TSTP Solution File: ITP194^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP194^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 03:19:04 EDT 2023
% Result : Theorem 0.86s 1.06s
% Output : Proof 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.16 % Problem : ITP194^1 : TPTP v8.1.2. Released v7.5.0.
% 0.16/0.17 % Command : do_cvc5 %s %d
% 0.17/0.38 % Computer : n002.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun Aug 27 11:36:04 EDT 2023
% 0.17/0.39 % CPUTime :
% 0.24/0.55 %----Proving TH0
% 0.24/0.56 %------------------------------------------------------------------------------
% 0.24/0.56 % File : ITP194^1 : TPTP v8.1.2. Released v7.5.0.
% 0.24/0.56 % Domain : Interactive Theorem Proving
% 0.24/0.56 % Problem : Sledgehammer Sturm_Tarski problem prob_257__5870986_1
% 0.24/0.56 % Version : Especial.
% 0.24/0.56 % English :
% 0.24/0.56
% 0.24/0.56 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.24/0.56 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.24/0.56 % Source : [Des21]
% 0.24/0.56 % Names : Sturm_Tarski/prob_257__5870986_1 [Des21]
% 0.24/0.56
% 0.24/0.56 % Status : Theorem
% 0.24/0.56 % Rating : 0.23 v8.1.0, 0.18 v7.5.0
% 0.24/0.56 % Syntax : Number of formulae : 415 ( 169 unt; 64 typ; 0 def)
% 0.24/0.56 % Number of atoms : 985 ( 326 equ; 0 cnn)
% 0.24/0.56 % Maximal formula atoms : 12 ( 2 avg)
% 0.24/0.56 % Number of connectives : 2504 ( 135 ~; 28 |; 37 &;1867 @)
% 0.24/0.56 % ( 0 <=>; 437 =>; 0 <=; 0 <~>)
% 0.24/0.56 % Maximal formula depth : 14 ( 6 avg)
% 0.24/0.56 % Number of types : 9 ( 8 usr)
% 0.24/0.56 % Number of type conns : 151 ( 151 >; 0 *; 0 +; 0 <<)
% 0.24/0.56 % Number of symbols : 59 ( 56 usr; 14 con; 0-6 aty)
% 0.24/0.56 % Number of variables : 907 ( 68 ^; 823 !; 16 ?; 907 :)
% 0.24/0.56 % SPC : TH0_THM_EQU_NAR
% 0.24/0.56
% 0.24/0.56 % Comments : This file was generated by Sledgehammer 2021-02-23 15:41:56.214
% 0.24/0.56 %------------------------------------------------------------------------------
% 0.24/0.56 % Could-be-implicit typings (8)
% 0.24/0.56 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.24/0.56 poly_poly_poly_real: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.24/0.56 poly_poly_real: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J,type,
% 0.24/0.56 poly_poly_nat: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 poly_real: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.24/0.56 poly_nat: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.24/0.56 set_real: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Real__Oreal,type,
% 0.24/0.56 real: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Nat__Onat,type,
% 0.24/0.56 nat: $tType ).
% 0.24/0.56
% 0.24/0.56 % Explicit typings (56)
% 0.24/0.56 thf(sy_c_Groups_Osgn__class_Osgn_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.24/0.56 sgn_sg2128174761y_real: poly_poly_real > poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Osgn__class_Osgn_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 sgn_sgn_poly_real: poly_real > poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Osgn__class_Osgn_001t__Real__Oreal,type,
% 0.24/0.56 sgn_sgn_real: real > real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.24/0.56 zero_zero_nat: nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.24/0.56 zero_zero_poly_nat: poly_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J,type,
% 0.24/0.56 zero_z1059985641ly_nat: poly_poly_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.24/0.56 zero_z935034829y_real: poly_poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.24/0.56 zero_z1423781445y_real: poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 zero_zero_poly_real: poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.24/0.56 zero_zero_real: real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_If_001t__Nat__Onat,type,
% 0.24/0.56 if_nat: $o > nat > nat > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_If_001t__Real__Oreal,type,
% 0.24/0.56 if_real: $o > real > real > real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.24/0.56 ord_less_nat: nat > nat > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.24/0.56 ord_le38482960y_real: poly_poly_real > poly_poly_real > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 ord_less_poly_real: poly_real > poly_real > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 0.24/0.56 ord_less_real: real > real > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.24/0.56 ord_less_eq_nat: nat > nat > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.24/0.56 ord_le893774876y_real: poly_poly_real > poly_poly_real > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 ord_le1180086932y_real: poly_real > poly_real > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.24/0.56 ord_less_eq_real: real > real > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
% 0.24/0.56 ord_min_nat: nat > nat > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Orderings_Oord__class_Omin_001t__Real__Oreal,type,
% 0.24/0.56 ord_min_real: real > real > real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.24/0.56 divide924636027y_real: poly_poly_real > poly_poly_poly_real > poly_poly_poly_real > poly_poly_poly_real > nat > nat > poly_poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 divide1142363123y_real: poly_real > poly_poly_real > poly_poly_real > poly_poly_real > nat > nat > poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Odivide__poly__main_001t__Real__Oreal,type,
% 0.24/0.56 divide1561404011n_real: real > poly_real > poly_real > poly_real > nat > nat > poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Ois__zero_001t__Nat__Onat,type,
% 0.24/0.56 is_zero_nat: poly_nat > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 is_zero_poly_real: poly_poly_real > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Ois__zero_001t__Real__Oreal,type,
% 0.24/0.56 is_zero_real: poly_real > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.24/0.56 order_poly_poly_real: poly_poly_real > poly_poly_poly_real > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 order_poly_real: poly_real > poly_poly_real > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Oorder_001t__Real__Oreal,type,
% 0.24/0.56 order_real: real > poly_real > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly_001t__Nat__Onat,type,
% 0.24/0.56 poly_nat2: poly_nat > nat > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.24/0.56 poly_poly_nat2: poly_poly_nat > poly_nat > poly_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.24/0.56 poly_poly_poly_real2: poly_poly_poly_real > poly_poly_real > poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 poly_poly_real2: poly_poly_real > poly_real > poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly_001t__Real__Oreal,type,
% 0.24/0.56 poly_real2: poly_real > real > real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly__cutoff_001t__Nat__Onat,type,
% 0.24/0.56 poly_cutoff_nat: nat > poly_nat > poly_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 poly_c1404107022y_real: nat > poly_poly_real > poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly__cutoff_001t__Real__Oreal,type,
% 0.24/0.56 poly_cutoff_real: nat > poly_real > poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly__shift_001t__Nat__Onat,type,
% 0.24/0.56 poly_shift_nat: nat > poly_nat > poly_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly__shift_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 poly_shift_poly_real: nat > poly_poly_real > poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Opoly__shift_001t__Real__Oreal,type,
% 0.24/0.56 poly_shift_real: nat > poly_real > poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Oreflect__poly_001t__Nat__Onat,type,
% 0.24/0.56 reflect_poly_nat: poly_nat > poly_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.24/0.56 reflec781175074ly_nat: poly_poly_nat > poly_poly_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.24/0.56 reflec144234502y_real: poly_poly_poly_real > poly_poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.24/0.56 reflec1522834046y_real: poly_poly_real > poly_poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Polynomial_Oreflect__poly_001t__Real__Oreal,type,
% 0.24/0.56 reflect_poly_real: poly_real > poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 0.24/0.56 collect_real: ( real > $o ) > set_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Osgn__neg__inf_001t__Real__Oreal,type,
% 0.24/0.56 sturm_1076696862f_real: poly_real > real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Osgn__pos__inf_001t__Real__Oreal,type,
% 0.24/0.56 sturm_1308388506f_real: poly_real > real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__Real__Oreal,type,
% 0.24/0.56 member_real: real > set_real > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_lb1____,type,
% 0.24/0.56 lb1: real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_lb2____,type,
% 0.24/0.56 lb2: real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_lb____,type,
% 0.24/0.56 lb: real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_p,type,
% 0.24/0.56 p: poly_real ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_thesis,type,
% 0.24/0.56 thesis: $o ).
% 0.24/0.56
% 0.24/0.56 % Relevant facts (345)
% 0.24/0.56 thf(fact_0_lb1,axiom,
% 0.24/0.56 ! [X: real] :
% 0.24/0.56 ( ( ( poly_real2 @ p @ X )
% 0.24/0.56 = zero_zero_real )
% 0.24/0.56 => ( ord_less_real @ lb1 @ X ) ) ).
% 0.24/0.56
% 0.24/0.56 % lb1
% 0.24/0.56 thf(fact_1_lb__def,axiom,
% 0.24/0.56 ( lb
% 0.24/0.56 = ( ord_min_real @ lb1 @ lb2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % lb_def
% 0.24/0.56 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb1_O_A_092_060forall_062x_O_Apoly_Ap_Ax_A_061_A0_A_092_060longrightarrow_062_Alb1_A_060_Ax_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.24/0.56 ~ ! [Lb1: real] :
% 0.24/0.56 ~ ! [X: real] :
% 0.24/0.56 ( ( ( poly_real2 @ p @ X )
% 0.24/0.56 = zero_zero_real )
% 0.24/0.56 => ( ord_less_real @ Lb1 @ X ) ) ).
% 0.24/0.56
% 0.24/0.56 % \<open>\<And>thesis. (\<And>lb1. \<forall>x. poly p x = 0 \<longrightarrow> lb1 < x \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.24/0.56 thf(fact_3_assms,axiom,
% 0.24/0.56 p != zero_zero_poly_real ).
% 0.24/0.56
% 0.24/0.56 % assms
% 0.24/0.56 thf(fact_4_poly__0,axiom,
% 0.24/0.56 ! [X2: poly_nat] :
% 0.24/0.56 ( ( poly_poly_nat2 @ zero_z1059985641ly_nat @ X2 )
% 0.24/0.56 = zero_zero_poly_nat ) ).
% 0.24/0.56
% 0.24/0.56 % poly_0
% 0.24/0.56 thf(fact_5_poly__0,axiom,
% 0.24/0.56 ! [X2: poly_poly_real] :
% 0.24/0.56 ( ( poly_poly_poly_real2 @ zero_z935034829y_real @ X2 )
% 0.24/0.56 = zero_z1423781445y_real ) ).
% 0.24/0.56
% 0.24/0.56 % poly_0
% 0.24/0.56 thf(fact_6_poly__0,axiom,
% 0.24/0.56 ! [X2: poly_real] :
% 0.24/0.56 ( ( poly_poly_real2 @ zero_z1423781445y_real @ X2 )
% 0.24/0.56 = zero_zero_poly_real ) ).
% 0.24/0.56
% 0.24/0.56 % poly_0
% 0.24/0.56 thf(fact_7_poly__0,axiom,
% 0.24/0.56 ! [X2: nat] :
% 0.24/0.56 ( ( poly_nat2 @ zero_zero_poly_nat @ X2 )
% 0.24/0.56 = zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % poly_0
% 0.24/0.56 thf(fact_8_poly__0,axiom,
% 0.24/0.56 ! [X2: real] :
% 0.24/0.56 ( ( poly_real2 @ zero_zero_poly_real @ X2 )
% 0.24/0.56 = zero_zero_real ) ).
% 0.24/0.56
% 0.24/0.56 % poly_0
% 0.24/0.56 thf(fact_9_not__gr__zero,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.24/0.56 = ( N = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % not_gr_zero
% 0.24/0.56 thf(fact_10_poly__IVT__neg,axiom,
% 0.24/0.56 ! [A: real,B: real,P: poly_real] :
% 0.24/0.56 ( ( ord_less_real @ A @ B )
% 0.24/0.56 => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ A ) )
% 0.24/0.56 => ( ( ord_less_real @ ( poly_real2 @ P @ B ) @ zero_zero_real )
% 0.24/0.56 => ? [X3: real] :
% 0.24/0.56 ( ( ord_less_real @ A @ X3 )
% 0.24/0.56 & ( ord_less_real @ X3 @ B )
% 0.24/0.56 & ( ( poly_real2 @ P @ X3 )
% 0.24/0.56 = zero_zero_real ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % poly_IVT_neg
% 0.24/0.56 thf(fact_11_poly__IVT__pos,axiom,
% 0.24/0.56 ! [A: real,B: real,P: poly_real] :
% 0.24/0.56 ( ( ord_less_real @ A @ B )
% 0.24/0.56 => ( ( ord_less_real @ ( poly_real2 @ P @ A ) @ zero_zero_real )
% 0.24/0.56 => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ B ) )
% 0.24/0.56 => ? [X3: real] :
% 0.24/0.56 ( ( ord_less_real @ A @ X3 )
% 0.24/0.56 & ( ord_less_real @ X3 @ B )
% 0.24/0.56 & ( ( poly_real2 @ P @ X3 )
% 0.24/0.56 = zero_zero_real ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % poly_IVT_pos
% 0.24/0.56 thf(fact_12_poly__all__0__iff__0,axiom,
% 0.24/0.56 ! [P: poly_poly_poly_real] :
% 0.24/0.56 ( ( ! [X4: poly_poly_real] :
% 0.24/0.56 ( ( poly_poly_poly_real2 @ P @ X4 )
% 0.24/0.56 = zero_z1423781445y_real ) )
% 0.24/0.56 = ( P = zero_z935034829y_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % poly_all_0_iff_0
% 0.24/0.56 thf(fact_13_poly__all__0__iff__0,axiom,
% 0.24/0.56 ! [P: poly_real] :
% 0.24/0.56 ( ( ! [X4: real] :
% 0.24/0.56 ( ( poly_real2 @ P @ X4 )
% 0.24/0.56 = zero_zero_real ) )
% 0.24/0.56 = ( P = zero_zero_poly_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % poly_all_0_iff_0
% 0.24/0.56 thf(fact_14_poly__all__0__iff__0,axiom,
% 0.24/0.56 ! [P: poly_poly_real] :
% 0.24/0.56 ( ( ! [X4: poly_real] :
% 0.24/0.56 ( ( poly_poly_real2 @ P @ X4 )
% 0.24/0.56 = zero_zero_poly_real ) )
% 0.24/0.56 = ( P = zero_z1423781445y_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % poly_all_0_iff_0
% 0.24/0.56 thf(fact_15_less__numeral__extra_I3_J,axiom,
% 0.24/0.56 ~ ( ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real ) ).
% 0.24/0.56
% 0.24/0.56 % less_numeral_extra(3)
% 0.24/0.56 thf(fact_16_less__numeral__extra_I3_J,axiom,
% 0.24/0.56 ~ ( ord_le38482960y_real @ zero_z1423781445y_real @ zero_z1423781445y_real ) ).
% 0.24/0.56
% 0.24/0.56 % less_numeral_extra(3)
% 0.24/0.56 thf(fact_17_less__numeral__extra_I3_J,axiom,
% 0.24/0.56 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.24/0.56
% 0.24/0.56 % less_numeral_extra(3)
% 0.24/0.56 thf(fact_18_less__numeral__extra_I3_J,axiom,
% 0.24/0.56 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % less_numeral_extra(3)
% 0.24/0.56 thf(fact_19_field__lbound__gt__zero,axiom,
% 0.24/0.56 ! [D1: real,D2: real] :
% 0.24/0.56 ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.24/0.56 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.24/0.56 => ? [E: real] :
% 0.24/0.56 ( ( ord_less_real @ zero_zero_real @ E )
% 0.24/0.56 & ( ord_less_real @ E @ D1 )
% 0.24/0.56 & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % field_lbound_gt_zero
% 0.24/0.56 thf(fact_20_gr__zeroI,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( N != zero_zero_nat )
% 0.24/0.56 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.24/0.56
% 0.24/0.56 % gr_zeroI
% 0.24/0.56 thf(fact_21_not__less__zero,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % not_less_zero
% 0.24/0.56 thf(fact_22_gr__implies__not__zero,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( ord_less_nat @ M @ N )
% 0.24/0.56 => ( N != zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % gr_implies_not_zero
% 0.24/0.56 thf(fact_23_zero__less__iff__neq__zero,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.24/0.56 = ( N != zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % zero_less_iff_neq_zero
% 0.24/0.56 thf(fact_24_zero__reorient,axiom,
% 0.24/0.56 ! [X2: real] :
% 0.24/0.56 ( ( zero_zero_real = X2 )
% 0.24/0.56 = ( X2 = zero_zero_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % zero_reorient
% 0.24/0.56 thf(fact_25_zero__reorient,axiom,
% 0.24/0.56 ! [X2: poly_real] :
% 0.24/0.56 ( ( zero_zero_poly_real = X2 )
% 0.24/0.56 = ( X2 = zero_zero_poly_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % zero_reorient
% 0.24/0.56 thf(fact_26_zero__reorient,axiom,
% 0.24/0.56 ! [X2: nat] :
% 0.24/0.56 ( ( zero_zero_nat = X2 )
% 0.24/0.56 = ( X2 = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % zero_reorient
% 0.24/0.56 thf(fact_27_zero__reorient,axiom,
% 0.24/0.56 ! [X2: poly_nat] :
% 0.24/0.56 ( ( zero_zero_poly_nat = X2 )
% 0.24/0.56 = ( X2 = zero_zero_poly_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % zero_reorient
% 0.24/0.56 thf(fact_28_zero__reorient,axiom,
% 0.24/0.56 ! [X2: poly_poly_real] :
% 0.24/0.56 ( ( zero_z1423781445y_real = X2 )
% 0.24/0.56 = ( X2 = zero_z1423781445y_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % zero_reorient
% 0.24/0.56 thf(fact_29_poly__eq__poly__eq__iff,axiom,
% 0.24/0.56 ! [P: poly_real,Q: poly_real] :
% 0.24/0.56 ( ( ( poly_real2 @ P )
% 0.24/0.56 = ( poly_real2 @ Q ) )
% 0.24/0.56 = ( P = Q ) ) ).
% 0.24/0.56
% 0.24/0.56 % poly_eq_poly_eq_iff
% 0.24/0.56 thf(fact_30_poly__eq__poly__eq__iff,axiom,
% 0.24/0.56 ! [P: poly_poly_real,Q: poly_poly_real] :
% 0.24/0.56 ( ( ( poly_poly_real2 @ P )
% 0.24/0.56 = ( poly_poly_real2 @ Q ) )
% 0.24/0.56 = ( P = Q ) ) ).
% 0.24/0.56
% 0.24/0.56 % poly_eq_poly_eq_iff
% 0.24/0.56 thf(fact_31_min__less__iff__conj,axiom,
% 0.24/0.56 ! [Z: real,X2: real,Y: real] :
% 0.24/0.56 ( ( ord_less_real @ Z @ ( ord_min_real @ X2 @ Y ) )
% 0.24/0.56 = ( ( ord_less_real @ Z @ X2 )
% 0.24/0.56 & ( ord_less_real @ Z @ Y ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_less_iff_conj
% 0.24/0.56 thf(fact_32_min__less__iff__conj,axiom,
% 0.24/0.56 ! [Z: nat,X2: nat,Y: nat] :
% 0.24/0.56 ( ( ord_less_nat @ Z @ ( ord_min_nat @ X2 @ Y ) )
% 0.24/0.56 = ( ( ord_less_nat @ Z @ X2 )
% 0.24/0.56 & ( ord_less_nat @ Z @ Y ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_less_iff_conj
% 0.24/0.56 thf(fact_33_min_Oidem,axiom,
% 0.24/0.56 ! [A: real] :
% 0.24/0.56 ( ( ord_min_real @ A @ A )
% 0.24/0.56 = A ) ).
% 0.24/0.56
% 0.24/0.56 % min.idem
% 0.24/0.56 thf(fact_34_min_Oidem,axiom,
% 0.24/0.56 ! [A: nat] :
% 0.24/0.56 ( ( ord_min_nat @ A @ A )
% 0.24/0.56 = A ) ).
% 0.24/0.56
% 0.24/0.56 % min.idem
% 0.24/0.56 thf(fact_35_min_Oleft__idem,axiom,
% 0.24/0.56 ! [A: real,B: real] :
% 0.24/0.56 ( ( ord_min_real @ A @ ( ord_min_real @ A @ B ) )
% 0.24/0.56 = ( ord_min_real @ A @ B ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.left_idem
% 0.24/0.56 thf(fact_36_min_Oleft__idem,axiom,
% 0.24/0.56 ! [A: nat,B: nat] :
% 0.24/0.56 ( ( ord_min_nat @ A @ ( ord_min_nat @ A @ B ) )
% 0.24/0.56 = ( ord_min_nat @ A @ B ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.left_idem
% 0.24/0.56 thf(fact_37_min_Oright__idem,axiom,
% 0.24/0.56 ! [A: real,B: real] :
% 0.24/0.56 ( ( ord_min_real @ ( ord_min_real @ A @ B ) @ B )
% 0.24/0.56 = ( ord_min_real @ A @ B ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.right_idem
% 0.24/0.56 thf(fact_38_min_Oright__idem,axiom,
% 0.24/0.56 ! [A: nat,B: nat] :
% 0.24/0.56 ( ( ord_min_nat @ ( ord_min_nat @ A @ B ) @ B )
% 0.24/0.56 = ( ord_min_nat @ A @ B ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.right_idem
% 0.24/0.56 thf(fact_39_min_Ostrict__coboundedI2,axiom,
% 0.24/0.56 ! [B: real,C: real,A: real] :
% 0.24/0.56 ( ( ord_less_real @ B @ C )
% 0.24/0.56 => ( ord_less_real @ ( ord_min_real @ A @ B ) @ C ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.strict_coboundedI2
% 0.24/0.56 thf(fact_40_min_Ostrict__coboundedI2,axiom,
% 0.24/0.56 ! [B: nat,C: nat,A: nat] :
% 0.24/0.56 ( ( ord_less_nat @ B @ C )
% 0.24/0.56 => ( ord_less_nat @ ( ord_min_nat @ A @ B ) @ C ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.strict_coboundedI2
% 0.24/0.56 thf(fact_41_min_Ostrict__coboundedI1,axiom,
% 0.24/0.56 ! [A: real,C: real,B: real] :
% 0.24/0.56 ( ( ord_less_real @ A @ C )
% 0.24/0.56 => ( ord_less_real @ ( ord_min_real @ A @ B ) @ C ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.strict_coboundedI1
% 0.24/0.56 thf(fact_42_min_Ostrict__coboundedI1,axiom,
% 0.24/0.56 ! [A: nat,C: nat,B: nat] :
% 0.24/0.56 ( ( ord_less_nat @ A @ C )
% 0.24/0.56 => ( ord_less_nat @ ( ord_min_nat @ A @ B ) @ C ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.strict_coboundedI1
% 0.24/0.56 thf(fact_43_min_Ostrict__order__iff,axiom,
% 0.24/0.56 ( ord_less_real
% 0.24/0.56 = ( ^ [A2: real,B2: real] :
% 0.24/0.56 ( ( A2
% 0.24/0.56 = ( ord_min_real @ A2 @ B2 ) )
% 0.24/0.56 & ( A2 != B2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.strict_order_iff
% 0.24/0.56 thf(fact_44_min_Ostrict__order__iff,axiom,
% 0.24/0.56 ( ord_less_nat
% 0.24/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.24/0.56 ( ( A2
% 0.24/0.56 = ( ord_min_nat @ A2 @ B2 ) )
% 0.24/0.56 & ( A2 != B2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.strict_order_iff
% 0.24/0.56 thf(fact_45_min_Ostrict__boundedE,axiom,
% 0.24/0.56 ! [A: real,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_real @ A @ ( ord_min_real @ B @ C ) )
% 0.24/0.56 => ~ ( ( ord_less_real @ A @ B )
% 0.24/0.56 => ~ ( ord_less_real @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.strict_boundedE
% 0.24/0.56 thf(fact_46_min_Ostrict__boundedE,axiom,
% 0.24/0.56 ! [A: nat,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_nat @ A @ ( ord_min_nat @ B @ C ) )
% 0.24/0.56 => ~ ( ( ord_less_nat @ A @ B )
% 0.24/0.56 => ~ ( ord_less_nat @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.strict_boundedE
% 0.24/0.56 thf(fact_47_min__less__iff__disj,axiom,
% 0.24/0.56 ! [X2: real,Y: real,Z: real] :
% 0.24/0.56 ( ( ord_less_real @ ( ord_min_real @ X2 @ Y ) @ Z )
% 0.24/0.56 = ( ( ord_less_real @ X2 @ Z )
% 0.24/0.56 | ( ord_less_real @ Y @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_less_iff_disj
% 0.24/0.56 thf(fact_48_min__less__iff__disj,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat,Z: nat] :
% 0.24/0.56 ( ( ord_less_nat @ ( ord_min_nat @ X2 @ Y ) @ Z )
% 0.24/0.56 = ( ( ord_less_nat @ X2 @ Z )
% 0.24/0.56 | ( ord_less_nat @ Y @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_less_iff_disj
% 0.24/0.56 thf(fact_49_is__zero__null,axiom,
% 0.24/0.56 ( is_zero_real
% 0.24/0.56 = ( ^ [P2: poly_real] : ( P2 = zero_zero_poly_real ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % is_zero_null
% 0.24/0.56 thf(fact_50_is__zero__null,axiom,
% 0.24/0.56 ( is_zero_nat
% 0.24/0.56 = ( ^ [P2: poly_nat] : ( P2 = zero_zero_poly_nat ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % is_zero_null
% 0.24/0.56 thf(fact_51_is__zero__null,axiom,
% 0.24/0.56 ( is_zero_poly_real
% 0.24/0.56 = ( ^ [P2: poly_poly_real] : ( P2 = zero_z1423781445y_real ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % is_zero_null
% 0.24/0.56 thf(fact_52_min_Oleft__commute,axiom,
% 0.24/0.56 ! [B: real,A: real,C: real] :
% 0.24/0.56 ( ( ord_min_real @ B @ ( ord_min_real @ A @ C ) )
% 0.24/0.56 = ( ord_min_real @ A @ ( ord_min_real @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.left_commute
% 0.24/0.56 thf(fact_53_min_Oleft__commute,axiom,
% 0.24/0.56 ! [B: nat,A: nat,C: nat] :
% 0.24/0.56 ( ( ord_min_nat @ B @ ( ord_min_nat @ A @ C ) )
% 0.24/0.56 = ( ord_min_nat @ A @ ( ord_min_nat @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.left_commute
% 0.24/0.56 thf(fact_54_min_Ocommute,axiom,
% 0.24/0.56 ( ord_min_real
% 0.24/0.56 = ( ^ [A2: real,B2: real] : ( ord_min_real @ B2 @ A2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.commute
% 0.24/0.56 thf(fact_55_min_Ocommute,axiom,
% 0.24/0.56 ( ord_min_nat
% 0.24/0.56 = ( ^ [A2: nat,B2: nat] : ( ord_min_nat @ B2 @ A2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.commute
% 0.24/0.56 thf(fact_56_min_Oassoc,axiom,
% 0.24/0.56 ! [A: real,B: real,C: real] :
% 0.24/0.56 ( ( ord_min_real @ ( ord_min_real @ A @ B ) @ C )
% 0.24/0.56 = ( ord_min_real @ A @ ( ord_min_real @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.assoc
% 0.24/0.56 thf(fact_57_min_Oassoc,axiom,
% 0.24/0.56 ! [A: nat,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_min_nat @ ( ord_min_nat @ A @ B ) @ C )
% 0.24/0.56 = ( ord_min_nat @ A @ ( ord_min_nat @ B @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.assoc
% 0.24/0.56 thf(fact_58_poly__cutoff__0,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( poly_cutoff_real @ N @ zero_zero_poly_real )
% 0.24/0.56 = zero_zero_poly_real ) ).
% 0.24/0.56
% 0.24/0.56 % poly_cutoff_0
% 0.24/0.56 thf(fact_59_poly__cutoff__0,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( poly_cutoff_nat @ N @ zero_zero_poly_nat )
% 0.24/0.56 = zero_zero_poly_nat ) ).
% 0.24/0.56
% 0.24/0.56 % poly_cutoff_0
% 0.24/0.56 thf(fact_60_poly__cutoff__0,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( poly_c1404107022y_real @ N @ zero_z1423781445y_real )
% 0.24/0.56 = zero_z1423781445y_real ) ).
% 0.24/0.56
% 0.24/0.56 % poly_cutoff_0
% 0.24/0.56 thf(fact_61_last__non__root__interval,axiom,
% 0.24/0.56 ! [P: poly_real,Ub: real] :
% 0.24/0.56 ( ( P != zero_zero_poly_real )
% 0.24/0.56 => ~ ! [Lb: real] :
% 0.24/0.56 ( ( ord_less_real @ Lb @ Ub )
% 0.24/0.56 => ~ ! [Z2: real] :
% 0.24/0.56 ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 0.24/0.56 & ( ord_less_real @ Z2 @ Ub ) )
% 0.24/0.56 => ( ( poly_real2 @ P @ Z2 )
% 0.24/0.56 != zero_zero_real ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % last_non_root_interval
% 0.24/0.56 thf(fact_62_next__non__root__interval,axiom,
% 0.24/0.56 ! [P: poly_real,Lb2: real] :
% 0.24/0.56 ( ( P != zero_zero_poly_real )
% 0.24/0.56 => ~ ! [Ub2: real] :
% 0.24/0.56 ( ( ord_less_real @ Lb2 @ Ub2 )
% 0.24/0.56 => ~ ! [Z2: real] :
% 0.24/0.56 ( ( ( ord_less_real @ Lb2 @ Z2 )
% 0.24/0.56 & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 0.24/0.56 => ( ( poly_real2 @ P @ Z2 )
% 0.24/0.56 != zero_zero_real ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % next_non_root_interval
% 0.24/0.56 thf(fact_63_reflect__poly__at__0__eq__0__iff,axiom,
% 0.24/0.56 ! [P: poly_real] :
% 0.24/0.56 ( ( ( poly_real2 @ ( reflect_poly_real @ P ) @ zero_zero_real )
% 0.24/0.56 = zero_zero_real )
% 0.24/0.56 = ( P = zero_zero_poly_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % reflect_poly_at_0_eq_0_iff
% 0.24/0.56 thf(fact_64_reflect__poly__at__0__eq__0__iff,axiom,
% 0.24/0.56 ! [P: poly_poly_real] :
% 0.24/0.56 ( ( ( poly_poly_real2 @ ( reflec1522834046y_real @ P ) @ zero_zero_poly_real )
% 0.24/0.56 = zero_zero_poly_real )
% 0.24/0.56 = ( P = zero_z1423781445y_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % reflect_poly_at_0_eq_0_iff
% 0.24/0.56 thf(fact_65_reflect__poly__at__0__eq__0__iff,axiom,
% 0.24/0.56 ! [P: poly_nat] :
% 0.24/0.56 ( ( ( poly_nat2 @ ( reflect_poly_nat @ P ) @ zero_zero_nat )
% 0.24/0.56 = zero_zero_nat )
% 0.24/0.56 = ( P = zero_zero_poly_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % reflect_poly_at_0_eq_0_iff
% 0.24/0.56 thf(fact_66_reflect__poly__at__0__eq__0__iff,axiom,
% 0.24/0.56 ! [P: poly_poly_nat] :
% 0.24/0.56 ( ( ( poly_poly_nat2 @ ( reflec781175074ly_nat @ P ) @ zero_zero_poly_nat )
% 0.24/0.56 = zero_zero_poly_nat )
% 0.24/0.56 = ( P = zero_z1059985641ly_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % reflect_poly_at_0_eq_0_iff
% 0.24/0.56 thf(fact_67_reflect__poly__at__0__eq__0__iff,axiom,
% 0.24/0.56 ! [P: poly_poly_poly_real] :
% 0.24/0.56 ( ( ( poly_poly_poly_real2 @ ( reflec144234502y_real @ P ) @ zero_z1423781445y_real )
% 0.24/0.56 = zero_z1423781445y_real )
% 0.24/0.56 = ( P = zero_z935034829y_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % reflect_poly_at_0_eq_0_iff
% 0.24/0.56 thf(fact_68_lb2,axiom,
% 0.24/0.56 ! [X: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X @ lb2 )
% 0.24/0.56 => ( ( sgn_sgn_real @ ( poly_real2 @ p @ X ) )
% 0.24/0.56 = ( sturm_1076696862f_real @ p ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % lb2
% 0.24/0.56 thf(fact_69_poly__shift__0,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( poly_shift_real @ N @ zero_zero_poly_real )
% 0.24/0.56 = zero_zero_poly_real ) ).
% 0.24/0.56
% 0.24/0.56 % poly_shift_0
% 0.24/0.56 thf(fact_70_poly__shift__0,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( poly_shift_nat @ N @ zero_zero_poly_nat )
% 0.24/0.56 = zero_zero_poly_nat ) ).
% 0.24/0.56
% 0.24/0.56 % poly_shift_0
% 0.24/0.56 thf(fact_71_poly__shift__0,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( poly_shift_poly_real @ N @ zero_z1423781445y_real )
% 0.24/0.56 = zero_z1423781445y_real ) ).
% 0.24/0.56
% 0.24/0.56 % poly_shift_0
% 0.24/0.56 thf(fact_72_order__root,axiom,
% 0.24/0.56 ! [P: poly_real,A: real] :
% 0.24/0.56 ( ( ( poly_real2 @ P @ A )
% 0.24/0.56 = zero_zero_real )
% 0.24/0.56 = ( ( P = zero_zero_poly_real )
% 0.24/0.56 | ( ( order_real @ A @ P )
% 0.24/0.56 != zero_zero_nat ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_root
% 0.24/0.56 thf(fact_73_order__root,axiom,
% 0.24/0.56 ! [P: poly_poly_real,A: poly_real] :
% 0.24/0.56 ( ( ( poly_poly_real2 @ P @ A )
% 0.24/0.56 = zero_zero_poly_real )
% 0.24/0.56 = ( ( P = zero_z1423781445y_real )
% 0.24/0.56 | ( ( order_poly_real @ A @ P )
% 0.24/0.56 != zero_zero_nat ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_root
% 0.24/0.56 thf(fact_74_order__root,axiom,
% 0.24/0.56 ! [P: poly_poly_poly_real,A: poly_poly_real] :
% 0.24/0.56 ( ( ( poly_poly_poly_real2 @ P @ A )
% 0.24/0.56 = zero_z1423781445y_real )
% 0.24/0.56 = ( ( P = zero_z935034829y_real )
% 0.24/0.56 | ( ( order_poly_poly_real @ A @ P )
% 0.24/0.56 != zero_zero_nat ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_root
% 0.24/0.56 thf(fact_75_divide__poly__main__0,axiom,
% 0.24/0.56 ! [R: poly_real,D: poly_real,Dr: nat,N: nat] :
% 0.24/0.56 ( ( divide1561404011n_real @ zero_zero_real @ zero_zero_poly_real @ R @ D @ Dr @ N )
% 0.24/0.56 = zero_zero_poly_real ) ).
% 0.24/0.56
% 0.24/0.56 % divide_poly_main_0
% 0.24/0.56 thf(fact_76_divide__poly__main__0,axiom,
% 0.24/0.56 ! [R: poly_poly_real,D: poly_poly_real,Dr: nat,N: nat] :
% 0.24/0.56 ( ( divide1142363123y_real @ zero_zero_poly_real @ zero_z1423781445y_real @ R @ D @ Dr @ N )
% 0.24/0.56 = zero_z1423781445y_real ) ).
% 0.24/0.56
% 0.24/0.56 % divide_poly_main_0
% 0.24/0.56 thf(fact_77_divide__poly__main__0,axiom,
% 0.24/0.56 ! [R: poly_poly_poly_real,D: poly_poly_poly_real,Dr: nat,N: nat] :
% 0.24/0.56 ( ( divide924636027y_real @ zero_z1423781445y_real @ zero_z935034829y_real @ R @ D @ Dr @ N )
% 0.24/0.56 = zero_z935034829y_real ) ).
% 0.24/0.56
% 0.24/0.56 % divide_poly_main_0
% 0.24/0.56 thf(fact_78_not__eq__pos__or__neg__iff__1,axiom,
% 0.24/0.56 ! [Lb2: real,Ub: real,P: poly_real] :
% 0.24/0.56 ( ( ! [Z3: real] :
% 0.24/0.56 ( ( ( ord_less_real @ Lb2 @ Z3 )
% 0.24/0.56 & ( ord_less_eq_real @ Z3 @ Ub ) )
% 0.24/0.56 => ( ( poly_real2 @ P @ Z3 )
% 0.24/0.56 != zero_zero_real ) ) )
% 0.24/0.56 = ( ! [Z3: real] :
% 0.24/0.56 ( ( ( ord_less_real @ Lb2 @ Z3 )
% 0.24/0.56 & ( ord_less_eq_real @ Z3 @ Ub ) )
% 0.24/0.56 => ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ Z3 ) ) )
% 0.24/0.56 | ! [Z3: real] :
% 0.24/0.56 ( ( ( ord_less_real @ Lb2 @ Z3 )
% 0.24/0.56 & ( ord_less_eq_real @ Z3 @ Ub ) )
% 0.24/0.56 => ( ord_less_real @ ( poly_real2 @ P @ Z3 ) @ zero_zero_real ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % not_eq_pos_or_neg_iff_1
% 0.24/0.56 thf(fact_79__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb2_O_A_092_060forall_062x_092_060le_062lb2_O_Asgn_A_Ipoly_Ap_Ax_J_A_061_Asgn__neg__inf_Ap_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.24/0.56 ~ ! [Lb22: real] :
% 0.24/0.56 ~ ! [X: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X @ Lb22 )
% 0.24/0.56 => ( ( sgn_sgn_real @ ( poly_real2 @ p @ X ) )
% 0.24/0.56 = ( sturm_1076696862f_real @ p ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % \<open>\<And>thesis. (\<And>lb2. \<forall>x\<le>lb2. sgn (poly p x) = sgn_neg_inf p \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.24/0.56 thf(fact_80_le__zero__eq,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.24/0.56 = ( N = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_zero_eq
% 0.24/0.56 thf(fact_81_min_Obounded__iff,axiom,
% 0.24/0.56 ! [A: real,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ ( ord_min_real @ B @ C ) )
% 0.24/0.56 = ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 & ( ord_less_eq_real @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.bounded_iff
% 0.24/0.56 thf(fact_82_min_Obounded__iff,axiom,
% 0.24/0.56 ! [A: nat,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ ( ord_min_nat @ B @ C ) )
% 0.24/0.56 = ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 & ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.bounded_iff
% 0.24/0.56 thf(fact_83_reflect__poly__0,axiom,
% 0.24/0.56 ( ( reflect_poly_real @ zero_zero_poly_real )
% 0.24/0.56 = zero_zero_poly_real ) ).
% 0.24/0.56
% 0.24/0.56 % reflect_poly_0
% 0.24/0.56 thf(fact_84_reflect__poly__0,axiom,
% 0.24/0.56 ( ( reflect_poly_nat @ zero_zero_poly_nat )
% 0.24/0.56 = zero_zero_poly_nat ) ).
% 0.24/0.56
% 0.24/0.56 % reflect_poly_0
% 0.24/0.56 thf(fact_85_reflect__poly__0,axiom,
% 0.24/0.56 ( ( reflec1522834046y_real @ zero_z1423781445y_real )
% 0.24/0.56 = zero_z1423781445y_real ) ).
% 0.24/0.56
% 0.24/0.56 % reflect_poly_0
% 0.24/0.56 thf(fact_86_mem__Collect__eq,axiom,
% 0.24/0.56 ! [A: real,P3: real > $o] :
% 0.24/0.56 ( ( member_real @ A @ ( collect_real @ P3 ) )
% 0.24/0.56 = ( P3 @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % mem_Collect_eq
% 0.24/0.56 thf(fact_87_Collect__mem__eq,axiom,
% 0.24/0.56 ! [A3: set_real] :
% 0.24/0.56 ( ( collect_real
% 0.24/0.56 @ ^ [X4: real] : ( member_real @ X4 @ A3 ) )
% 0.24/0.56 = A3 ) ).
% 0.24/0.56
% 0.24/0.56 % Collect_mem_eq
% 0.24/0.56 thf(fact_88_that,axiom,
% 0.24/0.56 ! [Lb2: real] :
% 0.24/0.56 ( ! [X3: real] :
% 0.24/0.56 ( ( ( poly_real2 @ p @ X3 )
% 0.24/0.56 = zero_zero_real )
% 0.24/0.56 => ( ord_less_real @ Lb2 @ X3 ) )
% 0.24/0.56 => ( ! [X3: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X3 @ Lb2 )
% 0.24/0.56 => ( ( sgn_sgn_real @ ( poly_real2 @ p @ X3 ) )
% 0.24/0.56 = ( sturm_1076696862f_real @ p ) ) )
% 0.24/0.56 => thesis ) ) ).
% 0.24/0.56
% 0.24/0.56 % that
% 0.24/0.56 thf(fact_89_complete__real,axiom,
% 0.24/0.56 ! [S: set_real] :
% 0.24/0.56 ( ? [X: real] : ( member_real @ X @ S )
% 0.24/0.56 => ( ? [Z2: real] :
% 0.24/0.56 ! [X3: real] :
% 0.24/0.56 ( ( member_real @ X3 @ S )
% 0.24/0.56 => ( ord_less_eq_real @ X3 @ Z2 ) )
% 0.24/0.56 => ? [Y2: real] :
% 0.24/0.56 ( ! [X: real] :
% 0.24/0.56 ( ( member_real @ X @ S )
% 0.24/0.56 => ( ord_less_eq_real @ X @ Y2 ) )
% 0.24/0.56 & ! [Z2: real] :
% 0.24/0.56 ( ! [X3: real] :
% 0.24/0.56 ( ( member_real @ X3 @ S )
% 0.24/0.56 => ( ord_less_eq_real @ X3 @ Z2 ) )
% 0.24/0.56 => ( ord_less_eq_real @ Y2 @ Z2 ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % complete_real
% 0.24/0.56 thf(fact_90_zero__le,axiom,
% 0.24/0.56 ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 0.24/0.56
% 0.24/0.56 % zero_le
% 0.24/0.56 thf(fact_91_le__numeral__extra_I3_J,axiom,
% 0.24/0.56 ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real ).
% 0.24/0.56
% 0.24/0.56 % le_numeral_extra(3)
% 0.24/0.56 thf(fact_92_le__numeral__extra_I3_J,axiom,
% 0.24/0.56 ord_le893774876y_real @ zero_z1423781445y_real @ zero_z1423781445y_real ).
% 0.24/0.56
% 0.24/0.56 % le_numeral_extra(3)
% 0.24/0.56 thf(fact_93_le__numeral__extra_I3_J,axiom,
% 0.24/0.56 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.24/0.56
% 0.24/0.56 % le_numeral_extra(3)
% 0.24/0.56 thf(fact_94_le__numeral__extra_I3_J,axiom,
% 0.24/0.56 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.24/0.56
% 0.24/0.56 % le_numeral_extra(3)
% 0.24/0.56 thf(fact_95_less__eq__real__def,axiom,
% 0.24/0.56 ( ord_less_eq_real
% 0.24/0.56 = ( ^ [X4: real,Y3: real] :
% 0.24/0.56 ( ( ord_less_real @ X4 @ Y3 )
% 0.24/0.56 | ( X4 = Y3 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_eq_real_def
% 0.24/0.56 thf(fact_96_min_Omono,axiom,
% 0.24/0.56 ! [A: real,C: real,B: real,D: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ C )
% 0.24/0.56 => ( ( ord_less_eq_real @ B @ D )
% 0.24/0.56 => ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ ( ord_min_real @ C @ D ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.mono
% 0.24/0.56 thf(fact_97_min_Omono,axiom,
% 0.24/0.56 ! [A: nat,C: nat,B: nat,D: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ C )
% 0.24/0.56 => ( ( ord_less_eq_nat @ B @ D )
% 0.24/0.56 => ( ord_less_eq_nat @ ( ord_min_nat @ A @ B ) @ ( ord_min_nat @ C @ D ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.mono
% 0.24/0.56 thf(fact_98_min_OorderE,axiom,
% 0.24/0.56 ! [A: real,B: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( A
% 0.24/0.56 = ( ord_min_real @ A @ B ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.orderE
% 0.24/0.56 thf(fact_99_min_OorderE,axiom,
% 0.24/0.56 ! [A: nat,B: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( A
% 0.24/0.56 = ( ord_min_nat @ A @ B ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.orderE
% 0.24/0.56 thf(fact_100_min_OorderI,axiom,
% 0.24/0.56 ! [A: real,B: real] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( ord_min_real @ A @ B ) )
% 0.24/0.56 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.orderI
% 0.24/0.56 thf(fact_101_min_OorderI,axiom,
% 0.24/0.56 ! [A: nat,B: nat] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( ord_min_nat @ A @ B ) )
% 0.24/0.56 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.orderI
% 0.24/0.56 thf(fact_102_min_Oabsorb1,axiom,
% 0.24/0.56 ! [A: real,B: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( ( ord_min_real @ A @ B )
% 0.24/0.56 = A ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.absorb1
% 0.24/0.56 thf(fact_103_min_Oabsorb1,axiom,
% 0.24/0.56 ! [A: nat,B: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( ( ord_min_nat @ A @ B )
% 0.24/0.56 = A ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.absorb1
% 0.24/0.56 thf(fact_104_min_Oabsorb2,axiom,
% 0.24/0.56 ! [B: real,A: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ B @ A )
% 0.24/0.56 => ( ( ord_min_real @ A @ B )
% 0.24/0.56 = B ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.absorb2
% 0.24/0.56 thf(fact_105_min_Oabsorb2,axiom,
% 0.24/0.56 ! [B: nat,A: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.56 => ( ( ord_min_nat @ A @ B )
% 0.24/0.56 = B ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.absorb2
% 0.24/0.56 thf(fact_106_min_OboundedE,axiom,
% 0.24/0.56 ! [A: real,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ ( ord_min_real @ B @ C ) )
% 0.24/0.56 => ~ ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ~ ( ord_less_eq_real @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.boundedE
% 0.24/0.56 thf(fact_107_min_OboundedE,axiom,
% 0.24/0.56 ! [A: nat,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ ( ord_min_nat @ B @ C ) )
% 0.24/0.56 => ~ ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ~ ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.boundedE
% 0.24/0.56 thf(fact_108_min_OboundedI,axiom,
% 0.24/0.56 ! [A: real,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_real @ A @ C )
% 0.24/0.56 => ( ord_less_eq_real @ A @ ( ord_min_real @ B @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.boundedI
% 0.24/0.56 thf(fact_109_min_OboundedI,axiom,
% 0.24/0.56 ! [A: nat,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_nat @ A @ C )
% 0.24/0.56 => ( ord_less_eq_nat @ A @ ( ord_min_nat @ B @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.boundedI
% 0.24/0.56 thf(fact_110_min_Oorder__iff,axiom,
% 0.24/0.56 ( ord_less_eq_real
% 0.24/0.56 = ( ^ [A2: real,B2: real] :
% 0.24/0.56 ( A2
% 0.24/0.56 = ( ord_min_real @ A2 @ B2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.order_iff
% 0.24/0.56 thf(fact_111_min_Oorder__iff,axiom,
% 0.24/0.56 ( ord_less_eq_nat
% 0.24/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.24/0.56 ( A2
% 0.24/0.56 = ( ord_min_nat @ A2 @ B2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.order_iff
% 0.24/0.56 thf(fact_112_min_Ocobounded1,axiom,
% 0.24/0.56 ! [A: real,B: real] : ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ A ) ).
% 0.24/0.56
% 0.24/0.56 % min.cobounded1
% 0.24/0.56 thf(fact_113_min_Ocobounded1,axiom,
% 0.24/0.56 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( ord_min_nat @ A @ B ) @ A ) ).
% 0.24/0.56
% 0.24/0.56 % min.cobounded1
% 0.24/0.56 thf(fact_114_min_Ocobounded2,axiom,
% 0.24/0.56 ! [A: real,B: real] : ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ B ) ).
% 0.24/0.56
% 0.24/0.56 % min.cobounded2
% 0.24/0.56 thf(fact_115_min_Ocobounded2,axiom,
% 0.24/0.56 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( ord_min_nat @ A @ B ) @ B ) ).
% 0.24/0.56
% 0.24/0.56 % min.cobounded2
% 0.24/0.56 thf(fact_116_min_Oabsorb__iff1,axiom,
% 0.24/0.56 ( ord_less_eq_real
% 0.24/0.56 = ( ^ [A2: real,B2: real] :
% 0.24/0.56 ( ( ord_min_real @ A2 @ B2 )
% 0.24/0.56 = A2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.absorb_iff1
% 0.24/0.56 thf(fact_117_min_Oabsorb__iff1,axiom,
% 0.24/0.56 ( ord_less_eq_nat
% 0.24/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.24/0.56 ( ( ord_min_nat @ A2 @ B2 )
% 0.24/0.56 = A2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.absorb_iff1
% 0.24/0.56 thf(fact_118_min_Oabsorb__iff2,axiom,
% 0.24/0.56 ( ord_less_eq_real
% 0.24/0.56 = ( ^ [B2: real,A2: real] :
% 0.24/0.56 ( ( ord_min_real @ A2 @ B2 )
% 0.24/0.56 = B2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.absorb_iff2
% 0.24/0.56 thf(fact_119_min_Oabsorb__iff2,axiom,
% 0.24/0.56 ( ord_less_eq_nat
% 0.24/0.56 = ( ^ [B2: nat,A2: nat] :
% 0.24/0.56 ( ( ord_min_nat @ A2 @ B2 )
% 0.24/0.56 = B2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.absorb_iff2
% 0.24/0.56 thf(fact_120_min_OcoboundedI1,axiom,
% 0.24/0.56 ! [A: real,C: real,B: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ C )
% 0.24/0.56 => ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ C ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.coboundedI1
% 0.24/0.56 thf(fact_121_min_OcoboundedI1,axiom,
% 0.24/0.56 ! [A: nat,C: nat,B: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ C )
% 0.24/0.56 => ( ord_less_eq_nat @ ( ord_min_nat @ A @ B ) @ C ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.coboundedI1
% 0.24/0.56 thf(fact_122_min_OcoboundedI2,axiom,
% 0.24/0.56 ! [B: real,C: real,A: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ B @ C )
% 0.24/0.56 => ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ C ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.coboundedI2
% 0.24/0.56 thf(fact_123_min_OcoboundedI2,axiom,
% 0.24/0.56 ! [B: nat,C: nat,A: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.56 => ( ord_less_eq_nat @ ( ord_min_nat @ A @ B ) @ C ) ) ).
% 0.24/0.56
% 0.24/0.56 % min.coboundedI2
% 0.24/0.56 thf(fact_124_min__le__iff__disj,axiom,
% 0.24/0.56 ! [X2: real,Y: real,Z: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ ( ord_min_real @ X2 @ Y ) @ Z )
% 0.24/0.56 = ( ( ord_less_eq_real @ X2 @ Z )
% 0.24/0.56 | ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_le_iff_disj
% 0.24/0.56 thf(fact_125_min__le__iff__disj,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat,Z: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ ( ord_min_nat @ X2 @ Y ) @ Z )
% 0.24/0.56 = ( ( ord_less_eq_nat @ X2 @ Z )
% 0.24/0.56 | ( ord_less_eq_nat @ Y @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_le_iff_disj
% 0.24/0.56 thf(fact_126_order__0I,axiom,
% 0.24/0.56 ! [P: poly_real,A: real] :
% 0.24/0.56 ( ( ( poly_real2 @ P @ A )
% 0.24/0.56 != zero_zero_real )
% 0.24/0.56 => ( ( order_real @ A @ P )
% 0.24/0.56 = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_0I
% 0.24/0.56 thf(fact_127_order__0I,axiom,
% 0.24/0.56 ! [P: poly_poly_real,A: poly_real] :
% 0.24/0.56 ( ( ( poly_poly_real2 @ P @ A )
% 0.24/0.56 != zero_zero_poly_real )
% 0.24/0.56 => ( ( order_poly_real @ A @ P )
% 0.24/0.56 = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_0I
% 0.24/0.56 thf(fact_128_order__0I,axiom,
% 0.24/0.56 ! [P: poly_poly_poly_real,A: poly_poly_real] :
% 0.24/0.56 ( ( ( poly_poly_poly_real2 @ P @ A )
% 0.24/0.56 != zero_z1423781445y_real )
% 0.24/0.56 => ( ( order_poly_poly_real @ A @ P )
% 0.24/0.56 = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_0I
% 0.24/0.56 thf(fact_129_not__eq__pos__or__neg__iff__2,axiom,
% 0.24/0.56 ! [Lb2: real,Ub: real,P: poly_real] :
% 0.24/0.56 ( ( ! [Z3: real] :
% 0.24/0.56 ( ( ( ord_less_eq_real @ Lb2 @ Z3 )
% 0.24/0.56 & ( ord_less_real @ Z3 @ Ub ) )
% 0.24/0.56 => ( ( poly_real2 @ P @ Z3 )
% 0.24/0.56 != zero_zero_real ) ) )
% 0.24/0.56 = ( ! [Z3: real] :
% 0.24/0.56 ( ( ( ord_less_eq_real @ Lb2 @ Z3 )
% 0.24/0.56 & ( ord_less_real @ Z3 @ Ub ) )
% 0.24/0.56 => ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ Z3 ) ) )
% 0.24/0.56 | ! [Z3: real] :
% 0.24/0.56 ( ( ( ord_less_eq_real @ Lb2 @ Z3 )
% 0.24/0.56 & ( ord_less_real @ Z3 @ Ub ) )
% 0.24/0.56 => ( ord_less_real @ ( poly_real2 @ P @ Z3 ) @ zero_zero_real ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % not_eq_pos_or_neg_iff_2
% 0.24/0.56 thf(fact_130_zero__le__sgn__iff,axiom,
% 0.24/0.56 ! [X2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X2 ) )
% 0.24/0.56 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % zero_le_sgn_iff
% 0.24/0.56 thf(fact_131_sgn__le__0__iff,axiom,
% 0.24/0.56 ! [X2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X2 ) @ zero_zero_real )
% 0.24/0.56 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_le_0_iff
% 0.24/0.56 thf(fact_132_sgn__greater,axiom,
% 0.24/0.56 ! [A: poly_real] :
% 0.24/0.56 ( ( ord_less_poly_real @ zero_zero_poly_real @ ( sgn_sgn_poly_real @ A ) )
% 0.24/0.56 = ( ord_less_poly_real @ zero_zero_poly_real @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_greater
% 0.24/0.56 thf(fact_133_sgn__greater,axiom,
% 0.24/0.56 ! [A: poly_poly_real] :
% 0.24/0.56 ( ( ord_le38482960y_real @ zero_z1423781445y_real @ ( sgn_sg2128174761y_real @ A ) )
% 0.24/0.56 = ( ord_le38482960y_real @ zero_z1423781445y_real @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_greater
% 0.24/0.56 thf(fact_134_sgn__greater,axiom,
% 0.24/0.56 ! [A: real] :
% 0.24/0.56 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 0.24/0.56 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_greater
% 0.24/0.56 thf(fact_135_sgn__less,axiom,
% 0.24/0.56 ! [A: poly_real] :
% 0.24/0.56 ( ( ord_less_poly_real @ ( sgn_sgn_poly_real @ A ) @ zero_zero_poly_real )
% 0.24/0.56 = ( ord_less_poly_real @ A @ zero_zero_poly_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_less
% 0.24/0.56 thf(fact_136_sgn__less,axiom,
% 0.24/0.56 ! [A: poly_poly_real] :
% 0.24/0.56 ( ( ord_le38482960y_real @ ( sgn_sg2128174761y_real @ A ) @ zero_z1423781445y_real )
% 0.24/0.56 = ( ord_le38482960y_real @ A @ zero_z1423781445y_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_less
% 0.24/0.56 thf(fact_137_sgn__less,axiom,
% 0.24/0.56 ! [A: real] :
% 0.24/0.56 ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 0.24/0.56 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_less
% 0.24/0.56 thf(fact_138_root__ub,axiom,
% 0.24/0.56 ! [P: poly_real] :
% 0.24/0.56 ( ( P != zero_zero_poly_real )
% 0.24/0.56 => ~ ! [Ub2: real] :
% 0.24/0.56 ( ! [X: real] :
% 0.24/0.56 ( ( ( poly_real2 @ P @ X )
% 0.24/0.56 = zero_zero_real )
% 0.24/0.56 => ( ord_less_real @ X @ Ub2 ) )
% 0.24/0.56 => ~ ! [X: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ Ub2 @ X )
% 0.24/0.56 => ( ( sgn_sgn_real @ ( poly_real2 @ P @ X ) )
% 0.24/0.56 = ( sturm_1308388506f_real @ P ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % root_ub
% 0.24/0.56 thf(fact_139_sgn__0,axiom,
% 0.24/0.56 ( ( sgn_sgn_real @ zero_zero_real )
% 0.24/0.56 = zero_zero_real ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_0
% 0.24/0.56 thf(fact_140_sgn__0,axiom,
% 0.24/0.56 ( ( sgn_sgn_poly_real @ zero_zero_poly_real )
% 0.24/0.56 = zero_zero_poly_real ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_0
% 0.24/0.56 thf(fact_141_sgn__0,axiom,
% 0.24/0.56 ( ( sgn_sg2128174761y_real @ zero_z1423781445y_real )
% 0.24/0.56 = zero_z1423781445y_real ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_0
% 0.24/0.56 thf(fact_142_sgn__zero,axiom,
% 0.24/0.56 ( ( sgn_sgn_real @ zero_zero_real )
% 0.24/0.56 = zero_zero_real ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_zero
% 0.24/0.56 thf(fact_143_sgn__sgn,axiom,
% 0.24/0.56 ! [A: real] :
% 0.24/0.56 ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 0.24/0.56 = ( sgn_sgn_real @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_sgn
% 0.24/0.56 thf(fact_144_linorder__neqE__linordered__idom,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( X2 != Y )
% 0.24/0.56 => ( ~ ( ord_less_real @ X2 @ Y )
% 0.24/0.56 => ( ord_less_real @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % linorder_neqE_linordered_idom
% 0.24/0.56 thf(fact_145_sgn__eq__0__iff,axiom,
% 0.24/0.56 ! [A: real] :
% 0.24/0.56 ( ( ( sgn_sgn_real @ A )
% 0.24/0.56 = zero_zero_real )
% 0.24/0.56 = ( A = zero_zero_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_eq_0_iff
% 0.24/0.56 thf(fact_146_sgn__eq__0__iff,axiom,
% 0.24/0.56 ! [A: poly_real] :
% 0.24/0.56 ( ( ( sgn_sgn_poly_real @ A )
% 0.24/0.56 = zero_zero_poly_real )
% 0.24/0.56 = ( A = zero_zero_poly_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_eq_0_iff
% 0.24/0.56 thf(fact_147_sgn__eq__0__iff,axiom,
% 0.24/0.56 ! [A: poly_poly_real] :
% 0.24/0.56 ( ( ( sgn_sg2128174761y_real @ A )
% 0.24/0.56 = zero_z1423781445y_real )
% 0.24/0.56 = ( A = zero_z1423781445y_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_eq_0_iff
% 0.24/0.56 thf(fact_148_sgn__0__0,axiom,
% 0.24/0.56 ! [A: real] :
% 0.24/0.56 ( ( ( sgn_sgn_real @ A )
% 0.24/0.56 = zero_zero_real )
% 0.24/0.56 = ( A = zero_zero_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_0_0
% 0.24/0.56 thf(fact_149_sgn__0__0,axiom,
% 0.24/0.56 ! [A: poly_real] :
% 0.24/0.56 ( ( ( sgn_sgn_poly_real @ A )
% 0.24/0.56 = zero_zero_poly_real )
% 0.24/0.56 = ( A = zero_zero_poly_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_0_0
% 0.24/0.56 thf(fact_150_sgn__0__0,axiom,
% 0.24/0.56 ! [A: poly_poly_real] :
% 0.24/0.56 ( ( ( sgn_sg2128174761y_real @ A )
% 0.24/0.56 = zero_z1423781445y_real )
% 0.24/0.56 = ( A = zero_z1423781445y_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_0_0
% 0.24/0.56 thf(fact_151_sgn__zero__iff,axiom,
% 0.24/0.56 ! [X2: real] :
% 0.24/0.56 ( ( ( sgn_sgn_real @ X2 )
% 0.24/0.56 = zero_zero_real )
% 0.24/0.56 = ( X2 = zero_zero_real ) ) ).
% 0.24/0.56
% 0.24/0.56 % sgn_zero_iff
% 0.24/0.56 thf(fact_152_le0,axiom,
% 0.24/0.56 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.24/0.56
% 0.24/0.56 % le0
% 0.24/0.56 thf(fact_153_bot__nat__0_Oextremum,axiom,
% 0.24/0.56 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.24/0.56
% 0.24/0.56 % bot_nat_0.extremum
% 0.24/0.56 thf(fact_154_neq0__conv,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( N != zero_zero_nat )
% 0.24/0.56 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.24/0.56
% 0.24/0.56 % neq0_conv
% 0.24/0.56 thf(fact_155_less__nat__zero__code,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % less_nat_zero_code
% 0.24/0.56 thf(fact_156_bot__nat__0_Onot__eq__extremum,axiom,
% 0.24/0.56 ! [A: nat] :
% 0.24/0.56 ( ( A != zero_zero_nat )
% 0.24/0.56 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % bot_nat_0.not_eq_extremum
% 0.24/0.56 thf(fact_157_min__0R,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( ord_min_nat @ N @ zero_zero_nat )
% 0.24/0.56 = zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % min_0R
% 0.24/0.56 thf(fact_158_min__0L,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( ord_min_nat @ zero_zero_nat @ N )
% 0.24/0.56 = zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % min_0L
% 0.24/0.56 thf(fact_159_le__refl,axiom,
% 0.24/0.56 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.24/0.56
% 0.24/0.56 % le_refl
% 0.24/0.56 thf(fact_160_le__trans,axiom,
% 0.24/0.56 ! [I: nat,J: nat,K: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ I @ J )
% 0.24/0.56 => ( ( ord_less_eq_nat @ J @ K )
% 0.24/0.56 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_trans
% 0.24/0.56 thf(fact_161_eq__imp__le,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( M = N )
% 0.24/0.56 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.24/0.56
% 0.24/0.56 % eq_imp_le
% 0.24/0.56 thf(fact_162_le__antisym,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ M @ N )
% 0.24/0.56 => ( ( ord_less_eq_nat @ N @ M )
% 0.24/0.56 => ( M = N ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_antisym
% 0.24/0.56 thf(fact_163_nat__le__linear,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ M @ N )
% 0.24/0.56 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.24/0.56
% 0.24/0.56 % nat_le_linear
% 0.24/0.56 thf(fact_164_Nat_Oex__has__greatest__nat,axiom,
% 0.24/0.56 ! [P3: nat > $o,K: nat,B: nat] :
% 0.24/0.56 ( ( P3 @ K )
% 0.24/0.56 => ( ! [Y2: nat] :
% 0.24/0.56 ( ( P3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.24/0.56 => ? [X3: nat] :
% 0.24/0.56 ( ( P3 @ X3 )
% 0.24/0.56 & ! [Y4: nat] :
% 0.24/0.56 ( ( P3 @ Y4 )
% 0.24/0.56 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Nat.ex_has_greatest_nat
% 0.24/0.56 thf(fact_165_less__mono__imp__le__mono,axiom,
% 0.24/0.56 ! [F: nat > nat,I: nat,J: nat] :
% 0.24/0.56 ( ! [I2: nat,J2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ I2 @ J2 )
% 0.24/0.56 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.24/0.56 => ( ( ord_less_eq_nat @ I @ J )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_mono_imp_le_mono
% 0.24/0.56 thf(fact_166_le__neq__implies__less,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ M @ N )
% 0.24/0.56 => ( ( M != N )
% 0.24/0.56 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_neq_implies_less
% 0.24/0.56 thf(fact_167_less__or__eq__imp__le,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( ( ord_less_nat @ M @ N )
% 0.24/0.56 | ( M = N ) )
% 0.24/0.56 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_or_eq_imp_le
% 0.24/0.56 thf(fact_168_le__eq__less__or__eq,axiom,
% 0.24/0.56 ( ord_less_eq_nat
% 0.24/0.56 = ( ^ [M2: nat,N2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ M2 @ N2 )
% 0.24/0.56 | ( M2 = N2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_eq_less_or_eq
% 0.24/0.56 thf(fact_169_less__imp__le__nat,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( ord_less_nat @ M @ N )
% 0.24/0.56 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_imp_le_nat
% 0.24/0.56 thf(fact_170_nat__less__le,axiom,
% 0.24/0.56 ( ord_less_nat
% 0.24/0.56 = ( ^ [M2: nat,N2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.24/0.56 & ( M2 != N2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % nat_less_le
% 0.24/0.56 thf(fact_171_linorder__neqE__nat,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( X2 != Y )
% 0.24/0.56 => ( ~ ( ord_less_nat @ X2 @ Y )
% 0.24/0.56 => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % linorder_neqE_nat
% 0.24/0.56 thf(fact_172_infinite__descent,axiom,
% 0.24/0.56 ! [P3: nat > $o,N: nat] :
% 0.24/0.56 ( ! [N3: nat] :
% 0.24/0.56 ( ~ ( P3 @ N3 )
% 0.24/0.56 => ? [M3: nat] :
% 0.24/0.56 ( ( ord_less_nat @ M3 @ N3 )
% 0.24/0.56 & ~ ( P3 @ M3 ) ) )
% 0.24/0.56 => ( P3 @ N ) ) ).
% 0.24/0.56
% 0.24/0.56 % infinite_descent
% 0.24/0.56 thf(fact_173_nat__less__induct,axiom,
% 0.24/0.56 ! [P3: nat > $o,N: nat] :
% 0.24/0.56 ( ! [N3: nat] :
% 0.24/0.56 ( ! [M3: nat] :
% 0.24/0.56 ( ( ord_less_nat @ M3 @ N3 )
% 0.24/0.56 => ( P3 @ M3 ) )
% 0.24/0.56 => ( P3 @ N3 ) )
% 0.24/0.56 => ( P3 @ N ) ) ).
% 0.24/0.56
% 0.24/0.56 % nat_less_induct
% 0.24/0.56 thf(fact_174_less__irrefl__nat,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ~ ( ord_less_nat @ N @ N ) ).
% 0.24/0.56
% 0.24/0.56 % less_irrefl_nat
% 0.24/0.56 thf(fact_175_less__not__refl3,axiom,
% 0.24/0.56 ! [S2: nat,T: nat] :
% 0.24/0.56 ( ( ord_less_nat @ S2 @ T )
% 0.24/0.56 => ( S2 != T ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_not_refl3
% 0.24/0.56 thf(fact_176_less__not__refl2,axiom,
% 0.24/0.56 ! [N: nat,M: nat] :
% 0.24/0.56 ( ( ord_less_nat @ N @ M )
% 0.24/0.56 => ( M != N ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_not_refl2
% 0.24/0.56 thf(fact_177_less__not__refl,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ~ ( ord_less_nat @ N @ N ) ).
% 0.24/0.56
% 0.24/0.56 % less_not_refl
% 0.24/0.56 thf(fact_178_nat__neq__iff,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( M != N )
% 0.24/0.56 = ( ( ord_less_nat @ M @ N )
% 0.24/0.56 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % nat_neq_iff
% 0.24/0.56 thf(fact_179_bot__nat__0_Oextremum__strict,axiom,
% 0.24/0.56 ! [A: nat] :
% 0.24/0.56 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % bot_nat_0.extremum_strict
% 0.24/0.56 thf(fact_180_infinite__descent0,axiom,
% 0.24/0.56 ! [P3: nat > $o,N: nat] :
% 0.24/0.56 ( ( P3 @ zero_zero_nat )
% 0.24/0.56 => ( ! [N3: nat] :
% 0.24/0.56 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.24/0.56 => ( ~ ( P3 @ N3 )
% 0.24/0.56 => ? [M3: nat] :
% 0.24/0.56 ( ( ord_less_nat @ M3 @ N3 )
% 0.24/0.56 & ~ ( P3 @ M3 ) ) ) )
% 0.24/0.56 => ( P3 @ N ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % infinite_descent0
% 0.24/0.56 thf(fact_181_gr__implies__not0,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( ord_less_nat @ M @ N )
% 0.24/0.56 => ( N != zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % gr_implies_not0
% 0.24/0.56 thf(fact_182_less__zeroE,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % less_zeroE
% 0.24/0.56 thf(fact_183_not__less0,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.24/0.56
% 0.24/0.56 % not_less0
% 0.24/0.56 thf(fact_184_not__gr0,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.24/0.56 = ( N = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % not_gr0
% 0.24/0.56 thf(fact_185_gr0I,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( N != zero_zero_nat )
% 0.24/0.56 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.24/0.56
% 0.24/0.56 % gr0I
% 0.24/0.56 thf(fact_186_less__eq__nat_Osimps_I1_J,axiom,
% 0.24/0.56 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.24/0.56
% 0.24/0.56 % less_eq_nat.simps(1)
% 0.24/0.56 thf(fact_187_le__0__eq,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.24/0.56 = ( N = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_0_eq
% 0.24/0.56 thf(fact_188_ex__least__nat__le,axiom,
% 0.24/0.56 ! [P3: nat > $o,N: nat] :
% 0.24/0.56 ( ( P3 @ N )
% 0.24/0.56 => ( ~ ( P3 @ zero_zero_nat )
% 0.24/0.56 => ? [K2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ K2 @ N )
% 0.24/0.56 & ! [I3: nat] :
% 0.24/0.56 ( ( ord_less_nat @ I3 @ K2 )
% 0.24/0.56 => ~ ( P3 @ I3 ) )
% 0.24/0.56 & ( P3 @ K2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ex_least_nat_le
% 0.24/0.56 thf(fact_189_bot__nat__0_Oextremum__unique,axiom,
% 0.24/0.56 ! [A: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.24/0.56 = ( A = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % bot_nat_0.extremum_unique
% 0.24/0.56 thf(fact_190_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.24/0.56 ! [A: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.24/0.56 => ( A = zero_zero_nat ) ) ).
% 0.24/0.56
% 0.24/0.56 % bot_nat_0.extremum_uniqueI
% 0.24/0.56 thf(fact_191_order__refl,axiom,
% 0.24/0.56 ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 0.24/0.56
% 0.24/0.56 % order_refl
% 0.24/0.56 thf(fact_192_order__refl,axiom,
% 0.24/0.56 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.24/0.56
% 0.24/0.56 % order_refl
% 0.24/0.56 thf(fact_193_min__absorb1,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X2 @ Y )
% 0.24/0.56 => ( ( ord_min_real @ X2 @ Y )
% 0.24/0.56 = X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_absorb1
% 0.24/0.56 thf(fact_194_min__absorb1,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X2 @ Y )
% 0.24/0.56 => ( ( ord_min_nat @ X2 @ Y )
% 0.24/0.56 = X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_absorb1
% 0.24/0.56 thf(fact_195_min__absorb2,axiom,
% 0.24/0.56 ! [Y: real,X2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ Y @ X2 )
% 0.24/0.56 => ( ( ord_min_real @ X2 @ Y )
% 0.24/0.56 = Y ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_absorb2
% 0.24/0.56 thf(fact_196_min__absorb2,axiom,
% 0.24/0.56 ! [Y: nat,X2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ Y @ X2 )
% 0.24/0.56 => ( ( ord_min_nat @ X2 @ Y )
% 0.24/0.56 = Y ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_absorb2
% 0.24/0.56 thf(fact_197_min__def,axiom,
% 0.24/0.56 ( ord_min_real
% 0.24/0.56 = ( ^ [A2: real,B2: real] : ( if_real @ ( ord_less_eq_real @ A2 @ B2 ) @ A2 @ B2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_def
% 0.24/0.56 thf(fact_198_min__def,axiom,
% 0.24/0.56 ( ord_min_nat
% 0.24/0.56 = ( ^ [A2: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A2 @ B2 ) @ A2 @ B2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % min_def
% 0.24/0.56 thf(fact_199_nat__descend__induct,axiom,
% 0.24/0.56 ! [N: nat,P3: nat > $o,M: nat] :
% 0.24/0.56 ( ! [K2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ N @ K2 )
% 0.24/0.56 => ( P3 @ K2 ) )
% 0.24/0.56 => ( ! [K2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ K2 @ N )
% 0.24/0.56 => ( ! [I3: nat] :
% 0.24/0.56 ( ( ord_less_nat @ K2 @ I3 )
% 0.24/0.56 => ( P3 @ I3 ) )
% 0.24/0.56 => ( P3 @ K2 ) ) )
% 0.24/0.56 => ( P3 @ M ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % nat_descend_induct
% 0.24/0.56 thf(fact_200_dual__order_Oantisym,axiom,
% 0.24/0.56 ! [B: real,A: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ B @ A )
% 0.24/0.56 => ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( A = B ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % dual_order.antisym
% 0.24/0.56 thf(fact_201_dual__order_Oantisym,axiom,
% 0.24/0.56 ! [B: nat,A: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.56 => ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( A = B ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % dual_order.antisym
% 0.24/0.56 thf(fact_202_dual__order_Oeq__iff,axiom,
% 0.24/0.56 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 0.24/0.56 = ( ^ [A2: real,B2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ B2 @ A2 )
% 0.24/0.56 & ( ord_less_eq_real @ A2 @ B2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % dual_order.eq_iff
% 0.24/0.56 thf(fact_203_dual__order_Oeq__iff,axiom,
% 0.24/0.56 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 0.24/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.24/0.56 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % dual_order.eq_iff
% 0.24/0.56 thf(fact_204_dual__order_Otrans,axiom,
% 0.24/0.56 ! [B: real,A: real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ B @ A )
% 0.24/0.56 => ( ( ord_less_eq_real @ C @ B )
% 0.24/0.56 => ( ord_less_eq_real @ C @ A ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % dual_order.trans
% 0.24/0.56 thf(fact_205_dual__order_Otrans,axiom,
% 0.24/0.56 ! [B: nat,A: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.56 => ( ( ord_less_eq_nat @ C @ B )
% 0.24/0.56 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % dual_order.trans
% 0.24/0.56 thf(fact_206_linorder__wlog,axiom,
% 0.24/0.56 ! [P3: real > real > $o,A: real,B: real] :
% 0.24/0.56 ( ! [A4: real,B3: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A4 @ B3 )
% 0.24/0.56 => ( P3 @ A4 @ B3 ) )
% 0.24/0.56 => ( ! [A4: real,B3: real] :
% 0.24/0.56 ( ( P3 @ B3 @ A4 )
% 0.24/0.56 => ( P3 @ A4 @ B3 ) )
% 0.24/0.56 => ( P3 @ A @ B ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % linorder_wlog
% 0.24/0.56 thf(fact_207_linorder__wlog,axiom,
% 0.24/0.56 ! [P3: nat > nat > $o,A: nat,B: nat] :
% 0.24/0.56 ( ! [A4: nat,B3: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A4 @ B3 )
% 0.24/0.56 => ( P3 @ A4 @ B3 ) )
% 0.24/0.56 => ( ! [A4: nat,B3: nat] :
% 0.24/0.56 ( ( P3 @ B3 @ A4 )
% 0.24/0.56 => ( P3 @ A4 @ B3 ) )
% 0.24/0.56 => ( P3 @ A @ B ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % linorder_wlog
% 0.24/0.56 thf(fact_208_dual__order_Orefl,axiom,
% 0.24/0.56 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 0.24/0.56
% 0.24/0.56 % dual_order.refl
% 0.24/0.56 thf(fact_209_dual__order_Orefl,axiom,
% 0.24/0.56 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.24/0.56
% 0.24/0.56 % dual_order.refl
% 0.24/0.56 thf(fact_210_order__trans,axiom,
% 0.24/0.56 ! [X2: real,Y: real,Z: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X2 @ Y )
% 0.24/0.56 => ( ( ord_less_eq_real @ Y @ Z )
% 0.24/0.56 => ( ord_less_eq_real @ X2 @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_trans
% 0.24/0.56 thf(fact_211_order__trans,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat,Z: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X2 @ Y )
% 0.24/0.56 => ( ( ord_less_eq_nat @ Y @ Z )
% 0.24/0.56 => ( ord_less_eq_nat @ X2 @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_trans
% 0.24/0.56 thf(fact_212_order__class_Oorder_Oantisym,axiom,
% 0.24/0.56 ! [A: real,B: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_real @ B @ A )
% 0.24/0.56 => ( A = B ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_class.order.antisym
% 0.24/0.56 thf(fact_213_order__class_Oorder_Oantisym,axiom,
% 0.24/0.56 ! [A: nat,B: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_nat @ B @ A )
% 0.24/0.56 => ( A = B ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_class.order.antisym
% 0.24/0.56 thf(fact_214_ord__le__eq__trans,axiom,
% 0.24/0.56 ! [A: real,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( ( B = C )
% 0.24/0.56 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_le_eq_trans
% 0.24/0.56 thf(fact_215_ord__le__eq__trans,axiom,
% 0.24/0.56 ! [A: nat,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( ( B = C )
% 0.24/0.56 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_le_eq_trans
% 0.24/0.56 thf(fact_216_ord__eq__le__trans,axiom,
% 0.24/0.56 ! [A: real,B: real,C: real] :
% 0.24/0.56 ( ( A = B )
% 0.24/0.56 => ( ( ord_less_eq_real @ B @ C )
% 0.24/0.56 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_le_trans
% 0.24/0.56 thf(fact_217_ord__eq__le__trans,axiom,
% 0.24/0.56 ! [A: nat,B: nat,C: nat] :
% 0.24/0.56 ( ( A = B )
% 0.24/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.56 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_le_trans
% 0.24/0.56 thf(fact_218_order__class_Oorder_Oeq__iff,axiom,
% 0.24/0.56 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 0.24/0.56 = ( ^ [A2: real,B2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A2 @ B2 )
% 0.24/0.56 & ( ord_less_eq_real @ B2 @ A2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_class.order.eq_iff
% 0.24/0.56 thf(fact_219_order__class_Oorder_Oeq__iff,axiom,
% 0.24/0.56 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 0.24/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.24/0.56 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_class.order.eq_iff
% 0.24/0.56 thf(fact_220_antisym__conv,axiom,
% 0.24/0.56 ! [Y: real,X2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ Y @ X2 )
% 0.24/0.56 => ( ( ord_less_eq_real @ X2 @ Y )
% 0.24/0.56 = ( X2 = Y ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % antisym_conv
% 0.24/0.56 thf(fact_221_antisym__conv,axiom,
% 0.24/0.56 ! [Y: nat,X2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ Y @ X2 )
% 0.24/0.56 => ( ( ord_less_eq_nat @ X2 @ Y )
% 0.24/0.56 = ( X2 = Y ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % antisym_conv
% 0.24/0.56 thf(fact_222_le__cases3,axiom,
% 0.24/0.56 ! [X2: real,Y: real,Z: real] :
% 0.24/0.56 ( ( ( ord_less_eq_real @ X2 @ Y )
% 0.24/0.56 => ~ ( ord_less_eq_real @ Y @ Z ) )
% 0.24/0.56 => ( ( ( ord_less_eq_real @ Y @ X2 )
% 0.24/0.56 => ~ ( ord_less_eq_real @ X2 @ Z ) )
% 0.24/0.56 => ( ( ( ord_less_eq_real @ X2 @ Z )
% 0.24/0.56 => ~ ( ord_less_eq_real @ Z @ Y ) )
% 0.24/0.56 => ( ( ( ord_less_eq_real @ Z @ Y )
% 0.24/0.56 => ~ ( ord_less_eq_real @ Y @ X2 ) )
% 0.24/0.56 => ( ( ( ord_less_eq_real @ Y @ Z )
% 0.24/0.56 => ~ ( ord_less_eq_real @ Z @ X2 ) )
% 0.24/0.56 => ~ ( ( ord_less_eq_real @ Z @ X2 )
% 0.24/0.56 => ~ ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_cases3
% 0.24/0.56 thf(fact_223_le__cases3,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat,Z: nat] :
% 0.24/0.56 ( ( ( ord_less_eq_nat @ X2 @ Y )
% 0.24/0.56 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 0.24/0.56 => ( ( ( ord_less_eq_nat @ Y @ X2 )
% 0.24/0.56 => ~ ( ord_less_eq_nat @ X2 @ Z ) )
% 0.24/0.56 => ( ( ( ord_less_eq_nat @ X2 @ Z )
% 0.24/0.56 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 0.24/0.56 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 0.24/0.56 => ~ ( ord_less_eq_nat @ Y @ X2 ) )
% 0.24/0.56 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 0.24/0.56 => ~ ( ord_less_eq_nat @ Z @ X2 ) )
% 0.24/0.56 => ~ ( ( ord_less_eq_nat @ Z @ X2 )
% 0.24/0.56 => ~ ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_cases3
% 0.24/0.56 thf(fact_224_order_Otrans,axiom,
% 0.24/0.56 ! [A: real,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_real @ B @ C )
% 0.24/0.56 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order.trans
% 0.24/0.56 thf(fact_225_order_Otrans,axiom,
% 0.24/0.56 ! [A: nat,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.56 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order.trans
% 0.24/0.56 thf(fact_226_le__cases,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ~ ( ord_less_eq_real @ X2 @ Y )
% 0.24/0.56 => ( ord_less_eq_real @ Y @ X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_cases
% 0.24/0.56 thf(fact_227_le__cases,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ~ ( ord_less_eq_nat @ X2 @ Y )
% 0.24/0.56 => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % le_cases
% 0.24/0.56 thf(fact_228_eq__refl,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( X2 = Y )
% 0.24/0.56 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 0.24/0.56
% 0.24/0.56 % eq_refl
% 0.24/0.56 thf(fact_229_eq__refl,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( X2 = Y )
% 0.24/0.56 => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 0.24/0.56
% 0.24/0.56 % eq_refl
% 0.24/0.56 thf(fact_230_linear,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X2 @ Y )
% 0.24/0.56 | ( ord_less_eq_real @ Y @ X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % linear
% 0.24/0.56 thf(fact_231_linear,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X2 @ Y )
% 0.24/0.56 | ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % linear
% 0.24/0.56 thf(fact_232_antisym,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X2 @ Y )
% 0.24/0.56 => ( ( ord_less_eq_real @ Y @ X2 )
% 0.24/0.56 => ( X2 = Y ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % antisym
% 0.24/0.56 thf(fact_233_antisym,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X2 @ Y )
% 0.24/0.56 => ( ( ord_less_eq_nat @ Y @ X2 )
% 0.24/0.56 => ( X2 = Y ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % antisym
% 0.24/0.56 thf(fact_234_eq__iff,axiom,
% 0.24/0.56 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 0.24/0.56 = ( ^ [X4: real,Y3: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X4 @ Y3 )
% 0.24/0.56 & ( ord_less_eq_real @ Y3 @ X4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % eq_iff
% 0.24/0.56 thf(fact_235_eq__iff,axiom,
% 0.24/0.56 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 0.24/0.56 = ( ^ [X4: nat,Y3: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.24/0.56 & ( ord_less_eq_nat @ Y3 @ X4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % eq_iff
% 0.24/0.56 thf(fact_236_ord__le__eq__subst,axiom,
% 0.24/0.56 ! [A: real,B: real,F: real > real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( ( ( F @ B )
% 0.24/0.56 = C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_le_eq_subst
% 0.24/0.56 thf(fact_237_ord__le__eq__subst,axiom,
% 0.24/0.56 ! [A: real,B: real,F: real > nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( ( ( F @ B )
% 0.24/0.56 = C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_le_eq_subst
% 0.24/0.56 thf(fact_238_ord__le__eq__subst,axiom,
% 0.24/0.56 ! [A: nat,B: nat,F: nat > real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( ( ( F @ B )
% 0.24/0.56 = C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_le_eq_subst
% 0.24/0.56 thf(fact_239_ord__le__eq__subst,axiom,
% 0.24/0.56 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( ( ( F @ B )
% 0.24/0.56 = C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_le_eq_subst
% 0.24/0.56 thf(fact_240_ord__eq__le__subst,axiom,
% 0.24/0.56 ! [A: real,F: real > real,B: real,C: real] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_eq_real @ B @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_le_subst
% 0.24/0.56 thf(fact_241_ord__eq__le__subst,axiom,
% 0.24/0.56 ! [A: nat,F: real > nat,B: real,C: real] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_eq_real @ B @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_le_subst
% 0.24/0.56 thf(fact_242_ord__eq__le__subst,axiom,
% 0.24/0.56 ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_le_subst
% 0.24/0.56 thf(fact_243_ord__eq__le__subst,axiom,
% 0.24/0.56 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_le_subst
% 0.24/0.56 thf(fact_244_order__subst2,axiom,
% 0.24/0.56 ! [A: real,B: real,F: real > real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_subst2
% 0.24/0.56 thf(fact_245_order__subst2,axiom,
% 0.24/0.56 ! [A: real,B: real,F: real > nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_subst2
% 0.24/0.56 thf(fact_246_order__subst2,axiom,
% 0.24/0.56 ! [A: nat,B: nat,F: nat > real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_subst2
% 0.24/0.56 thf(fact_247_order__subst2,axiom,
% 0.24/0.56 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.56 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_subst2
% 0.24/0.56 thf(fact_248_order__subst1,axiom,
% 0.24/0.56 ! [A: real,F: real > real,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_eq_real @ B @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_subst1
% 0.24/0.56 thf(fact_249_order__subst1,axiom,
% 0.24/0.56 ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_subst1
% 0.24/0.56 thf(fact_250_order__subst1,axiom,
% 0.24/0.56 ! [A: nat,F: real > nat,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_eq_real @ B @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_subst1
% 0.24/0.56 thf(fact_251_order__subst1,axiom,
% 0.24/0.56 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_subst1
% 0.24/0.56 thf(fact_252_ord__eq__less__subst,axiom,
% 0.24/0.56 ! [A: real,F: real > real,B: real,C: real] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_real @ B @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_less_subst
% 0.24/0.56 thf(fact_253_ord__eq__less__subst,axiom,
% 0.24/0.56 ! [A: nat,F: real > nat,B: real,C: real] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_real @ B @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_less_subst
% 0.24/0.56 thf(fact_254_ord__eq__less__subst,axiom,
% 0.24/0.56 ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_nat @ B @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_less_subst
% 0.24/0.56 thf(fact_255_ord__eq__less__subst,axiom,
% 0.24/0.56 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.24/0.56 ( ( A
% 0.24/0.56 = ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_nat @ B @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_eq_less_subst
% 0.24/0.56 thf(fact_256_ord__less__eq__subst,axiom,
% 0.24/0.56 ! [A: real,B: real,F: real > real,C: real] :
% 0.24/0.56 ( ( ord_less_real @ A @ B )
% 0.24/0.56 => ( ( ( F @ B )
% 0.24/0.56 = C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_less_eq_subst
% 0.24/0.56 thf(fact_257_ord__less__eq__subst,axiom,
% 0.24/0.56 ! [A: real,B: real,F: real > nat,C: nat] :
% 0.24/0.56 ( ( ord_less_real @ A @ B )
% 0.24/0.56 => ( ( ( F @ B )
% 0.24/0.56 = C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_less_eq_subst
% 0.24/0.56 thf(fact_258_ord__less__eq__subst,axiom,
% 0.24/0.56 ! [A: nat,B: nat,F: nat > real,C: real] :
% 0.24/0.56 ( ( ord_less_nat @ A @ B )
% 0.24/0.56 => ( ( ( F @ B )
% 0.24/0.56 = C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_less_eq_subst
% 0.24/0.56 thf(fact_259_ord__less__eq__subst,axiom,
% 0.24/0.56 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.24/0.56 ( ( ord_less_nat @ A @ B )
% 0.24/0.56 => ( ( ( F @ B )
% 0.24/0.56 = C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ord_less_eq_subst
% 0.24/0.56 thf(fact_260_order__less__subst1,axiom,
% 0.24/0.56 ! [A: real,F: real > real,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_real @ B @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_less_subst1
% 0.24/0.56 thf(fact_261_order__less__subst1,axiom,
% 0.24/0.56 ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_nat @ B @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_less_subst1
% 0.24/0.56 thf(fact_262_order__less__subst1,axiom,
% 0.24/0.56 ! [A: nat,F: real > nat,B: real,C: real] :
% 0.24/0.56 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_real @ B @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_less_subst1
% 0.24/0.56 thf(fact_263_order__less__subst1,axiom,
% 0.24/0.56 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.24/0.56 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.24/0.56 => ( ( ord_less_nat @ B @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_less_subst1
% 0.24/0.56 thf(fact_264_order__less__subst2,axiom,
% 0.24/0.56 ! [A: real,B: real,F: real > real,C: real] :
% 0.24/0.56 ( ( ord_less_real @ A @ B )
% 0.24/0.56 => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_less_subst2
% 0.24/0.56 thf(fact_265_order__less__subst2,axiom,
% 0.24/0.56 ! [A: real,B: real,F: real > nat,C: nat] :
% 0.24/0.56 ( ( ord_less_real @ A @ B )
% 0.24/0.56 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.24/0.56 => ( ! [X3: real,Y2: real] :
% 0.24/0.56 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_less_subst2
% 0.24/0.56 thf(fact_266_order__less__subst2,axiom,
% 0.24/0.56 ! [A: nat,B: nat,F: nat > real,C: real] :
% 0.24/0.56 ( ( ord_less_nat @ A @ B )
% 0.24/0.56 => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_less_subst2
% 0.24/0.56 thf(fact_267_order__less__subst2,axiom,
% 0.24/0.56 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.24/0.56 ( ( ord_less_nat @ A @ B )
% 0.24/0.56 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.24/0.56 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.56 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.56 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % order_less_subst2
% 0.24/0.56 thf(fact_268_lt__ex,axiom,
% 0.24/0.56 ! [X2: real] :
% 0.24/0.56 ? [Y2: real] : ( ord_less_real @ Y2 @ X2 ) ).
% 0.24/0.56
% 0.24/0.56 % lt_ex
% 0.24/0.56 thf(fact_269_gt__ex,axiom,
% 0.24/0.56 ! [X2: real] :
% 0.24/0.56 ? [X_1: real] : ( ord_less_real @ X2 @ X_1 ) ).
% 0.24/0.56
% 0.24/0.56 % gt_ex
% 0.24/0.56 thf(fact_270_gt__ex,axiom,
% 0.24/0.56 ! [X2: nat] :
% 0.24/0.56 ? [X_1: nat] : ( ord_less_nat @ X2 @ X_1 ) ).
% 0.24/0.56
% 0.24/0.56 % gt_ex
% 0.24/0.56 thf(fact_271_neqE,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( X2 != Y )
% 0.24/0.56 => ( ~ ( ord_less_real @ X2 @ Y )
% 0.24/0.56 => ( ord_less_real @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % neqE
% 0.24/0.56 thf(fact_272_neqE,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( X2 != Y )
% 0.24/0.56 => ( ~ ( ord_less_nat @ X2 @ Y )
% 0.24/0.56 => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % neqE
% 0.24/0.56 thf(fact_273_neq__iff,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( X2 != Y )
% 0.24/0.56 = ( ( ord_less_real @ X2 @ Y )
% 0.24/0.56 | ( ord_less_real @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % neq_iff
% 0.24/0.56 thf(fact_274_neq__iff,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( X2 != Y )
% 0.24/0.56 = ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.56 | ( ord_less_nat @ Y @ X2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % neq_iff
% 0.24/0.56 thf(fact_275_order_Oasym,axiom,
% 0.24/0.56 ! [A: real,B: real] :
% 0.24/0.56 ( ( ord_less_real @ A @ B )
% 0.24/0.56 => ~ ( ord_less_real @ B @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % order.asym
% 0.24/0.56 thf(fact_276_order_Oasym,axiom,
% 0.24/0.56 ! [A: nat,B: nat] :
% 0.24/0.56 ( ( ord_less_nat @ A @ B )
% 0.24/0.56 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % order.asym
% 0.24/0.56 thf(fact_277_dense,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.56 => ? [Z5: real] :
% 0.24/0.56 ( ( ord_less_real @ X2 @ Z5 )
% 0.24/0.56 & ( ord_less_real @ Z5 @ Y ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % dense
% 0.24/0.56 thf(fact_278_less__imp__neq,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.56 => ( X2 != Y ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_imp_neq
% 0.24/0.56 thf(fact_279_less__imp__neq,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.56 => ( X2 != Y ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_imp_neq
% 0.24/0.56 thf(fact_280_less__asym,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.56 => ~ ( ord_less_real @ Y @ X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_asym
% 0.24/0.56 thf(fact_281_less__asym,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.56 => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_asym
% 0.24/0.56 thf(fact_282_less__asym_H,axiom,
% 0.24/0.56 ! [A: real,B: real] :
% 0.24/0.56 ( ( ord_less_real @ A @ B )
% 0.24/0.56 => ~ ( ord_less_real @ B @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_asym'
% 0.24/0.56 thf(fact_283_less__asym_H,axiom,
% 0.24/0.56 ! [A: nat,B: nat] :
% 0.24/0.56 ( ( ord_less_nat @ A @ B )
% 0.24/0.56 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_asym'
% 0.24/0.56 thf(fact_284_less__trans,axiom,
% 0.24/0.56 ! [X2: real,Y: real,Z: real] :
% 0.24/0.56 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.56 => ( ( ord_less_real @ Y @ Z )
% 0.24/0.56 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_trans
% 0.24/0.56 thf(fact_285_less__trans,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat,Z: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.56 => ( ( ord_less_nat @ Y @ Z )
% 0.24/0.56 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_trans
% 0.24/0.56 thf(fact_286_less__linear,axiom,
% 0.24/0.56 ! [X2: real,Y: real] :
% 0.24/0.56 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.56 | ( X2 = Y )
% 0.24/0.56 | ( ord_less_real @ Y @ X2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % less_linear
% 0.24/0.56 thf(fact_287_less__linear,axiom,
% 0.24/0.56 ! [X2: nat,Y: nat] :
% 0.24/0.56 ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.57 | ( X2 = Y )
% 0.24/0.57 | ( ord_less_nat @ Y @ X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_linear
% 0.24/0.57 thf(fact_288_less__irrefl,axiom,
% 0.24/0.57 ! [X2: real] :
% 0.24/0.57 ~ ( ord_less_real @ X2 @ X2 ) ).
% 0.24/0.57
% 0.24/0.57 % less_irrefl
% 0.24/0.57 thf(fact_289_less__irrefl,axiom,
% 0.24/0.57 ! [X2: nat] :
% 0.24/0.57 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 0.24/0.57
% 0.24/0.57 % less_irrefl
% 0.24/0.57 thf(fact_290_ord__eq__less__trans,axiom,
% 0.24/0.57 ! [A: real,B: real,C: real] :
% 0.24/0.57 ( ( A = B )
% 0.24/0.57 => ( ( ord_less_real @ B @ C )
% 0.24/0.57 => ( ord_less_real @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ord_eq_less_trans
% 0.24/0.57 thf(fact_291_ord__eq__less__trans,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( A = B )
% 0.24/0.57 => ( ( ord_less_nat @ B @ C )
% 0.24/0.57 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ord_eq_less_trans
% 0.24/0.57 thf(fact_292_ord__less__eq__trans,axiom,
% 0.24/0.57 ! [A: real,B: real,C: real] :
% 0.24/0.57 ( ( ord_less_real @ A @ B )
% 0.24/0.57 => ( ( B = C )
% 0.24/0.57 => ( ord_less_real @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ord_less_eq_trans
% 0.24/0.57 thf(fact_293_ord__less__eq__trans,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( ord_less_nat @ A @ B )
% 0.24/0.57 => ( ( B = C )
% 0.24/0.57 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ord_less_eq_trans
% 0.24/0.57 thf(fact_294_dual__order_Oasym,axiom,
% 0.24/0.57 ! [B: real,A: real] :
% 0.24/0.57 ( ( ord_less_real @ B @ A )
% 0.24/0.57 => ~ ( ord_less_real @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % dual_order.asym
% 0.24/0.57 thf(fact_295_dual__order_Oasym,axiom,
% 0.24/0.57 ! [B: nat,A: nat] :
% 0.24/0.57 ( ( ord_less_nat @ B @ A )
% 0.24/0.57 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.24/0.57
% 0.24/0.57 % dual_order.asym
% 0.24/0.57 thf(fact_296_less__imp__not__eq,axiom,
% 0.24/0.57 ! [X2: real,Y: real] :
% 0.24/0.57 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.57 => ( X2 != Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_imp_not_eq
% 0.24/0.57 thf(fact_297_less__imp__not__eq,axiom,
% 0.24/0.57 ! [X2: nat,Y: nat] :
% 0.24/0.57 ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.57 => ( X2 != Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_imp_not_eq
% 0.24/0.57 thf(fact_298_less__not__sym,axiom,
% 0.24/0.57 ! [X2: real,Y: real] :
% 0.24/0.57 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.57 => ~ ( ord_less_real @ Y @ X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_not_sym
% 0.24/0.57 thf(fact_299_less__not__sym,axiom,
% 0.24/0.57 ! [X2: nat,Y: nat] :
% 0.24/0.57 ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.57 => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_not_sym
% 0.24/0.57 thf(fact_300_less__induct,axiom,
% 0.24/0.57 ! [P3: nat > $o,A: nat] :
% 0.24/0.57 ( ! [X3: nat] :
% 0.24/0.57 ( ! [Y4: nat] :
% 0.24/0.57 ( ( ord_less_nat @ Y4 @ X3 )
% 0.24/0.57 => ( P3 @ Y4 ) )
% 0.24/0.57 => ( P3 @ X3 ) )
% 0.24/0.57 => ( P3 @ A ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_induct
% 0.24/0.57 thf(fact_301_antisym__conv3,axiom,
% 0.24/0.57 ! [Y: real,X2: real] :
% 0.24/0.57 ( ~ ( ord_less_real @ Y @ X2 )
% 0.24/0.57 => ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 0.24/0.57 = ( X2 = Y ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % antisym_conv3
% 0.24/0.57 thf(fact_302_antisym__conv3,axiom,
% 0.24/0.57 ! [Y: nat,X2: nat] :
% 0.24/0.57 ( ~ ( ord_less_nat @ Y @ X2 )
% 0.24/0.57 => ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 0.24/0.57 = ( X2 = Y ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % antisym_conv3
% 0.24/0.57 thf(fact_303_less__imp__not__eq2,axiom,
% 0.24/0.57 ! [X2: real,Y: real] :
% 0.24/0.57 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.57 => ( Y != X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_imp_not_eq2
% 0.24/0.57 thf(fact_304_less__imp__not__eq2,axiom,
% 0.24/0.57 ! [X2: nat,Y: nat] :
% 0.24/0.57 ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.57 => ( Y != X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_imp_not_eq2
% 0.24/0.57 thf(fact_305_less__imp__triv,axiom,
% 0.24/0.57 ! [X2: real,Y: real,P3: $o] :
% 0.24/0.57 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.57 => ( ( ord_less_real @ Y @ X2 )
% 0.24/0.57 => P3 ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_imp_triv
% 0.24/0.57 thf(fact_306_less__imp__triv,axiom,
% 0.24/0.57 ! [X2: nat,Y: nat,P3: $o] :
% 0.24/0.57 ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.57 => ( ( ord_less_nat @ Y @ X2 )
% 0.24/0.57 => P3 ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_imp_triv
% 0.24/0.57 thf(fact_307_linorder__cases,axiom,
% 0.24/0.57 ! [X2: real,Y: real] :
% 0.24/0.57 ( ~ ( ord_less_real @ X2 @ Y )
% 0.24/0.57 => ( ( X2 != Y )
% 0.24/0.57 => ( ord_less_real @ Y @ X2 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % linorder_cases
% 0.24/0.57 thf(fact_308_linorder__cases,axiom,
% 0.24/0.57 ! [X2: nat,Y: nat] :
% 0.24/0.57 ( ~ ( ord_less_nat @ X2 @ Y )
% 0.24/0.57 => ( ( X2 != Y )
% 0.24/0.57 => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % linorder_cases
% 0.24/0.57 thf(fact_309_dual__order_Oirrefl,axiom,
% 0.24/0.57 ! [A: real] :
% 0.24/0.57 ~ ( ord_less_real @ A @ A ) ).
% 0.24/0.57
% 0.24/0.57 % dual_order.irrefl
% 0.24/0.57 thf(fact_310_dual__order_Oirrefl,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ~ ( ord_less_nat @ A @ A ) ).
% 0.24/0.57
% 0.24/0.57 % dual_order.irrefl
% 0.24/0.57 thf(fact_311_order_Ostrict__trans,axiom,
% 0.24/0.57 ! [A: real,B: real,C: real] :
% 0.24/0.57 ( ( ord_less_real @ A @ B )
% 0.24/0.57 => ( ( ord_less_real @ B @ C )
% 0.24/0.57 => ( ord_less_real @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % order.strict_trans
% 0.24/0.57 thf(fact_312_order_Ostrict__trans,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( ord_less_nat @ A @ B )
% 0.24/0.57 => ( ( ord_less_nat @ B @ C )
% 0.24/0.57 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % order.strict_trans
% 0.24/0.57 thf(fact_313_less__imp__not__less,axiom,
% 0.24/0.57 ! [X2: real,Y: real] :
% 0.24/0.57 ( ( ord_less_real @ X2 @ Y )
% 0.24/0.57 => ~ ( ord_less_real @ Y @ X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_imp_not_less
% 0.24/0.57 thf(fact_314_less__imp__not__less,axiom,
% 0.24/0.57 ! [X2: nat,Y: nat] :
% 0.24/0.57 ( ( ord_less_nat @ X2 @ Y )
% 0.24/0.57 => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_imp_not_less
% 0.24/0.57 thf(fact_315_exists__least__iff,axiom,
% 0.24/0.57 ( ( ^ [P4: nat > $o] :
% 0.24/0.57 ? [X5: nat] : ( P4 @ X5 ) )
% 0.24/0.57 = ( ^ [P5: nat > $o] :
% 0.24/0.57 ? [N2: nat] :
% 0.24/0.57 ( ( P5 @ N2 )
% 0.24/0.57 & ! [M2: nat] :
% 0.24/0.57 ( ( ord_less_nat @ M2 @ N2 )
% 0.24/0.57 => ~ ( P5 @ M2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % exists_least_iff
% 0.24/0.57 thf(fact_316_linorder__less__wlog,axiom,
% 0.24/0.57 ! [P3: real > real > $o,A: real,B: real] :
% 0.24/0.57 ( ! [A4: real,B3: real] :
% 0.24/0.57 ( ( ord_less_real @ A4 @ B3 )
% 0.24/0.57 => ( P3 @ A4 @ B3 ) )
% 0.24/0.57 => ( ! [A4: real] : ( P3 @ A4 @ A4 )
% 0.24/0.57 => ( ! [A4: real,B3: real] :
% 0.24/0.57 ( ( P3 @ B3 @ A4 )
% 0.24/0.57 => ( P3 @ A4 @ B3 ) )
% 0.24/0.57 => ( P3 @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % linorder_less_wlog
% 0.24/0.57 thf(fact_317_linorder__less__wlog,axiom,
% 0.24/0.57 ! [P3: nat > nat > $o,A: nat,B: nat] :
% 0.24/0.57 ( ! [A4: nat,B3: nat] :
% 0.24/0.57 ( ( ord_less_nat @ A4 @ B3 )
% 0.24/0.57 => ( P3 @ A4 @ B3 ) )
% 0.24/0.57 => ( ! [A4: nat] : ( P3 @ A4 @ A4 )
% 0.24/0.57 => ( ! [A4: nat,B3: nat] :
% 0.24/0.57 ( ( P3 @ B3 @ A4 )
% 0.24/0.57 => ( P3 @ A4 @ B3 ) )
% 0.24/0.57 => ( P3 @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % linorder_less_wlog
% 0.24/0.57 thf(fact_318_dual__order_Ostrict__trans,axiom,
% 0.24/0.57 ! [B: real,A: real,C: real] :
% 0.24/0.57 ( ( ord_less_real @ B @ A )
% 0.24/0.57 => ( ( ord_less_real @ C @ B )
% 0.24/0.57 => ( ord_less_real @ C @ A ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % dual_order.strict_trans
% 0.24/0.57 thf(fact_319_dual__order_Ostrict__trans,axiom,
% 0.24/0.57 ! [B: nat,A: nat,C: nat] :
% 0.24/0.57 ( ( ord_less_nat @ B @ A )
% 0.24/0.57 => ( ( ord_less_nat @ C @ B )
% 0.24/0.57 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % dual_order.strict_trans
% 0.24/0.57 thf(fact_320_not__less__iff__gr__or__eq,axiom,
% 0.24/0.57 ! [X2: real,Y: real] :
% 0.24/0.57 ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 0.24/0.57 = ( ( ord_less_real @ Y @ X2 )
% 0.24/0.57 | ( X2 = Y ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % not_less_iff_gr_or_eq
% 0.24/0.57 thf(fact_321_not__less__iff__gr__or__eq,axiom,
% 0.24/0.57 ! [X2: nat,Y: nat] :
% 0.24/0.57 ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 0.24/0.57 = ( ( ord_less_nat @ Y @ X2 )
% 0.24/0.57 | ( X2 = Y ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % not_less_iff_gr_or_eq
% 0.24/0.57 thf(fact_322_order_Ostrict__implies__not__eq,axiom,
% 0.24/0.57 ! [A: real,B: real] :
% 0.24/0.57 ( ( ord_less_real @ A @ B )
% 0.24/0.57 => ( A != B ) ) ).
% 0.24/0.57
% 0.24/0.57 % order.strict_implies_not_eq
% 0.24/0.57 thf(fact_323_order_Ostrict__implies__not__eq,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( ord_less_nat @ A @ B )
% 0.24/0.57 => ( A != B ) ) ).
% 0.24/0.57
% 0.24/0.57 % order.strict_implies_not_eq
% 0.24/0.57 thf(fact_324_dual__order_Ostrict__implies__not__eq,axiom,
% 0.24/0.57 ! [B: real,A: real] :
% 0.24/0.57 ( ( ord_less_real @ B @ A )
% 0.24/0.57 => ( A != B ) ) ).
% 0.24/0.57
% 0.24/0.57 % dual_order.strict_implies_not_eq
% 0.24/0.57 thf(fact_325_dual__order_Ostrict__implies__not__eq,axiom,
% 0.24/0.57 ! [B: nat,A: nat] :
% 0.24/0.57 ( ( ord_less_nat @ B @ A )
% 0.24/0.57 => ( A != B ) ) ).
% 0.24/0.57
% 0.24/0.57 % dual_order.strict_implies_not_eq
% 0.24/0.57 thf(fact_326_leD,axiom,
% 0.24/0.57 ! [Y: real,X2: real] :
% 0.24/0.57 ( ( ord_less_eq_real @ Y @ X2 )
% 0.24/0.57 => ~ ( ord_less_real @ X2 @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % leD
% 0.24/0.57 thf(fact_327_leD,axiom,
% 0.24/0.57 ! [Y: nat,X2: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ Y @ X2 )
% 0.24/0.57 => ~ ( ord_less_nat @ X2 @ Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % leD
% 0.24/0.57 thf(fact_328_leI,axiom,
% 0.24/0.57 ! [X2: real,Y: real] :
% 0.24/0.57 ( ~ ( ord_less_real @ X2 @ Y )
% 0.24/0.57 => ( ord_less_eq_real @ Y @ X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % leI
% 0.24/0.57 thf(fact_329_leI,axiom,
% 0.24/0.57 ! [X2: nat,Y: nat] :
% 0.24/0.57 ( ~ ( ord_less_nat @ X2 @ Y )
% 0.24/0.57 => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % leI
% 0.24/0.57 thf(fact_330_le__less,axiom,
% 0.24/0.57 ( ord_less_eq_real
% 0.24/0.57 = ( ^ [X4: real,Y3: real] :
% 0.24/0.57 ( ( ord_less_real @ X4 @ Y3 )
% 0.24/0.57 | ( X4 = Y3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_less
% 0.24/0.57 thf(fact_331_le__less,axiom,
% 0.24/0.57 ( ord_less_eq_nat
% 0.24/0.57 = ( ^ [X4: nat,Y3: nat] :
% 0.24/0.57 ( ( ord_less_nat @ X4 @ Y3 )
% 0.24/0.57 | ( X4 = Y3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % le_less
% 0.24/0.57 thf(fact_332_less__le,axiom,
% 0.24/0.57 ( ord_less_real
% 0.24/0.57 = ( ^ [X4: real,Y3: real] :
% 0.24/0.57 ( ( ord_less_eq_real @ X4 @ Y3 )
% 0.24/0.57 & ( X4 != Y3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_le
% 0.24/0.57 thf(fact_333_less__le,axiom,
% 0.24/0.57 ( ord_less_nat
% 0.24/0.57 = ( ^ [X4: nat,Y3: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.24/0.57 & ( X4 != Y3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % less_le
% 0.24/0.57 thf(fact_334_order__le__less__subst1,axiom,
% 0.24/0.57 ! [A: real,F: real > real,B: real,C: real] :
% 0.24/0.57 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.24/0.57 => ( ( ord_less_real @ B @ C )
% 0.24/0.57 => ( ! [X3: real,Y2: real] :
% 0.24/0.57 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.57 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.57 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % order_le_less_subst1
% 0.24/0.57 thf(fact_335_order__le__less__subst1,axiom,
% 0.24/0.57 ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.24/0.57 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.24/0.57 => ( ( ord_less_nat @ B @ C )
% 0.24/0.57 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.57 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.57 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.57 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % order_le_less_subst1
% 0.24/0.57 thf(fact_336_order__le__less__subst1,axiom,
% 0.24/0.57 ! [A: nat,F: real > nat,B: real,C: real] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.24/0.57 => ( ( ord_less_real @ B @ C )
% 0.24/0.57 => ( ! [X3: real,Y2: real] :
% 0.24/0.57 ( ( ord_less_real @ X3 @ Y2 )
% 0.24/0.57 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.57 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % order_le_less_subst1
% 0.24/0.57 thf(fact_337_order__le__less__subst1,axiom,
% 0.24/0.57 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.24/0.57 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.24/0.57 => ( ( ord_less_nat @ B @ C )
% 0.24/0.57 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.57 ( ( ord_less_nat @ X3 @ Y2 )
% 0.24/0.57 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.57 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % order_le_less_subst1
% 0.24/0.57 thf(fact_338_order__le__less__subst2,axiom,
% 0.24/0.57 ! [A: real,B: real,F: real > real,C: real] :
% 0.24/0.57 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.57 => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.24/0.57 => ( ! [X3: real,Y2: real] :
% 0.24/0.57 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.57 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.62 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.62
% 0.24/0.62 % order_le_less_subst2
% 0.24/0.62 thf(fact_339_order__le__less__subst2,axiom,
% 0.24/0.62 ! [A: real,B: real,F: real > nat,C: nat] :
% 0.24/0.62 ( ( ord_less_eq_real @ A @ B )
% 0.24/0.62 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.24/0.62 => ( ! [X3: real,Y2: real] :
% 0.24/0.62 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.62 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.62 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.62
% 0.24/0.62 % order_le_less_subst2
% 0.24/0.62 thf(fact_340_order__le__less__subst2,axiom,
% 0.24/0.62 ! [A: nat,B: nat,F: nat > real,C: real] :
% 0.24/0.62 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.62 => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.24/0.62 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.62 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.62 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.62 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.62
% 0.24/0.62 % order_le_less_subst2
% 0.24/0.62 thf(fact_341_order__le__less__subst2,axiom,
% 0.24/0.62 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.24/0.62 ( ( ord_less_eq_nat @ A @ B )
% 0.24/0.62 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.24/0.62 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.62 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.62 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.62 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.24/0.62
% 0.24/0.62 % order_le_less_subst2
% 0.24/0.62 thf(fact_342_order__less__le__subst1,axiom,
% 0.24/0.62 ! [A: nat,F: real > nat,B: real,C: real] :
% 0.24/0.62 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.24/0.62 => ( ( ord_less_eq_real @ B @ C )
% 0.24/0.62 => ( ! [X3: real,Y2: real] :
% 0.24/0.62 ( ( ord_less_eq_real @ X3 @ Y2 )
% 0.24/0.62 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.62 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.62
% 0.24/0.62 % order_less_le_subst1
% 0.24/0.62 thf(fact_343_order__less__le__subst1,axiom,
% 0.24/0.62 ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.24/0.62 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.24/0.62 => ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.62 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.62 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.62 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.62 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.62
% 0.24/0.62 % order_less_le_subst1
% 0.24/0.62 thf(fact_344_order__less__le__subst1,axiom,
% 0.24/0.62 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.24/0.62 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.24/0.62 => ( ( ord_less_eq_nat @ B @ C )
% 0.24/0.62 => ( ! [X3: nat,Y2: nat] :
% 0.24/0.62 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.24/0.62 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.24/0.62 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.24/0.62
% 0.24/0.62 % order_less_le_subst1
% 0.24/0.62
% 0.24/0.62 % Helper facts (5)
% 0.24/0.62 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.24/0.62 ! [X2: nat,Y: nat] :
% 0.24/0.62 ( ( if_nat @ $false @ X2 @ Y )
% 0.24/0.62 = Y ) ).
% 0.24/0.62
% 0.24/0.62 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.24/0.62 ! [X2: nat,Y: nat] :
% 0.24/0.62 ( ( if_nat @ $true @ X2 @ Y )
% 0.24/0.62 = X2 ) ).
% 0.24/0.62
% 0.24/0.62 thf(help_If_3_1_If_001t__Real__Oreal_T,axiom,
% 0.24/0.62 ! [P3: $o] :
% 0.24/0.62 ( ( P3 = $true )
% 0.24/0.62 | ( P3 = $false ) ) ).
% 0.24/0.62
% 0.24/0.62 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.24/0.62 ! [X2: real,Y: real] :
% 0.24/0.62 ( ( if_real @ $false @ X2 @ Y )
% 0.24/0.62 = Y ) ).
% 0.24/0.62
% 0.24/0.62 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.24/0.62 ! [X2: real,Y: real] :
% 0.24/0.62 ( ( if_real @ $true @ X2 @ Y )
% 0.24/0.62 = X2 ) ).
% 0.24/0.62
% 0.24/0.62 % Conjectures (1)
% 0.24/0.62 thf(conj_0,conjecture,
% 0.24/0.62 ! [X3: real] :
% 0.24/0.62 ( ( ( poly_real2 @ p @ X3 )
% 0.24/0.62 != zero_zero_real )
% 0.24/0.62 | ( ord_less_real @ lb @ X3 ) ) ).
% 0.24/0.62
% 0.24/0.62 %------------------------------------------------------------------------------
% 0.24/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.g5IF97zu7m/cvc5---1.0.5_12990.p...
% 0.24/0.62 (declare-sort $$unsorted 0)
% 0.24/0.62 (declare-sort tptp.poly_poly_poly_real 0)
% 0.24/0.62 (declare-sort tptp.poly_poly_real 0)
% 0.24/0.62 (declare-sort tptp.poly_poly_nat 0)
% 0.24/0.62 (declare-sort tptp.poly_real 0)
% 0.24/0.62 (declare-sort tptp.poly_nat 0)
% 0.24/0.62 (declare-sort tptp.set_real 0)
% 0.24/0.62 (declare-sort tptp.real 0)
% 0.24/0.62 (declare-sort tptp.nat 0)
% 0.24/0.62 (declare-fun tptp.sgn_sg2128174761y_real (tptp.poly_poly_real) tptp.poly_poly_real)
% 0.24/0.62 (declare-fun tptp.sgn_sgn_poly_real (tptp.poly_real) tptp.poly_real)
% 0.24/0.62 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 0.24/0.62 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.24/0.62 (declare-fun tptp.zero_zero_poly_nat () tptp.poly_nat)
% 0.24/0.62 (declare-fun tptp.zero_z1059985641ly_nat () tptp.poly_poly_nat)
% 0.24/0.62 (declare-fun tptp.zero_z935034829y_real () tptp.poly_poly_poly_real)
% 0.24/0.63 (declare-fun tptp.zero_z1423781445y_real () tptp.poly_poly_real)
% 0.24/0.63 (declare-fun tptp.zero_zero_poly_real () tptp.poly_real)
% 0.24/0.63 (declare-fun tptp.zero_zero_real () tptp.real)
% 0.24/0.63 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 0.24/0.63 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 0.24/0.63 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.24/0.63 (declare-fun tptp.ord_le38482960y_real (tptp.poly_poly_real tptp.poly_poly_real) Bool)
% 0.24/0.63 (declare-fun tptp.ord_less_poly_real (tptp.poly_real tptp.poly_real) Bool)
% 0.24/0.63 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 0.24/0.63 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.24/0.63 (declare-fun tptp.ord_le893774876y_real (tptp.poly_poly_real tptp.poly_poly_real) Bool)
% 0.24/0.63 (declare-fun tptp.ord_le1180086932y_real (tptp.poly_real tptp.poly_real) Bool)
% 0.24/0.63 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 0.24/0.63 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 0.24/0.63 (declare-fun tptp.ord_min_real (tptp.real tptp.real) tptp.real)
% 0.24/0.63 (declare-fun tptp.divide924636027y_real (tptp.poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat) tptp.poly_poly_poly_real)
% 0.24/0.63 (declare-fun tptp.divide1142363123y_real (tptp.poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat) tptp.poly_poly_real)
% 0.24/0.63 (declare-fun tptp.divide1561404011n_real (tptp.real tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat) tptp.poly_real)
% 0.24/0.63 (declare-fun tptp.is_zero_nat (tptp.poly_nat) Bool)
% 0.24/0.63 (declare-fun tptp.is_zero_poly_real (tptp.poly_poly_real) Bool)
% 0.24/0.63 (declare-fun tptp.is_zero_real (tptp.poly_real) Bool)
% 0.24/0.63 (declare-fun tptp.order_poly_poly_real (tptp.poly_poly_real tptp.poly_poly_poly_real) tptp.nat)
% 0.24/0.63 (declare-fun tptp.order_poly_real (tptp.poly_real tptp.poly_poly_real) tptp.nat)
% 0.24/0.63 (declare-fun tptp.order_real (tptp.real tptp.poly_real) tptp.nat)
% 0.24/0.63 (declare-fun tptp.poly_nat2 (tptp.poly_nat tptp.nat) tptp.nat)
% 0.24/0.63 (declare-fun tptp.poly_poly_nat2 (tptp.poly_poly_nat tptp.poly_nat) tptp.poly_nat)
% 0.24/0.63 (declare-fun tptp.poly_poly_poly_real2 (tptp.poly_poly_poly_real tptp.poly_poly_real) tptp.poly_poly_real)
% 0.24/0.63 (declare-fun tptp.poly_poly_real2 (tptp.poly_poly_real tptp.poly_real) tptp.poly_real)
% 0.24/0.63 (declare-fun tptp.poly_real2 (tptp.poly_real tptp.real) tptp.real)
% 0.24/0.63 (declare-fun tptp.poly_cutoff_nat (tptp.nat tptp.poly_nat) tptp.poly_nat)
% 0.24/0.63 (declare-fun tptp.poly_c1404107022y_real (tptp.nat tptp.poly_poly_real) tptp.poly_poly_real)
% 0.24/0.63 (declare-fun tptp.poly_cutoff_real (tptp.nat tptp.poly_real) tptp.poly_real)
% 0.24/0.63 (declare-fun tptp.poly_shift_nat (tptp.nat tptp.poly_nat) tptp.poly_nat)
% 0.24/0.63 (declare-fun tptp.poly_shift_poly_real (tptp.nat tptp.poly_poly_real) tptp.poly_poly_real)
% 0.24/0.63 (declare-fun tptp.poly_shift_real (tptp.nat tptp.poly_real) tptp.poly_real)
% 0.24/0.63 (declare-fun tptp.reflect_poly_nat (tptp.poly_nat) tptp.poly_nat)
% 0.24/0.63 (declare-fun tptp.reflec781175074ly_nat (tptp.poly_poly_nat) tptp.poly_poly_nat)
% 0.24/0.63 (declare-fun tptp.reflec144234502y_real (tptp.poly_poly_poly_real) tptp.poly_poly_poly_real)
% 0.24/0.63 (declare-fun tptp.reflec1522834046y_real (tptp.poly_poly_real) tptp.poly_poly_real)
% 0.24/0.63 (declare-fun tptp.reflect_poly_real (tptp.poly_real) tptp.poly_real)
% 0.24/0.63 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 0.24/0.63 (declare-fun tptp.sturm_1076696862f_real (tptp.poly_real) tptp.real)
% 0.24/0.63 (declare-fun tptp.sturm_1308388506f_real (tptp.poly_real) tptp.real)
% 0.24/0.63 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 0.24/0.63 (declare-fun tptp.lb1 () tptp.real)
% 0.24/0.63 (declare-fun tptp.lb2 () tptp.real)
% 0.24/0.63 (declare-fun tptp.lb () tptp.real)
% 0.24/0.63 (declare-fun tptp.p () tptp.poly_real)
% 0.24/0.63 (declare-fun tptp.thesis () Bool)
% 0.24/0.63 (assert (forall ((X tptp.real)) (=> (= (@ (@ tptp.poly_real2 tptp.p) X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.lb1) X))))
% 0.24/0.63 (assert (= tptp.lb (@ (@ tptp.ord_min_real tptp.lb1) tptp.lb2)))
% 0.24/0.63 (assert (not (forall ((Lb1 tptp.real)) (not (forall ((X tptp.real)) (=> (= (@ (@ tptp.poly_real2 tptp.p) X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Lb1) X)))))))
% 0.24/0.63 (assert (not (= tptp.p tptp.zero_zero_poly_real)))
% 0.24/0.63 (assert (forall ((X2 tptp.poly_nat)) (= (@ (@ tptp.poly_poly_nat2 tptp.zero_z1059985641ly_nat) X2) tptp.zero_zero_poly_nat)))
% 0.24/0.63 (assert (forall ((X2 tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 tptp.zero_z935034829y_real) X2) tptp.zero_z1423781445y_real)))
% 0.24/0.63 (assert (forall ((X2 tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 tptp.zero_z1423781445y_real) X2) tptp.zero_zero_poly_real)))
% 0.24/0.63 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.poly_nat2 tptp.zero_zero_poly_nat) X2) tptp.zero_zero_nat)))
% 0.24/0.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.poly_real2 tptp.zero_zero_poly_real) X2) tptp.zero_zero_real)))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (P tptp.poly_real)) (let ((_let_1 (@ tptp.poly_real2 P))) (=> (@ (@ 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 ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B) (= (@ (@ tptp.poly_real2 P) X3) tptp.zero_zero_real)))))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (P tptp.poly_real)) (let ((_let_1 (@ tptp.poly_real2 P))) (=> (@ (@ 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 ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B) (= (@ (@ tptp.poly_real2 P) X3) tptp.zero_zero_real)))))))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_poly_real)) (= (forall ((X4 tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 P) X4) tptp.zero_z1423781445y_real)) (= P tptp.zero_z935034829y_real))))
% 0.24/0.63 (assert (forall ((P tptp.poly_real)) (= (forall ((X4 tptp.real)) (= (@ (@ tptp.poly_real2 P) X4) tptp.zero_zero_real)) (= P tptp.zero_zero_poly_real))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_real)) (= (forall ((X4 tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 P) X4) tptp.zero_zero_poly_real)) (= P tptp.zero_z1423781445y_real))))
% 0.24/0.63 (assert (not (@ (@ tptp.ord_less_poly_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)))
% 0.24/0.63 (assert (not (@ (@ tptp.ord_le38482960y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)))
% 0.24/0.63 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 0.24/0.63 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.24/0.63 (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)))))))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))))
% 0.24/0.63 (assert (forall ((X2 tptp.poly_real)) (= (= tptp.zero_zero_poly_real X2) (= X2 tptp.zero_zero_poly_real))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((X2 tptp.poly_nat)) (= (= tptp.zero_zero_poly_nat X2) (= X2 tptp.zero_zero_poly_nat))))
% 0.24/0.63 (assert (forall ((X2 tptp.poly_poly_real)) (= (= tptp.zero_z1423781445y_real X2) (= X2 tptp.zero_z1423781445y_real))))
% 0.24/0.63 (assert (forall ((P tptp.poly_real) (Q tptp.poly_real)) (= (= (@ tptp.poly_real2 P) (@ tptp.poly_real2 Q)) (= P Q))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_real) (Q tptp.poly_poly_real)) (= (= (@ tptp.poly_poly_real2 P) (@ tptp.poly_poly_real2 Q)) (= P Q))))
% 0.24/0.63 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_min_real X2) Y)) (and (@ _let_1 X2) (@ _let_1 Y))))))
% 0.24/0.63 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_min_nat X2) Y)) (and (@ _let_1 X2) (@ _let_1 Y))))))
% 0.24/0.63 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_min_real A) A) A)))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_min_nat A) A) A)))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_min_real A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.ord_min_real A) B))) (= (@ (@ tptp.ord_min_real _let_1) B) _let_1))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat A) B))) (= (@ (@ tptp.ord_min_nat _let_1) B) _let_1))))
% 0.24/0.63 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real (@ (@ tptp.ord_min_real A) B)) C))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A) B)) C))))
% 0.24/0.63 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) C) (@ (@ tptp.ord_less_real (@ (@ tptp.ord_min_real A) B)) C))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A) B)) C))))
% 0.24/0.63 (assert (= tptp.ord_less_real (lambda ((A2 tptp.real) (B2 tptp.real)) (and (= A2 (@ (@ tptp.ord_min_real A2) B2)) (not (= A2 B2))))))
% 0.24/0.63 (assert (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (= A2 (@ (@ tptp.ord_min_nat A2) B2)) (not (= A2 B2))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ (@ tptp.ord_min_real B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ (@ tptp.ord_min_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_min_real X2) Y)) Z) (or (@ (@ tptp.ord_less_real X2) Z) (@ (@ tptp.ord_less_real Y) Z)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat X2) Y)) Z) (or (@ (@ tptp.ord_less_nat X2) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 0.24/0.63 (assert (= tptp.is_zero_real (lambda ((P2 tptp.poly_real)) (= P2 tptp.zero_zero_poly_real))))
% 0.24/0.63 (assert (= tptp.is_zero_nat (lambda ((P2 tptp.poly_nat)) (= P2 tptp.zero_zero_poly_nat))))
% 0.24/0.63 (assert (= tptp.is_zero_poly_real (lambda ((P2 tptp.poly_poly_real)) (= P2 tptp.zero_z1423781445y_real))))
% 0.24/0.63 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_min_real B))) (let ((_let_2 (@ tptp.ord_min_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat B))) (let ((_let_2 (@ tptp.ord_min_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.63 (assert (= tptp.ord_min_real (lambda ((A2 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_min_real B2) A2))))
% 0.24/0.63 (assert (= tptp.ord_min_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_min_nat B2) A2))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_min_real A))) (= (@ (@ tptp.ord_min_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_min_real B) C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat A))) (= (@ (@ tptp.ord_min_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_min_nat B) C))))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_cutoff_real N) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_cutoff_nat N) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat)))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_c1404107022y_real N) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)))
% 0.24/0.63 (assert (forall ((P tptp.poly_real) (Ub tptp.real)) (=> (not (= P tptp.zero_zero_poly_real)) (not (forall ((Lb tptp.real)) (=> (@ (@ tptp.ord_less_real Lb) Ub) (not (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb) Z2) (@ (@ tptp.ord_less_real Z2) Ub)) (not (= (@ (@ tptp.poly_real2 P) Z2) tptp.zero_zero_real)))))))))))
% 0.24/0.63 (assert (forall ((P tptp.poly_real) (Lb2 tptp.real)) (=> (not (= P tptp.zero_zero_poly_real)) (not (forall ((Ub2 tptp.real)) (=> (@ (@ tptp.ord_less_real Lb2) Ub2) (not (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb2) Z2) (@ (@ tptp.ord_less_eq_real Z2) Ub2)) (not (= (@ (@ tptp.poly_real2 P) Z2) tptp.zero_zero_real)))))))))))
% 0.24/0.63 (assert (forall ((P tptp.poly_real)) (= (= (@ (@ tptp.poly_real2 (@ tptp.reflect_poly_real P)) tptp.zero_zero_real) tptp.zero_zero_real) (= P tptp.zero_zero_poly_real))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_real)) (= (= (@ (@ tptp.poly_poly_real2 (@ tptp.reflec1522834046y_real P)) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real) (= P tptp.zero_z1423781445y_real))))
% 0.24/0.63 (assert (forall ((P tptp.poly_nat)) (= (= (@ (@ tptp.poly_nat2 (@ tptp.reflect_poly_nat P)) tptp.zero_zero_nat) tptp.zero_zero_nat) (= P tptp.zero_zero_poly_nat))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_nat)) (= (= (@ (@ tptp.poly_poly_nat2 (@ tptp.reflec781175074ly_nat P)) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat) (= P tptp.zero_z1059985641ly_nat))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_poly_real)) (= (= (@ (@ tptp.poly_poly_poly_real2 (@ tptp.reflec144234502y_real P)) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real) (= P tptp.zero_z935034829y_real))))
% 0.24/0.63 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.lb2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.poly_real2 tptp.p) X)) (@ tptp.sturm_1076696862f_real tptp.p)))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_shift_real N) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_shift_nat N) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat)))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.poly_shift_poly_real N) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)))
% 0.24/0.63 (assert (forall ((P tptp.poly_real) (A tptp.real)) (= (= (@ (@ tptp.poly_real2 P) A) tptp.zero_zero_real) (or (= P tptp.zero_zero_poly_real) (not (= (@ (@ tptp.order_real A) P) tptp.zero_zero_nat))))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_real) (A tptp.poly_real)) (= (= (@ (@ tptp.poly_poly_real2 P) A) tptp.zero_zero_poly_real) (or (= P tptp.zero_z1423781445y_real) (not (= (@ (@ tptp.order_poly_real A) P) tptp.zero_zero_nat))))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_poly_real) (A tptp.poly_poly_real)) (= (= (@ (@ tptp.poly_poly_poly_real2 P) A) tptp.zero_z1423781445y_real) (or (= P tptp.zero_z935034829y_real) (not (= (@ (@ tptp.order_poly_poly_real A) P) tptp.zero_zero_nat))))))
% 0.24/0.63 (assert (forall ((R tptp.poly_real) (D tptp.poly_real) (Dr tptp.nat) (N tptp.nat)) (= (@ (@ (@ (@ (@ (@ tptp.divide1561404011n_real tptp.zero_zero_real) tptp.zero_zero_poly_real) R) D) Dr) N) tptp.zero_zero_poly_real)))
% 0.24/0.63 (assert (forall ((R tptp.poly_poly_real) (D tptp.poly_poly_real) (Dr tptp.nat) (N tptp.nat)) (= (@ (@ (@ (@ (@ (@ tptp.divide1142363123y_real tptp.zero_zero_poly_real) tptp.zero_z1423781445y_real) R) D) Dr) N) tptp.zero_z1423781445y_real)))
% 0.24/0.63 (assert (forall ((R tptp.poly_poly_poly_real) (D tptp.poly_poly_poly_real) (Dr tptp.nat) (N tptp.nat)) (= (@ (@ (@ (@ (@ (@ tptp.divide924636027y_real tptp.zero_z1423781445y_real) tptp.zero_z935034829y_real) R) D) Dr) N) tptp.zero_z935034829y_real)))
% 0.24/0.63 (assert (forall ((Lb2 tptp.real) (Ub tptp.real) (P tptp.poly_real)) (= (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb2) Z3) (@ (@ tptp.ord_less_eq_real Z3) Ub)) (not (= (@ (@ tptp.poly_real2 P) Z3) tptp.zero_zero_real)))) (or (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb2) Z3) (@ (@ tptp.ord_less_eq_real Z3) Ub)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.poly_real2 P) Z3)))) (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb2) Z3) (@ (@ tptp.ord_less_eq_real Z3) Ub)) (@ (@ tptp.ord_less_real (@ (@ tptp.poly_real2 P) Z3)) tptp.zero_zero_real)))))))
% 0.24/0.63 (assert (not (forall ((Lb22 tptp.real)) (not (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Lb22) (= (@ tptp.sgn_sgn_real (@ (@ tptp.poly_real2 tptp.p) X)) (@ tptp.sturm_1076696862f_real tptp.p))))))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ (@ tptp.ord_min_real B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (= (@ _let_1 (@ (@ tptp.ord_min_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 0.24/0.63 (assert (= (@ tptp.reflect_poly_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real))
% 0.24/0.63 (assert (= (@ tptp.reflect_poly_nat tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat))
% 0.24/0.63 (assert (= (@ tptp.reflec1522834046y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real))
% 0.24/0.63 (assert (forall ((A tptp.real) (P3 (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P3)) (@ P3 A))))
% 0.24/0.63 (assert (forall ((A3 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A3))) A3)))
% 0.24/0.63 (assert (forall ((Lb2 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (= (@ (@ tptp.poly_real2 tptp.p) X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Lb2) X3))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Lb2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.poly_real2 tptp.p) X3)) (@ tptp.sturm_1076696862f_real tptp.p)))) tptp.thesis))))
% 0.24/0.63 (assert (forall ((S tptp.set_real)) (=> (exists ((X tptp.real)) (@ (@ tptp.member_real X) S)) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S) (@ (@ tptp.ord_less_eq_real X3) Z2)))) (exists ((Y2 tptp.real)) (and (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) S) (@ (@ tptp.ord_less_eq_real X) Y2))) (forall ((Z2 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S) (@ (@ tptp.ord_less_eq_real X3) Z2))) (@ (@ tptp.ord_less_eq_real Y2) Z2)))))))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)))
% 0.24/0.63 (assert (@ (@ tptp.ord_le1180086932y_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real))
% 0.24/0.63 (assert (@ (@ tptp.ord_le893774876y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real))
% 0.24/0.63 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 0.24/0.63 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 0.24/0.63 (assert (= tptp.ord_less_eq_real (lambda ((X4 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y3) (= X4 Y3)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_eq_real B) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) (@ (@ tptp.ord_min_real C) D))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) (@ (@ tptp.ord_min_nat C) D))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (= A (@ (@ tptp.ord_min_real A) B)))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A (@ (@ tptp.ord_min_nat A) B)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A (@ (@ tptp.ord_min_real A) B)) (@ (@ tptp.ord_less_eq_real A) B))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_min_nat A) B)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (= (@ (@ tptp.ord_min_real A) B) A))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_min_nat A) B) A))))
% 0.24/0.63 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.ord_min_real A) B) B))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_min_nat A) B) B))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ (@ tptp.ord_min_real B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ (@ tptp.ord_min_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.ord_min_real B) C)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.ord_min_nat B) C)))))))
% 0.24/0.63 (assert (= tptp.ord_less_eq_real (lambda ((A2 tptp.real) (B2 tptp.real)) (= A2 (@ (@ tptp.ord_min_real A2) B2)))))
% 0.24/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (= A2 (@ (@ tptp.ord_min_nat A2) B2)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) A)))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) A)))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) B)))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) B)))
% 0.24/0.63 (assert (= tptp.ord_less_eq_real (lambda ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_min_real A2) B2) A2))))
% 0.24/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_min_nat A2) B2) A2))))
% 0.24/0.63 (assert (= tptp.ord_less_eq_real (lambda ((B2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_min_real A2) B2) B2))))
% 0.24/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_min_nat A2) B2) B2))))
% 0.24/0.63 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) C))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) C))))
% 0.24/0.63 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) C))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) C))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real X2) Y)) Z) (or (@ (@ tptp.ord_less_eq_real X2) Z) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat X2) Y)) Z) (or (@ (@ tptp.ord_less_eq_nat X2) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))))
% 0.24/0.63 (assert (forall ((P tptp.poly_real) (A tptp.real)) (=> (not (= (@ (@ tptp.poly_real2 P) A) tptp.zero_zero_real)) (= (@ (@ tptp.order_real A) P) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_real) (A tptp.poly_real)) (=> (not (= (@ (@ tptp.poly_poly_real2 P) A) tptp.zero_zero_poly_real)) (= (@ (@ tptp.order_poly_real A) P) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((P tptp.poly_poly_poly_real) (A tptp.poly_poly_real)) (=> (not (= (@ (@ tptp.poly_poly_poly_real2 P) A) tptp.zero_z1423781445y_real)) (= (@ (@ tptp.order_poly_poly_real A) P) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((Lb2 tptp.real) (Ub tptp.real) (P tptp.poly_real)) (= (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb2) Z3) (@ (@ tptp.ord_less_real Z3) Ub)) (not (= (@ (@ tptp.poly_real2 P) Z3) tptp.zero_zero_real)))) (or (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb2) Z3) (@ (@ tptp.ord_less_real Z3) Ub)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.poly_real2 P) Z3)))) (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb2) Z3) (@ (@ tptp.ord_less_real Z3) Ub)) (@ (@ tptp.ord_less_real (@ (@ tptp.poly_real2 P) Z3)) tptp.zero_zero_real)))))))
% 0.24/0.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X2)) (@ _let_1 X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 0.24/0.63 (assert (forall ((A tptp.poly_real)) (let ((_let_1 (@ tptp.ord_less_poly_real tptp.zero_zero_poly_real))) (= (@ _let_1 (@ tptp.sgn_sgn_poly_real A)) (@ _let_1 A)))))
% 0.24/0.63 (assert (forall ((A tptp.poly_poly_real)) (let ((_let_1 (@ tptp.ord_le38482960y_real tptp.zero_z1423781445y_real))) (= (@ _let_1 (@ tptp.sgn_sg2128174761y_real A)) (@ _let_1 A)))))
% 0.24/0.63 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A)) (@ _let_1 A)))))
% 0.24/0.63 (assert (forall ((A tptp.poly_real)) (= (@ (@ tptp.ord_less_poly_real (@ tptp.sgn_sgn_poly_real A)) tptp.zero_zero_poly_real) (@ (@ tptp.ord_less_poly_real A) tptp.zero_zero_poly_real))))
% 0.24/0.63 (assert (forall ((A tptp.poly_poly_real)) (= (@ (@ tptp.ord_le38482960y_real (@ tptp.sgn_sg2128174761y_real A)) tptp.zero_z1423781445y_real) (@ (@ tptp.ord_le38482960y_real A) tptp.zero_z1423781445y_real))))
% 0.24/0.63 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 0.24/0.63 (assert (forall ((P tptp.poly_real)) (=> (not (= P tptp.zero_zero_poly_real)) (not (forall ((Ub2 tptp.real)) (=> (forall ((X tptp.real)) (=> (= (@ (@ tptp.poly_real2 P) X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) Ub2))) (not (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Ub2) X) (= (@ tptp.sgn_sgn_real (@ (@ tptp.poly_real2 P) X)) (@ tptp.sturm_1308388506f_real P)))))))))))
% 0.24/0.63 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 0.24/0.63 (assert (= (@ tptp.sgn_sgn_poly_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real))
% 0.24/0.63 (assert (= (@ tptp.sgn_sg2128174761y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real))
% 0.24/0.63 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 0.24/0.63 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2)))))
% 0.24/0.63 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 0.24/0.63 (assert (forall ((A tptp.poly_real)) (= (= (@ tptp.sgn_sgn_poly_real A) tptp.zero_zero_poly_real) (= A tptp.zero_zero_poly_real))))
% 0.24/0.63 (assert (forall ((A tptp.poly_poly_real)) (= (= (@ tptp.sgn_sg2128174761y_real A) tptp.zero_z1423781445y_real) (= A tptp.zero_z1423781445y_real))))
% 0.24/0.63 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 0.24/0.63 (assert (forall ((A tptp.poly_real)) (= (= (@ tptp.sgn_sgn_poly_real A) tptp.zero_zero_poly_real) (= A tptp.zero_zero_poly_real))))
% 0.24/0.63 (assert (forall ((A tptp.poly_poly_real)) (= (= (@ tptp.sgn_sg2128174761y_real A) tptp.zero_z1423781445y_real) (= A tptp.zero_z1423781445y_real))))
% 0.24/0.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sgn_sgn_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.24/0.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P3 K) (=> (forall ((Y2 tptp.nat)) (=> (@ P3 Y2) (@ (@ tptp.ord_less_eq_nat Y2) B))) (exists ((X3 tptp.nat)) (and (@ P3 X3) (forall ((Y4 tptp.nat)) (=> (@ P3 Y4) (@ (@ tptp.ord_less_eq_nat Y4) X3)))))))))
% 0.24/0.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.24/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M2) N2) (= M2 N2)))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.24/0.63 (assert (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (not (= M2 N2))))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2)))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P3 N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P3 M3)))))) (@ P3 N))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ P3 M3))) (@ P3 N3))) (@ P3 N))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.24/0.63 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 0.24/0.63 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P3 tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P3 N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P3 M3))))))) (@ P3 N)))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P3 N) (=> (not (@ P3 tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K2) (not (@ P3 I3)))) (@ P3 K2)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) X2)))
% 0.24/0.63 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (= (@ (@ tptp.ord_min_real X2) Y) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (= (@ (@ tptp.ord_min_nat X2) Y) X2))))
% 0.24/0.63 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (= (@ (@ tptp.ord_min_real X2) Y) Y))))
% 0.24/0.63 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= (@ (@ tptp.ord_min_nat X2) Y) Y))))
% 0.24/0.63 (assert (= tptp.ord_min_real (lambda ((A2 tptp.real) (B2 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real A2) B2)) A2) B2))))
% 0.24/0.63 (assert (= tptp.ord_min_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A2) B2)) A2) B2))))
% 0.24/0.63 (assert (forall ((N tptp.nat) (P3 (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P3 K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I3) (@ P3 I3))) (@ P3 K2)))) (@ P3 M)))))
% 0.24/0.63 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (= A B)))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 0.24/0.63 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((A2 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A2) (@ (@ tptp.ord_less_eq_real A2) B2)))))
% 0.24/0.63 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 0.24/0.63 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A4) B3) (@ (@ P3 A4) B3))) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ P3 B3) A4) (@ (@ P3 A4) B3))) (@ (@ P3 A) B)))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ P3 A4) B3))) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P3 B3) A4) (@ (@ P3 A4) B3))) (@ (@ P3 A) B)))))
% 0.24/0.63 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real B) A) (= A B)))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_eq_real A) C)))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 0.24/0.63 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((A2 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A2) B2) (@ (@ tptp.ord_less_eq_real B2) A2)))))
% 0.24/0.63 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat B2) A2)))))
% 0.24/0.63 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (= (@ (@ tptp.ord_less_eq_real X2) Y) (= X2 Y)))))
% 0.24/0.63 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y) (= X2 Y)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_real Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_real Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _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)))))))))))))))))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _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)))))))))))))))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real X2) Y)) (@ (@ tptp.ord_less_eq_real Y) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_nat X2) Y))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real Y) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (= X2 Y)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= X2 Y)))))
% 0.24/0.63 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((X4 tptp.real) (Y3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_real Y3) X4)))))
% 0.24/0.63 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((X4 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X4)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((X2 tptp.real)) (exists ((Y2 tptp.real)) (@ (@ tptp.ord_less_real Y2) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X2) X_1))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_1))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real Y) X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_nat X2) Y) (@ (@ tptp.ord_less_nat Y) X2)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (exists ((Z5 tptp.real)) (and (@ (@ tptp.ord_less_real X2) Z5) (@ (@ tptp.ord_less_real Z5) Y))))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= X2 Y)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= X2 Y)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y) (@ (@ tptp.ord_less_real Y) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y) (= X2 Y) (@ (@ tptp.ord_less_nat Y) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real X2) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= X2 Y)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= X2 Y)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y4) X3) (@ P3 Y4))) (@ P3 X3))) (@ P3 A))))
% 0.24/0.63 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X2)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (= X2 Y)))))
% 0.24/0.63 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (= X2 Y)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= Y X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= Y X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (P3 Bool)) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_real Y) X2) P3))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (P3 Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y) (=> (@ (@ tptp.ord_less_nat Y) X2) P3))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_real Y) X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_nat Y) X2)))))
% 0.24/0.63 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))))
% 0.24/0.63 (assert (= (lambda ((P4 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P5 N2) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (@ P5 M2)))))))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A4) B3) (@ (@ P3 A4) B3))) (=> (forall ((A4 tptp.real)) (@ (@ P3 A4) A4)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ P3 B3) A4) (@ (@ P3 A4) B3))) (@ (@ P3 A) B))))))
% 0.24/0.63 (assert (forall ((P3 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B3) (@ (@ P3 A4) B3))) (=> (forall ((A4 tptp.nat)) (@ (@ P3 A4) A4)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P3 B3) A4) (@ (@ P3 A4) B3))) (@ (@ P3 A) B))))))
% 0.24/0.63 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (or (@ (@ tptp.ord_less_real Y) X2) (= X2 Y)))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (or (@ (@ tptp.ord_less_nat Y) X2) (= X2 Y)))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 0.24/0.63 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 0.24/0.63 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (not (@ (@ tptp.ord_less_real X2) Y)))))
% 0.24/0.63 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (not (@ (@ tptp.ord_less_nat X2) Y)))))
% 0.24/0.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_eq_real Y) X2))))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 0.24/0.63 (assert (= tptp.ord_less_eq_real (lambda ((X4 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y3) (= X4 Y3)))))
% 0.24/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y3) (= X4 Y3)))))
% 0.24/0.63 (assert (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y3) (not (= X4 Y3))))))
% 0.24/0.63 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y3) (not (= X4 Y3))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 0.24/0.63 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.86/1.06 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 0.86/1.06 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.86/1.06 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.86/1.06 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.86/1.06 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.86/1.06 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X2) Y) Y)))
% 0.86/1.06 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X2) Y) X2)))
% 0.86/1.06 (assert (forall ((P3 Bool)) (or (= P3 true) (= P3 false))))
% 0.86/1.06 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X2) Y) Y)))
% 0.86/1.06 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X2) Y) X2)))
% 0.86/1.06 (assert (not (forall ((X3 tptp.real)) (or (not (= (@ (@ tptp.poly_real2 tptp.p) X3) tptp.zero_zero_real)) (@ (@ tptp.ord_less_real tptp.lb) X3)))))
% 0.86/1.06 (set-info :filename cvc5---1.0.5_12990)
% 0.86/1.06 (check-sat-assuming ( true ))
% 0.86/1.06 ------- get file name : TPTP file name is ITP194^1
% 0.86/1.06 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12990.smt2...
% 0.86/1.06 --- Run --ho-elim --full-saturate-quant at 10...
% 0.86/1.06 % SZS status Theorem for ITP194^1
% 0.86/1.06 % SZS output start Proof for ITP194^1
% 0.86/1.06 (
% 0.86/1.06 (let ((_let_1 (not (forall ((X3 tptp.real)) (or (not (= (@ (@ tptp.poly_real2 tptp.p) X3) tptp.zero_zero_real)) (@ (@ tptp.ord_less_real tptp.lb) X3)))))) (let ((_let_2 (= tptp.ord_less_eq_real (lambda ((X4 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y3) (= X4 Y3)))))) (let ((_let_3 (forall ((X2 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (or (@ (@ tptp.ord_less_real Y) X2) (= X2 Y)))))) (let ((_let_4 (= tptp.ord_min_real (lambda ((A2 tptp.real) (B2 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real A2) B2)) A2) B2))))) (let ((_let_5 (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_6 (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) C))))) (let ((_let_7 (= tptp.ord_less_eq_real (lambda ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_min_real A2) B2) A2))))) (let ((_let_8 (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (= A2 (@ (@ tptp.ord_min_nat A2) B2)))))) (let ((_let_9 (lambda ((A2 tptp.real) (B2 tptp.real)) (= A2 (@ (@ tptp.ord_min_real A2) B2))))) (let ((_let_10 (= tptp.ord_less_eq_real _let_9))) (let ((_let_11 (= tptp.ord_less_eq_real (lambda ((X4 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y3) (= X4 Y3)))))) (let ((_let_12 (= tptp.ord_min_real (lambda ((A2 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_min_real B2) A2))))) (let ((_let_13 (= tptp.is_zero_poly_real (lambda ((P2 tptp.poly_poly_real)) (= P2 tptp.zero_z1423781445y_real))))) (let ((_let_14 (= tptp.is_zero_nat (lambda ((P2 tptp.poly_nat)) (= P2 tptp.zero_zero_poly_nat))))) (let ((_let_15 (= tptp.is_zero_real (lambda ((P2 tptp.poly_real)) (= P2 tptp.zero_zero_poly_real))))) (let ((_let_16 (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (= A2 (@ (@ tptp.ord_min_nat A2) B2)) (not (= A2 B2))))))) (let ((_let_17 (= tptp.ord_less_real (lambda ((A2 tptp.real) (B2 tptp.real)) (and (= A2 (@ (@ tptp.ord_min_real A2) B2)) (not (= A2 B2))))))) (let ((_let_18 (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) C) (@ (@ tptp.ord_less_real (@ (@ tptp.ord_min_real A) B)) C))))) (let ((_let_19 (forall ((A tptp.real)) (= (@ (@ tptp.ord_min_real A) A) A)))) (let ((_let_20 (@ (@ tptp.ord_min_real tptp.lb1) tptp.lb2))) (let ((_let_21 (= tptp.lb _let_20))) (let ((_let_22 (forall ((X tptp.real)) (=> (= (@ (@ tptp.poly_real2 tptp.p) X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.lb1) X))))) (let ((_let_23 (ho_46 k_45 tptp.lb1))) (let ((_let_24 (ho_47 _let_23 tptp.lb2))) (let ((_let_25 (= tptp.lb1 _let_24))) (let ((_let_26 (= tptp.lb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_168))) (let ((_let_27 (= _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_168))) (let ((_let_28 (ho_90 k_89 tptp.p))) (let ((_let_29 (= tptp.zero_zero_real (ho_47 _let_28 tptp.lb1)))) (let ((_let_30 (= tptp.zero_zero_real (ho_47 _let_28 _let_24)))) (let ((_let_31 (forall ((BOUND_VARIABLE_20813 tptp.real)) (let ((_let_1 (ho_47 (ho_46 k_45 tptp.lb1) tptp.lb2))) (or (not (= tptp.zero_zero_real (ho_47 (ho_90 k_89 tptp.p) BOUND_VARIABLE_20813))) (= _let_1 (ho_47 (ho_46 k_45 _let_1) BOUND_VARIABLE_20813))))))) (let ((_let_32 (= _let_24 (ho_47 (ho_46 k_45 _let_24) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_168)))) (let ((_let_33 (= tptp.zero_zero_real (ho_47 _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_168)))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32))) (let ((_let_36 (= tptp.lb1 (ho_47 _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_168)))) (let ((_let_37 (or _let_34 _let_36))) (let ((_let_38 (= k_45 k_88))) (let ((_let_39 (= k_45 k_69))) (let ((_let_40 (= tptp.lb1 (ho_47 _let_23 tptp.lb1)))) (let ((_let_41 (not _let_25))) (let ((_let_42 (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_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_43 (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_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_44 (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_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> tptp.nat tptp.poly_nat tptp.poly_nat)|) (e |u_(-> tptp.poly_nat tptp.poly_nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.poly_nat tptp.poly_nat)|)) (not (forall ((ii tptp.nat)) (= (ho_111 v ii) (ite (= i ii) e (ho_111 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> tptp.nat tptp.poly_nat tptp.poly_nat)|) (y |u_(-> tptp.nat tptp.poly_nat tptp.poly_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_111 x z) (ho_111 y z)))) (= x y))))) (let ((_let_48 (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_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_49 (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_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_50 (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_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_51 (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_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_52 (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_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_53 (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_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> tptp.real Bool)|) (e Bool) (i tptp.real)) (not (forall ((v |u_(-> tptp.real Bool)|)) (not (forall ((ii tptp.real)) (= (ho_44 v ii) (ite (= i ii) e (ho_44 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> tptp.real Bool)|) (y |u_(-> tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_44 x z) (ho_44 y z)))) (= x y))))) (let ((_let_56 (forall ((u |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (e |u_(-> tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_146 v ii) (ite (= i ii) e (ho_146 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (y |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_58 (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_103 v ii) (ite (= i ii) e (ho_103 u ii)))))))))) (let ((_let_59 (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_103 x z) (ho_103 y z)))) (= x y))))) (let ((_let_60 (forall ((u |u_(-> tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (e |u_(-> tptp.nat tptp.nat tptp.poly_poly_real)|) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_147 v ii) (ite (= i ii) e (ho_147 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (y |u_(-> tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_147 x z) (ho_147 y z)))) (= x y))))) (let ((_let_62 (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_104 v ii) (ite (= i ii) e (ho_104 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> tptp.poly_real Bool)|) (y |u_(-> tptp.poly_real Bool)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_64 (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_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_65 (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_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> tptp.nat tptp.poly_poly_poly_real)|) (e tptp.poly_poly_poly_real) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.poly_poly_poly_real)|)) (not (forall ((ii tptp.nat)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.nat tptp.poly_poly_poly_real)|) (y |u_(-> tptp.nat tptp.poly_poly_poly_real)|)) (or (not (forall ((z tptp.nat)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> tptp.poly_nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.poly_nat)) (not (forall ((v |u_(-> tptp.poly_nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.poly_nat)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> tptp.poly_nat tptp.nat tptp.nat)|) (y |u_(-> tptp.poly_nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.poly_nat)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_70 (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_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_71 (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_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> tptp.poly_poly_nat tptp.poly_nat tptp.poly_nat)|) (e |u_(-> tptp.poly_nat tptp.poly_nat)|) (i tptp.poly_poly_nat)) (not (forall ((v |u_(-> tptp.poly_poly_nat tptp.poly_nat tptp.poly_nat)|)) (not (forall ((ii tptp.poly_poly_nat)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> tptp.poly_poly_nat tptp.poly_nat tptp.poly_nat)|) (y |u_(-> tptp.poly_poly_nat tptp.poly_nat tptp.poly_nat)|)) (or (not (forall ((z tptp.poly_poly_nat)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_74 (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_107 v ii) (ite (= i ii) e (ho_107 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.poly_poly_real Bool)|) (y |u_(-> tptp.poly_poly_real Bool)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (e |u_(-> tptp.nat tptp.poly_poly_poly_real)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (not (forall ((ii tptp.nat)) (= (ho_155 v ii) (ite (= i ii) e (ho_155 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (y |u_(-> tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (or (not (forall ((z tptp.nat)) (= (ho_155 x z) (ho_155 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> tptp.poly_nat tptp.poly_nat)|) (e tptp.poly_nat) (i tptp.poly_nat)) (not (forall ((v |u_(-> tptp.poly_nat tptp.poly_nat)|)) (not (forall ((ii tptp.poly_nat)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> tptp.poly_nat tptp.poly_nat)|) (y |u_(-> tptp.poly_nat tptp.poly_nat)|)) (or (not (forall ((z tptp.poly_nat)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_80 (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_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_81 (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_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_82 (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_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_83 (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_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_84 (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_95 v ii) (ite (= i ii) e (ho_95 u ii)))))))))) (let ((_let_85 (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_95 x z) (ho_95 y z)))) (= x y))))) (let ((_let_86 (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_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> tptp.real tptp.set_real Bool)|) (y |u_(-> tptp.real tptp.set_real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> tptp.nat tptp.poly_poly_real)|) (e tptp.poly_poly_real) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.poly_poly_real)|)) (not (forall ((ii tptp.nat)) (= (ho_149 v ii) (ite (= i ii) e (ho_149 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> tptp.nat tptp.poly_poly_real)|) (y |u_(-> tptp.nat tptp.poly_poly_real)|)) (or (not (forall ((z tptp.nat)) (= (ho_149 x z) (ho_149 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> tptp.nat tptp.real)|) (e tptp.real) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.real)|)) (not (forall ((ii tptp.nat)) (= (ho_165 v ii) (ite (= i ii) e (ho_165 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_165 x z) (ho_165 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> Bool tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat tptp.nat)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii Bool)) (= (ho_68 v ii) (ite (= i ii) e (ho_68 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> Bool tptp.nat tptp.nat tptp.nat)|) (y |u_(-> Bool tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_68 x z) (ho_68 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> tptp.poly_poly_nat tptp.poly_poly_nat)|) (e tptp.poly_poly_nat) (i tptp.poly_poly_nat)) (not (forall ((v |u_(-> tptp.poly_poly_nat tptp.poly_poly_nat)|)) (not (forall ((ii tptp.poly_poly_nat)) (= (ho_118 v ii) (ite (= i ii) e (ho_118 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> tptp.poly_poly_nat tptp.poly_poly_nat)|) (y |u_(-> tptp.poly_poly_nat tptp.poly_poly_nat)|)) (or (not (forall ((z tptp.poly_poly_nat)) (= (ho_118 x z) (ho_118 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_37 v ii) (ite (= i ii) e (ho_37 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (e |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_145 v ii) (ite (= i ii) e (ho_145 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (y |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_102 (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_43 v ii) (ite (= i ii) e (ho_43 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> tptp.real tptp.real Bool)|) (y |u_(-> tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_43 x z) (ho_43 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> tptp.nat tptp.nat tptp.poly_poly_real)|) (e |u_(-> tptp.nat tptp.poly_poly_real)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.poly_poly_real)|)) (not (forall ((ii tptp.nat)) (= (ho_148 v ii) (ite (= i ii) e (ho_148 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> tptp.nat tptp.nat tptp.poly_poly_real)|) (y |u_(-> tptp.nat tptp.nat tptp.poly_poly_real)|)) (or (not (forall ((z tptp.nat)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> tptp.real tptp.real tptp.real)|) (e |u_(-> tptp.real tptp.real)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.real tptp.real)|)) (not (forall ((ii tptp.real)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> tptp.real tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_40 v ii) (ite (= i ii) e (ho_40 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> tptp.poly_poly_poly_real tptp.nat)|) (e tptp.nat) (i tptp.poly_poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_poly_real tptp.nat)|)) (not (forall ((ii tptp.poly_poly_poly_real)) (= (ho_135 v ii) (ite (= i ii) e (ho_135 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> tptp.poly_poly_poly_real tptp.nat)|) (y |u_(-> tptp.poly_poly_poly_real tptp.nat)|)) (or (not (forall ((z tptp.poly_poly_poly_real)) (= (ho_135 x z) (ho_135 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> tptp.poly_poly_real tptp.poly_poly_poly_real tptp.nat)|) (e |u_(-> tptp.poly_poly_poly_real tptp.nat)|) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.poly_poly_poly_real tptp.nat)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_134 v ii) (ite (= i ii) e (ho_134 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> tptp.poly_poly_real tptp.poly_poly_poly_real tptp.nat)|) (y |u_(-> tptp.poly_poly_real tptp.poly_poly_poly_real tptp.nat)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> Bool tptp.real tptp.real tptp.real)|) (e |u_(-> tptp.real tptp.real tptp.real)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.real tptp.real tptp.real)|)) (not (forall ((ii Bool)) (= (ho_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> Bool tptp.real tptp.real tptp.real)|) (y |u_(-> Bool tptp.real tptp.real tptp.real)|)) (or (not (forall ((z Bool)) (= (ho_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real)|) (e tptp.poly_poly_poly_real) (i tptp.poly_poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_poly_real)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real)|) (y |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_poly_real)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> tptp.poly_real tptp.nat)|) (e tptp.nat) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.nat)|)) (not (forall ((ii tptp.poly_real)) (= (ho_129 v ii) (ite (= i ii) e (ho_129 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> tptp.poly_real tptp.nat)|) (y |u_(-> tptp.poly_real tptp.nat)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_124 (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_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> tptp.set_real Bool)|) (y |u_(-> tptp.set_real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> tptp.poly_real tptp.real)|) (e tptp.real) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.real)|)) (not (forall ((ii tptp.poly_real)) (= (ho_123 v ii) (ite (= i ii) e (ho_123 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> tptp.poly_real tptp.real)|) (y |u_(-> tptp.poly_real tptp.real)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> tptp.real tptp.poly_real tptp.nat)|) (e |u_(-> tptp.poly_real tptp.nat)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.poly_real tptp.nat)|)) (not (forall ((ii tptp.real)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> tptp.real tptp.poly_real tptp.nat)|) (y |u_(-> tptp.real tptp.poly_real tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> tptp.poly_poly_real tptp.nat)|) (e tptp.nat) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.nat)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> tptp.poly_poly_real tptp.nat)|) (y |u_(-> tptp.poly_poly_real tptp.nat)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> tptp.poly_real tptp.poly_poly_real tptp.nat)|) (e |u_(-> tptp.poly_poly_real tptp.nat)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.poly_poly_real tptp.nat)|)) (not (forall ((ii tptp.poly_real)) (= (ho_131 v ii) (ite (= i ii) e (ho_131 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> tptp.poly_real tptp.poly_poly_real tptp.nat)|) (y |u_(-> tptp.poly_real tptp.poly_poly_real tptp.nat)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> tptp.nat tptp.poly_real)|) (e tptp.poly_real) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.poly_real)|)) (not (forall ((ii tptp.nat)) (= (ho_142 v ii) (ite (= i ii) e (ho_142 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> tptp.nat tptp.poly_real)|) (y |u_(-> tptp.nat tptp.poly_real)|)) (or (not (forall ((z tptp.nat)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> tptp.nat tptp.nat tptp.poly_real)|) (e |u_(-> tptp.nat tptp.poly_real)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.poly_real)|)) (not (forall ((ii tptp.nat)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> tptp.nat tptp.nat tptp.poly_real)|) (y |u_(-> tptp.nat tptp.nat tptp.poly_real)|)) (or (not (forall ((z tptp.nat)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (e |u_(-> tptp.nat tptp.nat tptp.poly_real)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|)) (not (forall ((ii tptp.poly_real)) (= (ho_140 v ii) (ite (= i ii) e (ho_140 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (y |u_(-> tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (e |u_(-> tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|)) (not (forall ((ii tptp.poly_real)) (= (ho_139 v ii) (ite (= i ii) e (ho_139 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (y |u_(-> tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (e |u_(-> tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|)) (not (forall ((ii tptp.poly_real)) (= (ho_138 v ii) (ite (= i ii) e (ho_138 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (y |u_(-> tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_138 x z) (ho_138 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> tptp.real tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (e |u_(-> tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|)) (not (forall ((ii tptp.real)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> tptp.real tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|) (y |u_(-> tptp.real tptp.poly_real tptp.poly_real tptp.poly_real tptp.nat tptp.nat tptp.poly_real)|)) (or (not (forall ((z tptp.real)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (e |u_(-> tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (i tptp.poly_poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_poly_real)) (= (ho_153 v ii) (ite (= i ii) e (ho_153 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (y |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_poly_real)) (= (ho_153 x z) (ho_153 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> tptp.poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (e |u_(-> tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (i tptp.poly_real)) (not (forall ((v |u_(-> tptp.poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|)) (not (forall ((ii tptp.poly_real)) (= (ho_144 v ii) (ite (= i ii) e (ho_144 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> tptp.poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|) (y |u_(-> tptp.poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.poly_poly_real tptp.nat tptp.nat tptp.poly_poly_real)|)) (or (not (forall ((z tptp.poly_real)) (= (ho_144 x z) (ho_144 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (e |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (i tptp.poly_poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_poly_real)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (y |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_poly_real)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (e |u_(-> tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (i tptp.poly_poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_poly_real)) (= (ho_154 v ii) (ite (= i ii) e (ho_154 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (y |u_(-> tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_poly_real)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> tptp.poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (e |u_(-> tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (i tptp.poly_poly_real)) (not (forall ((v |u_(-> tptp.poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (not (forall ((ii tptp.poly_poly_real)) (= (ho_151 v ii) (ite (= i ii) e (ho_151 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> tptp.poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|) (y |u_(-> tptp.poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.poly_poly_poly_real tptp.nat tptp.nat tptp.poly_poly_poly_real)|)) (or (not (forall ((z tptp.poly_poly_real)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_156 (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_158 v ii) (ite (= i ii) e (ho_158 u ii)))))))))) (let ((_let_157 (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_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> tptp.real tptp.nat)|) (e tptp.nat) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.nat)|)) (not (forall ((ii tptp.real)) (= (ho_164 v ii) (ite (= i ii) e (ho_164 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> tptp.real tptp.nat)|) (y |u_(-> tptp.real tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_164 x z) (ho_164 y z)))) (= x y))))) (let ((_let_160 (forall ((BOUND_VARIABLE_22793 tptp.nat) (BOUND_VARIABLE_22794 tptp.nat)) (= (ho_38 (ho_37 k_36 BOUND_VARIABLE_22793) BOUND_VARIABLE_22794) (and (= BOUND_VARIABLE_22793 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22793) BOUND_VARIABLE_22794)) (not (= BOUND_VARIABLE_22793 BOUND_VARIABLE_22794))))))) (let ((_let_161 (forall ((BOUND_VARIABLE_22781 tptp.real) (BOUND_VARIABLE_22782 tptp.real)) (= (ho_44 (ho_43 k_42 BOUND_VARIABLE_22781) BOUND_VARIABLE_22782) (and (= BOUND_VARIABLE_22781 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22781) BOUND_VARIABLE_22782)) (not (= BOUND_VARIABLE_22781 BOUND_VARIABLE_22782))))))) (let ((_let_162 (forall ((BOUND_VARIABLE_22767 tptp.real) (BOUND_VARIABLE_22768 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22767 BOUND_VARIABLE_22768))) (let ((_let_2 (not _let_1))) (= (ho_44 (ho_43 k_48 BOUND_VARIABLE_22767) BOUND_VARIABLE_22768) (and (or (and (= BOUND_VARIABLE_22767 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22767) BOUND_VARIABLE_22768)) _let_2) _let_1) _let_2))))))) (let ((_let_163 (forall ((BOUND_VARIABLE_22754 tptp.nat) (BOUND_VARIABLE_22755 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_22754 BOUND_VARIABLE_22755))) (= (ho_38 (ho_37 k_49 BOUND_VARIABLE_22754) BOUND_VARIABLE_22755) (or (and (= BOUND_VARIABLE_22754 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22754) BOUND_VARIABLE_22755)) (not _let_1)) _let_1)))))) (let ((_let_164 (forall ((BOUND_VARIABLE_22741 tptp.real) (BOUND_VARIABLE_22742 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22741 BOUND_VARIABLE_22742))) (= (ho_44 (ho_43 k_50 BOUND_VARIABLE_22741) BOUND_VARIABLE_22742) (or (and (= BOUND_VARIABLE_22741 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22741) BOUND_VARIABLE_22742)) (not _let_1)) _let_1)))))) (let ((_let_165 (forall ((BOUND_VARIABLE_22963 |u_(-> tptp.nat Bool)|)) (= (ho_52 k_51 BOUND_VARIABLE_22963) (not (forall ((X5 tptp.nat)) (not (ho_38 BOUND_VARIABLE_22963 X5)))))))) (let ((_let_166 (forall ((BOUND_VARIABLE_22978 |u_(-> tptp.nat Bool)|)) (= (ho_52 k_53 BOUND_VARIABLE_22978) (not (forall ((N2 tptp.nat)) (or (not (ho_38 BOUND_VARIABLE_22978 N2)) (not (forall ((M2 tptp.nat)) (or (not (= M2 (ho_41 (ho_40 k_39 M2) N2))) (= N2 M2) (not (ho_38 BOUND_VARIABLE_22978 M2)))))))))))) (let ((_let_167 (forall ((BOUND_VARIABLE_22710 tptp.nat) (BOUND_VARIABLE_22711 tptp.nat)) (= (= BOUND_VARIABLE_22710 BOUND_VARIABLE_22711) (ho_38 (ho_37 k_54 BOUND_VARIABLE_22710) BOUND_VARIABLE_22711))))) (let ((_let_168 (forall ((BOUND_VARIABLE_22697 tptp.nat) (BOUND_VARIABLE_22698 tptp.nat)) (= (ho_38 (ho_37 k_55 BOUND_VARIABLE_22697) BOUND_VARIABLE_22698) (and (= BOUND_VARIABLE_22697 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22697) BOUND_VARIABLE_22698)) (= BOUND_VARIABLE_22698 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22698) BOUND_VARIABLE_22697))))))) (let ((_let_169 (forall ((BOUND_VARIABLE_22690 tptp.real) (BOUND_VARIABLE_22691 tptp.real)) (= (= BOUND_VARIABLE_22690 BOUND_VARIABLE_22691) (ho_44 (ho_43 k_56 BOUND_VARIABLE_22690) BOUND_VARIABLE_22691))))) (let ((_let_170 (forall ((BOUND_VARIABLE_22671 tptp.real) (BOUND_VARIABLE_22672 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22671 BOUND_VARIABLE_22672))) (let ((_let_2 (not _let_1))) (= (ho_44 (ho_43 k_57 BOUND_VARIABLE_22671) BOUND_VARIABLE_22672) (and (or (and (= BOUND_VARIABLE_22671 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22671) BOUND_VARIABLE_22672)) _let_2) _let_1) (or (and (= BOUND_VARIABLE_22672 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22672) BOUND_VARIABLE_22671)) _let_2) _let_1)))))))) (let ((_let_171 (forall ((BOUND_VARIABLE_22664 tptp.nat) (BOUND_VARIABLE_22665 tptp.nat)) (= (= BOUND_VARIABLE_22664 BOUND_VARIABLE_22665) (ho_38 (ho_37 k_58 BOUND_VARIABLE_22664) BOUND_VARIABLE_22665))))) (let ((_let_172 (forall ((BOUND_VARIABLE_22651 tptp.nat) (BOUND_VARIABLE_22652 tptp.nat)) (= (ho_38 (ho_37 k_59 BOUND_VARIABLE_22651) BOUND_VARIABLE_22652) (and (= BOUND_VARIABLE_22651 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22651) BOUND_VARIABLE_22652)) (= BOUND_VARIABLE_22652 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22652) BOUND_VARIABLE_22651))))))) (let ((_let_173 (forall ((BOUND_VARIABLE_22644 tptp.real) (BOUND_VARIABLE_22645 tptp.real)) (= (= BOUND_VARIABLE_22644 BOUND_VARIABLE_22645) (ho_44 (ho_43 k_60 BOUND_VARIABLE_22644) BOUND_VARIABLE_22645))))) (let ((_let_174 (forall ((BOUND_VARIABLE_22625 tptp.real) (BOUND_VARIABLE_22626 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22625 BOUND_VARIABLE_22626))) (let ((_let_2 (not _let_1))) (= (ho_44 (ho_43 k_61 BOUND_VARIABLE_22625) BOUND_VARIABLE_22626) (and (or (and (= BOUND_VARIABLE_22625 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22625) BOUND_VARIABLE_22626)) _let_2) _let_1) (or (and (= BOUND_VARIABLE_22626 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22626) BOUND_VARIABLE_22625)) _let_2) _let_1)))))))) (let ((_let_175 (forall ((BOUND_VARIABLE_22618 tptp.nat) (BOUND_VARIABLE_22619 tptp.nat)) (= (= BOUND_VARIABLE_22618 BOUND_VARIABLE_22619) (ho_38 (ho_37 k_62 BOUND_VARIABLE_22618) BOUND_VARIABLE_22619))))) (let ((_let_176 (forall ((BOUND_VARIABLE_22605 tptp.nat) (BOUND_VARIABLE_22606 tptp.nat)) (= (ho_38 (ho_37 k_63 BOUND_VARIABLE_22605) BOUND_VARIABLE_22606) (and (= BOUND_VARIABLE_22606 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22606) BOUND_VARIABLE_22605)) (= BOUND_VARIABLE_22605 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22605) BOUND_VARIABLE_22606))))))) (let ((_let_177 (forall ((BOUND_VARIABLE_22598 tptp.real) (BOUND_VARIABLE_22599 tptp.real)) (= (= BOUND_VARIABLE_22598 BOUND_VARIABLE_22599) (ho_44 (ho_43 k_64 BOUND_VARIABLE_22598) BOUND_VARIABLE_22599))))) (let ((_let_178 (forall ((BOUND_VARIABLE_22579 tptp.real) (BOUND_VARIABLE_22580 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22579 BOUND_VARIABLE_22580))) (let ((_let_2 (not _let_1))) (= (ho_44 (ho_43 k_65 BOUND_VARIABLE_22579) BOUND_VARIABLE_22580) (and (or (and (= BOUND_VARIABLE_22580 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22580) BOUND_VARIABLE_22579)) _let_2) _let_1) (or (and (= BOUND_VARIABLE_22579 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22579) BOUND_VARIABLE_22580)) _let_2) _let_1)))))))) (let ((_let_179 (forall ((BOUND_VARIABLE_22567 tptp.nat) (BOUND_VARIABLE_22568 tptp.nat)) (= (ho_41 (ho_40 k_66 BOUND_VARIABLE_22567) BOUND_VARIABLE_22568) (ho_41 (ho_40 (ho_68 k_67 (= BOUND_VARIABLE_22567 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22567) BOUND_VARIABLE_22568))) BOUND_VARIABLE_22567) BOUND_VARIABLE_22568))))) (let ((_let_180 (forall ((BOUND_VARIABLE_22551 tptp.real) (BOUND_VARIABLE_22552 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22551 BOUND_VARIABLE_22552))) (= (ho_47 (ho_46 k_69 BOUND_VARIABLE_22551) BOUND_VARIABLE_22552) (ho_47 (ho_46 (ho_71 k_70 (or (and (= BOUND_VARIABLE_22551 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22551) BOUND_VARIABLE_22552)) (not _let_1)) _let_1)) BOUND_VARIABLE_22551) BOUND_VARIABLE_22552)))))) (let ((_let_181 (forall ((BOUND_VARIABLE_22539 tptp.nat) (BOUND_VARIABLE_22540 tptp.nat)) (= (ho_38 (ho_37 k_72 BOUND_VARIABLE_22539) BOUND_VARIABLE_22540) (and (= BOUND_VARIABLE_22539 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22539) BOUND_VARIABLE_22540)) (not (= BOUND_VARIABLE_22539 BOUND_VARIABLE_22540))))))) (let ((_let_182 (forall ((BOUND_VARIABLE_22527 tptp.nat) (BOUND_VARIABLE_22528 tptp.nat)) (= (ho_38 (ho_37 k_73 BOUND_VARIABLE_22527) BOUND_VARIABLE_22528) (and (= BOUND_VARIABLE_22527 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22527) BOUND_VARIABLE_22528)) (not (= BOUND_VARIABLE_22527 BOUND_VARIABLE_22528))))))) (let ((_let_183 (forall ((BOUND_VARIABLE_22514 tptp.nat) (BOUND_VARIABLE_22515 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_22514 BOUND_VARIABLE_22515))) (= (ho_38 (ho_37 k_74 BOUND_VARIABLE_22514) BOUND_VARIABLE_22515) (or (and (= BOUND_VARIABLE_22514 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22514) BOUND_VARIABLE_22515)) (not _let_1)) _let_1)))))) (let ((_let_184 (forall ((BOUND_VARIABLE_22505 tptp.nat) (BOUND_VARIABLE_22506 tptp.nat)) (= (ho_38 (ho_37 k_75 BOUND_VARIABLE_22505) BOUND_VARIABLE_22506) (= BOUND_VARIABLE_22505 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22506) BOUND_VARIABLE_22505)))))) (let ((_let_185 (forall ((BOUND_VARIABLE_22496 tptp.real) (BOUND_VARIABLE_22497 tptp.real)) (= (ho_44 (ho_43 k_76 BOUND_VARIABLE_22496) BOUND_VARIABLE_22497) (= BOUND_VARIABLE_22496 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22497) BOUND_VARIABLE_22496)))))) (let ((_let_186 (forall ((BOUND_VARIABLE_22487 tptp.nat) (BOUND_VARIABLE_22488 tptp.nat)) (= (ho_38 (ho_37 k_77 BOUND_VARIABLE_22487) BOUND_VARIABLE_22488) (= BOUND_VARIABLE_22487 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22487) BOUND_VARIABLE_22488)))))) (let ((_let_187 (forall ((BOUND_VARIABLE_22478 tptp.nat) (BOUND_VARIABLE_22479 tptp.nat)) (= (ho_38 (ho_37 k_78 BOUND_VARIABLE_22478) BOUND_VARIABLE_22479) (= BOUND_VARIABLE_22478 (ho_41 (ho_40 k_39 BOUND_VARIABLE_22478) BOUND_VARIABLE_22479)))))) (let ((_let_188 (forall ((BOUND_VARIABLE_22469 tptp.real) (BOUND_VARIABLE_22470 tptp.real)) (= (ho_44 (ho_43 k_79 BOUND_VARIABLE_22469) BOUND_VARIABLE_22470) (= BOUND_VARIABLE_22469 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22469) BOUND_VARIABLE_22470)))))) (let ((_let_189 (forall ((BOUND_VARIABLE_22460 tptp.real) (BOUND_VARIABLE_22461 tptp.real)) (= (ho_44 (ho_43 k_80 BOUND_VARIABLE_22460) BOUND_VARIABLE_22461) (= BOUND_VARIABLE_22460 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22460) BOUND_VARIABLE_22461)))))) (let ((_let_190 (forall ((BOUND_VARIABLE_22447 tptp.real) (BOUND_VARIABLE_22448 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22447 BOUND_VARIABLE_22448))) (= (ho_44 (ho_43 k_81 BOUND_VARIABLE_22447) BOUND_VARIABLE_22448) (or (and (= BOUND_VARIABLE_22447 (ho_47 (ho_46 k_45 BOUND_VARIABLE_22447) BOUND_VARIABLE_22448)) (not _let_1)) _let_1)))))) (let ((_let_191 (forall ((BOUND_VARIABLE_22439 tptp.set_real) (BOUND_VARIABLE_22440 tptp.real)) (= (ho_44 (ho_83 k_82 BOUND_VARIABLE_22439) BOUND_VARIABLE_22440) (ho_86 (ho_85 k_84 BOUND_VARIABLE_22440) BOUND_VARIABLE_22439))))) (let ((_let_192 (forall ((BOUND_VARIABLE_22431 tptp.nat) (BOUND_VARIABLE_22432 tptp.nat)) (= (ho_41 (ho_40 k_87 BOUND_VARIABLE_22431) BOUND_VARIABLE_22432) (ho_41 (ho_40 k_39 BOUND_VARIABLE_22432) BOUND_VARIABLE_22431))))) (let ((_let_193 (forall ((BOUND_VARIABLE_22423 tptp.real) (BOUND_VARIABLE_22424 tptp.real)) (= (ho_47 (ho_46 k_88 BOUND_VARIABLE_22423) BOUND_VARIABLE_22424) (ho_47 (ho_46 k_45 BOUND_VARIABLE_22424) BOUND_VARIABLE_22423))))) (let ((_let_194 (not _let_29))) (let ((_let_195 (forall ((BOUND_VARIABLE_20866 tptp.real)) (or (not (= tptp.zero_zero_real (ho_47 (ho_90 k_89 tptp.p) BOUND_VARIABLE_20866))) (= tptp.lb1 (ho_47 (ho_46 k_45 tptp.lb1) BOUND_VARIABLE_20866)))))) (let ((_let_196 (forall ((BOUND_VARIABLE_22793 tptp.nat) (BOUND_VARIABLE_22794 tptp.nat)) (= (and (= BOUND_VARIABLE_22793 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22793) BOUND_VARIABLE_22794)) (not (= BOUND_VARIABLE_22793 BOUND_VARIABLE_22794))) (ll_35 BOUND_VARIABLE_22793 BOUND_VARIABLE_22794))))) (let ((_let_197 (forall ((BOUND_VARIABLE_22781 tptp.real) (BOUND_VARIABLE_22782 tptp.real)) (= (and (= BOUND_VARIABLE_22781 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22781) BOUND_VARIABLE_22782)) (not (= BOUND_VARIABLE_22781 BOUND_VARIABLE_22782))) (ll_34 BOUND_VARIABLE_22781 BOUND_VARIABLE_22782))))) (let ((_let_198 (forall ((BOUND_VARIABLE_22767 tptp.real) (BOUND_VARIABLE_22768 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22767 BOUND_VARIABLE_22768))) (let ((_let_2 (not _let_1))) (= (and (or (and (= BOUND_VARIABLE_22767 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22767) BOUND_VARIABLE_22768)) _let_2) _let_1) _let_2) (ll_33 BOUND_VARIABLE_22767 BOUND_VARIABLE_22768))))))) (let ((_let_199 (forall ((BOUND_VARIABLE_22754 tptp.nat) (BOUND_VARIABLE_22755 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_22754 BOUND_VARIABLE_22755))) (= (or (and (= BOUND_VARIABLE_22754 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22754) BOUND_VARIABLE_22755)) (not _let_1)) _let_1) (ll_32 BOUND_VARIABLE_22754 BOUND_VARIABLE_22755)))))) (let ((_let_200 (forall ((BOUND_VARIABLE_22741 tptp.real) (BOUND_VARIABLE_22742 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22741 BOUND_VARIABLE_22742))) (= (or (and (= BOUND_VARIABLE_22741 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22741) BOUND_VARIABLE_22742)) (not _let_1)) _let_1) (ll_31 BOUND_VARIABLE_22741 BOUND_VARIABLE_22742)))))) (let ((_let_201 (forall ((BOUND_VARIABLE_22732 (-> tptp.nat Bool))) (= (not (forall ((X5 tptp.nat)) (not (@ BOUND_VARIABLE_22732 X5)))) (ll_30 BOUND_VARIABLE_22732))))) (let ((_let_202 (forall ((BOUND_VARIABLE_22717 (-> tptp.nat Bool))) (= (not (forall ((N2 tptp.nat)) (or (not (@ BOUND_VARIABLE_22717 N2)) (not (forall ((M2 tptp.nat)) (or (not (= M2 (@ (@ tptp.ord_min_nat M2) N2))) (= N2 M2) (not (@ BOUND_VARIABLE_22717 M2)))))))) (ll_29 BOUND_VARIABLE_22717))))) (let ((_let_203 (forall ((BOUND_VARIABLE_22710 tptp.nat) (BOUND_VARIABLE_22711 tptp.nat)) (= (= BOUND_VARIABLE_22710 BOUND_VARIABLE_22711) (ll_28 BOUND_VARIABLE_22710 BOUND_VARIABLE_22711))))) (let ((_let_204 (forall ((BOUND_VARIABLE_22697 tptp.nat) (BOUND_VARIABLE_22698 tptp.nat)) (= (and (= BOUND_VARIABLE_22697 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22697) BOUND_VARIABLE_22698)) (= BOUND_VARIABLE_22698 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22698) BOUND_VARIABLE_22697))) (ll_27 BOUND_VARIABLE_22697 BOUND_VARIABLE_22698))))) (let ((_let_205 (forall ((BOUND_VARIABLE_22690 tptp.real) (BOUND_VARIABLE_22691 tptp.real)) (= (= BOUND_VARIABLE_22690 BOUND_VARIABLE_22691) (ll_26 BOUND_VARIABLE_22690 BOUND_VARIABLE_22691))))) (let ((_let_206 (forall ((BOUND_VARIABLE_22671 tptp.real) (BOUND_VARIABLE_22672 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22671 BOUND_VARIABLE_22672))) (let ((_let_2 (not _let_1))) (= (and (or (and (= BOUND_VARIABLE_22671 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22671) BOUND_VARIABLE_22672)) _let_2) _let_1) (or (and (= BOUND_VARIABLE_22672 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22672) BOUND_VARIABLE_22671)) _let_2) _let_1)) (ll_25 BOUND_VARIABLE_22671 BOUND_VARIABLE_22672))))))) (let ((_let_207 (forall ((BOUND_VARIABLE_22664 tptp.nat) (BOUND_VARIABLE_22665 tptp.nat)) (= (= BOUND_VARIABLE_22664 BOUND_VARIABLE_22665) (ll_24 BOUND_VARIABLE_22664 BOUND_VARIABLE_22665))))) (let ((_let_208 (forall ((BOUND_VARIABLE_22651 tptp.nat) (BOUND_VARIABLE_22652 tptp.nat)) (= (and (= BOUND_VARIABLE_22651 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22651) BOUND_VARIABLE_22652)) (= BOUND_VARIABLE_22652 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22652) BOUND_VARIABLE_22651))) (ll_23 BOUND_VARIABLE_22651 BOUND_VARIABLE_22652))))) (let ((_let_209 (forall ((BOUND_VARIABLE_22644 tptp.real) (BOUND_VARIABLE_22645 tptp.real)) (= (= BOUND_VARIABLE_22644 BOUND_VARIABLE_22645) (ll_22 BOUND_VARIABLE_22644 BOUND_VARIABLE_22645))))) (let ((_let_210 (forall ((BOUND_VARIABLE_22625 tptp.real) (BOUND_VARIABLE_22626 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22625 BOUND_VARIABLE_22626))) (let ((_let_2 (not _let_1))) (= (and (or (and (= BOUND_VARIABLE_22625 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22625) BOUND_VARIABLE_22626)) _let_2) _let_1) (or (and (= BOUND_VARIABLE_22626 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22626) BOUND_VARIABLE_22625)) _let_2) _let_1)) (ll_21 BOUND_VARIABLE_22625 BOUND_VARIABLE_22626))))))) (let ((_let_211 (forall ((BOUND_VARIABLE_22618 tptp.nat) (BOUND_VARIABLE_22619 tptp.nat)) (= (= BOUND_VARIABLE_22618 BOUND_VARIABLE_22619) (ll_20 BOUND_VARIABLE_22618 BOUND_VARIABLE_22619))))) (let ((_let_212 (forall ((BOUND_VARIABLE_22605 tptp.nat) (BOUND_VARIABLE_22606 tptp.nat)) (= (and (= BOUND_VARIABLE_22606 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22606) BOUND_VARIABLE_22605)) (= BOUND_VARIABLE_22605 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22605) BOUND_VARIABLE_22606))) (ll_19 BOUND_VARIABLE_22605 BOUND_VARIABLE_22606))))) (let ((_let_213 (forall ((BOUND_VARIABLE_22598 tptp.real) (BOUND_VARIABLE_22599 tptp.real)) (= (= BOUND_VARIABLE_22598 BOUND_VARIABLE_22599) (ll_18 BOUND_VARIABLE_22598 BOUND_VARIABLE_22599))))) (let ((_let_214 (forall ((BOUND_VARIABLE_22579 tptp.real) (BOUND_VARIABLE_22580 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22579 BOUND_VARIABLE_22580))) (let ((_let_2 (not _let_1))) (= (and (or (and (= BOUND_VARIABLE_22580 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22580) BOUND_VARIABLE_22579)) _let_2) _let_1) (or (and (= BOUND_VARIABLE_22579 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22579) BOUND_VARIABLE_22580)) _let_2) _let_1)) (ll_17 BOUND_VARIABLE_22579 BOUND_VARIABLE_22580))))))) (let ((_let_215 (forall ((BOUND_VARIABLE_22567 tptp.nat) (BOUND_VARIABLE_22568 tptp.nat)) (= (@ (@ (@ tptp.if_nat (= BOUND_VARIABLE_22567 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22567) BOUND_VARIABLE_22568))) BOUND_VARIABLE_22567) BOUND_VARIABLE_22568) (ll_16 BOUND_VARIABLE_22567 BOUND_VARIABLE_22568))))) (let ((_let_216 (forall ((BOUND_VARIABLE_22551 tptp.real) (BOUND_VARIABLE_22552 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22551 BOUND_VARIABLE_22552))) (= (@ (@ (@ tptp.if_real (or (and (= BOUND_VARIABLE_22551 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22551) BOUND_VARIABLE_22552)) (not _let_1)) _let_1)) BOUND_VARIABLE_22551) BOUND_VARIABLE_22552) (ll_15 BOUND_VARIABLE_22551 BOUND_VARIABLE_22552)))))) (let ((_let_217 (forall ((BOUND_VARIABLE_22539 tptp.nat) (BOUND_VARIABLE_22540 tptp.nat)) (= (and (= BOUND_VARIABLE_22539 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22539) BOUND_VARIABLE_22540)) (not (= BOUND_VARIABLE_22539 BOUND_VARIABLE_22540))) (ll_14 BOUND_VARIABLE_22539 BOUND_VARIABLE_22540))))) (let ((_let_218 (forall ((BOUND_VARIABLE_22527 tptp.nat) (BOUND_VARIABLE_22528 tptp.nat)) (= (and (= BOUND_VARIABLE_22527 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22527) BOUND_VARIABLE_22528)) (not (= BOUND_VARIABLE_22527 BOUND_VARIABLE_22528))) (ll_13 BOUND_VARIABLE_22527 BOUND_VARIABLE_22528))))) (let ((_let_219 (forall ((BOUND_VARIABLE_22514 tptp.nat) (BOUND_VARIABLE_22515 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_22514 BOUND_VARIABLE_22515))) (= (or (and (= BOUND_VARIABLE_22514 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22514) BOUND_VARIABLE_22515)) (not _let_1)) _let_1) (ll_12 BOUND_VARIABLE_22514 BOUND_VARIABLE_22515)))))) (let ((_let_220 (forall ((BOUND_VARIABLE_22505 tptp.nat) (BOUND_VARIABLE_22506 tptp.nat)) (= (= BOUND_VARIABLE_22505 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22506) BOUND_VARIABLE_22505)) (ll_11 BOUND_VARIABLE_22505 BOUND_VARIABLE_22506))))) (let ((_let_221 (forall ((BOUND_VARIABLE_22496 tptp.real) (BOUND_VARIABLE_22497 tptp.real)) (= (= BOUND_VARIABLE_22496 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22497) BOUND_VARIABLE_22496)) (ll_10 BOUND_VARIABLE_22496 BOUND_VARIABLE_22497))))) (let ((_let_222 (forall ((BOUND_VARIABLE_22487 tptp.nat) (BOUND_VARIABLE_22488 tptp.nat)) (= (= BOUND_VARIABLE_22487 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22487) BOUND_VARIABLE_22488)) (ll_9 BOUND_VARIABLE_22487 BOUND_VARIABLE_22488))))) (let ((_let_223 (forall ((BOUND_VARIABLE_22478 tptp.nat) (BOUND_VARIABLE_22479 tptp.nat)) (= (= BOUND_VARIABLE_22478 (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22478) BOUND_VARIABLE_22479)) (ll_8 BOUND_VARIABLE_22478 BOUND_VARIABLE_22479))))) (let ((_let_224 (forall ((BOUND_VARIABLE_22469 tptp.real) (BOUND_VARIABLE_22470 tptp.real)) (= (= BOUND_VARIABLE_22469 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22469) BOUND_VARIABLE_22470)) (ll_7 BOUND_VARIABLE_22469 BOUND_VARIABLE_22470))))) (let ((_let_225 (forall ((BOUND_VARIABLE_22460 tptp.real) (BOUND_VARIABLE_22461 tptp.real)) (= (= BOUND_VARIABLE_22460 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22460) BOUND_VARIABLE_22461)) (ll_6 BOUND_VARIABLE_22460 BOUND_VARIABLE_22461))))) (let ((_let_226 (forall ((BOUND_VARIABLE_22447 tptp.real) (BOUND_VARIABLE_22448 tptp.real)) (let ((_let_1 (= BOUND_VARIABLE_22447 BOUND_VARIABLE_22448))) (= (or (and (= BOUND_VARIABLE_22447 (@ (@ tptp.ord_min_real BOUND_VARIABLE_22447) BOUND_VARIABLE_22448)) (not _let_1)) _let_1) (ll_5 BOUND_VARIABLE_22447 BOUND_VARIABLE_22448)))))) (let ((_let_227 (forall ((BOUND_VARIABLE_22439 tptp.set_real) (BOUND_VARIABLE_22440 tptp.real)) (= (@ (@ tptp.member_real BOUND_VARIABLE_22440) BOUND_VARIABLE_22439) (ll_4 BOUND_VARIABLE_22439 BOUND_VARIABLE_22440))))) (let ((_let_228 (forall ((BOUND_VARIABLE_22431 tptp.nat) (BOUND_VARIABLE_22432 tptp.nat)) (= (@ (@ tptp.ord_min_nat BOUND_VARIABLE_22432) BOUND_VARIABLE_22431) (ll_3 BOUND_VARIABLE_22431 BOUND_VARIABLE_22432))))) (let ((_let_229 (forall ((BOUND_VARIABLE_22423 tptp.real) (BOUND_VARIABLE_22424 tptp.real)) (= (@ (@ tptp.ord_min_real BOUND_VARIABLE_22424) BOUND_VARIABLE_22423) (ll_2 BOUND_VARIABLE_22423 BOUND_VARIABLE_22424))))) (let ((_let_230 (@ tptp.poly_real2 tptp.p))) (let ((_let_231 (and (forall ((BOUND_VARIABLE_20866 tptp.real)) (or (not (= tptp.zero_zero_real (@ (@ tptp.poly_real2 tptp.p) BOUND_VARIABLE_20866))) (= tptp.lb1 (@ (@ tptp.ord_min_real tptp.lb1) BOUND_VARIABLE_20866)))) (not (= tptp.zero_zero_real (@ _let_230 tptp.lb1))) _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 ((_let_232 (ASSUME :args (_let_21)))) (let ((_let_233 (ASSUME :args (_let_17)))) (let ((_let_234 (ASSUME :args (_let_16)))) (let ((_let_235 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_236 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_237 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_238 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_237 _let_236 _let_235 _let_234 _let_233 _let_232) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_239 (AND_INTRO (ASSUME :args (_let_8)) _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232))) (let ((_let_240 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_22)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_239 :args ((forall ((X tptp.real)) (or (not (= tptp.zero_zero_real (@ (@ tptp.poly_real2 tptp.p) X))) (@ (@ tptp.ord_less_real tptp.lb1) X))) SB_DEFAULT SBA_FIXPOINT)))) (PREPROCESS :args ((and _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)))) :args (_let_231)) (PREPROCESS :args ((= _let_231 (and _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 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160))))) (PREPROCESS :args ((and _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)))) :args ((and _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 _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 ((_let_241 (not _let_30))) (let ((_let_242 (or))) (let ((_let_243 (REFL :args (_let_241)))) (let ((_let_244 (_let_41))) (let ((_let_245 (REFL :args _let_244))) (let ((_let_246 (and _let_194 _let_25))) (let ((_let_247 (_let_194 _let_25))) 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tptp.ord_less_real Lb1) X)))))) (not (= tptp.p tptp.zero_zero_poly_real)) (forall ((X2 tptp.poly_nat)) (= (@ (@ tptp.poly_poly_nat2 tptp.zero_z1059985641ly_nat) X2) tptp.zero_zero_poly_nat)) (forall ((X2 tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 tptp.zero_z935034829y_real) X2) tptp.zero_z1423781445y_real)) (forall ((X2 tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 tptp.zero_z1423781445y_real) X2) tptp.zero_zero_poly_real)) (forall ((X2 tptp.nat)) (= (@ (@ tptp.poly_nat2 tptp.zero_zero_poly_nat) X2) tptp.zero_zero_nat)) (forall ((X2 tptp.real)) (= (@ (@ tptp.poly_real2 tptp.zero_zero_poly_real) X2) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((A tptp.real) (B tptp.real) (P tptp.poly_real)) (let ((_let_1 (@ tptp.poly_real2 P))) (=> (@ (@ 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 ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B) (= (@ (@ tptp.poly_real2 P) X3) tptp.zero_zero_real)))))))) (forall ((A tptp.real) (B tptp.real) (P tptp.poly_real)) (let ((_let_1 (@ tptp.poly_real2 P))) (=> (@ (@ 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 ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B) (= (@ (@ tptp.poly_real2 P) X3) tptp.zero_zero_real)))))))) (forall ((P tptp.poly_poly_poly_real)) (= (forall ((X4 tptp.poly_poly_real)) (= (@ (@ tptp.poly_poly_poly_real2 P) X4) tptp.zero_z1423781445y_real)) (= P tptp.zero_z935034829y_real))) (forall ((P tptp.poly_real)) (= (forall ((X4 tptp.real)) (= (@ (@ tptp.poly_real2 P) X4) tptp.zero_zero_real)) (= P tptp.zero_zero_poly_real))) (forall ((P tptp.poly_poly_real)) (= (forall ((X4 tptp.poly_real)) (= (@ (@ tptp.poly_poly_real2 P) X4) tptp.zero_zero_poly_real)) (= P tptp.zero_z1423781445y_real))) (not (@ (@ tptp.ord_less_poly_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)) (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)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) (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 ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))) (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.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))) (forall ((X2 tptp.poly_nat)) (= (= tptp.zero_zero_poly_nat X2) (= X2 tptp.zero_zero_poly_nat))) (forall ((X2 tptp.poly_poly_real)) (= (= tptp.zero_z1423781445y_real X2) (= X2 tptp.zero_z1423781445y_real))) (forall ((P tptp.poly_real) (Q tptp.poly_real)) (= (= (@ tptp.poly_real2 P) (@ tptp.poly_real2 Q)) (= P Q))) (forall ((P tptp.poly_poly_real) (Q tptp.poly_poly_real)) (= (= (@ tptp.poly_poly_real2 P) (@ tptp.poly_poly_real2 Q)) (= P Q))) (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_min_real X2) Y)) (and (@ _let_1 X2) (@ _let_1 Y))))) (forall ((Z tptp.nat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_min_nat X2) Y)) (and (@ _let_1 X2) (@ _let_1 Y))))) _let_19 (forall ((A tptp.nat)) (= (@ (@ tptp.ord_min_nat A) A) A)) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_min_real A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.ord_min_real A) B))) (= (@ (@ tptp.ord_min_real _let_1) B) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat A) B))) (= (@ (@ tptp.ord_min_nat _let_1) B) _let_1))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real (@ (@ tptp.ord_min_real A) B)) C))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A) B)) C))) _let_18 (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A) B)) C))) _let_17 _let_16 (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ (@ tptp.ord_min_real B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ (@ tptp.ord_min_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))) (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_min_real X2) Y)) Z) (or (@ (@ tptp.ord_less_real X2) Z) (@ (@ tptp.ord_less_real Y) Z)))) (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat X2) Y)) Z) (or (@ (@ tptp.ord_less_nat X2) Z) (@ (@ tptp.ord_less_nat Y) Z)))) _let_15 _let_14 _let_13 (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_min_real B))) (let ((_let_2 (@ tptp.ord_min_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat B))) (let ((_let_2 (@ tptp.ord_min_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) _let_12 (= tptp.ord_min_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_min_nat B2) A2))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_min_real A))) (= (@ (@ tptp.ord_min_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_min_real B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat A))) (= (@ (@ tptp.ord_min_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_min_nat B) C))))) (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_nat N) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.poly_c1404107022y_real N) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)) (forall ((P tptp.poly_real) (Ub tptp.real)) (=> (not (= P tptp.zero_zero_poly_real)) (not (forall ((Lb tptp.real)) (=> (@ (@ tptp.ord_less_real Lb) Ub) (not (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb) Z2) (@ (@ tptp.ord_less_real Z2) Ub)) (not (= (@ (@ tptp.poly_real2 P) Z2) tptp.zero_zero_real)))))))))) (forall ((P tptp.poly_real) (Lb2 tptp.real)) (=> (not (= P tptp.zero_zero_poly_real)) (not (forall ((Ub2 tptp.real)) (=> (@ (@ tptp.ord_less_real Lb2) Ub2) (not (forall ((Z2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb2) Z2) (@ (@ tptp.ord_less_eq_real Z2) Ub2)) (not (= (@ (@ tptp.poly_real2 P) Z2) tptp.zero_zero_real)))))))))) (forall ((P tptp.poly_real)) (= (= (@ (@ tptp.poly_real2 (@ tptp.reflect_poly_real P)) tptp.zero_zero_real) tptp.zero_zero_real) (= P tptp.zero_zero_poly_real))) (forall ((P tptp.poly_poly_real)) (= (= (@ (@ tptp.poly_poly_real2 (@ tptp.reflec1522834046y_real P)) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real) (= P tptp.zero_z1423781445y_real))) (forall ((P tptp.poly_nat)) (= (= (@ (@ tptp.poly_nat2 (@ tptp.reflect_poly_nat P)) tptp.zero_zero_nat) tptp.zero_zero_nat) (= P tptp.zero_zero_poly_nat))) (forall ((P tptp.poly_poly_nat)) (= (= (@ (@ tptp.poly_poly_nat2 (@ tptp.reflec781175074ly_nat P)) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat) (= P tptp.zero_z1059985641ly_nat))) (forall ((P tptp.poly_poly_poly_real)) (= (= (@ (@ tptp.poly_poly_poly_real2 (@ tptp.reflec144234502y_real P)) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real) (= P tptp.zero_z935034829y_real))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.lb2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.poly_real2 tptp.p) X)) (@ tptp.sturm_1076696862f_real tptp.p)))) (forall ((N tptp.nat)) (= (@ (@ tptp.poly_shift_real N) tptp.zero_zero_poly_real) tptp.zero_zero_poly_real)) (forall ((N tptp.nat)) (= (@ (@ tptp.poly_shift_nat N) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.poly_shift_poly_real N) tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real)) (forall ((P tptp.poly_real) (A tptp.real)) (= (= (@ (@ tptp.poly_real2 P) A) tptp.zero_zero_real) (or (= P tptp.zero_zero_poly_real) (not (= (@ (@ tptp.order_real A) P) tptp.zero_zero_nat))))) (forall ((P tptp.poly_poly_real) (A tptp.poly_real)) (= (= (@ (@ tptp.poly_poly_real2 P) A) tptp.zero_zero_poly_real) (or (= P tptp.zero_z1423781445y_real) (not (= (@ (@ tptp.order_poly_real A) P) tptp.zero_zero_nat))))) (forall ((P tptp.poly_poly_poly_real) (A tptp.poly_poly_real)) (= (= (@ (@ tptp.poly_poly_poly_real2 P) A) tptp.zero_z1423781445y_real) (or (= P tptp.zero_z935034829y_real) (not (= (@ (@ tptp.order_poly_poly_real A) P) tptp.zero_zero_nat))))) (forall ((R tptp.poly_real) (D tptp.poly_real) (Dr tptp.nat) (N tptp.nat)) (= (@ (@ (@ (@ (@ (@ tptp.divide1561404011n_real tptp.zero_zero_real) tptp.zero_zero_poly_real) R) D) Dr) N) tptp.zero_zero_poly_real)) (forall ((R tptp.poly_poly_real) (D tptp.poly_poly_real) (Dr tptp.nat) (N tptp.nat)) (= (@ (@ (@ (@ (@ (@ tptp.divide1142363123y_real tptp.zero_zero_poly_real) tptp.zero_z1423781445y_real) R) D) Dr) N) tptp.zero_z1423781445y_real)) (forall ((R tptp.poly_poly_poly_real) (D tptp.poly_poly_poly_real) (Dr tptp.nat) (N tptp.nat)) (= (@ (@ (@ (@ (@ (@ tptp.divide924636027y_real tptp.zero_z1423781445y_real) tptp.zero_z935034829y_real) R) D) Dr) N) tptp.zero_z935034829y_real)) (forall ((Lb2 tptp.real) (Ub tptp.real) (P tptp.poly_real)) (= (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb2) Z3) (@ (@ tptp.ord_less_eq_real Z3) Ub)) (not (= (@ (@ tptp.poly_real2 P) Z3) tptp.zero_zero_real)))) (or (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb2) Z3) (@ (@ tptp.ord_less_eq_real Z3) Ub)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.poly_real2 P) Z3)))) (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real Lb2) Z3) (@ (@ tptp.ord_less_eq_real Z3) Ub)) (@ (@ tptp.ord_less_real (@ (@ tptp.poly_real2 P) Z3)) tptp.zero_zero_real)))))) (not (forall ((Lb22 tptp.real)) (not (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Lb22) (= (@ tptp.sgn_sgn_real (@ (@ tptp.poly_real2 tptp.p) X)) (@ tptp.sturm_1076696862f_real tptp.p))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ (@ tptp.ord_min_real B) C)) (and (@ _let_1 B) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (= (@ _let_1 (@ (@ tptp.ord_min_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))) (= (@ tptp.reflect_poly_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real) (= (@ tptp.reflect_poly_nat tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat) (= (@ tptp.reflec1522834046y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real) (forall ((A tptp.real) (P3 (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P3)) (@ P3 A))) (forall ((A3 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A3))) A3)) (forall ((Lb2 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (= (@ (@ tptp.poly_real2 tptp.p) X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Lb2) X3))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Lb2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.poly_real2 tptp.p) X3)) (@ tptp.sturm_1076696862f_real tptp.p)))) tptp.thesis))) (forall ((S tptp.set_real)) (=> (exists ((X tptp.real)) (@ (@ tptp.member_real X) S)) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S) (@ (@ tptp.ord_less_eq_real X3) Z2)))) (exists ((Y2 tptp.real)) (and (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) S) (@ (@ tptp.ord_less_eq_real X) Y2))) (forall ((Z2 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S) (@ (@ tptp.ord_less_eq_real X3) Z2))) (@ (@ tptp.ord_less_eq_real Y2) Z2)))))))) (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)) (@ (@ tptp.ord_le1180086932y_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real) (@ (@ 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) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat) _let_11 (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_eq_real B) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) (@ (@ tptp.ord_min_real C) D))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) (@ (@ tptp.ord_min_nat C) D))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (= A (@ (@ tptp.ord_min_real A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A (@ (@ tptp.ord_min_nat A) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (= A (@ (@ tptp.ord_min_real A) B)) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_min_nat A) B)) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (= (@ (@ tptp.ord_min_real A) B) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_min_nat A) B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.ord_min_real A) B) B))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_min_nat A) B) B))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ (@ tptp.ord_min_real B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ (@ tptp.ord_min_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.ord_min_real B) C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.ord_min_nat B) C)))))) _let_10 _let_8 (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) A)) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) B)) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) B)) _let_7 (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_min_nat A2) B2) A2))) (= tptp.ord_less_eq_real (lambda ((B2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_min_real A2) B2) B2))) (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_min_nat A2) B2) B2))) _let_6 (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) C))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real A) B)) C))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A) B)) C))) (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_min_real X2) Y)) Z) (or (@ (@ tptp.ord_less_eq_real X2) Z) (@ (@ tptp.ord_less_eq_real Y) Z)))) (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat X2) Y)) Z) (or (@ (@ tptp.ord_less_eq_nat X2) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))) (forall ((P tptp.poly_real) (A tptp.real)) (=> (not (= (@ (@ tptp.poly_real2 P) A) tptp.zero_zero_real)) (= (@ (@ tptp.order_real A) P) tptp.zero_zero_nat))) (forall ((P tptp.poly_poly_real) (A tptp.poly_real)) (=> (not (= (@ (@ tptp.poly_poly_real2 P) A) tptp.zero_zero_poly_real)) (= (@ (@ tptp.order_poly_real A) P) tptp.zero_zero_nat))) (forall ((P tptp.poly_poly_poly_real) (A tptp.poly_poly_real)) (=> (not (= (@ (@ tptp.poly_poly_poly_real2 P) A) tptp.zero_z1423781445y_real)) (= (@ (@ tptp.order_poly_poly_real A) P) tptp.zero_zero_nat))) (forall ((Lb2 tptp.real) (Ub tptp.real) (P tptp.poly_real)) (= (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb2) Z3) (@ (@ tptp.ord_less_real Z3) Ub)) (not (= (@ (@ tptp.poly_real2 P) Z3) tptp.zero_zero_real)))) (or (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb2) Z3) (@ (@ tptp.ord_less_real Z3) Ub)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.poly_real2 P) Z3)))) (forall ((Z3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real Lb2) Z3) (@ (@ tptp.ord_less_real Z3) Ub)) (@ (@ tptp.ord_less_real (@ (@ tptp.poly_real2 P) Z3)) tptp.zero_zero_real)))))) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X2)) (@ _let_1 X2)))) (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))) (forall ((A tptp.poly_real)) (let ((_let_1 (@ tptp.ord_less_poly_real tptp.zero_zero_poly_real))) (= (@ _let_1 (@ tptp.sgn_sgn_poly_real A)) (@ _let_1 A)))) (forall ((A tptp.poly_poly_real)) (let ((_let_1 (@ tptp.ord_le38482960y_real tptp.zero_z1423781445y_real))) (= (@ _let_1 (@ tptp.sgn_sg2128174761y_real A)) (@ _let_1 A)))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A)) (@ _let_1 A)))) (forall ((A tptp.poly_real)) (= (@ (@ tptp.ord_less_poly_real (@ tptp.sgn_sgn_poly_real A)) tptp.zero_zero_poly_real) (@ (@ tptp.ord_less_poly_real A) tptp.zero_zero_poly_real))) (forall ((A tptp.poly_poly_real)) (= (@ (@ tptp.ord_le38482960y_real (@ tptp.sgn_sg2128174761y_real A)) tptp.zero_z1423781445y_real) (@ (@ tptp.ord_le38482960y_real A) tptp.zero_z1423781445y_real))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((P tptp.poly_real)) (=> (not (= P tptp.zero_zero_poly_real)) (not (forall ((Ub2 tptp.real)) (=> (forall ((X tptp.real)) (=> (= (@ (@ tptp.poly_real2 P) X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) Ub2))) (not (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Ub2) X) (= (@ tptp.sgn_sgn_real (@ (@ tptp.poly_real2 P) X)) (@ tptp.sturm_1308388506f_real P)))))))))) _let_5 (= (@ tptp.sgn_sgn_poly_real tptp.zero_zero_poly_real) tptp.zero_zero_poly_real) (= (@ tptp.sgn_sg2128174761y_real tptp.zero_z1423781445y_real) tptp.zero_z1423781445y_real) _let_5 (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2)))) (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.poly_real)) (= (= (@ tptp.sgn_sgn_poly_real A) tptp.zero_zero_poly_real) (= A tptp.zero_zero_poly_real))) (forall ((A tptp.poly_poly_real)) (= (= (@ tptp.sgn_sg2128174761y_real A) tptp.zero_z1423781445y_real) (= A tptp.zero_z1423781445y_real))) (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.poly_real)) (= (= (@ tptp.sgn_sgn_poly_real A) tptp.zero_zero_poly_real) (= A tptp.zero_zero_poly_real))) (forall ((A tptp.poly_poly_real)) (= (= (@ tptp.sgn_sg2128174761y_real A) tptp.zero_z1423781445y_real) (= A tptp.zero_z1423781445y_real))) (forall ((X2 tptp.real)) (= (= (@ tptp.sgn_sgn_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((P3 (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P3 K) (=> (forall ((Y2 tptp.nat)) (=> (@ P3 Y2) (@ (@ tptp.ord_less_eq_nat Y2) B))) (exists ((X3 tptp.nat)) (and (@ P3 X3) (forall ((Y4 tptp.nat)) (=> (@ P3 Y4) (@ (@ tptp.ord_less_eq_nat Y4) X3)))))))) (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M2) N2) (= M2 N2)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (not (= M2 N2))))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2)))) (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P3 N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P3 M3)))))) (@ P3 N))) (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ P3 M3))) (@ P3 N3))) (@ P3 N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P3 tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P3 N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P3 M3))))))) (@ P3 N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P3 N) (=> (not (@ P3 tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K2) (not (@ P3 I3)))) (@ P3 K2)))))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) X2)) (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)) (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (= (@ (@ tptp.ord_min_real X2) Y) X2))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (= (@ (@ tptp.ord_min_nat X2) Y) X2))) (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (= (@ (@ tptp.ord_min_real X2) Y) Y))) (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= (@ (@ tptp.ord_min_nat X2) Y) Y))) _let_4 (= tptp.ord_min_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A2) B2)) A2) B2))) (forall ((N tptp.nat) (P3 (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P3 K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I3) (@ P3 I3))) (@ P3 K2)))) (@ P3 M)))) (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.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))) (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((A2 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A2) (@ (@ tptp.ord_less_eq_real A2) B2)))) (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat A2) B2)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((P3 (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A4) B3) (@ (@ P3 A4) B3))) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ P3 B3) A4) (@ (@ P3 A4) B3))) (@ (@ P3 A) B)))) (forall ((P3 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ P3 A4) B3))) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P3 B3) A4) (@ (@ P3 A4) B3))) (@ (@ P3 A) B)))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)) (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))) (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((A tptp.real) (B tptp.real)) 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(F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ 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B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B)) (=> (@ 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(@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ 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C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((X2 tptp.real)) (exists ((Y2 tptp.real)) (@ (@ tptp.ord_less_real Y2) X2))) (forall ((X2 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X2) X_1))) (forall ((X2 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_1))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2)))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2)))) (forall ((X2 tptp.real) (Y tptp.real)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real Y) X2)))) (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_nat X2) Y) (@ (@ tptp.ord_less_nat Y) X2)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (exists ((Z5 tptp.real)) (and (@ (@ tptp.ord_less_real X2) Z5) (@ (@ tptp.ord_less_real Z5) Y))))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= X2 Y)))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= X2 Y)))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))) (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))) (forall ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y) (@ (@ tptp.ord_less_real Y) X2))) (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y) (= X2 Y) (@ (@ tptp.ord_less_nat Y) X2))) (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real X2) X2))) (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= X2 Y)))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= X2 Y)))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))) (forall ((P3 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y4) X3) (@ P3 Y4))) (@ P3 X3))) (@ P3 A))) (forall ((Y tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X2)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (= X2 Y)))) (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (= X2 Y)))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= Y X2)))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= Y X2)))) (forall ((X2 tptp.real) (Y tptp.real) (P3 Bool)) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_real Y) X2) P3))) (forall ((X2 tptp.nat) (Y tptp.nat) (P3 Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y) (=> (@ (@ tptp.ord_less_nat Y) X2) P3))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_real Y) X2)))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_nat Y) X2)))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))) (= (lambda ((P4 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P5 N2) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (@ P5 M2)))))))) (forall ((P3 (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A4) B3) (@ (@ P3 A4) B3))) (=> (forall ((A4 tptp.real)) (@ (@ P3 A4) A4)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ P3 B3) A4) (@ (@ P3 A4) B3))) (@ (@ P3 A) B))))) (forall ((P3 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B3) (@ (@ P3 A4) B3))) (=> (forall ((A4 tptp.nat)) (@ (@ P3 A4) A4)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P3 B3) A4) (@ (@ P3 A4) B3))) (@ (@ P3 A) B))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) _let_3 (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (or (@ (@ tptp.ord_less_nat Y) X2) (= X2 Y)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))) (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (not (@ (@ tptp.ord_less_real X2) Y)))) (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (not (@ (@ tptp.ord_less_nat X2) Y)))) (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_eq_real Y) X2))) (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))) _let_2 (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y3) (= X4 Y3)))) (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y3) (not (= X4 Y3))))) (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y3) (not (= X4 Y3))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X3 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X2) Y) Y)) (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X2) Y) X2)) (forall ((P3 Bool)) (or (= P3 true) (= P3 false))) (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X2) Y) Y)) (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X2) Y) X2)) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.86/1.06 )
% 0.86/1.06 % SZS output end Proof for ITP194^1
% 0.86/1.06 % cvc5---1.0.5 exiting
% 0.86/1.06 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------