ Z3 )
% 0.25/0.57 => ( ord_less_real @ X2 @ Z3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_le_trans
% 0.25/0.57 thf(fact_260_less__le__trans,axiom,
% 0.25/0.57 ! [X2: int,Y2: int,Z3: int] :
% 0.25/0.57 ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.57 => ( ( ord_less_eq_int @ Y2 @ Z3 )
% 0.25/0.57 => ( ord_less_int @ X2 @ Z3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_le_trans
% 0.25/0.57 thf(fact_261_dense__ge,axiom,
% 0.25/0.57 ! [Z3: real,Y2: real] :
% 0.25/0.57 ( ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ Z3 @ X4 )
% 0.25/0.57 => ( ord_less_eq_real @ Y2 @ X4 ) )
% 0.25/0.57 => ( ord_less_eq_real @ Y2 @ Z3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % dense_ge
% 0.25/0.57 thf(fact_262_dense__le,axiom,
% 0.25/0.57 ! [Y2: real,Z3: real] :
% 0.25/0.57 ( ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ X4 @ Y2 )
% 0.25/0.57 => ( ord_less_eq_real @ X4 @ Z3 ) )
% 0.25/0.57 => ( ord_less_eq_real @ Y2 @ Z3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % dense_le
% 0.25/0.57 thf(fact_263_le__less__linear,axiom,
% 0.25/0.57 ! [X2: real,Y2: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.57 | ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % le_less_linear
% 0.25/0.57 thf(fact_264_le__less__linear,axiom,
% 0.25/0.57 ! [X2: int,Y2: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.57 | ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % le_less_linear
% 0.25/0.57 thf(fact_265_le__imp__less__or__eq,axiom,
% 0.25/0.57 ! [X2: real,Y2: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.25/0.57 => ( ( ord_less_real @ X2 @ Y2 )
% 0.25/0.57 | ( X2 = Y2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % le_imp_less_or_eq
% 0.25/0.57 thf(fact_266_le__imp__less__or__eq,axiom,
% 0.25/0.57 ! [X2: int,Y2: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.25/0.57 => ( ( ord_less_int @ X2 @ Y2 )
% 0.25/0.57 | ( X2 = Y2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % le_imp_less_or_eq
% 0.25/0.57 thf(fact_267_less__le__not__le,axiom,
% 0.25/0.57 ( ord_less_real
% 0.25/0.57 = ( ^ [X: real,Y: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ X @ Y )
% 0.25/0.57 & ~ ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_le_not_le
% 0.25/0.57 thf(fact_268_less__le__not__le,axiom,
% 0.25/0.57 ( ord_less_int
% 0.25/0.57 = ( ^ [X: int,Y: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ X @ Y )
% 0.25/0.57 & ~ ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_le_not_le
% 0.25/0.57 thf(fact_269_not__le__imp__less,axiom,
% 0.25/0.57 ! [Y2: real,X2: real] :
% 0.25/0.57 ( ~ ( ord_less_eq_real @ Y2 @ X2 )
% 0.25/0.57 => ( ord_less_real @ X2 @ Y2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_le_imp_less
% 0.25/0.57 thf(fact_270_not__le__imp__less,axiom,
% 0.25/0.57 ! [Y2: int,X2: int] :
% 0.25/0.57 ( ~ ( ord_less_eq_int @ Y2 @ X2 )
% 0.25/0.57 => ( ord_less_int @ X2 @ Y2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_le_imp_less
% 0.25/0.57 thf(fact_271_order_Ostrict__trans1,axiom,
% 0.25/0.57 ! [A: real,B: real,C2: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ A @ B )
% 0.25/0.57 => ( ( ord_less_real @ B @ C2 )
% 0.25/0.57 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order.strict_trans1
% 0.25/0.57 thf(fact_272_order_Ostrict__trans1,axiom,
% 0.25/0.57 ! [A: int,B: int,C2: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ A @ B )
% 0.25/0.57 => ( ( ord_less_int @ B @ C2 )
% 0.25/0.57 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order.strict_trans1
% 0.25/0.57 thf(fact_273_order_Ostrict__trans2,axiom,
% 0.25/0.57 ! [A: real,B: real,C2: real] :
% 0.25/0.57 ( ( ord_less_real @ A @ B )
% 0.25/0.57 => ( ( ord_less_eq_real @ B @ C2 )
% 0.25/0.57 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order.strict_trans2
% 0.25/0.57 thf(fact_274_order_Ostrict__trans2,axiom,
% 0.25/0.57 ! [A: int,B: int,C2: int] :
% 0.25/0.57 ( ( ord_less_int @ A @ B )
% 0.25/0.57 => ( ( ord_less_eq_int @ B @ C2 )
% 0.25/0.57 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order.strict_trans2
% 0.25/0.57 thf(fact_275_order_Oorder__iff__strict,axiom,
% 0.25/0.57 ( ord_less_eq_real
% 0.25/0.57 = ( ^ [A4: real,B4: real] :
% 0.25/0.57 ( ( ord_less_real @ A4 @ B4 )
% 0.25/0.57 | ( A4 = B4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order.order_iff_strict
% 0.25/0.57 thf(fact_276_order_Oorder__iff__strict,axiom,
% 0.25/0.57 ( ord_less_eq_int
% 0.25/0.57 = ( ^ [A4: int,B4: int] :
% 0.25/0.57 ( ( ord_less_int @ A4 @ B4 )
% 0.25/0.57 | ( A4 = B4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order.order_iff_strict
% 0.25/0.57 thf(fact_277_order_Ostrict__iff__order,axiom,
% 0.25/0.57 ( ord_less_real
% 0.25/0.57 = ( ^ [A4: real,B4: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ A4 @ B4 )
% 0.25/0.57 & ( A4 != B4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order.strict_iff_order
% 0.25/0.57 thf(fact_278_order_Ostrict__iff__order,axiom,
% 0.25/0.57 ( ord_less_int
% 0.25/0.57 = ( ^ [A4: int,B4: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ A4 @ B4 )
% 0.25/0.57 & ( A4 != B4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % order.strict_iff_order
% 0.25/0.57 thf(fact_279_dual__order_Ostrict__trans1,axiom,
% 0.25/0.57 ! [B: real,A: real,C2: real] :
% 0.25/0.57 ( ( ord_less_eq_real @ B @ A )
% 0.25/0.57 => ( ( ord_less_real @ C2 @ B )
% 0.25/0.57 => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % dual_order.strict_trans1
% 0.25/0.57 thf(fact_280_dual__order_Ostrict__trans1,axiom,
% 0.25/0.57 ! [B: int,A: int,C2: int] :
% 0.25/0.57 ( ( ord_less_eq_int @ B @ A )
% 0.25/0.57 => ( ( ord_less_int @ C2 @ B )
% 0.25/0.57 => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % dual_order.strict_trans1
% 0.25/0.57 thf(fact_281_dual__order_Ostrict__trans2,axiom,
% 0.25/0.57 ! [B: real,A: real,C2: real] :
% 0.25/0.57 ( ( ord_less_real @ B @ A )
% 0.25/0.57 => ( ( ord_less_eq_real @ C2 @ B )
% 0.25/0.57 => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % dual_order.strict_trans2
% 0.25/0.57 thf(fact_282_dual__order_Ostrict__trans2,axiom,
% 0.25/0.57 ! [B: int,A: int,C2: int] :
% 0.25/0.57 ( ( ord_less_int @ B @ A )
% 0.25/0.57 => ( ( ord_less_eq_int @ C2 @ B )
% 0.25/0.57 => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % dual_order.strict_trans2
% 0.25/0.57 thf(fact_283_dense__ge__bounded,axiom,
% 0.25/0.57 ! [Z3: real,X2: real,Y2: real] :
% 0.25/0.57 ( ( ord_less_real @ Z3 @ X2 )
% 0.25/0.57 => ( ! [W: real] :
% 0.25/0.57 ( ( ord_less_real @ Z3 @ W )
% 0.25/0.57 => ( ( ord_less_real @ W @ X2 )
% 0.25/0.57 => ( ord_less_eq_real @ Y2 @ W ) ) )
% 0.25/0.57 => ( ord_less_eq_real @ Y2 @ Z3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % dense_ge_bounded
% 0.25/0.57 thf(fact_284_minf_I8_J,axiom,
% 0.25/0.57 ! [T2: real] :
% 0.25/0.57 ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ X3 @ Z5 )
% 0.25/0.57 => ~ ( ord_less_eq_real @ T2 @ X3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % minf(8)
% 0.25/0.57 thf(fact_285_minf_I8_J,axiom,
% 0.25/0.57 ! [T2: int] :
% 0.25/0.57 ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ X3 @ Z5 )
% 0.25/0.57 => ~ ( ord_less_eq_int @ T2 @ X3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % minf(8)
% 0.25/0.57 thf(fact_286_minf_I6_J,axiom,
% 0.25/0.57 ! [T2: real] :
% 0.25/0.57 ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ X3 @ Z5 )
% 0.25/0.57 => ( ord_less_eq_real @ X3 @ T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % minf(6)
% 0.25/0.57 thf(fact_287_minf_I6_J,axiom,
% 0.25/0.57 ! [T2: int] :
% 0.25/0.57 ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ X3 @ Z5 )
% 0.25/0.57 => ( ord_less_eq_int @ X3 @ T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % minf(6)
% 0.25/0.57 thf(fact_288_pinf_I8_J,axiom,
% 0.25/0.57 ! [T2: real] :
% 0.25/0.57 ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ Z5 @ X3 )
% 0.25/0.57 => ( ord_less_eq_real @ T2 @ X3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(8)
% 0.25/0.57 thf(fact_289_pinf_I8_J,axiom,
% 0.25/0.57 ! [T2: int] :
% 0.25/0.57 ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ Z5 @ X3 )
% 0.25/0.57 => ( ord_less_eq_int @ T2 @ X3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(8)
% 0.25/0.57 thf(fact_290_pinf_I6_J,axiom,
% 0.25/0.57 ! [T2: real] :
% 0.25/0.57 ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ Z5 @ X3 )
% 0.25/0.57 => ~ ( ord_less_eq_real @ X3 @ T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(6)
% 0.25/0.57 thf(fact_291_pinf_I6_J,axiom,
% 0.25/0.57 ! [T2: int] :
% 0.25/0.57 ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ Z5 @ X3 )
% 0.25/0.57 => ~ ( ord_less_eq_int @ X3 @ T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(6)
% 0.25/0.57 thf(fact_292_verit__comp__simplify1_I3_J,axiom,
% 0.25/0.57 ! [B7: real,A6: real] :
% 0.25/0.57 ( ( ~ ( ord_less_eq_real @ B7 @ A6 ) )
% 0.25/0.57 = ( ord_less_real @ A6 @ B7 ) ) ).
% 0.25/0.57
% 0.25/0.57 % verit_comp_simplify1(3)
% 0.25/0.57 thf(fact_293_verit__comp__simplify1_I3_J,axiom,
% 0.25/0.57 ! [B7: int,A6: int] :
% 0.25/0.57 ( ( ~ ( ord_less_eq_int @ B7 @ A6 ) )
% 0.25/0.57 = ( ord_less_int @ A6 @ B7 ) ) ).
% 0.25/0.57
% 0.25/0.57 % verit_comp_simplify1(3)
% 0.25/0.57 thf(fact_294_is__zero__null,axiom,
% 0.25/0.57 ( is_zero_real
% 0.25/0.57 = ( ^ [P3: poly_real] : ( P3 = zero_zero_poly_real ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % is_zero_null
% 0.25/0.57 thf(fact_295_is__zero__null,axiom,
% 0.25/0.57 ( is_zero_int
% 0.25/0.57 = ( ^ [P3: poly_int] : ( P3 = zero_zero_poly_int ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % is_zero_null
% 0.25/0.57 thf(fact_296_is__zero__null,axiom,
% 0.25/0.57 ( is_zero_poly_real
% 0.25/0.57 = ( ^ [P3: poly_poly_real] : ( P3 = zero_z1423781445y_real ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % is_zero_null
% 0.25/0.57 thf(fact_297_poly__cutoff__0,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( poly_cutoff_real @ N @ zero_zero_poly_real )
% 0.25/0.57 = zero_zero_poly_real ) ).
% 0.25/0.57
% 0.25/0.57 % poly_cutoff_0
% 0.25/0.57 thf(fact_298_poly__cutoff__0,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( poly_cutoff_int @ N @ zero_zero_poly_int )
% 0.25/0.57 = zero_zero_poly_int ) ).
% 0.25/0.57
% 0.25/0.57 % poly_cutoff_0
% 0.25/0.57 thf(fact_299_poly__cutoff__0,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( poly_c1404107022y_real @ N @ zero_z1423781445y_real )
% 0.25/0.57 = zero_z1423781445y_real ) ).
% 0.25/0.57
% 0.25/0.57 % poly_cutoff_0
% 0.25/0.57 thf(fact_300_subsetI,axiom,
% 0.25/0.57 ! [A2: set_real,B3: set_real] :
% 0.25/0.57 ( ! [X4: real] :
% 0.25/0.57 ( ( member_real @ X4 @ A2 )
% 0.25/0.57 => ( member_real @ X4 @ B3 ) )
% 0.25/0.57 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % subsetI
% 0.25/0.57 thf(fact_301_in__mono,axiom,
% 0.25/0.57 ! [A2: set_real,B3: set_real,X2: real] :
% 0.25/0.57 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.25/0.57 => ( ( member_real @ X2 @ A2 )
% 0.25/0.57 => ( member_real @ X2 @ B3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % in_mono
% 0.25/0.57 thf(fact_302_subsetD,axiom,
% 0.25/0.57 ! [A2: set_real,B3: set_real,C2: real] :
% 0.25/0.57 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.25/0.57 => ( ( member_real @ C2 @ A2 )
% 0.25/0.57 => ( member_real @ C2 @ B3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % subsetD
% 0.25/0.57 thf(fact_303_subset__eq,axiom,
% 0.25/0.57 ( ord_less_eq_set_real
% 0.25/0.57 = ( ^ [A7: set_real,B5: set_real] :
% 0.25/0.57 ! [X: real] :
% 0.25/0.57 ( ( member_real @ X @ A7 )
% 0.25/0.57 => ( member_real @ X @ B5 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % subset_eq
% 0.25/0.57 thf(fact_304_subset__iff,axiom,
% 0.25/0.57 ( ord_less_eq_set_real
% 0.25/0.57 = ( ^ [A7: set_real,B5: set_real] :
% 0.25/0.57 ! [T3: real] :
% 0.25/0.57 ( ( member_real @ T3 @ A7 )
% 0.25/0.57 => ( member_real @ T3 @ B5 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % subset_iff
% 0.25/0.57 thf(fact_305_Collect__mono,axiom,
% 0.25/0.57 ! [P: real > $o,Q: real > $o] :
% 0.25/0.57 ( ! [X4: real] :
% 0.25/0.57 ( ( P @ X4 )
% 0.25/0.57 => ( Q @ X4 ) )
% 0.25/0.57 => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_mono
% 0.25/0.57 thf(fact_306_Collect__mono,axiom,
% 0.25/0.57 ! [P: int > $o,Q: int > $o] :
% 0.25/0.57 ( ! [X4: int] :
% 0.25/0.57 ( ( P @ X4 )
% 0.25/0.57 => ( Q @ X4 ) )
% 0.25/0.57 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_mono
% 0.25/0.57 thf(fact_307_Collect__subset,axiom,
% 0.25/0.57 ! [A2: set_real,P: real > $o] :
% 0.25/0.57 ( ord_less_eq_set_real
% 0.25/0.57 @ ( collect_real
% 0.25/0.57 @ ^ [X: real] :
% 0.25/0.57 ( ( member_real @ X @ A2 )
% 0.25/0.57 & ( P @ X ) ) )
% 0.25/0.57 @ A2 ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_subset
% 0.25/0.57 thf(fact_308_Collect__subset,axiom,
% 0.25/0.57 ! [A2: set_int,P: int > $o] :
% 0.25/0.57 ( ord_less_eq_set_int
% 0.25/0.57 @ ( collect_int
% 0.25/0.57 @ ^ [X: int] :
% 0.25/0.57 ( ( member_int @ X @ A2 )
% 0.25/0.57 & ( P @ X ) ) )
% 0.25/0.57 @ A2 ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_subset
% 0.25/0.57 thf(fact_309_less__eq__set__def,axiom,
% 0.25/0.57 ( ord_less_eq_set_real
% 0.25/0.57 = ( ^ [A7: set_real,B5: set_real] :
% 0.25/0.57 ( ord_less_eq_real_o
% 0.25/0.57 @ ^ [X: real] : ( member_real @ X @ A7 )
% 0.25/0.57 @ ^ [X: real] : ( member_real @ X @ B5 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_eq_set_def
% 0.25/0.57 thf(fact_310_Collect__mono__iff,axiom,
% 0.25/0.57 ! [P: real > $o,Q: real > $o] :
% 0.25/0.57 ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 0.25/0.57 = ( ! [X: real] :
% 0.25/0.57 ( ( P @ X )
% 0.25/0.57 => ( Q @ X ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_mono_iff
% 0.25/0.57 thf(fact_311_Collect__mono__iff,axiom,
% 0.25/0.57 ! [P: int > $o,Q: int > $o] :
% 0.25/0.57 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 0.25/0.57 = ( ! [X: int] :
% 0.25/0.57 ( ( P @ X )
% 0.25/0.57 => ( Q @ X ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_mono_iff
% 0.25/0.57 thf(fact_312_verit__la__disequality,axiom,
% 0.25/0.57 ! [A: real,B: real] :
% 0.25/0.57 ( ( A = B )
% 0.25/0.57 | ~ ( ord_less_eq_real @ A @ B )
% 0.25/0.57 | ~ ( ord_less_eq_real @ B @ A ) ) ).
% 0.25/0.57
% 0.25/0.57 % verit_la_disequality
% 0.25/0.57 thf(fact_313_verit__la__disequality,axiom,
% 0.25/0.57 ! [A: int,B: int] :
% 0.25/0.57 ( ( A = B )
% 0.25/0.57 | ~ ( ord_less_eq_int @ A @ B )
% 0.25/0.57 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.25/0.57
% 0.25/0.57 % verit_la_disequality
% 0.25/0.57 thf(fact_314_verit__comp__simplify1_I1_J,axiom,
% 0.25/0.57 ! [A: real] :
% 0.25/0.57 ~ ( ord_less_real @ A @ A ) ).
% 0.25/0.57
% 0.25/0.57 % verit_comp_simplify1(1)
% 0.25/0.57 thf(fact_315_verit__comp__simplify1_I1_J,axiom,
% 0.25/0.57 ! [A: int] :
% 0.25/0.57 ~ ( ord_less_int @ A @ A ) ).
% 0.25/0.57
% 0.25/0.57 % verit_comp_simplify1(1)
% 0.25/0.57 thf(fact_316_pinf_I1_J,axiom,
% 0.25/0.57 ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.25/0.57 ( ? [Z: real] :
% 0.25/0.57 ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ Z @ X4 )
% 0.25/0.57 => ( ( P @ X4 )
% 0.25/0.57 = ( P4 @ X4 ) ) )
% 0.25/0.57 => ( ? [Z: real] :
% 0.25/0.57 ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ Z @ X4 )
% 0.25/0.57 => ( ( Q @ X4 )
% 0.25/0.57 = ( Q3 @ X4 ) ) )
% 0.25/0.57 => ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ Z5 @ X3 )
% 0.25/0.57 => ( ( ( P @ X3 )
% 0.25/0.57 & ( Q @ X3 ) )
% 0.25/0.57 = ( ( P4 @ X3 )
% 0.25/0.57 & ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(1)
% 0.25/0.57 thf(fact_317_pinf_I1_J,axiom,
% 0.25/0.57 ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.25/0.57 ( ? [Z: int] :
% 0.25/0.57 ! [X4: int] :
% 0.25/0.57 ( ( ord_less_int @ Z @ X4 )
% 0.25/0.57 => ( ( P @ X4 )
% 0.25/0.57 = ( P4 @ X4 ) ) )
% 0.25/0.57 => ( ? [Z: int] :
% 0.25/0.57 ! [X4: int] :
% 0.25/0.57 ( ( ord_less_int @ Z @ X4 )
% 0.25/0.57 => ( ( Q @ X4 )
% 0.25/0.57 = ( Q3 @ X4 ) ) )
% 0.25/0.57 => ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ Z5 @ X3 )
% 0.25/0.57 => ( ( ( P @ X3 )
% 0.25/0.57 & ( Q @ X3 ) )
% 0.25/0.57 = ( ( P4 @ X3 )
% 0.25/0.57 & ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(1)
% 0.25/0.57 thf(fact_318_pinf_I2_J,axiom,
% 0.25/0.57 ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.25/0.57 ( ? [Z: real] :
% 0.25/0.57 ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ Z @ X4 )
% 0.25/0.57 => ( ( P @ X4 )
% 0.25/0.57 = ( P4 @ X4 ) ) )
% 0.25/0.57 => ( ? [Z: real] :
% 0.25/0.57 ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ Z @ X4 )
% 0.25/0.57 => ( ( Q @ X4 )
% 0.25/0.57 = ( Q3 @ X4 ) ) )
% 0.25/0.57 => ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ Z5 @ X3 )
% 0.25/0.57 => ( ( ( P @ X3 )
% 0.25/0.57 | ( Q @ X3 ) )
% 0.25/0.57 = ( ( P4 @ X3 )
% 0.25/0.57 | ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(2)
% 0.25/0.57 thf(fact_319_pinf_I2_J,axiom,
% 0.25/0.57 ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.25/0.57 ( ? [Z: int] :
% 0.25/0.57 ! [X4: int] :
% 0.25/0.57 ( ( ord_less_int @ Z @ X4 )
% 0.25/0.57 => ( ( P @ X4 )
% 0.25/0.57 = ( P4 @ X4 ) ) )
% 0.25/0.57 => ( ? [Z: int] :
% 0.25/0.57 ! [X4: int] :
% 0.25/0.57 ( ( ord_less_int @ Z @ X4 )
% 0.25/0.57 => ( ( Q @ X4 )
% 0.25/0.57 = ( Q3 @ X4 ) ) )
% 0.25/0.57 => ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ Z5 @ X3 )
% 0.25/0.57 => ( ( ( P @ X3 )
% 0.25/0.57 | ( Q @ X3 ) )
% 0.25/0.57 = ( ( P4 @ X3 )
% 0.25/0.57 | ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(2)
% 0.25/0.57 thf(fact_320_pinf_I3_J,axiom,
% 0.25/0.57 ! [T2: real] :
% 0.25/0.57 ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ Z5 @ X3 )
% 0.25/0.57 => ( X3 != T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(3)
% 0.25/0.57 thf(fact_321_pinf_I3_J,axiom,
% 0.25/0.57 ! [T2: int] :
% 0.25/0.57 ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ Z5 @ X3 )
% 0.25/0.57 => ( X3 != T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(3)
% 0.25/0.57 thf(fact_322_pinf_I4_J,axiom,
% 0.25/0.57 ! [T2: real] :
% 0.25/0.57 ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ Z5 @ X3 )
% 0.25/0.57 => ( X3 != T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(4)
% 0.25/0.57 thf(fact_323_pinf_I4_J,axiom,
% 0.25/0.57 ! [T2: int] :
% 0.25/0.57 ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ Z5 @ X3 )
% 0.25/0.57 => ( X3 != T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(4)
% 0.25/0.57 thf(fact_324_pinf_I5_J,axiom,
% 0.25/0.57 ! [T2: real] :
% 0.25/0.57 ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ Z5 @ X3 )
% 0.25/0.57 => ~ ( ord_less_real @ X3 @ T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(5)
% 0.25/0.57 thf(fact_325_pinf_I5_J,axiom,
% 0.25/0.57 ! [T2: int] :
% 0.25/0.57 ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ Z5 @ X3 )
% 0.25/0.57 => ~ ( ord_less_int @ X3 @ T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(5)
% 0.25/0.57 thf(fact_326_pinf_I7_J,axiom,
% 0.25/0.57 ! [T2: real] :
% 0.25/0.57 ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ Z5 @ X3 )
% 0.25/0.57 => ( ord_less_real @ T2 @ X3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(7)
% 0.25/0.57 thf(fact_327_pinf_I7_J,axiom,
% 0.25/0.57 ! [T2: int] :
% 0.25/0.57 ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ Z5 @ X3 )
% 0.25/0.57 => ( ord_less_int @ T2 @ X3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % pinf(7)
% 0.25/0.57 thf(fact_328_minf_I1_J,axiom,
% 0.25/0.57 ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.25/0.57 ( ? [Z: real] :
% 0.25/0.57 ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ X4 @ Z )
% 0.25/0.57 => ( ( P @ X4 )
% 0.25/0.57 = ( P4 @ X4 ) ) )
% 0.25/0.57 => ( ? [Z: real] :
% 0.25/0.57 ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ X4 @ Z )
% 0.25/0.57 => ( ( Q @ X4 )
% 0.25/0.57 = ( Q3 @ X4 ) ) )
% 0.25/0.57 => ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ X3 @ Z5 )
% 0.25/0.57 => ( ( ( P @ X3 )
% 0.25/0.57 & ( Q @ X3 ) )
% 0.25/0.57 = ( ( P4 @ X3 )
% 0.25/0.57 & ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % minf(1)
% 0.25/0.57 thf(fact_329_minf_I1_J,axiom,
% 0.25/0.57 ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.25/0.57 ( ? [Z: int] :
% 0.25/0.57 ! [X4: int] :
% 0.25/0.57 ( ( ord_less_int @ X4 @ Z )
% 0.25/0.57 => ( ( P @ X4 )
% 0.25/0.57 = ( P4 @ X4 ) ) )
% 0.25/0.57 => ( ? [Z: int] :
% 0.25/0.57 ! [X4: int] :
% 0.25/0.57 ( ( ord_less_int @ X4 @ Z )
% 0.25/0.57 => ( ( Q @ X4 )
% 0.25/0.57 = ( Q3 @ X4 ) ) )
% 0.25/0.57 => ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ X3 @ Z5 )
% 0.25/0.57 => ( ( ( P @ X3 )
% 0.25/0.57 & ( Q @ X3 ) )
% 0.25/0.57 = ( ( P4 @ X3 )
% 0.25/0.57 & ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % minf(1)
% 0.25/0.57 thf(fact_330_minf_I2_J,axiom,
% 0.25/0.57 ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.25/0.57 ( ? [Z: real] :
% 0.25/0.57 ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ X4 @ Z )
% 0.25/0.57 => ( ( P @ X4 )
% 0.25/0.57 = ( P4 @ X4 ) ) )
% 0.25/0.57 => ( ? [Z: real] :
% 0.25/0.57 ! [X4: real] :
% 0.25/0.57 ( ( ord_less_real @ X4 @ Z )
% 0.25/0.57 => ( ( Q @ X4 )
% 0.25/0.57 = ( Q3 @ X4 ) ) )
% 0.25/0.57 => ? [Z5: real] :
% 0.25/0.57 ! [X3: real] :
% 0.25/0.57 ( ( ord_less_real @ X3 @ Z5 )
% 0.25/0.57 => ( ( ( P @ X3 )
% 0.25/0.57 | ( Q @ X3 ) )
% 0.25/0.57 = ( ( P4 @ X3 )
% 0.25/0.57 | ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % minf(2)
% 0.25/0.57 thf(fact_331_minf_I2_J,axiom,
% 0.25/0.57 ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.25/0.57 ( ? [Z: int] :
% 0.25/0.57 ! [X4: int] :
% 0.25/0.57 ( ( ord_less_int @ X4 @ Z )
% 0.25/0.57 => ( ( P @ X4 )
% 0.25/0.57 = ( P4 @ X4 ) ) )
% 0.25/0.57 => ( ? [Z: int] :
% 0.25/0.57 ! [X4: int] :
% 0.25/0.57 ( ( ord_less_int @ X4 @ Z )
% 0.25/0.57 => ( ( Q @ X4 )
% 0.25/0.57 = ( Q3 @ X4 ) ) )
% 0.25/0.57 => ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ X3 @ Z5 )
% 0.25/0.57 => ( ( ( P @ X3 )
% 0.25/0.57 | ( Q @ X3 ) )
% 0.25/0.57 = ( ( P4 @ X3 )
% 0.25/0.57 | ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % minf(2)
% 0.25/0.57 thf(fact_332_minf_I3_J,axiom,
% 0.25/0.57 ! [T2: int] :
% 0.25/0.57 ? [Z5: int] :
% 0.25/0.57 ! [X3: int] :
% 0.25/0.57 ( ( ord_less_int @ X3 @ Z5 )
% 0.25/0.57 => ( X3 != T2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % minf(3)
% 0.25/0.57 thf(fact_333_conj__le__cong,axiom,
% 0.25/0.57 ! [X2: int,X5: int,P: $o,P4: $o] :
% 0.25/0.57 ( ( X2 = X5 )
% 0.25/0.57 => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.25/0.57 => ( P = P4 ) )
% 0.25/0.57 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.25/0.57 & P )
% 0.25/0.57 = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.25/0.57 & P4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % conj_le_cong
% 0.25/0.57 thf(fact_334_imp__le__cong,axiom,
% 0.25/0.57 ! [X2: int,X5: int,P: $o,P4: $o] :
% 0.25/0.57 ( ( X2 = X5 )
% 0.25/0.57 => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.25/0.57 => ( P = P4 ) )
% 0.25/0.57 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.25/0.57 => P )
% 0.25/0.57 = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.25/0.57 => P4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % imp_le_cong
% 0.25/0.57 thf(fact_335_jump__poly__not__root,axiom,
% 0.25/0.57 ! [P2: poly_real,X2: real,Q2: poly_real] :
% 0.25/0.57 ( ( ( poly_real2 @ P2 @ X2 )
% 0.25/0.64 != zero_zero_real )
% 0.25/0.64 => ( ( sturm_276991412p_poly @ Q2 @ P2 @ X2 )
% 0.25/0.64 = zero_zero_int ) ) ).
% 0.25/0.64
% 0.25/0.64 % jump_poly_not_root
% 0.25/0.64 thf(fact_336_jump__poly0_I2_J,axiom,
% 0.25/0.64 ! [Q2: poly_real,X2: real] :
% 0.25/0.64 ( ( sturm_276991412p_poly @ Q2 @ zero_zero_poly_real @ X2 )
% 0.25/0.64 = zero_zero_int ) ).
% 0.25/0.64
% 0.25/0.64 % jump_poly0(2)
% 0.25/0.64 thf(fact_337_jump__poly0_I1_J,axiom,
% 0.25/0.64 ! [P2: poly_real,X2: real] :
% 0.25/0.64 ( ( sturm_276991412p_poly @ zero_zero_poly_real @ P2 @ X2 )
% 0.25/0.64 = zero_zero_int ) ).
% 0.25/0.64
% 0.25/0.64 % jump_poly0(1)
% 0.25/0.64 thf(fact_338_verit__la__generic,axiom,
% 0.25/0.64 ! [A: int,X2: int] :
% 0.25/0.64 ( ( ord_less_eq_int @ A @ X2 )
% 0.25/0.64 | ( A = X2 )
% 0.25/0.64 | ( ord_less_eq_int @ X2 @ A ) ) ).
% 0.25/0.64
% 0.25/0.64 % verit_la_generic
% 0.25/0.64 thf(fact_339_finite__interval__int1,axiom,
% 0.25/0.64 ! [A: int,B: int] :
% 0.25/0.64 ( finite_finite_int
% 0.25/0.64 @ ( collect_int
% 0.25/0.64 @ ^ [I: int] :
% 0.25/0.64 ( ( ord_less_eq_int @ A @ I )
% 0.25/0.64 & ( ord_less_eq_int @ I @ B ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % finite_interval_int1
% 0.25/0.64 thf(fact_340_finite__interval__int2,axiom,
% 0.25/0.64 ! [A: int,B: int] :
% 0.25/0.64 ( finite_finite_int
% 0.25/0.64 @ ( collect_int
% 0.25/0.64 @ ^ [I: int] :
% 0.25/0.64 ( ( ord_less_eq_int @ A @ I )
% 0.25/0.64 & ( ord_less_int @ I @ B ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % finite_interval_int2
% 0.25/0.64 thf(fact_341_finite__interval__int4,axiom,
% 0.25/0.64 ! [A: int,B: int] :
% 0.25/0.64 ( finite_finite_int
% 0.25/0.64 @ ( collect_int
% 0.25/0.64 @ ^ [I: int] :
% 0.25/0.64 ( ( ord_less_int @ A @ I )
% 0.25/0.64 & ( ord_less_int @ I @ B ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % finite_interval_int4
% 0.25/0.64 thf(fact_342_finite__interval__int3,axiom,
% 0.25/0.64 ! [A: int,B: int] :
% 0.25/0.64 ( finite_finite_int
% 0.25/0.64 @ ( collect_int
% 0.25/0.64 @ ^ [I: int] :
% 0.25/0.64 ( ( ord_less_int @ A @ I )
% 0.25/0.64 & ( ord_less_eq_int @ I @ B ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % finite_interval_int3
% 0.25/0.64 thf(fact_343_less__int__code_I1_J,axiom,
% 0.25/0.64 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.25/0.64
% 0.25/0.64 % less_int_code(1)
% 0.25/0.64 thf(fact_344_less__eq__int__code_I1_J,axiom,
% 0.25/0.64 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.25/0.64
% 0.25/0.64 % less_eq_int_code(1)
% 0.25/0.64 thf(fact_345_cindex__poly__0_I2_J,axiom,
% 0.25/0.64 ! [A: real,B: real,Q2: poly_real] :
% 0.25/0.64 ( ( sturm_308542325x_poly @ A @ B @ Q2 @ zero_zero_poly_real )
% 0.25/0.64 = zero_zero_int ) ).
% 0.25/0.64
% 0.25/0.64 % cindex_poly_0(2)
% 0.25/0.64 thf(fact_346_cindex__poly__0_I1_J,axiom,
% 0.25/0.64 ! [A: real,B: real,P2: poly_real] :
% 0.25/0.64 ( ( sturm_308542325x_poly @ A @ B @ zero_zero_poly_real @ P2 )
% 0.25/0.64 = zero_zero_int ) ).
% 0.25/0.64
% 0.25/0.64 % cindex_poly_0(1)
% 0.25/0.64 thf(fact_347_cindex__poly__cross,axiom,
% 0.25/0.64 ! [A: real,B: real,P2: poly_real] :
% 0.25/0.64 ( ( ord_less_real @ A @ B )
% 0.25/0.64 => ( ( ( poly_real2 @ P2 @ A )
% 0.25/0.64 != zero_zero_real )
% 0.25/0.64 => ( ( ( poly_real2 @ P2 @ B )
% 0.25/0.64 != zero_zero_real )
% 0.25/0.64 => ( ( sturm_308542325x_poly @ A @ B @ one_one_poly_real @ P2 )
% 0.25/0.64 = ( sturm_1953858694_cross @ P2 @ A @ B ) ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % cindex_poly_cross
% 0.25/0.64 thf(fact_348_cindex__poly__def,axiom,
% 0.25/0.64 ( sturm_308542325x_poly
% 0.25/0.64 = ( ^ [A4: real,B4: real,Q4: poly_real,P3: poly_real] :
% 0.25/0.64 ( groups2051521940al_int @ ( sturm_276991412p_poly @ Q4 @ P3 )
% 0.25/0.64 @ ( collect_real
% 0.25/0.64 @ ^ [X: real] :
% 0.25/0.64 ( ( ( poly_real2 @ P3 @ X )
% 0.25/0.64 = zero_zero_real )
% 0.25/0.64 & ( ord_less_real @ A4 @ X )
% 0.25/0.64 & ( ord_less_real @ X @ B4 ) ) ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % cindex_poly_def
% 0.25/0.64 thf(fact_349_int__one__le__iff__zero__less,axiom,
% 0.25/0.64 ! [Z3: int] :
% 0.25/0.64 ( ( ord_less_eq_int @ one_one_int @ Z3 )
% 0.25/0.64 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 0.25/0.64
% 0.25/0.64 % int_one_le_iff_zero_less
% 0.25/0.64
% 0.25/0.64 % Conjectures (1)
% 0.25/0.64 thf(conj_0,conjecture,
% 0.25/0.64 ( finite_finite_real
% 0.25/0.64 @ ( collect_real
% 0.25/0.64 @ ^ [X: real] :
% 0.25/0.64 ( ( ( poly_real2 @ p @ X )
% 0.25/0.64 = zero_zero_real )
% 0.25/0.64 & ( ord_less_real @ a @ X )
% 0.25/0.64 & ( ord_less_real @ X @ b ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 %------------------------------------------------------------------------------
% 0.25/0.64 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8tCQp6vfdW/cvc5---1.0.5_32595.p...
% 0.25/0.64 (declare-sort $$unsorted 0)
% 0.25/0.64 (declare-sort tptp.poly_poly_poly_real 0)
% 0.25/0.64 (declare-sort tptp.set_poly_poly_real 0)
% 0.25/0.64 (declare-sort tptp.poly_poly_real 0)
% 0.25/0.64 (declare-sort tptp.poly_poly_int 0)
% 0.25/0.64 (declare-sort tptp.set_poly_real 0)
% 0.25/0.64 (declare-sort tptp.set_poly_int 0)
% 0.25/0.64 (declare-sort tptp.set_set_real 0)
% 0.25/0.64 (declare-sort tptp.set_set_int 0)
% 0.25/0.64 (declare-sort tptp.poly_real 0)
% 0.25/0.64 (declare-sort tptp.poly_int 0)
% 0.25/0.64 (declare-sort tptp.set_real 0)
% 0.25/0.64 (declare-sort tptp.set_int 0)
% 0.25/0.64 (declare-sort tptp.real 0)
% 0.25/0.64 (declare-sort tptp.nat 0)
% 0.25/0.64 (declare-sort tptp.int 0)
% 0.25/0.64 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 0.25/0.64 (declare-fun tptp.finite385822667ly_int (tptp.set_poly_int) Bool)
% 0.25/0.64 (declare-fun tptp.finite1328464339y_real (tptp.set_poly_poly_real) Bool)
% 0.25/0.64 (declare-fun tptp.finite1810960971y_real (tptp.set_poly_real) Bool)
% 0.25/0.64 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 0.25/0.64 (declare-fun tptp.finite26677625et_int (tptp.set_set_int) Bool)
% 0.25/0.64 (declare-fun tptp.finite475462905t_real (tptp.set_set_real) Bool)
% 0.25/0.64 (declare-fun tptp.one_one_int () tptp.int)
% 0.25/0.64 (declare-fun tptp.one_one_poly_real () tptp.poly_real)
% 0.25/0.64 (declare-fun tptp.zero_zero_int () tptp.int)
% 0.25/0.64 (declare-fun tptp.zero_zero_poly_int () tptp.poly_int)
% 0.25/0.64 (declare-fun tptp.zero_z1549157189ly_int () tptp.poly_poly_int)
% 0.25/0.64 (declare-fun tptp.zero_z935034829y_real () tptp.poly_poly_poly_real)
% 0.25/0.64 (declare-fun tptp.zero_z1423781445y_real () tptp.poly_poly_real)
% 0.25/0.64 (declare-fun tptp.zero_zero_poly_real () tptp.poly_real)
% 0.25/0.64 (declare-fun tptp.zero_zero_real () tptp.real)
% 0.25/0.64 (declare-fun tptp.groups2051521940al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 0.25/0.64 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_poly_int (tptp.poly_int tptp.poly_int) Bool)
% 0.25/0.64 (declare-fun tptp.ord_le38482960y_real (tptp.poly_poly_real tptp.poly_poly_real) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_poly_real (tptp.poly_real tptp.poly_real) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_eq_poly_int (tptp.poly_int tptp.poly_int) Bool)
% 0.25/0.64 (declare-fun tptp.ord_le893774876y_real (tptp.poly_poly_real tptp.poly_poly_real) Bool)
% 0.25/0.64 (declare-fun tptp.ord_le1180086932y_real (tptp.poly_real tptp.poly_real) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 0.25/0.64 (declare-fun tptp.is_zero_int (tptp.poly_int) Bool)
% 0.25/0.64 (declare-fun tptp.is_zero_poly_real (tptp.poly_poly_real) Bool)
% 0.25/0.64 (declare-fun tptp.is_zero_real (tptp.poly_real) Bool)
% 0.25/0.64 (declare-fun tptp.poly_int2 (tptp.poly_int tptp.int) tptp.int)
% 0.25/0.64 (declare-fun tptp.poly_poly_int2 (tptp.poly_poly_int tptp.poly_int) tptp.poly_int)
% 0.25/0.64 (declare-fun tptp.poly_poly_poly_real2 (tptp.poly_poly_poly_real tptp.poly_poly_real) tptp.poly_poly_real)
% 0.25/0.64 (declare-fun tptp.poly_poly_real2 (tptp.poly_poly_real tptp.poly_real) tptp.poly_real)
% 0.25/0.64 (declare-fun tptp.poly_real2 (tptp.poly_real tptp.real) tptp.real)
% 0.25/0.64 (declare-fun tptp.poly_cutoff_int (tptp.nat tptp.poly_int) tptp.poly_int)
% 0.25/0.64 (declare-fun tptp.poly_c1404107022y_real (tptp.nat tptp.poly_poly_real) tptp.poly_poly_real)
% 0.25/0.64 (declare-fun tptp.poly_cutoff_real (tptp.nat tptp.poly_real) tptp.poly_real)
% 0.25/0.64 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 0.25/0.64 (declare-fun tptp.collect_poly_int ((-> tptp.poly_int Bool)) tptp.set_poly_int)
% 0.25/0.64 (declare-fun tptp.collec927113489y_real ((-> tptp.poly_poly_real Bool)) tptp.set_poly_poly_real)
% 0.25/0.64 (declare-fun tptp.collect_poly_real ((-> tptp.poly_real Bool)) tptp.set_poly_real)
% 0.25/0.64 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 0.25/0.64 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 0.25/0.64 (declare-fun tptp.collect_set_real ((-> tptp.set_real Bool)) tptp.set_set_real)
% 0.25/0.64 (declare-fun tptp.sturm_308542325x_poly (tptp.real tptp.real tptp.poly_real tptp.poly_real) tptp.int)
% 0.25/0.64 (declare-fun tptp.sturm_1953858694_cross (tptp.poly_real tptp.real tptp.real) tptp.int)
% 0.25/0.64 (declare-fun tptp.sturm_276991412p_poly (tptp.poly_real tptp.poly_real tptp.real) tptp.int)
% 0.25/0.64 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 0.25/0.64 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 0.25/0.64 (declare-fun tptp.a () tptp.real)
% 0.25/0.64 (declare-fun tptp.a2 () tptp.real)
% 0.25/0.64 (declare-fun tptp.b () tptp.real)
% 0.25/0.64 (declare-fun tptp.b2 () tptp.real)
% 0.25/0.64 (declare-fun tptp.p () tptp.poly_real)
% 0.25/0.64 (assert (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ (@ tptp.poly_real2 tptp.p) X) tptp.zero_zero_real)))))
% 0.25/0.64 (assert (@ (@ tptp.ord_less_real tptp.a2) tptp.b2))
% 0.25/0.64 (assert (@ (@ tptp.ord_less_real tptp.b2) tptp.b))
% 0.25/0.64 (assert (@ (@ tptp.ord_less_real tptp.a) tptp.a2))
% 0.25/0.64 (assert (not (= tptp.p tptp.zero_zero_poly_real)))
% 0.25/0.64 (assert (forall ((X2 tptp.poly_int)) (= (@ (@ tptp.poly_poly_int2 tptp.zero_z1549157189ly_int) X2) tptp.zero_zero_poly_int)))
% 0.25/0.64 (assert (forall ((X2 tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 tptp.zero_z935034829y_real) X2) tptp.zero_z1423781445y_real)))
% 0.25/0.64 (assert (forall ((X2 tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 tptp.zero_z1423781445y_real) X2) tptp.zero_zero_poly_real)))
% 0.25/0.64 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.poly_int2 tptp.zero_zero_poly_int) X2) tptp.zero_zero_int)))
% 0.25/0.64 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.poly_real2 tptp.zero_zero_poly_real) X2) tptp.zero_zero_real)))
% 0.25/0.64 (assert (forall ((X3 tptp.real)) (=> (or (and (@ (@ tptp.ord_less_real tptp.a) X3) (@ (@ tptp.ord_less_eq_real X3) tptp.a2)) (and (@ (@ tptp.ord_less_eq_real tptp.b2) X3) (@ (@ tptp.ord_less_real X3) tptp.b))) (not (= (@ (@ tptp.poly_real2 tptp.p) X3) tptp.zero_zero_real)))))
% 0.25/0.64 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (or (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ P X) (@ Q X))))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ P X) (@ Q X))))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X tptp.int)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_poly_int)) (=> (not (= P2 tptp.zero_z1549157189ly_int)) (@ tptp.finite385822667ly_int (@ tptp.collect_poly_int (lambda ((X tptp.poly_int)) (= (@ (@ tptp.poly_poly_int2 P2) X) tptp.zero_zero_poly_int)))))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_poly_poly_real)) (=> (not (= P2 tptp.zero_z935034829y_real)) (@ tptp.finite1328464339y_real (@ tptp.collec927113489y_real (lambda ((X tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 P2) X) tptp.zero_z1423781445y_real)))))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_real)) (=> (not (= P2 tptp.zero_zero_poly_real)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ (@ tptp.poly_real2 P2) X) tptp.zero_zero_real)))))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_int)) (=> (not (= P2 tptp.zero_zero_poly_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ (@ tptp.poly_int2 P2) X) tptp.zero_zero_int)))))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_poly_real)) (=> (not (= P2 tptp.zero_z1423781445y_real)) (@ tptp.finite1810960971y_real (@ tptp.collect_poly_real (lambda ((X tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 P2) X) tptp.zero_zero_poly_real)))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (P2 tptp.poly_real)) (let ((_let_1 (@ tptp.poly_real2 P2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ _let_1 A)) (=> (@ (@ tptp.ord_less_real (@ _let_1 B)) tptp.zero_zero_real) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B) (= (@ (@ tptp.poly_real2 P2) X4) tptp.zero_zero_real)))))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (P2 tptp.poly_real)) (let ((_let_1 (@ tptp.poly_real2 P2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ _let_1 B)) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B) (= (@ (@ tptp.poly_real2 P2) X4) tptp.zero_zero_real)))))))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_real)) (= (forall ((X tptp.real)) (= (@ (@ tptp.poly_real2 P2) X) tptp.zero_zero_real)) (= P2 tptp.zero_zero_poly_real))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_poly_real)) (= (forall ((X tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 P2) X) tptp.zero_zero_poly_real)) (= P2 tptp.zero_z1423781445y_real))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_int)) (= (forall ((X tptp.int)) (= (@ (@ tptp.poly_int2 P2) X) tptp.zero_zero_int)) (= P2 tptp.zero_zero_poly_int))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_poly_int)) (= (forall ((X tptp.poly_int)) (= (@ (@ tptp.poly_poly_int2 P2) X) tptp.zero_zero_poly_int)) (= P2 tptp.zero_z1549157189ly_int))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_poly_poly_real)) (= (forall ((X tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 P2) X) tptp.zero_z1423781445y_real)) (= P2 tptp.zero_z935034829y_real))))
% 0.25/0.64 (assert (not (@ (@ tptp.ord_less_poly_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)))
% 0.25/0.64 (assert (not (@ (@ tptp.ord_less_poly_int tptp.zero_zero_poly_int) tptp.zero_zero_poly_int)))
% 0.25/0.64 (assert (not (@ (@ tptp.ord_le38482960y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)))
% 0.25/0.64 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 0.25/0.64 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 0.25/0.64 (assert (@ (@ tptp.ord_le1180086932y_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real))
% 0.25/0.64 (assert (@ (@ tptp.ord_less_eq_poly_int tptp.zero_zero_poly_int) tptp.zero_zero_poly_int))
% 0.25/0.64 (assert (@ (@ tptp.ord_le893774876y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real))
% 0.25/0.64 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 0.25/0.64 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 0.25/0.64 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (forall ((B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real B2) A3) (@ P B2))) (@ P A3)))) (@ P A2)))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (forall ((B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B2) A3) (@ P B2))) (@ P A3)))) (@ P A2)))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real X4) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X4) (= X4 Xa))))))))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int X4) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X4) (= X4 Xa))))))))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real A) X4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X4) Xa) (= X4 Xa))))))))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int A) X4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X4) Xa) (= X4 Xa))))))))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_real) (Lb tptp.real)) (=> (not (= P2 tptp.zero_zero_poly_real)) (not (forall ((Ub tptp.real)) (=> (@ (@ tptp.ord_less_real Lb) Ub) (not (forall ((Z tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb) Z) (@ (@ tptp.ord_less_eq_real Z) Ub)) (not (= (@ (@ tptp.poly_real2 P2) Z) tptp.zero_zero_real)))))))))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_real) (Ub2 tptp.real)) (=> (not (= P2 tptp.zero_zero_poly_real)) (not (forall ((Lb2 tptp.real)) (=> (@ (@ tptp.ord_less_real Lb2) Ub2) (not (forall ((Z tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb2) Z) (@ (@ tptp.ord_less_real Z) Ub2)) (not (= (@ (@ tptp.poly_real2 P2) Z) tptp.zero_zero_real)))))))))))
% 0.25/0.64 (assert (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))))
% 0.25/0.64 (assert (forall ((X2 tptp.poly_real)) (= (= tptp.zero_zero_poly_real X2) (= X2 tptp.zero_zero_poly_real))))
% 0.25/0.64 (assert (forall ((X2 tptp.int)) (= (= tptp.zero_zero_int X2) (= X2 tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((X2 tptp.poly_int)) (= (= tptp.zero_zero_poly_int X2) (= X2 tptp.zero_zero_poly_int))))
% 0.25/0.64 (assert (forall ((X2 tptp.poly_poly_real)) (= (= tptp.zero_z1423781445y_real X2) (= X2 tptp.zero_z1423781445y_real))))
% 0.25/0.64 (assert (forall ((Lb tptp.real) (Ub2 tptp.real) (P2 tptp.poly_real)) (= (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb) Z2) (@ (@ tptp.ord_less_real Z2) Ub2)) (not (= (@ (@ tptp.poly_real2 P2) Z2) tptp.zero_zero_real)))) (or (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb) Z2) (@ (@ tptp.ord_less_real Z2) Ub2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.poly_real2 P2) Z2)))) (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb) Z2) (@ (@ tptp.ord_less_real Z2) Ub2)) (@ (@ tptp.ord_less_real (@ (@ tptp.poly_real2 P2) Z2)) tptp.zero_zero_real)))))))
% 0.25/0.64 (assert (forall ((Lb tptp.real) (Ub2 tptp.real) (P2 tptp.poly_real)) (= (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb) Z2) (@ (@ tptp.ord_less_eq_real Z2) Ub2)) (not (= (@ (@ tptp.poly_real2 P2) Z2) tptp.zero_zero_real)))) (or (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb) Z2) (@ (@ tptp.ord_less_eq_real Z2) Ub2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.poly_real2 P2) Z2)))) (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb) Z2) (@ (@ tptp.ord_less_eq_real Z2) Ub2)) (@ (@ tptp.ord_less_real (@ (@ tptp.poly_real2 P2) Z2)) tptp.zero_zero_real)))))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_real) (Q2 tptp.poly_real)) (= (= (@ tptp.poly_real2 P2) (@ tptp.poly_real2 Q2)) (= P2 Q2))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_int) (Q2 tptp.poly_int)) (= (= (@ tptp.poly_int2 P2) (@ tptp.poly_int2 Q2)) (= P2 Q2))))
% 0.25/0.64 (assert (forall ((P2 tptp.poly_poly_real) (Q2 tptp.poly_poly_real)) (= (= (@ tptp.poly_poly_real2 P2) (@ tptp.poly_poly_real2 Q2)) (= P2 Q2))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (R (-> tptp.real tptp.real Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_real B3) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) B3) (@ (@ R X4) Xa))))) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A2) (@ (@ R A4) X4)))))))))))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_int) (R (-> tptp.real tptp.int Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X4) Xa))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A2) (@ (@ R A4) X4)))))))))))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_real) (R (-> tptp.int tptp.real Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite_finite_real B3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) B3) (@ (@ R X4) Xa))))) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A4 tptp.int)) (and (@ (@ tptp.member_int A4) A2) (@ (@ R A4) X4)))))))))))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X4) Xa))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A4 tptp.int)) (and (@ (@ tptp.member_int A4) A2) (@ (@ R A4) X4)))))))))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.real Bool))) (=> (not (@ tptp.finite_finite_real (@ tptp.collect_real P))) (exists ((X_1 tptp.real)) (@ P X_1)))))
% 0.25/0.64 (assert (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_1 tptp.int)) (@ P X_1)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) X2)))
% 0.25/0.64 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) X2)))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (P2 tptp.poly_real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (not (= (@ (@ tptp.poly_real2 P2) X4) tptp.zero_zero_real)))) (= (@ (@ (@ tptp.sturm_1953858694_cross P2) A) B) tptp.zero_zero_int)))))
% 0.25/0.64 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) C) (@ (@ tptp.ord_less_eq_real C) B) (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_real X3) C)) (@ P X3))) (forall ((D tptp.real)) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_real X4) D)) (@ P X4))) (@ (@ tptp.ord_less_eq_real D) C))))))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C) (@ (@ tptp.ord_less_eq_int C) B) (forall ((X3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X3) (@ (@ tptp.ord_less_int X3) C)) (@ P X3))) (forall ((D tptp.int)) (=> (forall ((X4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X4) (@ (@ tptp.ord_less_int X4) D)) (@ P X4))) (@ (@ tptp.ord_less_eq_int D) C))))))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 0.25/0.64 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 0.25/0.64 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 0.25/0.64 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (= A4 B4))))))
% 0.25/0.64 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (= A4 B4))))))
% 0.25/0.64 (assert (= tptp.ord_less_eq_real (lambda ((B4 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B4) A4) (= A4 B4)))))
% 0.25/0.64 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A4) (= A4 B4)))))
% 0.25/0.64 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 0.25/0.64 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A2))) A2)))
% 0.25/0.64 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A2))) A2)))
% 0.25/0.64 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 0.25/0.64 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real X2) W) (=> (@ (@ tptp.ord_less_real W) Y2) (@ (@ tptp.ord_less_eq_real W) Z3)))) (@ (@ tptp.ord_less_eq_real Y2) Z3)))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite475462905t_real (@ tptp.collect_set_real (lambda ((B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real B5) A2)))))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite26677625et_int (@ tptp.collect_set_int (lambda ((B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B5) A2)))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ (@ tptp.sturm_1953858694_cross tptp.zero_zero_poly_real) A) B) tptp.zero_zero_int)))
% 0.25/0.64 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ tptp.finite_finite_real B3) (@ tptp.finite_finite_real A2)))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ tptp.finite_finite_int B3) (@ tptp.finite_finite_int A2)))))
% 0.25/0.64 (assert (forall ((S tptp.set_real) (T tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real S) T) (=> (not (@ tptp.finite_finite_real S)) (not (@ tptp.finite_finite_real T))))))
% 0.25/0.64 (assert (forall ((S tptp.set_int) (T tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int T))))))
% 0.25/0.64 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real)) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (@ tptp.finite_finite_real A2)))))
% 0.25/0.64 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ tptp.finite_finite_int A2)))))
% 0.25/0.64 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (= A B)))))
% 0.25/0.64 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 0.25/0.64 (assert (= (lambda ((Y3 tptp.real) (Z4 tptp.real)) (= Y3 Z4)) (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (@ (@ tptp.ord_less_eq_real A4) B4)))))
% 0.25/0.64 (assert (= (lambda ((Y3 tptp.int) (Z4 tptp.int)) (= Y3 Z4)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (@ (@ tptp.ord_less_eq_int A4) B4)))))
% 0.25/0.64 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.64 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A5 tptp.real) (B6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A5) B6) (@ (@ P A5) B6))) (=> (forall ((A5 tptp.real) (B6 tptp.real)) (=> (@ (@ P B6) A5) (@ (@ P A5) B6))) (@ (@ P A) B)))))
% 0.25/0.64 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A5) B6) (@ (@ P A5) B6))) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (=> (@ (@ P B6) A5) (@ (@ P A5) B6))) (@ (@ P A) B)))))
% 0.25/0.64 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)))
% 0.25/0.64 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) Z3) (@ _let_1 Z3))))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z3) (@ _let_1 Z3))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real B) A) (= A B)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ (@ tptp.ord_less_eq_real A) C2)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_eq_int A) C2)))))
% 0.25/0.64 (assert (= (lambda ((Y3 tptp.real) (Z4 tptp.real)) (= Y3 Z4)) (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (@ (@ tptp.ord_less_eq_real B4) A4)))))
% 0.25/0.64 (assert (= (lambda ((Y3 tptp.int) (Z4 tptp.int)) (= Y3 Z4)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ tptp.ord_less_eq_int B4) A4)))))
% 0.25/0.64 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (= (@ (@ tptp.ord_less_eq_real X2) Y2) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y2) X2) (= (@ (@ tptp.ord_less_eq_int X2) Y2) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_real Z3))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_real Y2))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_int Z3))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_int Y2))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ _let_1 C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real X2) Y2)) (@ (@ tptp.ord_less_eq_real Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X2) Y2)) (@ (@ tptp.ord_less_eq_int Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_int X2) Y2))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y2) (@ (@ tptp.ord_less_eq_int Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) X2) (= X2 Y2)))))
% 0.25/0.64 (assert (= (lambda ((Y3 tptp.real) (Z4 tptp.real)) (= Y3 Z4)) (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real Y) X)))))
% 0.25/0.64 (assert (= (lambda ((Y3 tptp.int) (Z4 tptp.int)) (= Y3 Z4)) (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X)))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((X2 tptp.real)) (exists ((Y4 tptp.real)) (@ (@ tptp.ord_less_real Y4) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int)) (exists ((Y4 tptp.int)) (@ (@ tptp.ord_less_int Y4) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X2) X_1))))
% 0.25/0.64 (assert (forall ((X2 tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X2) X_1))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (@ (@ tptp.ord_less_real Y2) X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (@ (@ tptp.ord_less_int Y2) X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (not (= X2 Y2)) (or (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real Y2) X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (not (= X2 Y2)) (or (@ (@ tptp.ord_less_int X2) Y2) (@ (@ tptp.ord_less_int Y2) X2)))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (exists ((Z5 tptp.real)) (and (@ (@ tptp.ord_less_real X2) Z5) (@ (@ tptp.ord_less_real Z5) Y2))))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (@ (@ tptp.ord_less_real Y2) X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (@ (@ tptp.ord_less_int Y2) X2)))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_real Y2) Z3) (@ _let_1 Z3))))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_int Y2) Z3) (@ _let_1 Z3))))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y2) (= X2 Y2) (@ (@ tptp.ord_less_real Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y2) (= X2 Y2) (@ (@ tptp.ord_less_int Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real X2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int)) (not (@ (@ tptp.ord_less_int X2) X2))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C2) (@ (@ tptp.ord_less_real A) C2)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 0.25/0.64 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 0.25/0.64 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (@ (@ tptp.ord_less_real Y2) X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (@ (@ tptp.ord_less_int Y2) X2)))))
% 0.25/0.64 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y2) X2)) (= (not (@ (@ tptp.ord_less_real X2) Y2)) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y2) X2)) (= (not (@ (@ tptp.ord_less_int X2) Y2)) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (= Y2 X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (= Y2 X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) P))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X2) Y2) (=> (@ (@ tptp.ord_less_int Y2) X2) P))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (=> (not (= X2 Y2)) (@ (@ tptp.ord_less_real Y2) X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (=> (not (= X2 Y2)) (@ (@ tptp.ord_less_int Y2) X2)))))
% 0.25/0.64 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 0.25/0.64 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C2) (@ _let_1 C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C2) (@ _let_1 C2))))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (@ (@ tptp.ord_less_real Y2) X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (@ (@ tptp.ord_less_int Y2) X2)))))
% 0.25/0.64 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A5 tptp.real) (B6 tptp.real)) (=> (@ (@ tptp.ord_less_real A5) B6) (@ (@ P A5) B6))) (=> (forall ((A5 tptp.real)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.real) (B6 tptp.real)) (=> (@ (@ P B6) A5) (@ (@ P A5) B6))) (@ (@ P A) B))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (=> (@ (@ tptp.ord_less_int A5) B6) (@ (@ P A5) B6))) (=> (forall ((A5 tptp.int)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (=> (@ (@ P B6) A5) (@ (@ P A5) B6))) (@ (@ P A) B))))))
% 0.25/0.64 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.64 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y2)) (or (@ (@ tptp.ord_less_real Y2) X2) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y2)) (or (@ (@ tptp.ord_less_int Y2) X2) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 0.25/0.64 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 0.25/0.64 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 0.25/0.64 (assert (forall ((A tptp.real)) (exists ((B6 tptp.real)) (or (@ (@ tptp.ord_less_real A) B6) (@ (@ tptp.ord_less_real B6) A)))))
% 0.25/0.64 (assert (forall ((S tptp.set_real)) (=> (exists ((X3 tptp.real)) (@ (@ tptp.member_real X3) S)) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z)))) (exists ((Y4 tptp.real)) (and (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S) (@ (@ tptp.ord_less_eq_real X3) Y4))) (forall ((Z tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z))) (@ (@ tptp.ord_less_eq_real Y4) Z)))))))))
% 0.25/0.64 (assert (forall ((D1 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ _let_1 D1) (@ _let_1 D2)))))))))
% 0.25/0.64 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (not (@ (@ tptp.ord_less_real X2) Y2)))))
% 0.25/0.64 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y2) X2) (not (@ (@ tptp.ord_less_int X2) Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (@ (@ tptp.ord_less_eq_real Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (@ (@ tptp.ord_less_eq_int Y2) X2))))
% 0.25/0.64 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 0.25/0.64 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 0.25/0.64 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (= X Y))))))
% 0.25/0.64 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (not (= X Y))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C2)))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X2) Y2)) (@ (@ tptp.ord_less_real Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X2) Y2)) (@ (@ tptp.ord_less_int Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y2)) (@ (@ tptp.ord_less_eq_real Y2) X2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y2)) (@ (@ tptp.ord_less_eq_int Y2) X2))))
% 0.25/0.64 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (= (@ (@ tptp.ord_less_eq_real X2) Y2) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (= (@ (@ tptp.ord_less_eq_int X2) Y2) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (= (not (@ (@ tptp.ord_less_real X2) Y2)) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (= (not (@ (@ tptp.ord_less_int X2) Y2)) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 0.25/0.64 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (@ (@ tptp.ord_less_eq_int X2) Y2))))
% 0.25/0.64 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_real Y2) Z3) (@ (@ tptp.ord_less_real X2) Z3)))))
% 0.25/0.65 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z3) (@ (@ tptp.ord_less_int X2) Z3)))))
% 0.25/0.65 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) Z3) (@ _let_1 Z3))))))
% 0.25/0.65 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z3) (@ _let_1 Z3))))))
% 0.25/0.65 (assert (forall ((Z3 tptp.real) (Y2 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (@ (@ tptp.ord_less_eq_real Y2) X4))) (@ (@ tptp.ord_less_eq_real Y2) Z3))))
% 0.25/0.65 (assert (forall ((Y2 tptp.real) (Z3 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y2) (@ (@ tptp.ord_less_eq_real X4) Z3))) (@ (@ tptp.ord_less_eq_real Y2) Z3))))
% 0.25/0.65 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_real Y2) X2))))
% 0.25/0.65 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y2) (@ (@ tptp.ord_less_int Y2) X2))))
% 0.25/0.65 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (or (@ (@ tptp.ord_less_real X2) Y2) (= X2 Y2)))))
% 0.25/0.65 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (or (@ (@ tptp.ord_less_int X2) Y2) (= X2 Y2)))))
% 0.25/0.65 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (@ (@ tptp.ord_less_eq_real Y) X))))))
% 0.25/0.65 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (not (@ (@ tptp.ord_less_eq_int Y) X))))))
% 0.25/0.65 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y2) X2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 0.25/0.65 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y2) X2)) (@ (@ tptp.ord_less_int X2) Y2))))
% 0.25/0.65 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C2) (@ (@ tptp.ord_less_real A) C2)))))
% 0.25/0.65 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))))
% 0.25/0.65 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ _let_1 C2))))))
% 0.25/0.65 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))))
% 0.25/0.65 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B4) (= A4 B4)))))
% 0.25/0.65 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B4) (= A4 B4)))))
% 0.25/0.65 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (= A4 B4))))))
% 0.25/0.65 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (= A4 B4))))))
% 0.25/0.65 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.65 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.65 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C2) B) (@ (@ tptp.ord_less_real C2) A)))))
% 0.25/0.65 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) B) (@ (@ tptp.ord_less_int C2) A)))))
% 0.25/0.65 (assert (forall ((Z3 tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) W) (=> (@ (@ tptp.ord_less_real W) X2) (@ (@ tptp.ord_less_eq_real Y2) W)))) (@ (@ tptp.ord_less_eq_real Y2) Z3)))))
% 0.25/0.65 (assert (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (not (@ (@ tptp.ord_less_eq_real T2) X3)))))))
% 0.25/0.65 (assert (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (not (@ (@ tptp.ord_less_eq_int T2) X3)))))))
% 0.25/0.65 (assert (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (@ (@ tptp.ord_less_eq_real X3) T2))))))
% 0.25/0.65 (assert (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (@ (@ tptp.ord_less_eq_int X3) T2))))))
% 0.25/0.65 (assert (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (@ (@ tptp.ord_less_eq_real T2) X3))))))
% 0.25/0.65 (assert (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (@ (@ tptp.ord_less_eq_int T2) X3))))))
% 0.25/0.65 (assert (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (not (@ (@ tptp.ord_less_eq_real X3) T2)))))))
% 0.25/0.65 (assert (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (not (@ (@ tptp.ord_less_eq_int X3) T2)))))))
% 0.25/0.65 (assert (forall ((B7 tptp.real) (A6 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B7) A6)) (@ (@ tptp.ord_less_real A6) B7))))
% 0.25/0.65 (assert (forall ((B7 tptp.int) (A6 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B7) A6)) (@ (@ tptp.ord_less_int A6) B7))))
% 0.25/0.65 (assert (= tptp.is_zero_real (lambda ((P3 tptp.poly_real)) (= P3 tptp.zero_zero_poly_real))))
% 0.25/0.65 (assert (= tptp.is_zero_int (lambda ((P3 tptp.poly_int)) (= P3 tptp.zero_zero_poly_int))))
% 0.25/0.65 (assert (= tptp.is_zero_poly_real (lambda ((P3 tptp.poly_poly_real)) (= P3 tptp.zero_z1423781445y_real))))
% 0.25/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_cutoff_real N) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)))
% 0.25/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_cutoff_int N) tptp.zero_zero_poly_int) tptp.zero_zero_poly_int)))
% 0.25/0.65 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_c1404107022y_real N) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)))
% 0.25/0.65 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_real A2) B3))))
% 0.25/0.65 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 0.25/0.65 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C2 tptp.real)) (let ((_let_1 (@ tptp.member_real C2))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 0.25/0.65 (assert (= tptp.ord_less_eq_set_real (lambda ((A7 tptp.set_real) (B5 tptp.set_real)) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 A7) (@ _let_1 B5)))))))
% 0.25/0.65 (assert (= tptp.ord_less_eq_set_real (lambda ((A7 tptp.set_real) (B5 tptp.set_real)) (forall ((T3 tptp.real)) (let ((_let_1 (@ tptp.member_real T3))) (=> (@ _let_1 A7) (@ _let_1 B5)))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))))
% 0.25/0.65 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 0.25/0.65 (assert (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A2) (@ P X))))) A2)))
% 0.25/0.65 (assert (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (@ P X))))) A2)))
% 0.25/0.65 (assert (= tptp.ord_less_eq_set_real (lambda ((A7 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A7))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B5))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)) (forall ((X tptp.real)) (=> (@ P X) (@ Q X))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X tptp.int)) (=> (@ P X) (@ Q X))))))
% 0.25/0.65 (assert (forall ((A tptp.real) (B tptp.real)) (or (= A B) (not (@ (@ tptp.ord_less_eq_real A) B)) (not (@ (@ tptp.ord_less_eq_real B) A)))))
% 0.25/0.65 (assert (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))))
% 0.25/0.65 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 0.25/0.65 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 0.25/0.65 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q3 (-> tptp.real Bool))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P4 X3) (@ Q3 X3))))))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X4) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P4 X3) (@ Q3 X3))))))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q3 (-> tptp.real Bool))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P4 X3) (@ Q3 X3))))))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X4) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P4 X3) (@ Q3 X3))))))))))
% 0.25/0.65 (assert (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (not (= X3 T2)))))))
% 0.25/0.65 (assert (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (not (= X3 T2)))))))
% 0.25/0.65 (assert (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (not (= X3 T2)))))))
% 0.25/0.65 (assert (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (not (= X3 T2)))))))
% 0.25/0.65 (assert (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (not (@ (@ tptp.ord_less_real X3) T2)))))))
% 0.25/0.65 (assert (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (not (@ (@ tptp.ord_less_int X3) T2)))))))
% 0.25/0.65 (assert (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (@ (@ tptp.ord_less_real T2) X3))))))
% 0.25/0.65 (assert (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (@ (@ tptp.ord_less_int T2) X3))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q3 (-> tptp.real Bool))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (and (@ P X3) (@ Q X3)) (and (@ P4 X3) (@ Q3 X3))))))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (and (@ P X3) (@ Q X3)) (and (@ P4 X3) (@ Q3 X3))))))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q3 (-> tptp.real Bool))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (or (@ P X3) (@ Q X3)) (or (@ P4 X3) (@ Q3 X3))))))))))
% 0.25/0.65 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (or (@ P X3) (@ Q X3)) (or (@ P4 X3) (@ Q3 X3))))))))))
% 0.25/0.65 (assert (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (not (= X3 T2)))))))
% 0.25/0.65 (assert (forall ((X2 tptp.int) (X5 tptp.int) (P Bool) (P4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X5))) (=> (= X2 X5) (=> (=> _let_2 (= P P4)) (= (and (@ _let_1 X2) P) (and _let_2 P4))))))))
% 0.25/0.65 (assert (forall ((X2 tptp.int) (X5 tptp.int) (P Bool) (P4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X5))) (=> (= X2 X5) (=> (=> _let_2 (= P P4)) (= (=> (@ _let_1 X2) P) (=> _let_2 P4))))))))
% 0.25/0.65 (assert (forall ((P2 tptp.poly_real) (X2 tptp.real) (Q2 tptp.poly_real)) (=> (not (= (@ (@ tptp.poly_real2 P2) X2) tptp.zero_zero_real)) (= (@ (@ (@ tptp.sturm_276991412p_poly Q2) P2) X2) tptp.zero_zero_int))))
% 0.25/0.65 (assert (forall ((Q2 tptp.poly_real) (X2 tptp.real)) (= (@ (@ (@ tptp.sturm_276991412p_poly Q2) tptp.zero_zero_poly_real) X2) tptp.zero_zero_int)))
% 0.25/0.65 (assert (forall ((P2 tptp.poly_real) (X2 tptp.real)) (= (@ (@ (@ tptp.sturm_276991412p_poly tptp.zero_zero_poly_real) P2) X2) tptp.zero_zero_int)))
% 0.25/0.65 (assert (forall ((A tptp.int) (X2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X2) (= A X2) (@ (@ tptp.ord_less_eq_int X2) A))))
% 0.25/0.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I) (@ (@ tptp.ord_less_eq_int I) B)))))))
% 0.25/0.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I) (@ (@ tptp.ord_less_int I) B)))))))
% 0.25/0.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_int A) I) (@ (@ tptp.ord_less_int I) B)))))))
% 0.25/0.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_int A) I) (@ (@ tptp.ord_less_eq_int I) B)))))))
% 0.25/0.65 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 0.25/0.65 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 0.25/0.65 (assert (forall ((A tptp.real) (B tptp.real) (Q2 tptp.poly_real)) (= (@ (@ (@ (@ tptp.sturm_308542325x_poly A) B) Q2) tptp.zero_zero_poly_real) tptp.zero_zero_int)))
% 0.25/0.65 (assert (forall ((A tptp.real) (B tptp.real) (P2 tptp.poly_real)) (= (@ (@ (@ (@ tptp.sturm_308542325x_poly A) B) tptp.zero_zero_poly_real) P2) tptp.zero_zero_int)))
% 0.25/0.65 (assert (forall ((A tptp.real) (B tptp.real) (P2 tptp.poly_real)) (let ((_let_1 (@ tptp.poly_real2 P2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (not (= (@ _let_1 A) tptp.zero_zero_real)) (=> (not (= (@ _let_1 B) tptp.zero_zero_real)) (= (@ (@ (@ (@ tptp.sturm_308542325x_poly A) B) tptp.one_one_poly_real) P2) (@ (@ (@ tptp.sturm_1953858694_cross P2) A) B))))))))
% 0.25/0.65 (assert (= tptp.sturm_308542325x_poly (lambda ((A4 tptp.real) (B4 tptp.real) (Q4 tptp.poly_real) (P3 tptp.poly_real)) (@ (@ tptp.groups2051521940al_int (@ (@ tptp.sturm_276991412p_poly Q4) P3)) (@ tptp.collect_real (lambda ((X tptp.real)) (and (= (@ (@ tptp.poly_real2 P3) X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A4) X) (@ (@ tptp.ord_less_real X) B4))))))))
% 62.91/63.20 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))))
% 62.91/63.20 (assert (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (= (@ (@ tptp.poly_real2 tptp.p) X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.a) X) (@ (@ tptp.ord_less_real X) tptp.b)))))))
% 62.91/63.20 (set-info :filename cvc5---1.0.5_32595)
% 62.91/63.20 (check-sat-assuming ( true ))
% 62.91/63.20 ------- get file name : TPTP file name is ITP193^1
% 62.91/63.20 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32595.smt2...
% 62.91/63.20 --- Run --ho-elim --full-saturate-quant at 10...
% 62.91/63.20 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 62.91/63.20 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 62.91/63.20 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 62.91/63.20 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 62.91/63.20 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 62.91/63.20 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 62.91/63.20 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 62.91/63.20 % SZS status Theorem for ITP193^1
% 62.91/63.20 % SZS output start Proof for ITP193^1
% 62.91/63.20 (
% 62.91/63.20 (let ((_let_1 (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (= (@ (@ tptp.poly_real2 tptp.p) X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.a) X) (@ (@ tptp.ord_less_real X) tptp.b)))))))) (let ((_let_2 (= tptp.sturm_308542325x_poly (lambda ((A4 tptp.real) (B4 tptp.real) (Q4 tptp.poly_real) (P3 tptp.poly_real)) (@ (@ tptp.groups2051521940al_int (@ (@ tptp.sturm_276991412p_poly Q4) P3)) (@ tptp.collect_real (lambda ((X tptp.real)) (and (= (@ (@ tptp.poly_real2 P3) X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A4) X) (@ (@ tptp.ord_less_real X) B4))))))))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_4 (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))) (let ((_let_5 (= tptp.ord_less_eq_set_real (lambda ((A7 tptp.set_real) (B5 tptp.set_real)) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 A7) (@ _let_1 B5)))))))) (let ((_let_6 (= tptp.is_zero_poly_real (lambda ((P3 tptp.poly_poly_real)) (= P3 tptp.zero_z1423781445y_real))))) (let ((_let_7 (= tptp.is_zero_int (lambda ((P3 tptp.poly_int)) (= P3 tptp.zero_zero_poly_int))))) (let ((_let_8 (= tptp.is_zero_real (lambda ((P3 tptp.poly_real)) (= P3 tptp.zero_zero_poly_real))))) (let ((_let_9 (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ tptp.finite_finite_real B3) (@ tptp.finite_finite_real A2)))))) (let ((_let_10 (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))) (let ((_let_11 (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (= A4 B4))))))) (let ((_let_12 (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))) (let ((_let_13 (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ (@ tptp.poly_real2 tptp.p) X) tptp.zero_zero_real)))))) (let ((_let_14 (forall ((BOUND_VARIABLE_18964 tptp.real)) (= (ho_64 k_183 BOUND_VARIABLE_18964) (= tptp.zero_zero_real (ho_74 (ho_73 k_72 tptp.p) BOUND_VARIABLE_18964)))))) (let ((_let_15 (= tptp.zero_zero_real (ho_74 (ho_73 k_72 tptp.p) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_250)))) (let ((_let_16 (ho_64 k_183 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_250))) (let ((_let_17 (= _let_16 _let_15))) (let ((_let_18 (forall ((u |u_(-> tptp.set_poly_int Bool)|) (e Bool) (i tptp.set_poly_int)) (not (forall ((v |u_(-> tptp.set_poly_int Bool)|)) (not (forall ((ii tptp.set_poly_int)) (= (ho_193 v ii) (ite (= i ii) e (ho_193 u ii)))))))))) (let ((_let_19 (forall ((x |u_(-> tptp.set_poly_int Bool)|) (y |u_(-> tptp.set_poly_int Bool)|)) (or (not (forall ((z tptp.set_poly_int)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_20 (forall ((u |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|) (e |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|) (i |u_(-> tptp.int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (not (forall ((ii |u_(-> tptp.int Bool)|)) (= (ho_178 v ii) (ite (= i ii) e (ho_178 u ii)))))))))) (let ((_let_21 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_178 x z) (ho_178 y z)))) (= x y))))) (let ((_let_22 (forall ((u |u_(-> tptp.poly_poly_int tptp.poly_int tptp.poly_int)|) (e |u_(-> tptp.poly_int tptp.poly_int)|) (i tptp.poly_poly_int)) (not (forall ((v |u_(-> tptp.poly_poly_int tptp.poly_int tptp.poly_int)|)) (not (forall ((ii tptp.poly_poly_int)) (= (ho_175 v ii) (ite (= i ii) e (ho_175 u ii)))))))))) (let ((_let_23 (forall ((x |u_(-> tptp.poly_poly_int tptp.poly_int tptp.poly_int)|) (y |u_(-> tptp.poly_poly_int tptp.poly_int tptp.poly_int)|)) (or (not (forall ((z tptp.poly_poly_int)) (= (ho_175 x z) (ho_175 y z)))) (= x y))))) (let ((_let_24 (forall ((u |u_(-> tptp.poly_poly_real Bool)|) (e Bool) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real Bool)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_167 v ii) (ite (= i ii) e (ho_167 u ii)))))))))) (let ((_let_25 (forall ((x |u_(-> tptp.poly_poly_real Bool)|) (y |u_(-> tptp.poly_poly_real Bool)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_167 x z) (ho_167 y z)))) (= x y))))) (let ((_let_26 (forall ((u |u_(-> tptp.real tptp.int Bool)|) (e |u_(-> tptp.int Bool)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.int Bool)|)) (not (forall ((ii tptp.real)) (= (ho_145 v ii) (ite (= i ii) e (ho_145 u ii)))))))))) (let ((_let_27 (forall ((x |u_(-> tptp.real tptp.int Bool)|) (y |u_(-> tptp.real tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_28 (forall ((u |u_(-> _u_(-> tptp.poly_poly_real Bool)_ tptp.set_poly_poly_real)|) (e tptp.set_poly_poly_real) (i |u_(-> tptp.poly_poly_real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.poly_poly_real Bool)_ tptp.set_poly_poly_real)|)) (not (forall ((ii |u_(-> tptp.poly_poly_real Bool)|)) (= (ho_195 v ii) (ite (= i ii) e (ho_195 u ii)))))))))) (let ((_let_29 (forall ((x |u_(-> _u_(-> tptp.poly_poly_real Bool)_ tptp.set_poly_poly_real)|) (y |u_(-> _u_(-> tptp.poly_poly_real Bool)_ tptp.set_poly_poly_real)|)) (or (not (forall ((z |u_(-> tptp.poly_poly_real Bool)|)) (= (ho_195 x z) (ho_195 y z)))) (= x y))))) (let ((_let_30 (forall ((u |u_(-> tptp.poly_real tptp.real Bool)|) (e |u_(-> tptp.real Bool)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.real Bool)|)) (not (forall ((ii tptp.poly_real)) (= (ho_164 v ii) (ite (= i ii) e (ho_164 u ii)))))))))) (let ((_let_31 (forall ((x |u_(-> tptp.poly_real tptp.real Bool)|) (y |u_(-> tptp.poly_real tptp.real Bool)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_164 x z) (ho_164 y z)))) (= x y))))) (let ((_let_32 (forall ((u |u_(-> tptp.poly_int tptp.int tptp.int)|) (e |u_(-> tptp.int tptp.int)|) (i tptp.poly_int)) (not (forall ((v |u_(-> tptp.poly_int tptp.int tptp.int)|)) (not (forall ((ii tptp.poly_int)) (= (ho_161 v ii) (ite (= i ii) e (ho_161 u ii)))))))))) (let ((_let_33 (forall ((x |u_(-> tptp.poly_int tptp.int tptp.int)|) (y |u_(-> tptp.poly_int tptp.int tptp.int)|)) (or (not (forall ((z tptp.poly_int)) (= (ho_161 x z) (ho_161 y z)))) (= x y))))) (let ((_let_34 (forall ((u |u_(-> tptp.set_int tptp.int Bool)|) (e |u_(-> tptp.int Bool)|) (i tptp.set_int)) (not (forall ((v |u_(-> tptp.set_int tptp.int Bool)|)) (not (forall ((ii tptp.set_int)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_35 (forall ((x |u_(-> tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_36 (forall ((u |u_(-> _u_(-> tptp.poly_real Bool)_ tptp.set_poly_real)|) (e tptp.set_poly_real) (i |u_(-> tptp.poly_real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.poly_real Bool)_ tptp.set_poly_real)|)) (not (forall ((ii |u_(-> tptp.poly_real Bool)|)) (= (ho_199 v ii) (ite (= i ii) e (ho_199 u ii)))))))))) (let ((_let_37 (forall ((x |u_(-> _u_(-> tptp.poly_real Bool)_ tptp.set_poly_real)|) (y |u_(-> _u_(-> tptp.poly_real Bool)_ tptp.set_poly_real)|)) (or (not (forall ((z |u_(-> tptp.poly_real Bool)|)) (= (ho_199 x z) (ho_199 y z)))) (= x y))))) (let ((_let_38 (forall ((u |u_(-> tptp.poly_real tptp.poly_real)|) (e tptp.poly_real) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.poly_real)|)) (not (forall ((ii tptp.poly_real)) (= (ho_157 v ii) (ite (= i ii) e (ho_157 u ii)))))))))) (let ((_let_39 (forall ((x |u_(-> tptp.poly_real tptp.poly_real)|) (y |u_(-> tptp.poly_real tptp.poly_real)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_157 x z) (ho_157 y z)))) (= x y))))) (let ((_let_40 (forall ((u |u_(-> tptp.set_int _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|) (e |u_(-> _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|) (i tptp.set_int)) (not (forall ((v |u_(-> tptp.set_int _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|)) (not (forall ((ii tptp.set_int)) (= (ho_143 v ii) (ite (= i ii) e (ho_143 u ii)))))))))) (let ((_let_41 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_143 x z) (ho_143 y z)))) (= x y))))) (let ((_let_42 (forall ((u |u_(-> tptp.poly_poly_real tptp.poly_real Bool)|) (e |u_(-> tptp.poly_real Bool)|) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.poly_real Bool)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_153 v ii) (ite (= i ii) e (ho_153 u ii)))))))))) (let ((_let_43 (forall ((x |u_(-> tptp.poly_poly_real tptp.poly_real Bool)|) (y |u_(-> tptp.poly_poly_real tptp.poly_real Bool)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_153 x z) (ho_153 y z)))) (= x y))))) (let ((_let_44 (forall ((u |u_(-> _u_(-> tptp.poly_int Bool)_ tptp.set_poly_int)|) (e tptp.set_poly_int) (i |u_(-> tptp.poly_int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.poly_int Bool)_ tptp.set_poly_int)|)) (not (forall ((ii |u_(-> tptp.poly_int Bool)|)) (= (ho_191 v ii) (ite (= i ii) e (ho_191 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> _u_(-> tptp.poly_int Bool)_ tptp.set_poly_int)|) (y |u_(-> _u_(-> tptp.poly_int Bool)_ tptp.set_poly_int)|)) (or (not (forall ((z |u_(-> tptp.poly_int Bool)|)) (= (ho_191 x z) (ho_191 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|) (e |u_(-> tptp.real tptp.real Bool)|) (i |u_(-> tptp.real tptp.real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|)) (not (forall ((ii |u_(-> tptp.real tptp.real Bool)|)) (= (ho_151 v ii) (ite (= i ii) e (ho_151 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real Bool)|)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|) (e |u_(-> tptp.int Bool)|) (i |u_(-> tptp.int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (not (forall ((ii |u_(-> tptp.int Bool)|)) (= (ho_95 v ii) (ite (= i ii) e (ho_95 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_95 x z) (ho_95 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> tptp.int tptp.int)|) (e tptp.int) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.int)|)) (not (forall ((ii tptp.int)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> tptp.set_int Bool)|) (e Bool) (i tptp.set_int)) (not (forall ((v |u_(-> tptp.set_int Bool)|)) (not (forall ((ii tptp.set_int)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> tptp.set_int Bool)|) (y |u_(-> tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> tptp.poly_real tptp.real tptp.int)|) (e |u_(-> tptp.real tptp.int)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.real tptp.int)|)) (not (forall ((ii tptp.poly_real)) (= (ho_234 v ii) (ite (= i ii) e (ho_234 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> tptp.poly_real tptp.real tptp.int)|) (y |u_(-> tptp.poly_real tptp.real tptp.int)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_234 x z) (ho_234 y z)))) (= x y))))) (let ((_let_56 (forall ((u |u_(-> tptp.set_real _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|) (e |u_(-> _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|) (i tptp.set_real)) (not (forall ((v |u_(-> tptp.set_real _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|)) (not (forall ((ii tptp.set_real)) (= (ho_147 v ii) (ite (= i ii) e (ho_147 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_147 x z) (ho_147 y z)))) (= x y))))) (let ((_let_58 (forall ((u |u_(-> _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|) (e |u_(-> tptp.int tptp.real Bool)|) (i |u_(-> tptp.real tptp.int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|)) (not (forall ((ii |u_(-> tptp.real tptp.int Bool)|)) (= (ho_148 v ii) (ite (= i ii) e (ho_148 u ii)))))))))) (let ((_let_59 (forall ((x |u_(-> _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int Bool)|)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_60 (forall ((u |u_(-> tptp.set_poly_poly_real Bool)|) (e Bool) (i tptp.set_poly_poly_real)) (not (forall ((v |u_(-> tptp.set_poly_poly_real Bool)|)) (not (forall ((ii tptp.set_poly_poly_real)) (= (ho_197 v ii) (ite (= i ii) e (ho_197 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> tptp.set_poly_poly_real Bool)|) (y |u_(-> tptp.set_poly_poly_real Bool)|)) (or (not (forall ((z tptp.set_poly_poly_real)) (= (ho_197 x z) (ho_197 y z)))) (= x y))))) (let ((_let_62 (forall ((u |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_real Bool)|) (e |u_(-> tptp.poly_poly_real Bool)|) (i tptp.poly_poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_real Bool)|)) (not (forall ((ii tptp.poly_poly_poly_real)) (= (ho_166 v ii) (ite (= i ii) e (ho_166 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_real Bool)|) (y |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_real Bool)|)) (or (not (forall ((z tptp.poly_poly_poly_real)) (= (ho_166 x z) (ho_166 y z)))) (= x y))))) (let ((_let_64 (forall ((u |u_(-> tptp.set_real _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|) (e |u_(-> _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|) (i tptp.set_real)) (not (forall ((v |u_(-> tptp.set_real _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|)) (not (forall ((ii tptp.set_real)) (= (ho_150 v ii) (ite (= i ii) e (ho_150 u ii)))))))))) (let ((_let_65 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_150 x z) (ho_150 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> tptp.int tptp.int tptp.int Bool)|) (e |u_(-> tptp.int tptp.int Bool)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.int tptp.int Bool)|)) (not (forall ((ii tptp.int)) (= (ho_81 v ii) (ite (= i ii) e (ho_81 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_81 x z) (ho_81 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> _u_(-> tptp.real Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.real Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.real Bool)|)) (= (ho_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> tptp.int tptp.real)|) (e tptp.real) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.real)|)) (not (forall ((ii tptp.int)) (= (ho_225 v ii) (ite (= i ii) e (ho_225 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> tptp.int tptp.real)|) (y |u_(-> tptp.int tptp.real)|)) (or (not (forall ((z tptp.int)) (= (ho_225 x z) (ho_225 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> tptp.poly_poly_real tptp.poly_poly_real)|) (e tptp.poly_poly_real) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_170 v ii) (ite (= i ii) e (ho_170 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> tptp.poly_poly_real tptp.poly_poly_real)|) (y |u_(-> tptp.poly_poly_real tptp.poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> tptp.int Bool)|) (e Bool) (i tptp.int)) (not (forall ((v |u_(-> tptp.int Bool)|)) (not (forall ((ii tptp.int)) (= (ho_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.int Bool)|) (y |u_(-> tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> tptp.poly_int tptp.int Bool)|) (e |u_(-> tptp.int Bool)|) (i tptp.poly_int)) (not (forall ((v |u_(-> tptp.poly_int tptp.int Bool)|)) (not (forall ((ii tptp.poly_int)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> tptp.poly_int tptp.int Bool)|) (y |u_(-> tptp.poly_int tptp.int Bool)|)) (or (not (forall ((z tptp.poly_int)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> tptp.real tptp.real tptp.real Bool)|) (e |u_(-> tptp.real tptp.real Bool)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.real tptp.real Bool)|)) (not (forall ((ii tptp.real)) (= (ho_77 v ii) (ite (= i ii) e (ho_77 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> tptp.real tptp.real tptp.real Bool)|) (y |u_(-> tptp.real tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_77 x z) (ho_77 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (e |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (i tptp.set_int)) (not (forall ((v |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|)) (not (forall ((ii tptp.set_int)) (= (ho_139 v ii) (ite (= i ii) e (ho_139 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> tptp.poly_real tptp.real tptp.real)|) (e |u_(-> tptp.real tptp.real)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.real tptp.real)|)) (not (forall ((ii tptp.poly_real)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> tptp.poly_real tptp.real tptp.real)|) (y |u_(-> tptp.poly_real tptp.real tptp.real)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> tptp.poly_real tptp.real tptp.real tptp.real Bool)|) (e |u_(-> tptp.real tptp.real tptp.real Bool)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.real tptp.real tptp.real Bool)|)) (not (forall ((ii tptp.poly_real)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> tptp.poly_real tptp.real tptp.real tptp.real Bool)|) (y |u_(-> tptp.poly_real tptp.real tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> tptp.real tptp.real)|) (e tptp.real) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.real)|)) (not (forall ((ii tptp.real)) (= (ho_74 v ii) (ite (= i ii) e (ho_74 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_74 x z) (ho_74 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> tptp.poly_int tptp.poly_int)|) (e tptp.poly_int) (i tptp.poly_int)) (not (forall ((v |u_(-> tptp.poly_int tptp.poly_int)|)) (not (forall ((ii tptp.poly_int)) (= (ho_176 v ii) (ite (= i ii) e (ho_176 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> tptp.poly_int tptp.poly_int)|) (y |u_(-> tptp.poly_int tptp.poly_int)|)) (or (not (forall ((z tptp.poly_int)) (= (ho_176 x z) (ho_176 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> tptp.set_real Bool)|) (e Bool) (i tptp.set_real)) (not (forall ((v |u_(-> tptp.set_real Bool)|)) (not (forall ((ii tptp.set_real)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> tptp.set_real Bool)|) (y |u_(-> tptp.set_real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> tptp.int tptp.set_int Bool)|) (e |u_(-> tptp.set_int Bool)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.set_int Bool)|)) (not (forall ((ii tptp.int)) (= (ho_97 v ii) (ite (= i ii) e (ho_97 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> tptp.int tptp.set_int Bool)|) (y |u_(-> tptp.int tptp.set_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> tptp.real tptp.real Bool)|) (e |u_(-> tptp.real Bool)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.real Bool)|)) (not (forall ((ii tptp.real)) (= (ho_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> tptp.real tptp.real Bool)|) (y |u_(-> tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int)|) (e tptp.set_int) (i |u_(-> tptp.int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int)|)) (not (forall ((ii |u_(-> tptp.int Bool)|)) (= (ho_188 v ii) (ite (= i ii) e (ho_188 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_188 x z) (ho_188 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> _u_(-> tptp.real Bool)_ tptp.set_real)|) (e tptp.set_real) (i |u_(-> tptp.real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.real Bool)_ tptp.set_real)|)) (not (forall ((ii |u_(-> tptp.real Bool)|)) (= (ho_185 v ii) (ite (= i ii) e (ho_185 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.set_real)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.set_real)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_185 x z) (ho_185 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> tptp.poly_real Bool)|) (e Bool) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real Bool)|)) (not (forall ((ii tptp.poly_real)) (= (ho_154 v ii) (ite (= i ii) e (ho_154 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> tptp.poly_real Bool)|) (y |u_(-> tptp.poly_real Bool)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> tptp.real Bool)|) (e Bool) (i tptp.real)) (not (forall ((v |u_(-> tptp.real Bool)|)) (not (forall ((ii tptp.real)) (= (ho_64 v ii) (ite (= i ii) e (ho_64 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> tptp.real Bool)|) (y |u_(-> tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_64 x z) (ho_64 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> tptp.poly_int Bool)|) (e Bool) (i tptp.poly_int)) (not (forall ((v |u_(-> tptp.poly_int Bool)|)) (not (forall ((ii tptp.poly_int)) (= (ho_173 v ii) (ite (= i ii) e (ho_173 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> tptp.poly_int Bool)|) (y |u_(-> tptp.poly_int Bool)|)) (or (not (forall ((z tptp.poly_int)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|) (e |u_(-> _u_(-> tptp.real Bool)_ tptp.real Bool)|) (i |u_(-> tptp.real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (not (forall ((ii |u_(-> tptp.real Bool)|)) (= (ho_180 v ii) (ite (= i ii) e (ho_180 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_180 x z) (ho_180 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.real Bool)_ Bool)|) (i |u_(-> tptp.real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.real Bool)|)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> tptp.set_real tptp.set_real Bool)|) (e |u_(-> tptp.set_real Bool)|) (i tptp.set_real)) (not (forall ((v |u_(-> tptp.set_real tptp.set_real Bool)|)) (not (forall ((ii tptp.set_real)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> tptp.set_real tptp.set_real Bool)|) (y |u_(-> tptp.set_real tptp.set_real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_real tptp.poly_poly_real)|) (e |u_(-> tptp.poly_poly_real tptp.poly_poly_real)|) (i tptp.poly_poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_real tptp.poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_poly_real)) (= (ho_169 v ii) (ite (= i ii) e (ho_169 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_real tptp.poly_poly_real)|) (y |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_real tptp.poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_poly_real)) (= (ho_169 x z) (ho_169 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|) (e |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|) (i tptp.set_int)) (not (forall ((v |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (not (forall ((ii tptp.set_int)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> tptp.set_poly_real Bool)|) (e Bool) (i tptp.set_poly_real)) (not (forall ((v |u_(-> tptp.set_poly_real Bool)|)) (not (forall ((ii tptp.set_poly_real)) (= (ho_201 v ii) (ite (= i ii) e (ho_201 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> tptp.set_poly_real Bool)|) (y |u_(-> tptp.set_poly_real Bool)|)) (or (not (forall ((z tptp.set_poly_real)) (= (ho_201 x z) (ho_201 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> tptp.poly_poly_int tptp.poly_int Bool)|) (e |u_(-> tptp.poly_int Bool)|) (i tptp.poly_poly_int)) (not (forall ((v |u_(-> tptp.poly_poly_int tptp.poly_int Bool)|)) (not (forall ((ii tptp.poly_poly_int)) (= (ho_172 v ii) (ite (= i ii) e (ho_172 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> tptp.poly_poly_int tptp.poly_int Bool)|) (y |u_(-> tptp.poly_poly_int tptp.poly_int Bool)|)) (or (not (forall ((z tptp.poly_poly_int)) (= (ho_172 x z) (ho_172 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> tptp.int tptp.real Bool)|) (e |u_(-> tptp.real Bool)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.real Bool)|)) (not (forall ((ii tptp.int)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> tptp.int tptp.real Bool)|) (y |u_(-> tptp.int tptp.real Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> tptp.real tptp.set_real Bool)|) (e |u_(-> tptp.set_real Bool)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.set_real Bool)|)) (not (forall ((ii tptp.real)) (= (ho_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> tptp.real tptp.set_real Bool)|) (y |u_(-> tptp.real tptp.set_real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> _u_(-> tptp.real Bool)_ tptp.real Bool)|) (e |u_(-> tptp.real Bool)|) (i |u_(-> tptp.real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (not (forall ((ii |u_(-> tptp.real Bool)|)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> tptp.set_real tptp.real Bool)|) (e |u_(-> tptp.real Bool)|) (i tptp.set_real)) (not (forall ((v |u_(-> tptp.set_real tptp.real Bool)|)) (not (forall ((ii tptp.set_real)) (= (ho_63 v ii) (ite (= i ii) e (ho_63 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> tptp.set_real tptp.real Bool)|) (y |u_(-> tptp.set_real tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> tptp.set_real _u_(-> tptp.real Bool)_ tptp.real Bool)|) (e |u_(-> _u_(-> tptp.real Bool)_ tptp.real Bool)|) (i tptp.set_real)) (not (forall ((v |u_(-> tptp.set_real _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (not (forall ((ii tptp.set_real)) (= (ho_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> tptp.set_int tptp.set_int Bool)|) (e |u_(-> tptp.set_int Bool)|) (i tptp.set_int)) (not (forall ((v |u_(-> tptp.set_int tptp.set_int Bool)|)) (not (forall ((ii tptp.set_int)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> tptp.set_int tptp.set_int Bool)|) (y |u_(-> tptp.set_int tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> tptp.int tptp.int Bool)|) (e |u_(-> tptp.int Bool)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.int Bool)|)) (not (forall ((ii tptp.int)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (e |u_(-> tptp.int tptp.int Bool)|) (i |u_(-> tptp.int tptp.int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|)) (not (forall ((ii |u_(-> tptp.int tptp.int Bool)|)) (= (ho_140 v ii) (ite (= i ii) e (ho_140 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> tptp.poly_int tptp.poly_int Bool)|) (e |u_(-> tptp.poly_int Bool)|) (i tptp.poly_int)) (not (forall ((v |u_(-> tptp.poly_int tptp.poly_int Bool)|)) (not (forall ((ii tptp.poly_int)) (= (ho_205 v ii) (ite (= i ii) e (ho_205 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> tptp.poly_int tptp.poly_int Bool)|) (y |u_(-> tptp.poly_int tptp.poly_int Bool)|)) (or (not (forall ((z tptp.poly_int)) (= (ho_205 x z) (ho_205 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> tptp.poly_poly_real tptp.poly_real tptp.poly_real)|) (e |u_(-> tptp.poly_real tptp.poly_real)|) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.poly_real tptp.poly_real)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> tptp.poly_poly_real tptp.poly_real tptp.poly_real)|) (y |u_(-> tptp.poly_poly_real tptp.poly_real tptp.poly_real)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|) (e |u_(-> tptp.real tptp.int Bool)|) (i |u_(-> tptp.int tptp.real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|)) (not (forall ((ii |u_(-> tptp.int tptp.real Bool)|)) (= (ho_144 v ii) (ite (= i ii) e (ho_144 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real Bool)|)) (= (ho_144 x z) (ho_144 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> tptp.poly_real tptp.poly_real Bool)|) (e |u_(-> tptp.poly_real Bool)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.poly_real Bool)|)) (not (forall ((ii tptp.poly_real)) (= (ho_203 v ii) (ite (= i ii) e (ho_203 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> tptp.poly_real tptp.poly_real Bool)|) (y |u_(-> tptp.poly_real tptp.poly_real Bool)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_203 x z) (ho_203 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> tptp.poly_poly_real tptp.poly_poly_real Bool)|) (e |u_(-> tptp.poly_poly_real Bool)|) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.poly_poly_real Bool)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_207 v ii) (ite (= i ii) e (ho_207 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> tptp.poly_poly_real tptp.poly_poly_real Bool)|) (y |u_(-> tptp.poly_poly_real tptp.poly_poly_real Bool)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_207 x z) (ho_207 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> tptp.real tptp.int)|) (e tptp.int) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.int)|)) (not (forall ((ii tptp.real)) (= (ho_216 v ii) (ite (= i ii) e (ho_216 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> tptp.real tptp.int)|) (y |u_(-> tptp.real tptp.int)|)) (or (not (forall ((z tptp.real)) (= (ho_216 x z) (ho_216 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> tptp.real tptp.real tptp.int)|) (e |u_(-> tptp.real tptp.int)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.real tptp.int)|)) (not (forall ((ii tptp.real)) (= (ho_215 v ii) (ite (= i ii) e (ho_215 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> tptp.real tptp.real tptp.int)|) (y |u_(-> tptp.real tptp.real tptp.int)|)) (or (not (forall ((z tptp.real)) (= (ho_215 x z) (ho_215 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> tptp.poly_real tptp.real tptp.real tptp.int)|) (e |u_(-> tptp.real tptp.real tptp.int)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.real tptp.real tptp.int)|)) (not (forall ((ii tptp.poly_real)) (= (ho_214 v ii) (ite (= i ii) e (ho_214 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> tptp.poly_real tptp.real tptp.real tptp.int)|) (y |u_(-> tptp.poly_real tptp.real tptp.real tptp.int)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_214 x z) (ho_214 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> _u_(-> tptp.set_real Bool)_ tptp.set_set_real)|) (e tptp.set_set_real) (i |u_(-> tptp.set_real Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.set_real Bool)_ tptp.set_set_real)|)) (not (forall ((ii |u_(-> tptp.set_real Bool)|)) (= (ho_218 v ii) (ite (= i ii) e (ho_218 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> _u_(-> tptp.set_real Bool)_ tptp.set_set_real)|) (y |u_(-> _u_(-> tptp.set_real Bool)_ tptp.set_set_real)|)) (or (not (forall ((z |u_(-> tptp.set_real Bool)|)) (= (ho_218 x z) (ho_218 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> tptp.set_set_real Bool)|) (e Bool) (i tptp.set_set_real)) (not (forall ((v |u_(-> tptp.set_set_real Bool)|)) (not (forall ((ii tptp.set_set_real)) (= (ho_220 v ii) (ite (= i ii) e (ho_220 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> tptp.set_set_real Bool)|) (y |u_(-> tptp.set_set_real Bool)|)) (or (not (forall ((z tptp.set_set_real)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_156 (forall ((u |u_(-> _u_(-> tptp.set_int Bool)_ tptp.set_set_int)|) (e tptp.set_set_int) (i |u_(-> tptp.set_int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.set_int Bool)_ tptp.set_set_int)|)) (not (forall ((ii |u_(-> tptp.set_int Bool)|)) (= (ho_222 v ii) (ite (= i ii) e (ho_222 u ii)))))))))) (let ((_let_157 (forall ((x |u_(-> _u_(-> tptp.set_int Bool)_ tptp.set_set_int)|) (y |u_(-> _u_(-> tptp.set_int Bool)_ tptp.set_set_int)|)) (or (not (forall ((z |u_(-> tptp.set_int Bool)|)) (= (ho_222 x z) (ho_222 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> tptp.set_set_int Bool)|) (e Bool) (i tptp.set_set_int)) (not (forall ((v |u_(-> tptp.set_set_int Bool)|)) (not (forall ((ii tptp.set_set_int)) (= (ho_224 v ii) (ite (= i ii) e (ho_224 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> tptp.set_set_int Bool)|) (y |u_(-> tptp.set_set_int Bool)|)) (or (not (forall ((z tptp.set_set_int)) (= (ho_224 x z) (ho_224 y z)))) (= x y))))) (let ((_let_160 (forall ((u |u_(-> tptp.nat tptp.poly_real tptp.poly_real)|) (e |u_(-> tptp.poly_real tptp.poly_real)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.poly_real tptp.poly_real)|)) (not (forall ((ii tptp.nat)) (= (ho_227 v ii) (ite (= i ii) e (ho_227 u ii)))))))))) (let ((_let_161 (forall ((x |u_(-> tptp.nat tptp.poly_real tptp.poly_real)|) (y |u_(-> tptp.nat tptp.poly_real tptp.poly_real)|)) (or (not (forall ((z tptp.nat)) (= (ho_227 x z) (ho_227 y z)))) (= x y))))) (let ((_let_162 (forall ((u |u_(-> tptp.nat tptp.poly_int tptp.poly_int)|) (e |u_(-> tptp.poly_int tptp.poly_int)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.poly_int tptp.poly_int)|)) (not (forall ((ii tptp.nat)) (= (ho_229 v ii) (ite (= i ii) e (ho_229 u ii)))))))))) (let ((_let_163 (forall ((x |u_(-> tptp.nat tptp.poly_int tptp.poly_int)|) (y |u_(-> tptp.nat tptp.poly_int tptp.poly_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_229 x z) (ho_229 y z)))) (= x y))))) (let ((_let_164 (forall ((u |u_(-> tptp.nat tptp.poly_poly_real tptp.poly_poly_real)|) (e |u_(-> tptp.poly_poly_real tptp.poly_poly_real)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.poly_poly_real tptp.poly_poly_real)|)) (not (forall ((ii tptp.nat)) (= (ho_231 v ii) (ite (= i ii) e (ho_231 u ii)))))))))) (let ((_let_165 (forall ((x |u_(-> tptp.nat tptp.poly_poly_real tptp.poly_poly_real)|) (y |u_(-> tptp.nat tptp.poly_poly_real tptp.poly_poly_real)|)) (or (not (forall ((z tptp.nat)) (= (ho_231 x z) (ho_231 y z)))) (= x y))))) (let ((_let_166 (forall ((u |u_(-> tptp.poly_real tptp.poly_real tptp.real tptp.int)|) (e |u_(-> tptp.poly_real tptp.real tptp.int)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.poly_real tptp.real tptp.int)|)) (not (forall ((ii tptp.poly_real)) (= (ho_233 v ii) (ite (= i ii) e (ho_233 u ii)))))))))) (let ((_let_167 (forall ((x |u_(-> tptp.poly_real tptp.poly_real tptp.real tptp.int)|) (y |u_(-> tptp.poly_real tptp.poly_real tptp.real tptp.int)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_233 x z) (ho_233 y z)))) (= x y))))) (let ((_let_168 (forall ((u |u_(-> tptp.set_real tptp.int)|) (e tptp.int) (i tptp.set_real)) (not (forall ((v |u_(-> tptp.set_real tptp.int)|)) (not (forall ((ii tptp.set_real)) (= (ho_237 v ii) (ite (= i ii) e (ho_237 u ii)))))))))) (let ((_let_169 (forall ((x |u_(-> tptp.set_real tptp.int)|) (y |u_(-> tptp.set_real tptp.int)|)) (or (not (forall ((z tptp.set_real)) (= (ho_237 x z) (ho_237 y z)))) (= x y))))) (let ((_let_170 (forall ((u |u_(-> _u_(-> tptp.real tptp.int)_ tptp.set_real tptp.int)|) (e |u_(-> tptp.set_real tptp.int)|) (i |u_(-> tptp.real tptp.int)|)) (not (forall ((v |u_(-> _u_(-> tptp.real tptp.int)_ tptp.set_real tptp.int)|)) (not (forall ((ii |u_(-> tptp.real tptp.int)|)) (= (ho_236 v ii) (ite (= i ii) e (ho_236 u ii)))))))))) (let ((_let_171 (forall ((x |u_(-> _u_(-> tptp.real tptp.int)_ tptp.set_real tptp.int)|) (y |u_(-> _u_(-> tptp.real tptp.int)_ tptp.set_real tptp.int)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int)|)) (= (ho_236 x z) (ho_236 y z)))) (= x y))))) (let ((_let_172 (forall ((BOUND_VARIABLE_19625 tptp.set_real) (BOUND_VARIABLE_19626 tptp.real)) (= (ho_64 (ho_63 k_62 BOUND_VARIABLE_19625) BOUND_VARIABLE_19626) (ho_67 (ho_66 k_65 BOUND_VARIABLE_19626) BOUND_VARIABLE_19625))))) (let ((_let_173 (forall ((BOUND_VARIABLE_19617 tptp.set_real) (BOUND_VARIABLE_19618 tptp.real)) (= (ho_64 (ho_63 k_68 BOUND_VARIABLE_19617) BOUND_VARIABLE_19618) (ho_67 (ho_66 k_65 BOUND_VARIABLE_19618) BOUND_VARIABLE_19617))))) (let ((_let_174 (forall ((BOUND_VARIABLE_19606 tptp.real)) (= (ho_64 k_69 BOUND_VARIABLE_19606) (and (= tptp.zero_zero_real (ho_74 (ho_73 k_72 tptp.p) BOUND_VARIABLE_19606)) (ho_64 (ho_71 k_70 tptp.a) BOUND_VARIABLE_19606) (ho_64 (ho_71 k_70 BOUND_VARIABLE_19606) tptp.b)))))) (let ((_let_175 (forall ((BOUND_VARIABLE_19590 tptp.poly_real) (BOUND_VARIABLE_19591 tptp.real) (BOUND_VARIABLE_19592 tptp.real) (BOUND_VARIABLE_19593 tptp.real)) (= (ho_64 (ho_71 (ho_77 (ho_76 k_75 BOUND_VARIABLE_19590) BOUND_VARIABLE_19591) BOUND_VARIABLE_19592) BOUND_VARIABLE_19593) (and (= tptp.zero_zero_real (ho_74 (ho_73 k_72 BOUND_VARIABLE_19590) BOUND_VARIABLE_19593)) (ho_64 (ho_71 k_70 BOUND_VARIABLE_19591) BOUND_VARIABLE_19593) (ho_64 (ho_71 k_70 BOUND_VARIABLE_19593) BOUND_VARIABLE_19592)))))) (let ((_let_176 (forall ((BOUND_VARIABLE_19574 tptp.poly_real) (BOUND_VARIABLE_19575 tptp.real) (BOUND_VARIABLE_19576 tptp.real) (BOUND_VARIABLE_19577 tptp.real)) (= (ho_64 (ho_71 (ho_77 (ho_76 k_78 BOUND_VARIABLE_19574) BOUND_VARIABLE_19575) BOUND_VARIABLE_19576) BOUND_VARIABLE_19577) (and (= tptp.zero_zero_real (ho_74 (ho_73 k_72 BOUND_VARIABLE_19574) BOUND_VARIABLE_19577)) (ho_64 (ho_71 k_70 BOUND_VARIABLE_19575) BOUND_VARIABLE_19577) (ho_64 (ho_71 k_70 BOUND_VARIABLE_19577) BOUND_VARIABLE_19576)))))) (let ((_let_177 (forall ((BOUND_VARIABLE_19560 tptp.real) (BOUND_VARIABLE_19561 tptp.real) (BOUND_VARIABLE_19562 tptp.real)) (= (ho_64 (ho_71 (ho_77 k_79 BOUND_VARIABLE_19560) BOUND_VARIABLE_19561) BOUND_VARIABLE_19562) (and (= tptp.zero_zero_real (ho_74 (ho_73 k_72 tptp.zero_zero_poly_real) BOUND_VARIABLE_19562)) (ho_64 (ho_71 k_70 BOUND_VARIABLE_19560) BOUND_VARIABLE_19562) (ho_64 (ho_71 k_70 BOUND_VARIABLE_19562) BOUND_VARIABLE_19561)))))) (let ((_let_178 (forall ((BOUND_VARIABLE_19546 tptp.int) (BOUND_VARIABLE_19547 tptp.int) (BOUND_VARIABLE_19548 tptp.int)) (= (ho_83 (ho_82 (ho_81 k_80 BOUND_VARIABLE_19546) BOUND_VARIABLE_19547) BOUND_VARIABLE_19548) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19548) BOUND_VARIABLE_19546) (ho_83 (ho_82 k_84 BOUND_VARIABLE_19547) BOUND_VARIABLE_19548) (not (= BOUND_VARIABLE_19547 BOUND_VARIABLE_19548))))))) (let ((_let_179 (forall ((BOUND_VARIABLE_19530 tptp.int) (BOUND_VARIABLE_19531 tptp.int) (BOUND_VARIABLE_19532 tptp.int)) (= (ho_83 (ho_82 (ho_81 k_85 BOUND_VARIABLE_19530) BOUND_VARIABLE_19531) BOUND_VARIABLE_19532) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19530) BOUND_VARIABLE_19532) (not (= BOUND_VARIABLE_19530 BOUND_VARIABLE_19532)) (ho_83 (ho_82 k_84 BOUND_VARIABLE_19532) BOUND_VARIABLE_19531) (not (= BOUND_VARIABLE_19531 BOUND_VARIABLE_19532))))))) (let ((_let_180 (forall ((BOUND_VARIABLE_19516 tptp.int) (BOUND_VARIABLE_19517 tptp.int) (BOUND_VARIABLE_19518 tptp.int)) (= (ho_83 (ho_82 (ho_81 k_86 BOUND_VARIABLE_19516) BOUND_VARIABLE_19517) BOUND_VARIABLE_19518) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19516) BOUND_VARIABLE_19518) (ho_83 (ho_82 k_84 BOUND_VARIABLE_19518) BOUND_VARIABLE_19517) (not (= BOUND_VARIABLE_19517 BOUND_VARIABLE_19518))))))) (let ((_let_181 (forall ((BOUND_VARIABLE_19504 tptp.int) (BOUND_VARIABLE_19505 tptp.int) (BOUND_VARIABLE_19506 tptp.int)) (= (ho_83 (ho_82 (ho_81 k_87 BOUND_VARIABLE_19504) BOUND_VARIABLE_19505) BOUND_VARIABLE_19506) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19504) BOUND_VARIABLE_19506) (ho_83 (ho_82 k_84 BOUND_VARIABLE_19506) BOUND_VARIABLE_19505)))))) (let ((_let_182 (forall ((BOUND_VARIABLE_19476 tptp.set_real) (BOUND_VARIABLE_19477 tptp.set_real)) (= (ho_90 (ho_89 k_88 (ho_63 k_62 BOUND_VARIABLE_19476)) (ho_63 k_68 BOUND_VARIABLE_19477)) (ho_67 (ho_92 k_91 BOUND_VARIABLE_19476) BOUND_VARIABLE_19477))))) (let ((_let_183 (forall ((BOUND_VARIABLE_19465 tptp.set_int) (BOUND_VARIABLE_19971 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_19467 tptp.int)) (= (ho_83 (ho_95 (ho_94 k_93 BOUND_VARIABLE_19465) BOUND_VARIABLE_19971) BOUND_VARIABLE_19467) (and (ho_98 (ho_97 k_96 BOUND_VARIABLE_19467) BOUND_VARIABLE_19465) (ho_83 BOUND_VARIABLE_19971 BOUND_VARIABLE_19467)))))) (let ((_let_184 (forall ((BOUND_VARIABLE_19454 tptp.set_real) (BOUND_VARIABLE_20000 |u_(-> tptp.real Bool)|) (BOUND_VARIABLE_19456 tptp.real)) (= (ho_64 (ho_101 (ho_100 k_99 BOUND_VARIABLE_19454) BOUND_VARIABLE_20000) BOUND_VARIABLE_19456) (and (ho_67 (ho_66 k_65 BOUND_VARIABLE_19456) BOUND_VARIABLE_19454) (ho_64 BOUND_VARIABLE_20000 BOUND_VARIABLE_19456)))))) (let ((_let_185 (forall ((BOUND_VARIABLE_19443 tptp.set_real) (BOUND_VARIABLE_19444 tptp.set_real)) (= (ho_67 (ho_92 k_102 BOUND_VARIABLE_19443) BOUND_VARIABLE_19444) (forall ((X tptp.real)) (let ((_let_1 (ho_66 k_65 X))) (or (not (ho_67 _let_1 BOUND_VARIABLE_19443)) (ho_67 _let_1 BOUND_VARIABLE_19444)))))))) (let ((_let_186 (forall ((BOUND_VARIABLE_19432 tptp.set_real) (BOUND_VARIABLE_19433 tptp.set_real)) (= (ho_67 (ho_92 k_103 BOUND_VARIABLE_19432) BOUND_VARIABLE_19433) (forall ((T3 tptp.real)) (let ((_let_1 (ho_66 k_65 T3))) (or (not (ho_67 _let_1 BOUND_VARIABLE_19432)) (ho_67 _let_1 BOUND_VARIABLE_19433)))))))) (let ((_let_187 (forall ((BOUND_VARIABLE_19421 tptp.int) (BOUND_VARIABLE_19422 tptp.int)) (= (ho_83 (ho_82 k_104 BOUND_VARIABLE_19421) BOUND_VARIABLE_19422) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19421) BOUND_VARIABLE_19422) (not (= BOUND_VARIABLE_19421 BOUND_VARIABLE_19422))))))) (let ((_let_188 (forall ((BOUND_VARIABLE_19409 tptp.real) (BOUND_VARIABLE_19410 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19409 BOUND_VARIABLE_19410))) (= (ho_64 (ho_71 k_105 BOUND_VARIABLE_19409) BOUND_VARIABLE_19410) (and (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19409) BOUND_VARIABLE_19410) _let_1) (not _let_1))))))) (let ((_let_189 (forall ((BOUND_VARIABLE_19397 tptp.int) (BOUND_VARIABLE_19398 tptp.int)) (let ((_let_1 (= BOUND_VARIABLE_19397 BOUND_VARIABLE_19398))) (= (ho_83 (ho_82 k_106 BOUND_VARIABLE_19397) BOUND_VARIABLE_19398) (or (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19397) BOUND_VARIABLE_19398) (not _let_1)) _let_1)))))) (let ((_let_190 (forall ((BOUND_VARIABLE_19387 tptp.real) (BOUND_VARIABLE_19388 tptp.real)) (= (ho_64 (ho_71 k_107 BOUND_VARIABLE_19387) BOUND_VARIABLE_19388) (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19387) BOUND_VARIABLE_19388) (= BOUND_VARIABLE_19387 BOUND_VARIABLE_19388)))))) (let ((_let_191 (forall ((BOUND_VARIABLE_19375 tptp.int) (BOUND_VARIABLE_19376 tptp.int)) (= (ho_83 (ho_82 k_108 BOUND_VARIABLE_19375) BOUND_VARIABLE_19376) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19375) BOUND_VARIABLE_19376) (not (ho_83 (ho_82 k_84 BOUND_VARIABLE_19376) BOUND_VARIABLE_19375))))))) (let ((_let_192 (forall ((BOUND_VARIABLE_19360 tptp.real) (BOUND_VARIABLE_19361 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19360 BOUND_VARIABLE_19361))) (= (and (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19360) BOUND_VARIABLE_19361) _let_1) (not (ho_64 (ho_71 k_70 BOUND_VARIABLE_19361) BOUND_VARIABLE_19360)) (not _let_1)) (ho_64 (ho_71 k_109 BOUND_VARIABLE_19360) BOUND_VARIABLE_19361)))))) (let ((_let_193 (forall ((BOUND_VARIABLE_19349 tptp.int) (BOUND_VARIABLE_19350 tptp.int)) (= (ho_83 (ho_82 k_110 BOUND_VARIABLE_19349) BOUND_VARIABLE_19350) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19349) BOUND_VARIABLE_19350) (not (= BOUND_VARIABLE_19349 BOUND_VARIABLE_19350))))))) (let ((_let_194 (forall ((BOUND_VARIABLE_19338 tptp.int) (BOUND_VARIABLE_19339 tptp.int)) (= (ho_83 (ho_82 k_111 BOUND_VARIABLE_19338) BOUND_VARIABLE_19339) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19338) BOUND_VARIABLE_19339) (not (= BOUND_VARIABLE_19338 BOUND_VARIABLE_19339))))))) (let ((_let_195 (forall ((BOUND_VARIABLE_19326 tptp.real) (BOUND_VARIABLE_19327 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19326 BOUND_VARIABLE_19327))) (= (ho_64 (ho_71 k_112 BOUND_VARIABLE_19326) BOUND_VARIABLE_19327) (and (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19326) BOUND_VARIABLE_19327) _let_1) (not _let_1))))))) (let ((_let_196 (forall ((BOUND_VARIABLE_19314 tptp.int) (BOUND_VARIABLE_19315 tptp.int)) (let ((_let_1 (= BOUND_VARIABLE_19314 BOUND_VARIABLE_19315))) (= (ho_83 (ho_82 k_113 BOUND_VARIABLE_19314) BOUND_VARIABLE_19315) (or (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19314) BOUND_VARIABLE_19315) (not _let_1)) _let_1)))))) (let ((_let_197 (forall ((BOUND_VARIABLE_19304 tptp.real) (BOUND_VARIABLE_19305 tptp.real)) (= (ho_64 (ho_71 k_114 BOUND_VARIABLE_19304) BOUND_VARIABLE_19305) (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19304) BOUND_VARIABLE_19305) (= BOUND_VARIABLE_19304 BOUND_VARIABLE_19305)))))) (let ((_let_198 (forall ((BOUND_VARIABLE_19297 tptp.int) (BOUND_VARIABLE_19298 tptp.int)) (= (= BOUND_VARIABLE_19297 BOUND_VARIABLE_19298) (ho_83 (ho_82 k_115 BOUND_VARIABLE_19297) BOUND_VARIABLE_19298))))) (let ((_let_199 (forall ((BOUND_VARIABLE_19286 tptp.int) (BOUND_VARIABLE_19287 tptp.int)) (= (ho_83 (ho_82 k_116 BOUND_VARIABLE_19286) BOUND_VARIABLE_19287) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19286) BOUND_VARIABLE_19287) (ho_83 (ho_82 k_84 BOUND_VARIABLE_19287) BOUND_VARIABLE_19286)))))) (let ((_let_200 (forall ((BOUND_VARIABLE_19279 tptp.real) (BOUND_VARIABLE_19280 tptp.real)) (= (= BOUND_VARIABLE_19279 BOUND_VARIABLE_19280) (ho_64 (ho_71 k_117 BOUND_VARIABLE_19279) BOUND_VARIABLE_19280))))) (let ((_let_201 (forall ((BOUND_VARIABLE_19265 tptp.real) (BOUND_VARIABLE_19266 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19265 BOUND_VARIABLE_19266))) (= (ho_64 (ho_71 k_118 BOUND_VARIABLE_19265) BOUND_VARIABLE_19266) (and (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19265) BOUND_VARIABLE_19266) _let_1) (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19266) BOUND_VARIABLE_19265) _let_1))))))) (let ((_let_202 (forall ((BOUND_VARIABLE_19258 tptp.int) (BOUND_VARIABLE_19259 tptp.int)) (= (= BOUND_VARIABLE_19258 BOUND_VARIABLE_19259) (ho_83 (ho_82 k_119 BOUND_VARIABLE_19258) BOUND_VARIABLE_19259))))) (let ((_let_203 (forall ((BOUND_VARIABLE_19247 tptp.int) (BOUND_VARIABLE_19248 tptp.int)) (= (ho_83 (ho_82 k_120 BOUND_VARIABLE_19247) BOUND_VARIABLE_19248) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19247) BOUND_VARIABLE_19248) (ho_83 (ho_82 k_84 BOUND_VARIABLE_19248) BOUND_VARIABLE_19247)))))) (let ((_let_204 (forall ((BOUND_VARIABLE_19240 tptp.real) (BOUND_VARIABLE_19241 tptp.real)) (= (= BOUND_VARIABLE_19240 BOUND_VARIABLE_19241) (ho_64 (ho_71 k_121 BOUND_VARIABLE_19240) BOUND_VARIABLE_19241))))) (let ((_let_205 (forall ((BOUND_VARIABLE_19226 tptp.real) (BOUND_VARIABLE_19227 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19226 BOUND_VARIABLE_19227))) (= (ho_64 (ho_71 k_122 BOUND_VARIABLE_19226) BOUND_VARIABLE_19227) (and (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19226) BOUND_VARIABLE_19227) _let_1) (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19227) BOUND_VARIABLE_19226) _let_1))))))) (let ((_let_206 (forall ((BOUND_VARIABLE_19219 tptp.int) (BOUND_VARIABLE_19220 tptp.int)) (= (= BOUND_VARIABLE_19219 BOUND_VARIABLE_19220) (ho_83 (ho_82 k_123 BOUND_VARIABLE_19219) BOUND_VARIABLE_19220))))) (let ((_let_207 (forall ((BOUND_VARIABLE_19208 tptp.int) (BOUND_VARIABLE_19209 tptp.int)) (= (ho_83 (ho_82 k_124 BOUND_VARIABLE_19208) BOUND_VARIABLE_19209) (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19209) BOUND_VARIABLE_19208) (ho_83 (ho_82 k_84 BOUND_VARIABLE_19208) BOUND_VARIABLE_19209)))))) (let ((_let_208 (forall ((BOUND_VARIABLE_19201 tptp.real) (BOUND_VARIABLE_19202 tptp.real)) (= (= BOUND_VARIABLE_19201 BOUND_VARIABLE_19202) (ho_64 (ho_71 k_125 BOUND_VARIABLE_19201) BOUND_VARIABLE_19202))))) (let ((_let_209 (forall ((BOUND_VARIABLE_19187 tptp.real) (BOUND_VARIABLE_19188 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19187 BOUND_VARIABLE_19188))) (= (ho_64 (ho_71 k_126 BOUND_VARIABLE_19187) BOUND_VARIABLE_19188) (and (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19188) BOUND_VARIABLE_19187) _let_1) (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19187) BOUND_VARIABLE_19188) _let_1))))))) (let ((_let_210 (forall ((BOUND_VARIABLE_19179 tptp.set_int) (BOUND_VARIABLE_19180 tptp.set_int)) (= (ho_98 (ho_128 k_127 BOUND_VARIABLE_19179) BOUND_VARIABLE_19180) (ho_98 (ho_128 k_129 BOUND_VARIABLE_19180) BOUND_VARIABLE_19179))))) (let ((_let_211 (forall ((BOUND_VARIABLE_19168 tptp.set_real) (BOUND_VARIABLE_19169 tptp.set_real)) (= (ho_67 (ho_92 k_130 BOUND_VARIABLE_19168) BOUND_VARIABLE_19169) (forall ((X tptp.real)) (let ((_let_1 (ho_66 k_65 X))) (or (not (ho_67 _let_1 BOUND_VARIABLE_19169)) (ho_67 _let_1 BOUND_VARIABLE_19168)))))))) (let ((_let_212 (forall ((BOUND_VARIABLE_19160 tptp.set_int) (BOUND_VARIABLE_19161 tptp.int)) (= (ho_83 (ho_132 k_131 BOUND_VARIABLE_19160) BOUND_VARIABLE_19161) (ho_98 (ho_97 k_96 BOUND_VARIABLE_19161) BOUND_VARIABLE_19160))))) (let ((_let_213 (forall ((BOUND_VARIABLE_19152 tptp.set_real) (BOUND_VARIABLE_19153 tptp.real)) (= (ho_64 (ho_63 k_133 BOUND_VARIABLE_19152) BOUND_VARIABLE_19153) (ho_67 (ho_66 k_65 BOUND_VARIABLE_19153) BOUND_VARIABLE_19152))))) (let ((_let_214 (forall ((BOUND_VARIABLE_19140 tptp.int) (BOUND_VARIABLE_19141 tptp.int)) (let ((_let_1 (= BOUND_VARIABLE_19140 BOUND_VARIABLE_19141))) (= (ho_83 (ho_82 k_134 BOUND_VARIABLE_19140) BOUND_VARIABLE_19141) (or (and (ho_83 (ho_82 k_84 BOUND_VARIABLE_19140) BOUND_VARIABLE_19141) (not _let_1)) _let_1)))))) (let ((_let_215 (forall ((BOUND_VARIABLE_19130 tptp.real) (BOUND_VARIABLE_19131 tptp.real)) (= (ho_64 (ho_71 k_135 BOUND_VARIABLE_19130) BOUND_VARIABLE_19131) (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19130) BOUND_VARIABLE_19131) (= BOUND_VARIABLE_19130 BOUND_VARIABLE_19131)))))) (let ((_let_216 (forall ((BOUND_VARIABLE_19120 tptp.real) (BOUND_VARIABLE_19121 tptp.real)) (= (ho_64 (ho_71 k_136 BOUND_VARIABLE_19120) BOUND_VARIABLE_19121) (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19120) BOUND_VARIABLE_19121) (= BOUND_VARIABLE_19120 BOUND_VARIABLE_19121)))))) (let ((_let_217 (forall ((BOUND_VARIABLE_19108 tptp.real) (BOUND_VARIABLE_19109 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19108 BOUND_VARIABLE_19109))) (= (ho_64 (ho_71 k_137 BOUND_VARIABLE_19108) BOUND_VARIABLE_19109) (and (or (ho_64 (ho_71 k_70 BOUND_VARIABLE_19108) BOUND_VARIABLE_19109) _let_1) (not _let_1))))))) (let ((_let_218 (forall ((BOUND_VARIABLE_19095 tptp.set_int) (BOUND_VARIABLE_20378 |u_(-> tptp.int tptp.int Bool)|) (BOUND_VARIABLE_19097 tptp.int) (BOUND_VARIABLE_19098 tptp.int)) (= (ho_83 (ho_82 (ho_140 (ho_139 k_138 BOUND_VARIABLE_19095) BOUND_VARIABLE_20378) BOUND_VARIABLE_19097) BOUND_VARIABLE_19098) (and (ho_98 (ho_97 k_96 BOUND_VARIABLE_19098) BOUND_VARIABLE_19095) (ho_83 (ho_82 BOUND_VARIABLE_20378 BOUND_VARIABLE_19098) BOUND_VARIABLE_19097)))))) (let ((_let_219 (forall ((BOUND_VARIABLE_19082 tptp.set_int) (BOUND_VARIABLE_20405 |u_(-> tptp.int tptp.real Bool)|) (BOUND_VARIABLE_19084 tptp.real) (BOUND_VARIABLE_19085 tptp.int)) (= (ho_83 (ho_145 (ho_144 (ho_143 k_142 BOUND_VARIABLE_19082) BOUND_VARIABLE_20405) BOUND_VARIABLE_19084) BOUND_VARIABLE_19085) (and (ho_98 (ho_97 k_96 BOUND_VARIABLE_19085) BOUND_VARIABLE_19082) (ho_64 (ho_141 BOUND_VARIABLE_20405 BOUND_VARIABLE_19085) BOUND_VARIABLE_19084)))))) (let ((_let_220 (forall ((BOUND_VARIABLE_19069 tptp.set_real) (BOUND_VARIABLE_20436 |u_(-> tptp.real tptp.int Bool)|) (BOUND_VARIABLE_19071 tptp.int) (BOUND_VARIABLE_19072 tptp.real)) (= (ho_64 (ho_141 (ho_148 (ho_147 k_146 BOUND_VARIABLE_19069) BOUND_VARIABLE_20436) BOUND_VARIABLE_19071) BOUND_VARIABLE_19072) (and (ho_67 (ho_66 k_65 BOUND_VARIABLE_19072) BOUND_VARIABLE_19069) (ho_83 (ho_145 BOUND_VARIABLE_20436 BOUND_VARIABLE_19072) BOUND_VARIABLE_19071)))))) (let ((_let_221 (forall ((BOUND_VARIABLE_19056 tptp.set_real) (BOUND_VARIABLE_20462 |u_(-> tptp.real tptp.real Bool)|) (BOUND_VARIABLE_19058 tptp.real) (BOUND_VARIABLE_19059 tptp.real)) (= (ho_64 (ho_71 (ho_151 (ho_150 k_149 BOUND_VARIABLE_19056) BOUND_VARIABLE_20462) BOUND_VARIABLE_19058) BOUND_VARIABLE_19059) (and (ho_67 (ho_66 k_65 BOUND_VARIABLE_19059) BOUND_VARIABLE_19056) (ho_64 (ho_71 BOUND_VARIABLE_20462 BOUND_VARIABLE_19059) BOUND_VARIABLE_19058)))))) (let ((_let_222 (forall ((BOUND_VARIABLE_19047 tptp.poly_poly_real) (BOUND_VARIABLE_19048 tptp.poly_real)) (= (ho_154 (ho_153 k_152 BOUND_VARIABLE_19047) BOUND_VARIABLE_19048) (= tptp.zero_zero_poly_real (ho_157 (ho_156 k_155 BOUND_VARIABLE_19047) BOUND_VARIABLE_19048)))))) (let ((_let_223 (forall ((BOUND_VARIABLE_19038 tptp.poly_int) (BOUND_VARIABLE_19039 tptp.int)) (= (ho_83 (ho_159 k_158 BOUND_VARIABLE_19038) BOUND_VARIABLE_19039) (= tptp.zero_zero_int (ho_162 (ho_161 k_160 BOUND_VARIABLE_19038) BOUND_VARIABLE_19039)))))) (let ((_let_224 (forall ((BOUND_VARIABLE_19029 tptp.poly_real) (BOUND_VARIABLE_19030 tptp.real)) (= (ho_64 (ho_164 k_163 BOUND_VARIABLE_19029) BOUND_VARIABLE_19030) (= tptp.zero_zero_real (ho_74 (ho_73 k_72 BOUND_VARIABLE_19029) BOUND_VARIABLE_19030)))))) (let ((_let_225 (forall ((BOUND_VARIABLE_19020 tptp.poly_poly_poly_real) (BOUND_VARIABLE_19021 tptp.poly_poly_real)) (= (ho_167 (ho_166 k_165 BOUND_VARIABLE_19020) BOUND_VARIABLE_19021) (= tptp.zero_z1423781445y_real (ho_170 (ho_169 k_168 BOUND_VARIABLE_19020) BOUND_VARIABLE_19021)))))) (let ((_let_226 (forall ((BOUND_VARIABLE_19011 tptp.poly_poly_int) (BOUND_VARIABLE_19012 tptp.poly_int)) (= (ho_173 (ho_172 k_171 BOUND_VARIABLE_19011) BOUND_VARIABLE_19012) (= tptp.zero_zero_poly_int (ho_176 (ho_175 k_174 BOUND_VARIABLE_19011) BOUND_VARIABLE_19012)))))) (let ((_let_227 (forall ((BOUND_VARIABLE_20590 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_20589 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_19003 tptp.int)) (= (ho_83 (ho_95 (ho_178 k_177 BOUND_VARIABLE_20590) BOUND_VARIABLE_20589) BOUND_VARIABLE_19003) (or (ho_83 BOUND_VARIABLE_20590 BOUND_VARIABLE_19003) (ho_83 BOUND_VARIABLE_20589 BOUND_VARIABLE_19003)))))) (let ((_let_228 (forall ((BOUND_VARIABLE_20609 |u_(-> tptp.real Bool)|) (BOUND_VARIABLE_20608 |u_(-> tptp.real Bool)|) (BOUND_VARIABLE_18993 tptp.real)) (= (ho_64 (ho_101 (ho_180 k_179 BOUND_VARIABLE_20609) BOUND_VARIABLE_20608) BOUND_VARIABLE_18993) (or (ho_64 BOUND_VARIABLE_20609 BOUND_VARIABLE_18993) (ho_64 BOUND_VARIABLE_20608 BOUND_VARIABLE_18993)))))) (let ((_let_229 (forall ((BOUND_VARIABLE_20628 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_20627 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_18983 tptp.int)) (= (ho_83 (ho_95 (ho_178 k_181 BOUND_VARIABLE_20628) BOUND_VARIABLE_20627) BOUND_VARIABLE_18983) (and (ho_83 BOUND_VARIABLE_20628 BOUND_VARIABLE_18983) (ho_83 BOUND_VARIABLE_20627 BOUND_VARIABLE_18983)))))) (let ((_let_230 (forall ((BOUND_VARIABLE_20643 |u_(-> tptp.real Bool)|) (BOUND_VARIABLE_20642 |u_(-> tptp.real Bool)|) (BOUND_VARIABLE_18973 tptp.real)) (= (ho_64 (ho_101 (ho_180 k_182 BOUND_VARIABLE_20643) BOUND_VARIABLE_20642) BOUND_VARIABLE_18973) (and (ho_64 BOUND_VARIABLE_20643 BOUND_VARIABLE_18973) (ho_64 BOUND_VARIABLE_20642 BOUND_VARIABLE_18973)))))) (let ((_let_231 (ho_185 k_184 k_183))) (let ((_let_232 (ho_67 k_186 _let_231))) (let ((_let_233 (forall ((BOUND_VARIABLE_19625 tptp.set_real) (BOUND_VARIABLE_19626 tptp.real)) (= (@ (@ tptp.member_real BOUND_VARIABLE_19626) BOUND_VARIABLE_19625) (ll_61 BOUND_VARIABLE_19625 BOUND_VARIABLE_19626))))) (let ((_let_234 (forall ((BOUND_VARIABLE_19617 tptp.set_real) (BOUND_VARIABLE_19618 tptp.real)) (= (@ (@ tptp.member_real BOUND_VARIABLE_19618) BOUND_VARIABLE_19617) (ll_60 BOUND_VARIABLE_19617 BOUND_VARIABLE_19618))))) (let ((_let_235 (forall ((BOUND_VARIABLE_19606 tptp.real)) (= (and (= tptp.zero_zero_real (@ (@ tptp.poly_real2 tptp.p) BOUND_VARIABLE_19606)) (@ (@ tptp.ord_less_real tptp.a) BOUND_VARIABLE_19606) (@ (@ tptp.ord_less_real BOUND_VARIABLE_19606) tptp.b)) (ll_59 BOUND_VARIABLE_19606))))) (let ((_let_236 (forall ((BOUND_VARIABLE_19590 tptp.poly_real) (BOUND_VARIABLE_19591 tptp.real) (BOUND_VARIABLE_19592 tptp.real) (BOUND_VARIABLE_19593 tptp.real)) (= (and (= tptp.zero_zero_real (@ (@ tptp.poly_real2 BOUND_VARIABLE_19590) BOUND_VARIABLE_19593)) (@ (@ tptp.ord_less_real BOUND_VARIABLE_19591) BOUND_VARIABLE_19593) (@ (@ tptp.ord_less_real BOUND_VARIABLE_19593) BOUND_VARIABLE_19592)) (ll_58 BOUND_VARIABLE_19590 BOUND_VARIABLE_19591 BOUND_VARIABLE_19592 BOUND_VARIABLE_19593))))) (let ((_let_237 (forall ((BOUND_VARIABLE_19574 tptp.poly_real) (BOUND_VARIABLE_19575 tptp.real) (BOUND_VARIABLE_19576 tptp.real) (BOUND_VARIABLE_19577 tptp.real)) (= (and (= tptp.zero_zero_real (@ (@ tptp.poly_real2 BOUND_VARIABLE_19574) BOUND_VARIABLE_19577)) (@ (@ tptp.ord_less_real BOUND_VARIABLE_19575) BOUND_VARIABLE_19577) (@ (@ tptp.ord_less_real BOUND_VARIABLE_19577) BOUND_VARIABLE_19576)) (ll_57 BOUND_VARIABLE_19574 BOUND_VARIABLE_19575 BOUND_VARIABLE_19576 BOUND_VARIABLE_19577))))) (let ((_let_238 (forall ((BOUND_VARIABLE_19560 tptp.real) (BOUND_VARIABLE_19561 tptp.real) (BOUND_VARIABLE_19562 tptp.real)) (= (and (= tptp.zero_zero_real (@ (@ tptp.poly_real2 tptp.zero_zero_poly_real) BOUND_VARIABLE_19562)) (@ (@ tptp.ord_less_real BOUND_VARIABLE_19560) BOUND_VARIABLE_19562) (@ (@ tptp.ord_less_real BOUND_VARIABLE_19562) BOUND_VARIABLE_19561)) (ll_56 BOUND_VARIABLE_19560 BOUND_VARIABLE_19561 BOUND_VARIABLE_19562))))) (let ((_let_239 (forall ((BOUND_VARIABLE_19546 tptp.int) (BOUND_VARIABLE_19547 tptp.int) (BOUND_VARIABLE_19548 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19548) BOUND_VARIABLE_19546) (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19547) BOUND_VARIABLE_19548) (not (= BOUND_VARIABLE_19547 BOUND_VARIABLE_19548))) (ll_55 BOUND_VARIABLE_19546 BOUND_VARIABLE_19547 BOUND_VARIABLE_19548))))) (let ((_let_240 (forall ((BOUND_VARIABLE_19530 tptp.int) (BOUND_VARIABLE_19531 tptp.int) (BOUND_VARIABLE_19532 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19530) BOUND_VARIABLE_19532) (not (= BOUND_VARIABLE_19530 BOUND_VARIABLE_19532)) (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19532) BOUND_VARIABLE_19531) (not (= BOUND_VARIABLE_19531 BOUND_VARIABLE_19532))) (ll_54 BOUND_VARIABLE_19530 BOUND_VARIABLE_19531 BOUND_VARIABLE_19532))))) (let ((_let_241 (forall ((BOUND_VARIABLE_19516 tptp.int) (BOUND_VARIABLE_19517 tptp.int) (BOUND_VARIABLE_19518 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19516) BOUND_VARIABLE_19518) (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19518) BOUND_VARIABLE_19517) (not (= BOUND_VARIABLE_19517 BOUND_VARIABLE_19518))) (ll_53 BOUND_VARIABLE_19516 BOUND_VARIABLE_19517 BOUND_VARIABLE_19518))))) (let ((_let_242 (forall ((BOUND_VARIABLE_19504 tptp.int) (BOUND_VARIABLE_19505 tptp.int) (BOUND_VARIABLE_19506 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19504) BOUND_VARIABLE_19506) (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19506) BOUND_VARIABLE_19505)) (ll_52 BOUND_VARIABLE_19504 BOUND_VARIABLE_19505 BOUND_VARIABLE_19506))))) (let ((_let_243 (forall ((BOUND_VARIABLE_19476 tptp.set_real) (BOUND_VARIABLE_19477 tptp.set_real)) (= (ll_51 BOUND_VARIABLE_19476 BOUND_VARIABLE_19477) (@ (@ tptp.ord_less_eq_real_o (@ ll_61 BOUND_VARIABLE_19476)) (@ ll_60 BOUND_VARIABLE_19477)))))) (let ((_let_244 (forall ((BOUND_VARIABLE_19465 tptp.set_int) (BOUND_VARIABLE_19466 (-> tptp.int Bool)) (BOUND_VARIABLE_19467 tptp.int)) (= (and (@ (@ tptp.member_int BOUND_VARIABLE_19467) BOUND_VARIABLE_19465) (@ BOUND_VARIABLE_19466 BOUND_VARIABLE_19467)) (ll_50 BOUND_VARIABLE_19465 BOUND_VARIABLE_19466 BOUND_VARIABLE_19467))))) (let ((_let_245 (forall ((BOUND_VARIABLE_19454 tptp.set_real) (BOUND_VARIABLE_19455 (-> tptp.real Bool)) (BOUND_VARIABLE_19456 tptp.real)) (= (and (@ (@ tptp.member_real BOUND_VARIABLE_19456) BOUND_VARIABLE_19454) (@ BOUND_VARIABLE_19455 BOUND_VARIABLE_19456)) (ll_49 BOUND_VARIABLE_19454 BOUND_VARIABLE_19455 BOUND_VARIABLE_19456))))) (let ((_let_246 (forall ((BOUND_VARIABLE_19443 tptp.set_real) (BOUND_VARIABLE_19444 tptp.set_real)) (= (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (or (not (@ _let_1 BOUND_VARIABLE_19443)) (@ _let_1 BOUND_VARIABLE_19444)))) (ll_48 BOUND_VARIABLE_19443 BOUND_VARIABLE_19444))))) (let ((_let_247 (forall ((BOUND_VARIABLE_19432 tptp.set_real) (BOUND_VARIABLE_19433 tptp.set_real)) (= (forall ((T3 tptp.real)) (let ((_let_1 (@ tptp.member_real T3))) (or (not (@ _let_1 BOUND_VARIABLE_19432)) (@ _let_1 BOUND_VARIABLE_19433)))) (ll_47 BOUND_VARIABLE_19432 BOUND_VARIABLE_19433))))) (let ((_let_248 (forall ((BOUND_VARIABLE_19421 tptp.int) (BOUND_VARIABLE_19422 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19421) BOUND_VARIABLE_19422) (not (= BOUND_VARIABLE_19421 BOUND_VARIABLE_19422))) (ll_46 BOUND_VARIABLE_19421 BOUND_VARIABLE_19422))))) (let ((_let_249 (forall ((BOUND_VARIABLE_19409 tptp.real) (BOUND_VARIABLE_19410 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19409 BOUND_VARIABLE_19410))) (= (and (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19409) BOUND_VARIABLE_19410) _let_1) (not _let_1)) (ll_45 BOUND_VARIABLE_19409 BOUND_VARIABLE_19410)))))) (let ((_let_250 (forall ((BOUND_VARIABLE_19397 tptp.int) (BOUND_VARIABLE_19398 tptp.int)) (let ((_let_1 (= BOUND_VARIABLE_19397 BOUND_VARIABLE_19398))) (= (or (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19397) BOUND_VARIABLE_19398) (not _let_1)) _let_1) (ll_44 BOUND_VARIABLE_19397 BOUND_VARIABLE_19398)))))) (let ((_let_251 (forall ((BOUND_VARIABLE_19387 tptp.real) (BOUND_VARIABLE_19388 tptp.real)) (= (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19387) BOUND_VARIABLE_19388) (= BOUND_VARIABLE_19387 BOUND_VARIABLE_19388)) (ll_43 BOUND_VARIABLE_19387 BOUND_VARIABLE_19388))))) (let ((_let_252 (forall ((BOUND_VARIABLE_19375 tptp.int) (BOUND_VARIABLE_19376 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19375) BOUND_VARIABLE_19376) (not (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19376) BOUND_VARIABLE_19375))) (ll_42 BOUND_VARIABLE_19375 BOUND_VARIABLE_19376))))) (let ((_let_253 (forall ((BOUND_VARIABLE_19360 tptp.real) (BOUND_VARIABLE_19361 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19360 BOUND_VARIABLE_19361))) (= (ll_41 BOUND_VARIABLE_19360 BOUND_VARIABLE_19361) (and (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19360) BOUND_VARIABLE_19361) _let_1) (not (@ (@ tptp.ord_less_real BOUND_VARIABLE_19361) BOUND_VARIABLE_19360)) (not _let_1))))))) (let ((_let_254 (forall ((BOUND_VARIABLE_19349 tptp.int) (BOUND_VARIABLE_19350 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19349) BOUND_VARIABLE_19350) (not (= BOUND_VARIABLE_19349 BOUND_VARIABLE_19350))) (ll_40 BOUND_VARIABLE_19349 BOUND_VARIABLE_19350))))) (let ((_let_255 (forall ((BOUND_VARIABLE_19338 tptp.int) (BOUND_VARIABLE_19339 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19338) BOUND_VARIABLE_19339) (not (= BOUND_VARIABLE_19338 BOUND_VARIABLE_19339))) (ll_39 BOUND_VARIABLE_19338 BOUND_VARIABLE_19339))))) (let ((_let_256 (forall ((BOUND_VARIABLE_19326 tptp.real) (BOUND_VARIABLE_19327 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19326 BOUND_VARIABLE_19327))) (= (and (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19326) BOUND_VARIABLE_19327) _let_1) (not _let_1)) (ll_38 BOUND_VARIABLE_19326 BOUND_VARIABLE_19327)))))) (let ((_let_257 (forall ((BOUND_VARIABLE_19314 tptp.int) (BOUND_VARIABLE_19315 tptp.int)) (let ((_let_1 (= BOUND_VARIABLE_19314 BOUND_VARIABLE_19315))) (= (or (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19314) BOUND_VARIABLE_19315) (not _let_1)) _let_1) (ll_37 BOUND_VARIABLE_19314 BOUND_VARIABLE_19315)))))) (let ((_let_258 (forall ((BOUND_VARIABLE_19304 tptp.real) (BOUND_VARIABLE_19305 tptp.real)) (= (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19304) BOUND_VARIABLE_19305) (= BOUND_VARIABLE_19304 BOUND_VARIABLE_19305)) (ll_36 BOUND_VARIABLE_19304 BOUND_VARIABLE_19305))))) (let ((_let_259 (forall ((BOUND_VARIABLE_19297 tptp.int) (BOUND_VARIABLE_19298 tptp.int)) (= (= BOUND_VARIABLE_19297 BOUND_VARIABLE_19298) (ll_35 BOUND_VARIABLE_19297 BOUND_VARIABLE_19298))))) (let ((_let_260 (forall ((BOUND_VARIABLE_19286 tptp.int) (BOUND_VARIABLE_19287 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19286) BOUND_VARIABLE_19287) (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19287) BOUND_VARIABLE_19286)) (ll_34 BOUND_VARIABLE_19286 BOUND_VARIABLE_19287))))) (let ((_let_261 (forall ((BOUND_VARIABLE_19279 tptp.real) (BOUND_VARIABLE_19280 tptp.real)) (= (= BOUND_VARIABLE_19279 BOUND_VARIABLE_19280) (ll_33 BOUND_VARIABLE_19279 BOUND_VARIABLE_19280))))) (let ((_let_262 (forall ((BOUND_VARIABLE_19265 tptp.real) (BOUND_VARIABLE_19266 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19265 BOUND_VARIABLE_19266))) (= (and (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19265) BOUND_VARIABLE_19266) _let_1) (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19266) BOUND_VARIABLE_19265) _let_1)) (ll_32 BOUND_VARIABLE_19265 BOUND_VARIABLE_19266)))))) (let ((_let_263 (forall ((BOUND_VARIABLE_19258 tptp.int) (BOUND_VARIABLE_19259 tptp.int)) (= (= BOUND_VARIABLE_19258 BOUND_VARIABLE_19259) (ll_31 BOUND_VARIABLE_19258 BOUND_VARIABLE_19259))))) (let ((_let_264 (forall ((BOUND_VARIABLE_19247 tptp.int) (BOUND_VARIABLE_19248 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19247) BOUND_VARIABLE_19248) (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19248) BOUND_VARIABLE_19247)) (ll_30 BOUND_VARIABLE_19247 BOUND_VARIABLE_19248))))) (let ((_let_265 (forall ((BOUND_VARIABLE_19240 tptp.real) (BOUND_VARIABLE_19241 tptp.real)) (= (= BOUND_VARIABLE_19240 BOUND_VARIABLE_19241) (ll_29 BOUND_VARIABLE_19240 BOUND_VARIABLE_19241))))) (let ((_let_266 (forall ((BOUND_VARIABLE_19226 tptp.real) (BOUND_VARIABLE_19227 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19226 BOUND_VARIABLE_19227))) (= (and (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19226) BOUND_VARIABLE_19227) _let_1) (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19227) BOUND_VARIABLE_19226) _let_1)) (ll_28 BOUND_VARIABLE_19226 BOUND_VARIABLE_19227)))))) (let ((_let_267 (forall ((BOUND_VARIABLE_19219 tptp.int) (BOUND_VARIABLE_19220 tptp.int)) (= (= BOUND_VARIABLE_19219 BOUND_VARIABLE_19220) (ll_27 BOUND_VARIABLE_19219 BOUND_VARIABLE_19220))))) (let ((_let_268 (forall ((BOUND_VARIABLE_19208 tptp.int) (BOUND_VARIABLE_19209 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19209) BOUND_VARIABLE_19208) (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19208) BOUND_VARIABLE_19209)) (ll_26 BOUND_VARIABLE_19208 BOUND_VARIABLE_19209))))) (let ((_let_269 (forall ((BOUND_VARIABLE_19201 tptp.real) (BOUND_VARIABLE_19202 tptp.real)) (= (= BOUND_VARIABLE_19201 BOUND_VARIABLE_19202) (ll_25 BOUND_VARIABLE_19201 BOUND_VARIABLE_19202))))) (let ((_let_270 (forall ((BOUND_VARIABLE_19187 tptp.real) (BOUND_VARIABLE_19188 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19187 BOUND_VARIABLE_19188))) (= (and (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19188) BOUND_VARIABLE_19187) _let_1) (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19187) BOUND_VARIABLE_19188) _let_1)) (ll_24 BOUND_VARIABLE_19187 BOUND_VARIABLE_19188)))))) (let ((_let_271 (forall ((BOUND_VARIABLE_19179 tptp.set_int) (BOUND_VARIABLE_19180 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int BOUND_VARIABLE_19180) BOUND_VARIABLE_19179) (ll_23 BOUND_VARIABLE_19179 BOUND_VARIABLE_19180))))) (let ((_let_272 (forall ((BOUND_VARIABLE_19168 tptp.set_real) (BOUND_VARIABLE_19169 tptp.set_real)) (= (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (or (not (@ _let_1 BOUND_VARIABLE_19169)) (@ _let_1 BOUND_VARIABLE_19168)))) (ll_22 BOUND_VARIABLE_19168 BOUND_VARIABLE_19169))))) (let ((_let_273 (forall ((BOUND_VARIABLE_19160 tptp.set_int) (BOUND_VARIABLE_19161 tptp.int)) (= (@ (@ tptp.member_int BOUND_VARIABLE_19161) BOUND_VARIABLE_19160) (ll_21 BOUND_VARIABLE_19160 BOUND_VARIABLE_19161))))) (let ((_let_274 (forall ((BOUND_VARIABLE_19152 tptp.set_real) (BOUND_VARIABLE_19153 tptp.real)) (= (@ (@ tptp.member_real BOUND_VARIABLE_19153) BOUND_VARIABLE_19152) (ll_20 BOUND_VARIABLE_19152 BOUND_VARIABLE_19153))))) (let ((_let_275 (forall ((BOUND_VARIABLE_19140 tptp.int) (BOUND_VARIABLE_19141 tptp.int)) (let ((_let_1 (= BOUND_VARIABLE_19140 BOUND_VARIABLE_19141))) (= (or (and (@ (@ tptp.ord_less_eq_int BOUND_VARIABLE_19140) BOUND_VARIABLE_19141) (not _let_1)) _let_1) (ll_19 BOUND_VARIABLE_19140 BOUND_VARIABLE_19141)))))) (let ((_let_276 (forall ((BOUND_VARIABLE_19130 tptp.real) (BOUND_VARIABLE_19131 tptp.real)) (= (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19130) BOUND_VARIABLE_19131) (= BOUND_VARIABLE_19130 BOUND_VARIABLE_19131)) (ll_18 BOUND_VARIABLE_19130 BOUND_VARIABLE_19131))))) (let ((_let_277 (forall ((BOUND_VARIABLE_19120 tptp.real) (BOUND_VARIABLE_19121 tptp.real)) (= (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19120) BOUND_VARIABLE_19121) (= BOUND_VARIABLE_19120 BOUND_VARIABLE_19121)) (ll_17 BOUND_VARIABLE_19120 BOUND_VARIABLE_19121))))) (let ((_let_278 (forall ((BOUND_VARIABLE_19108 tptp.real) (BOUND_VARIABLE_19109 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_19108 BOUND_VARIABLE_19109))) (= (and (or (@ (@ tptp.ord_less_real BOUND_VARIABLE_19108) BOUND_VARIABLE_19109) _let_1) (not _let_1)) (ll_16 BOUND_VARIABLE_19108 BOUND_VARIABLE_19109)))))) (let ((_let_279 (forall ((BOUND_VARIABLE_19095 tptp.set_int) (BOUND_VARIABLE_19096 (-> tptp.int tptp.int Bool)) (BOUND_VARIABLE_19097 tptp.int) (BOUND_VARIABLE_19098 tptp.int)) (= (and (@ (@ tptp.member_int BOUND_VARIABLE_19098) BOUND_VARIABLE_19095) (@ (@ BOUND_VARIABLE_19096 BOUND_VARIABLE_19098) BOUND_VARIABLE_19097)) (ll_15 BOUND_VARIABLE_19095 BOUND_VARIABLE_19096 BOUND_VARIABLE_19097 BOUND_VARIABLE_19098))))) (let ((_let_280 (forall ((BOUND_VARIABLE_19082 tptp.set_int) (BOUND_VARIABLE_19083 (-> tptp.int tptp.real Bool)) (BOUND_VARIABLE_19084 tptp.real) (BOUND_VARIABLE_19085 tptp.int)) (= (and (@ (@ tptp.member_int BOUND_VARIABLE_19085) BOUND_VARIABLE_19082) (@ (@ BOUND_VARIABLE_19083 BOUND_VARIABLE_19085) BOUND_VARIABLE_19084)) (ll_14 BOUND_VARIABLE_19082 BOUND_VARIABLE_19083 BOUND_VARIABLE_19084 BOUND_VARIABLE_19085))))) (let ((_let_281 (forall ((BOUND_VARIABLE_19069 tptp.set_real) (BOUND_VARIABLE_19070 (-> tptp.real tptp.int Bool)) (BOUND_VARIABLE_19071 tptp.int) (BOUND_VARIABLE_19072 tptp.real)) (= (and (@ (@ tptp.member_real BOUND_VARIABLE_19072) BOUND_VARIABLE_19069) (@ (@ BOUND_VARIABLE_19070 BOUND_VARIABLE_19072) BOUND_VARIABLE_19071)) (ll_13 BOUND_VARIABLE_19069 BOUND_VARIABLE_19070 BOUND_VARIABLE_19071 BOUND_VARIABLE_19072))))) (let ((_let_282 (forall ((BOUND_VARIABLE_19056 tptp.set_real) (BOUND_VARIABLE_19057 (-> tptp.real tptp.real Bool)) (BOUND_VARIABLE_19058 tptp.real) (BOUND_VARIABLE_19059 tptp.real)) (= (and (@ (@ tptp.member_real BOUND_VARIABLE_19059) BOUND_VARIABLE_19056) (@ (@ BOUND_VARIABLE_19057 BOUND_VARIABLE_19059) BOUND_VARIABLE_19058)) (ll_12 BOUND_VARIABLE_19056 BOUND_VARIABLE_19057 BOUND_VARIABLE_19058 BOUND_VARIABLE_19059))))) (let ((_let_283 (forall ((BOUND_VARIABLE_19047 tptp.poly_poly_real) (BOUND_VARIABLE_19048 tptp.poly_real)) (= (= tptp.zero_zero_poly_real (@ (@ tptp.poly_poly_real2 BOUND_VARIABLE_19047) BOUND_VARIABLE_19048)) (ll_11 BOUND_VARIABLE_19047 BOUND_VARIABLE_19048))))) (let ((_let_284 (forall ((BOUND_VARIABLE_19038 tptp.poly_int) (BOUND_VARIABLE_19039 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.poly_int2 BOUND_VARIABLE_19038) BOUND_VARIABLE_19039)) (ll_10 BOUND_VARIABLE_19038 BOUND_VARIABLE_19039))))) (let ((_let_285 (forall ((BOUND_VARIABLE_19029 tptp.poly_real) (BOUND_VARIABLE_19030 tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.poly_real2 BOUND_VARIABLE_19029) BOUND_VARIABLE_19030)) (ll_9 BOUND_VARIABLE_19029 BOUND_VARIABLE_19030))))) (let ((_let_286 (forall ((BOUND_VARIABLE_19020 tptp.poly_poly_poly_real) (BOUND_VARIABLE_19021 tptp.poly_poly_real)) (= (= tptp.zero_z1423781445y_real (@ (@ tptp.poly_poly_poly_real2 BOUND_VARIABLE_19020) BOUND_VARIABLE_19021)) (ll_8 BOUND_VARIABLE_19020 BOUND_VARIABLE_19021))))) (let ((_let_287 (forall ((BOUND_VARIABLE_19011 tptp.poly_poly_int) (BOUND_VARIABLE_19012 tptp.poly_int)) (= (= tptp.zero_zero_poly_int (@ (@ tptp.poly_poly_int2 BOUND_VARIABLE_19011) BOUND_VARIABLE_19012)) (ll_7 BOUND_VARIABLE_19011 BOUND_VARIABLE_19012))))) (let ((_let_288 (forall ((BOUND_VARIABLE_19001 (-> tptp.int Bool)) (BOUND_VARIABLE_19002 (-> tptp.int Bool)) (BOUND_VARIABLE_19003 tptp.int)) (= (or (@ BOUND_VARIABLE_19001 BOUND_VARIABLE_19003) (@ BOUND_VARIABLE_19002 BOUND_VARIABLE_19003)) (ll_6 BOUND_VARIABLE_19001 BOUND_VARIABLE_19002 BOUND_VARIABLE_19003))))) (let ((_let_289 (forall ((BOUND_VARIABLE_18991 (-> tptp.real Bool)) (BOUND_VARIABLE_18992 (-> tptp.real Bool)) (BOUND_VARIABLE_18993 tptp.real)) (= (or (@ BOUND_VARIABLE_18991 BOUND_VARIABLE_18993) (@ BOUND_VARIABLE_18992 BOUND_VARIABLE_18993)) (ll_5 BOUND_VARIABLE_18991 BOUND_VARIABLE_18992 BOUND_VARIABLE_18993))))) (let ((_let_290 (forall ((BOUND_VARIABLE_18981 (-> tptp.int Bool)) (BOUND_VARIABLE_18982 (-> tptp.int Bool)) (BOUND_VARIABLE_18983 tptp.int)) (= (and (@ BOUND_VARIABLE_18981 BOUND_VARIABLE_18983) (@ BOUND_VARIABLE_18982 BOUND_VARIABLE_18983)) (ll_4 BOUND_VARIABLE_18981 BOUND_VARIABLE_18982 BOUND_VARIABLE_18983))))) (let ((_let_291 (forall ((BOUND_VARIABLE_18971 (-> tptp.real Bool)) (BOUND_VARIABLE_18972 (-> tptp.real Bool)) (BOUND_VARIABLE_18973 tptp.real)) (= (and (@ BOUND_VARIABLE_18971 BOUND_VARIABLE_18973) (@ BOUND_VARIABLE_18972 BOUND_VARIABLE_18973)) (ll_3 BOUND_VARIABLE_18971 BOUND_VARIABLE_18972 BOUND_VARIABLE_18973))))) (let ((_let_292 (forall ((BOUND_VARIABLE_18964 tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.poly_real2 tptp.p) BOUND_VARIABLE_18964)) (ll_2 BOUND_VARIABLE_18964))))) (let ((_let_293 (@ tptp.finite_finite_real (@ tptp.collect_real ll_2)))) (let ((_let_294 (and _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233))) (let ((_let_295 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (= tptp.zero_zero_real (@ (@ tptp.poly_real2 tptp.p) X))))) _let_293))))) (PREPROCESS :args ((and _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233)))) :args (_let_294)) (PREPROCESS :args ((= _let_294 (and _let_232 _let_14 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172))))) (PREPROCESS :args ((and _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18)))) :args ((and _let_232 _let_14 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tptp.zero_z935034829y_real))) (not (@ (@ tptp.ord_less_poly_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)) (not (@ (@ tptp.ord_less_poly_int tptp.zero_zero_poly_int) tptp.zero_zero_poly_int)) (not (@ (@ tptp.ord_le38482960y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)) _let_4 (@ (@ tptp.ord_le1180086932y_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real) (@ (@ tptp.ord_less_eq_poly_int tptp.zero_zero_poly_int) tptp.zero_zero_poly_int) (@ (@ tptp.ord_le893774876y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real) _let_3 (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (forall ((B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real B2) A3) (@ P B2))) (@ P A3)))) (@ P A2)))) (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (forall ((B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B2) A3) (@ P B2))) (@ P A3)))) (@ P A2)))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real X4) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X4) (= X4 Xa))))))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int X4) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X4) (= X4 Xa))))))))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real A) X4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X4) Xa) (= X4 Xa))))))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int A) X4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X4) Xa) (= X4 Xa))))))))) (forall ((P2 tptp.poly_real) (Lb tptp.real)) (=> (not (= P2 tptp.zero_zero_poly_real)) (not (forall ((Ub tptp.real)) (=> (@ (@ tptp.ord_less_real Lb) Ub) (not (forall ((Z tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb) Z) (@ (@ tptp.ord_less_eq_real Z) Ub)) (not (= (@ (@ tptp.poly_real2 P2) Z) tptp.zero_zero_real)))))))))) (forall ((P2 tptp.poly_real) (Ub2 tptp.real)) (=> (not (= P2 tptp.zero_zero_poly_real)) (not (forall ((Lb2 tptp.real)) (=> (@ (@ tptp.ord_less_real Lb2) Ub2) (not (forall ((Z tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb2) Z) (@ (@ tptp.ord_less_real Z) Ub2)) (not (= (@ (@ tptp.poly_real2 P2) Z) tptp.zero_zero_real)))))))))) (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))) (forall ((X2 tptp.poly_real)) (= (= tptp.zero_zero_poly_real X2) (= X2 tptp.zero_zero_poly_real))) (forall ((X2 tptp.int)) (= (= tptp.zero_zero_int X2) (= X2 tptp.zero_zero_int))) (forall ((X2 tptp.poly_int)) (= (= tptp.zero_zero_poly_int X2) (= X2 tptp.zero_zero_poly_int))) (forall ((X2 tptp.poly_poly_real)) (= (= tptp.zero_z1423781445y_real X2) (= X2 tptp.zero_z1423781445y_real))) (forall ((Lb tptp.real) (Ub2 tptp.real) (P2 tptp.poly_real)) (= (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb) Z2) (@ (@ tptp.ord_less_real Z2) Ub2)) (not (= (@ (@ tptp.poly_real2 P2) Z2) tptp.zero_zero_real)))) (or (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb) Z2) (@ (@ tptp.ord_less_real Z2) Ub2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.poly_real2 P2) Z2)))) (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb) Z2) (@ (@ tptp.ord_less_real Z2) Ub2)) (@ (@ tptp.ord_less_real (@ (@ tptp.poly_real2 P2) Z2)) tptp.zero_zero_real)))))) (forall ((Lb tptp.real) (Ub2 tptp.real) (P2 tptp.poly_real)) (= (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb) Z2) (@ (@ tptp.ord_less_eq_real Z2) Ub2)) (not (= (@ (@ tptp.poly_real2 P2) Z2) tptp.zero_zero_real)))) (or (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb) Z2) (@ (@ tptp.ord_less_eq_real Z2) Ub2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.poly_real2 P2) Z2)))) (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb) Z2) (@ (@ tptp.ord_less_eq_real Z2) Ub2)) (@ (@ tptp.ord_less_real (@ (@ tptp.poly_real2 P2) Z2)) tptp.zero_zero_real)))))) (forall ((P2 tptp.poly_real) (Q2 tptp.poly_real)) (= (= (@ tptp.poly_real2 P2) (@ tptp.poly_real2 Q2)) (= P2 Q2))) (forall ((P2 tptp.poly_int) (Q2 tptp.poly_int)) (= (= (@ tptp.poly_int2 P2) (@ tptp.poly_int2 Q2)) (= P2 Q2))) (forall ((P2 tptp.poly_poly_real) (Q2 tptp.poly_poly_real)) (= (= (@ tptp.poly_poly_real2 P2) (@ tptp.poly_poly_real2 Q2)) (= P2 Q2))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (R (-> tptp.real tptp.real Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_real B3) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) B3) (@ (@ R X4) Xa))))) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A2) (@ (@ R A4) X4)))))))))))) (forall ((A2 tptp.set_real) (B3 tptp.set_int) (R (-> tptp.real tptp.int Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X4) Xa))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A2) (@ (@ R A4) X4)))))))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_real) (R (-> tptp.int tptp.real Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite_finite_real B3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) B3) (@ (@ R X4) Xa))))) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A4 tptp.int)) (and (@ (@ tptp.member_int A4) A2) (@ (@ R A4) X4)))))))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X4) Xa))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A4 tptp.int)) (and (@ (@ tptp.member_int A4) A2) (@ (@ R A4) X4)))))))))))) (forall ((P (-> tptp.real Bool))) (=> (not (@ tptp.finite_finite_real (@ tptp.collect_real P))) (exists ((X_1 tptp.real)) (@ P X_1)))) (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_1 tptp.int)) (@ P X_1)))) (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) X2)) (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) X2)) (forall ((A tptp.real) (B tptp.real) (P2 tptp.poly_real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (not (= (@ (@ tptp.poly_real2 P2) X4) tptp.zero_zero_real)))) (= (@ (@ (@ tptp.sturm_1953858694_cross P2) A) B) tptp.zero_zero_int)))) _let_12 (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) C) (@ (@ tptp.ord_less_eq_real C) B) (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_real X3) C)) (@ P X3))) (forall ((D tptp.real)) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_real X4) D)) (@ P X4))) (@ (@ tptp.ord_less_eq_real D) C))))))))) (forall ((A tptp.int) (B tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C) (@ (@ tptp.ord_less_eq_int C) B) (forall ((X3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X3) (@ (@ tptp.ord_less_int X3) C)) (@ P X3))) (forall ((D tptp.int)) (=> (forall ((X4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X4) (@ (@ tptp.ord_less_int X4) D)) (@ P X4))) (@ (@ tptp.ord_less_eq_int D) C))))))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))) (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (= A4 B4))))) _let_11 (= tptp.ord_less_eq_real (lambda ((B4 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B4) A4) (= A4 B4)))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A4) (= A4 B4)))) _let_10 (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))) (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A2))) A2)) (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A2))) A2)) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))) (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))) (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real X2) W) (=> (@ (@ tptp.ord_less_real W) Y2) (@ (@ tptp.ord_less_eq_real W) Z3)))) (@ (@ tptp.ord_less_eq_real Y2) Z3)))) (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite475462905t_real (@ tptp.collect_set_real (lambda ((B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real B5) A2)))))) (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite26677625et_int (@ tptp.collect_set_int (lambda ((B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B5) A2)))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ (@ tptp.sturm_1953858694_cross tptp.zero_zero_poly_real) A) B) tptp.zero_zero_int)) _let_9 (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ tptp.finite_finite_int B3) (@ tptp.finite_finite_int A2)))) (forall ((S tptp.set_real) (T tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real S) T) (=> (not (@ tptp.finite_finite_real S)) (not (@ tptp.finite_finite_real T))))) (forall ((S tptp.set_int) (T tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int T))))) (forall ((B3 tptp.set_real) (A2 tptp.set_real)) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (@ tptp.finite_finite_real A2)))) (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ tptp.finite_finite_int A2)))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))) (= (lambda ((Y3 tptp.real) (Z4 tptp.real)) (= Y3 Z4)) (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (@ (@ tptp.ord_less_eq_real A4) B4)))) (= (lambda ((Y3 tptp.int) (Z4 tptp.int)) (= Y3 Z4)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (@ (@ tptp.ord_less_eq_int A4) B4)))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A5 tptp.real) (B6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A5) B6) (@ (@ P A5) B6))) (=> (forall ((A5 tptp.real) (B6 tptp.real)) (=> (@ (@ P B6) A5) (@ (@ P A5) B6))) (@ (@ P A) B)))) (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A5) B6) (@ (@ P A5) B6))) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (=> (@ (@ P B6) A5) (@ (@ P A5) B6))) (@ (@ P A) B)))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)) (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) Z3) (@ _let_1 Z3))))) (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z3) (@ _let_1 Z3))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real B) A) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ (@ tptp.ord_less_eq_real A) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_eq_int A) C2)))) (= (lambda ((Y3 tptp.real) (Z4 tptp.real)) (= Y3 Z4)) (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (@ (@ tptp.ord_less_eq_real B4) A4)))) (= (lambda ((Y3 tptp.int) (Z4 tptp.int)) (= Y3 Z4)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ tptp.ord_less_eq_int B4) A4)))) (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (= (@ (@ tptp.ord_less_eq_real X2) Y2) (= X2 Y2)))) (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y2) X2) (= (@ (@ tptp.ord_less_eq_int X2) Y2) (= X2 Y2)))) (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_real Z3))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_real Y2))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_int Z3))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_int Y2))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real X2) Y2)) (@ (@ tptp.ord_less_eq_real Y2) X2))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X2) Y2)) (@ (@ tptp.ord_less_eq_int Y2) X2))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_real X2) Y2))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_int X2) Y2))) (forall ((X2 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real Y2) X2))) (forall ((X2 tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y2) (@ (@ tptp.ord_less_eq_int Y2) X2))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (= X2 Y2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) X2) (= X2 Y2)))) (= (lambda ((Y3 tptp.real) (Z4 tptp.real)) (= Y3 Z4)) (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real Y) X)))) (= (lambda ((Y3 tptp.int) (Z4 tptp.int)) (= Y3 Z4)) (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X)))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C2))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C2))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C2))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C2))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real A) (@ F C2)))))) (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A) (@ F C2)))))) (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real A) (@ F C2)))))) (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A) (@ F C2)))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C2))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C2))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C2))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C2))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C2)))))) (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C2)))))) (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C2)))))) (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C2)))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C2))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_int 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tptp.ord_less_int X2) X_1))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (@ (@ tptp.ord_less_real Y2) X2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (@ (@ tptp.ord_less_int Y2) X2)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (= (not (= X2 Y2)) (or (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real Y2) X2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (= (not (= X2 Y2)) (or (@ (@ tptp.ord_less_int X2) Y2) (@ (@ tptp.ord_less_int Y2) X2)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (exists ((Z5 tptp.real)) (and (@ (@ tptp.ord_less_real X2) Z5) (@ (@ tptp.ord_less_real Z5) Y2))))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (= X2 Y2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (= X2 Y2)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (@ (@ tptp.ord_less_real Y2) X2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (@ (@ tptp.ord_less_int Y2) X2)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))) (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_real Y2) Z3) (@ _let_1 Z3))))) (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_int Y2) Z3) (@ _let_1 Z3))))) (forall ((X2 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y2) (= X2 Y2) (@ (@ tptp.ord_less_real Y2) X2))) (forall ((X2 tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y2) (= X2 Y2) (@ (@ tptp.ord_less_int Y2) X2))) (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real X2) X2))) (forall ((X2 tptp.int)) (not (@ (@ tptp.ord_less_int X2) X2))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C2) (@ (@ tptp.ord_less_real A) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (= X2 Y2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (= X2 Y2)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (@ (@ tptp.ord_less_real Y2) X2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (@ (@ tptp.ord_less_int Y2) X2)))) (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y2) X2)) (= (not (@ (@ tptp.ord_less_real X2) Y2)) (= X2 Y2)))) (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y2) X2)) (= (not (@ (@ tptp.ord_less_int X2) Y2)) (= X2 Y2)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (= Y2 X2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (= Y2 X2)))) (forall ((X2 tptp.real) (Y2 tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) P))) (forall ((X2 tptp.int) (Y2 tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X2) Y2) (=> (@ (@ tptp.ord_less_int Y2) X2) P))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (=> (not (= X2 Y2)) (@ (@ tptp.ord_less_real Y2) X2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (=> (not (= X2 Y2)) (@ (@ tptp.ord_less_int Y2) X2)))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C2) (@ _let_1 C2))))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (not (@ (@ tptp.ord_less_real Y2) X2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (not (@ (@ tptp.ord_less_int Y2) X2)))) (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A5 tptp.real) (B6 tptp.real)) (=> (@ (@ tptp.ord_less_real A5) B6) (@ (@ P A5) B6))) (=> (forall ((A5 tptp.real)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.real) (B6 tptp.real)) (=> (@ (@ P B6) A5) (@ (@ P A5) B6))) (@ (@ P A) B))))) (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (=> (@ (@ tptp.ord_less_int A5) B6) (@ (@ P A5) B6))) (=> (forall ((A5 tptp.int)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (=> (@ (@ P B6) A5) (@ (@ P A5) B6))) (@ (@ P A) B))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((X2 tptp.real) (Y2 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y2)) (or (@ (@ tptp.ord_less_real Y2) X2) (= X2 Y2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y2)) (or (@ (@ tptp.ord_less_int Y2) X2) (= X2 Y2)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))) (forall ((A tptp.real)) (exists ((B6 tptp.real)) (or (@ (@ tptp.ord_less_real A) B6) (@ (@ tptp.ord_less_real B6) A)))) (forall ((S tptp.set_real)) (=> (exists ((X3 tptp.real)) (@ (@ tptp.member_real X3) S)) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z)))) (exists ((Y4 tptp.real)) (and (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S) (@ (@ tptp.ord_less_eq_real X3) Y4))) (forall ((Z tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z))) (@ (@ tptp.ord_less_eq_real Y4) Z)))))))) (forall ((D1 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ _let_1 D1) (@ _let_1 D2)))))))) (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (not (@ (@ tptp.ord_less_real X2) Y2)))) (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y2) X2) (not (@ (@ tptp.ord_less_int X2) Y2)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (@ (@ tptp.ord_less_eq_real Y2) X2))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (@ (@ tptp.ord_less_eq_int Y2) X2))) (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))) (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))) (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (= X Y))))) (= tptp.ord_less_int (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (not (= X Y))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C2)))))) (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C2)))))) (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C2)))))) (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C2)))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ 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tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C2))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C2 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tptp.ord_less_real Y2) X2))) (forall ((X2 tptp.int) (Y2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X2) Y2)) (@ (@ tptp.ord_less_int Y2) X2))) (forall ((X2 tptp.real) (Y2 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y2)) (@ (@ tptp.ord_less_eq_real Y2) X2))) (forall ((X2 tptp.int) (Y2 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y2)) (@ (@ tptp.ord_less_eq_int Y2) X2))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (= (@ (@ tptp.ord_less_eq_real X2) Y2) (= X2 Y2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (= (@ (@ tptp.ord_less_eq_int X2) Y2) (= X2 Y2)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (= (not (@ (@ tptp.ord_less_real X2) Y2)) (= X2 Y2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (= (not (@ (@ tptp.ord_less_int X2) Y2)) (= X2 Y2)))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_eq_real X2) Y2))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y2) (@ (@ tptp.ord_less_eq_int X2) Y2))) (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_real Y2) Z3) (@ (@ tptp.ord_less_real X2) Z3)))) (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z3) (@ (@ tptp.ord_less_int X2) Z3)))) (forall ((X2 tptp.real) (Y2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) Z3) (@ _let_1 Z3))))) (forall ((X2 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z3) (@ _let_1 Z3))))) (forall ((Z3 tptp.real) (Y2 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (@ (@ tptp.ord_less_eq_real Y2) X4))) (@ (@ tptp.ord_less_eq_real Y2) Z3))) (forall ((Y2 tptp.real) (Z3 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y2) (@ (@ tptp.ord_less_eq_real X4) Z3))) (@ (@ tptp.ord_less_eq_real Y2) Z3))) (forall ((X2 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_real Y2) X2))) (forall ((X2 tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y2) (@ (@ tptp.ord_less_int Y2) X2))) (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (or (@ (@ tptp.ord_less_real X2) Y2) (= X2 Y2)))) (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (or (@ (@ tptp.ord_less_int X2) Y2) (= X2 Y2)))) (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (@ (@ tptp.ord_less_eq_real Y) X))))) (= tptp.ord_less_int (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (not (@ (@ tptp.ord_less_eq_int Y) X))))) (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y2) X2)) (@ (@ tptp.ord_less_real X2) Y2))) (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y2) X2)) (@ (@ tptp.ord_less_int X2) Y2))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C2) (@ (@ tptp.ord_less_real A) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))) (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B4) (= A4 B4)))) (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B4) (= A4 B4)))) (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (= A4 B4))))) (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (= A4 B4))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C2) B) (@ (@ tptp.ord_less_real C2) A)))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) B) (@ (@ tptp.ord_less_int C2) A)))) (forall ((Z3 tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) W) (=> (@ (@ tptp.ord_less_real W) X2) (@ (@ tptp.ord_less_eq_real Y2) W)))) (@ (@ tptp.ord_less_eq_real Y2) Z3)))) (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (not (@ (@ tptp.ord_less_eq_real T2) X3)))))) (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (not (@ (@ tptp.ord_less_eq_int T2) X3)))))) (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (@ (@ tptp.ord_less_eq_real X3) T2))))) (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (@ (@ tptp.ord_less_eq_int X3) T2))))) (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (@ (@ tptp.ord_less_eq_real T2) X3))))) (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (@ (@ tptp.ord_less_eq_int T2) X3))))) (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (not (@ (@ tptp.ord_less_eq_real X3) T2)))))) (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (not (@ (@ tptp.ord_less_eq_int X3) T2)))))) (forall ((B7 tptp.real) (A6 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B7) A6)) (@ (@ tptp.ord_less_real A6) B7))) (forall ((B7 tptp.int) (A6 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B7) A6)) (@ (@ tptp.ord_less_int A6) B7))) _let_8 _let_7 _let_6 (forall ((N tptp.nat)) (= (@ (@ tptp.poly_cutoff_real N) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)) (forall ((N tptp.nat)) (= (@ (@ tptp.poly_cutoff_int N) tptp.zero_zero_poly_int) tptp.zero_zero_poly_int)) (forall ((N tptp.nat)) (= (@ (@ tptp.poly_c1404107022y_real N) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_real A2) B3))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C2 tptp.real)) (let ((_let_1 (@ tptp.member_real C2))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) _let_5 (= tptp.ord_less_eq_set_real (lambda ((A7 tptp.set_real) (B5 tptp.set_real)) (forall ((T3 tptp.real)) (let ((_let_1 (@ tptp.member_real T3))) (=> (@ _let_1 A7) (@ _let_1 B5)))))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))) (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))) (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A2) (@ P X))))) A2)) (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (@ P X))))) A2)) (= tptp.ord_less_eq_set_real (lambda ((A7 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A7))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B5))))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)) (forall ((X tptp.real)) (=> (@ P X) (@ Q X))))) (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X tptp.int)) (=> (@ P X) (@ Q X))))) (forall ((A tptp.real) (B tptp.real)) (or (= A B) (not (@ (@ tptp.ord_less_eq_real A) B)) (not (@ (@ tptp.ord_less_eq_real B) A)))) (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))) (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q3 (-> tptp.real Bool))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P4 X3) (@ Q3 X3))))))))) (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X4) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P4 X3) (@ Q3 X3))))))))) (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q3 (-> tptp.real Bool))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P4 X3) (@ Q3 X3))))))))) (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X4) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P4 X3) (@ Q3 X3))))))))) (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (not (= X3 T2)))))) (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (not (= X3 T2)))))) (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (not (= X3 T2)))))) (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (not (= X3 T2)))))) (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (not (@ (@ tptp.ord_less_real X3) T2)))))) (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (not (@ (@ tptp.ord_less_int X3) T2)))))) (forall ((T2 tptp.real)) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (@ (@ tptp.ord_less_real T2) X3))))) (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (@ (@ tptp.ord_less_int T2) X3))))) (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q3 (-> tptp.real Bool))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (and (@ P X3) (@ Q X3)) (and (@ P4 X3) (@ Q3 X3))))))))) (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (and (@ P X3) (@ Q X3)) (and (@ P4 X3) (@ Q3 X3))))))))) (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q3 (-> tptp.real Bool))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (or (@ P X3) (@ Q X3)) (or (@ P4 X3) (@ Q3 X3))))))))) (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z) (= (@ Q X4) (@ Q3 X4))))) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (or (@ P X3) (@ Q X3)) (or (@ P4 X3) (@ Q3 X3))))))))) (forall ((T2 tptp.int)) (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (not (= X3 T2)))))) (forall ((X2 tptp.int) (X5 tptp.int) (P Bool) (P4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X5))) (=> (= X2 X5) (=> (=> _let_2 (= P P4)) (= (and (@ _let_1 X2) P) (and _let_2 P4))))))) (forall ((X2 tptp.int) (X5 tptp.int) (P Bool) (P4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X5))) (=> (= X2 X5) (=> (=> _let_2 (= P P4)) (= (=> (@ _let_1 X2) P) (=> _let_2 P4))))))) (forall ((P2 tptp.poly_real) (X2 tptp.real) (Q2 tptp.poly_real)) (=> (not (= (@ (@ tptp.poly_real2 P2) X2) tptp.zero_zero_real)) (= (@ (@ (@ tptp.sturm_276991412p_poly Q2) P2) X2) tptp.zero_zero_int))) (forall ((Q2 tptp.poly_real) (X2 tptp.real)) (= (@ (@ (@ tptp.sturm_276991412p_poly Q2) tptp.zero_zero_poly_real) X2) tptp.zero_zero_int)) (forall ((P2 tptp.poly_real) (X2 tptp.real)) (= (@ (@ (@ tptp.sturm_276991412p_poly tptp.zero_zero_poly_real) P2) X2) tptp.zero_zero_int)) (forall ((A tptp.int) (X2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X2) (= A X2) (@ (@ tptp.ord_less_eq_int X2) A))) (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I) (@ (@ tptp.ord_less_eq_int I) B)))))) (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I) (@ (@ tptp.ord_less_int I) B)))))) (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_int A) I) (@ (@ tptp.ord_less_int I) B)))))) (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_int A) I) (@ (@ tptp.ord_less_eq_int I) B)))))) _let_4 _let_3 (forall ((A tptp.real) (B tptp.real) (Q2 tptp.poly_real)) (= (@ (@ (@ (@ tptp.sturm_308542325x_poly A) B) Q2) tptp.zero_zero_poly_real) tptp.zero_zero_int)) (forall ((A tptp.real) (B tptp.real) (P2 tptp.poly_real)) (= (@ (@ (@ (@ tptp.sturm_308542325x_poly A) B) tptp.zero_zero_poly_real) P2) tptp.zero_zero_int)) (forall ((A tptp.real) (B tptp.real) (P2 tptp.poly_real)) (let ((_let_1 (@ tptp.poly_real2 P2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (not (= (@ _let_1 A) tptp.zero_zero_real)) (=> (not (= (@ _let_1 B) tptp.zero_zero_real)) (= (@ (@ (@ (@ tptp.sturm_308542325x_poly A) B) tptp.one_one_poly_real) P2) (@ (@ (@ tptp.sturm_1953858694_cross P2) A) B))))))) _let_2 (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 62.91/63.21 )
% 62.91/63.21 % SZS output end Proof for ITP193^1
% 62.91/63.21 % cvc5---1.0.5 exiting
% 62.91/63.21 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------