TSTP Solution File: ITP044^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP044^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.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 03:17:44 EDT 2023
% Result : Theorem 0.65s 0.91s
% Output : Proof 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : ITP044^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.17 % Command : do_cvc5 %s %d
% 0.18/0.38 % Computer : n026.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Sun Aug 27 15:18:04 EDT 2023
% 0.18/0.38 % CPUTime :
% 0.25/0.55 %----Proving TH0
% 0.25/0.55 %------------------------------------------------------------------------------
% 0.25/0.55 % File : ITP044^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.55 % Domain : Interactive Theorem Proving
% 0.25/0.55 % Problem : Sledgehammer Descartes_Sign_Rule problem prob_761__5872108_1
% 0.25/0.55 % Version : Especial.
% 0.25/0.55 % English :
% 0.25/0.55
% 0.25/0.55 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.55 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.55 % Source : [Des21]
% 0.25/0.55 % Names : Descartes_Sign_Rule/prob_761__5872108_1 [Des21]
% 0.25/0.55
% 0.25/0.55 % Status : Theorem
% 0.25/0.55 % Rating : 0.31 v8.1.0, 0.36 v7.5.0
% 0.25/0.55 % Syntax : Number of formulae : 412 ( 240 unt; 65 typ; 0 def)
% 0.25/0.55 % Number of atoms : 790 ( 531 equ; 0 cnn)
% 0.25/0.55 % Maximal formula atoms : 10 ( 2 avg)
% 0.25/0.55 % Number of connectives : 2132 ( 114 ~; 47 |; 46 &;1703 @)
% 0.25/0.55 % ( 0 <=>; 222 =>; 0 <=; 0 <~>)
% 0.25/0.55 % Maximal formula depth : 17 ( 5 avg)
% 0.25/0.55 % Number of types : 10 ( 9 usr)
% 0.25/0.55 % Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% 0.25/0.55 % Number of symbols : 57 ( 56 usr; 17 con; 0-2 aty)
% 0.25/0.55 % Number of variables : 718 ( 16 ^; 697 !; 5 ?; 718 :)
% 0.25/0.55 % SPC : TH0_THM_EQU_NAR
% 0.25/0.55
% 0.25/0.55 % Comments : This file was generated by Sledgehammer 2021-02-23 15:42:44.488
% 0.25/0.55 %------------------------------------------------------------------------------
% 0.25/0.55 % Could-be-implicit typings (9)
% 0.25/0.55 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J,type,
% 0.25/0.55 poly_poly_a: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__List__Olist_It__Polynomial__Opoly_Itf__a_J_J,type,
% 0.25/0.55 list_poly_a: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.25/0.55 list_list_a: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.25/0.55 poly_nat: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.25/0.55 list_nat: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 poly_a: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.25/0.55 list_a: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__Nat__Onat,type,
% 0.25/0.55 nat: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_tf__a,type,
% 0.25/0.55 a: $tType ).
% 0.25/0.55
% 0.25/0.55 % Explicit typings (56)
% 0.25/0.55 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Opsums_001t__Nat__Onat,type,
% 0.25/0.55 descar226543321ms_nat: list_nat > list_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Opsums_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 descar282223555poly_a: list_poly_a > list_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Opsums_001tf__a,type,
% 0.25/0.55 descar1375166517sums_a: list_a > list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Oreduce__root_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 descar434775507poly_a: poly_a > poly_poly_a > poly_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Oreduce__root_001tf__a,type,
% 0.25/0.55 descar466059845root_a: a > poly_a > poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Osign__changes_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 descar357075861poly_a: list_poly_a > nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Osign__changes_001tf__a,type,
% 0.25/0.55 descar2095969287nges_a: list_a > nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.25/0.55 one_one_nat: nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.25/0.55 one_one_poly_nat: poly_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J,type,
% 0.25/0.55 one_one_poly_poly_a: poly_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 one_one_poly_a: poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Oone__class_Oone_001tf__a,type,
% 0.25/0.55 one_one_a: a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 0.25/0.55 times_times_nat: nat > nat > nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 times_times_poly_a: poly_a > poly_a > poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Otimes__class_Otimes_001tf__a,type,
% 0.25/0.55 times_times_a: a > a > a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 uminus_uminus_poly_a: poly_a > poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001tf__a,type,
% 0.25/0.55 uminus_uminus_a: a > a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.25/0.55 zero_zero_nat: nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.25/0.55 zero_zero_poly_nat: poly_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J,type,
% 0.25/0.55 zero_z2096148049poly_a: poly_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 zero_zero_poly_a: poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type,
% 0.25/0.55 zero_zero_a: a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.25/0.55 append_nat: list_nat > list_nat > list_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Oappend_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 append_poly_a: list_poly_a > list_poly_a > list_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Oappend_001tf__a,type,
% 0.25/0.55 append_a: list_a > list_a > list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__a_J,type,
% 0.25/0.55 cons_list_a: list_a > list_list_a > list_list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.25/0.55 cons_nat: nat > list_nat > list_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Olist_OCons_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 cons_poly_a: poly_a > list_poly_a > list_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 0.25/0.55 cons_a: a > list_a > list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__a_J,type,
% 0.25/0.55 nil_list_a: list_list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.25/0.55 nil_nat: list_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Olist_ONil_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 nil_poly_a: list_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Olist_ONil_001tf__a,type,
% 0.25/0.55 nil_a: list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Onull_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 null_poly_a: list_poly_a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_List_Onull_001tf__a,type,
% 0.25/0.55 null_a: list_a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.25/0.55 ord_less_nat: nat > nat > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 ord_less_poly_a: poly_a > poly_a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Orderings_Oord__class_Oless_001tf__a,type,
% 0.25/0.55 ord_less_a: a > a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_OPoly_001t__Nat__Onat,type,
% 0.25/0.55 poly_nat2: list_nat > poly_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_OPoly_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 poly_poly_a2: list_poly_a > poly_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_OPoly_001tf__a,type,
% 0.25/0.55 poly_a2: list_a > poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_Ocoeffs_001t__Nat__Onat,type,
% 0.25/0.55 coeffs_nat: poly_nat > list_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_Ocoeffs_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 coeffs_poly_a: poly_poly_a > list_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_Ocoeffs_001tf__a,type,
% 0.25/0.55 coeffs_a: poly_a > list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 is_zero_poly_a: poly_poly_a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_Ois__zero_001tf__a,type,
% 0.25/0.55 is_zero_a: poly_a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_OpCons_001t__Nat__Onat,type,
% 0.25/0.55 pCons_nat: nat > poly_nat > poly_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 pCons_poly_a: poly_a > poly_poly_a > poly_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_OpCons_001tf__a,type,
% 0.25/0.55 pCons_a: a > poly_a > poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_Osmult_001t__Nat__Onat,type,
% 0.25/0.55 smult_nat: nat > poly_nat > poly_nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_Osmult_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.25/0.55 smult_poly_a: poly_a > poly_poly_a > poly_poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Polynomial_Osmult_001tf__a,type,
% 0.25/0.55 smult_a: a > poly_a > poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_g,type,
% 0.25/0.55 g: poly_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_v,type,
% 0.25/0.55 v: poly_a > nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_xs____,type,
% 0.25/0.55 xs: list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_ys____,type,
% 0.25/0.55 ys: list_a ).
% 0.25/0.55
% 0.25/0.55 % Relevant facts (346)
% 0.25/0.55 thf(fact_0_v__def,axiom,
% 0.25/0.55 ( v
% 0.25/0.55 = ( ^ [F: poly_a] : ( descar2095969287nges_a @ ( coeffs_a @ F ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % v_def
% 0.25/0.55 thf(fact_1_nz,axiom,
% 0.25/0.55 g != zero_zero_poly_a ).
% 0.25/0.55
% 0.25/0.55 % nz
% 0.25/0.55 thf(fact_2_coeffs__eq__iff,axiom,
% 0.25/0.55 ( ( ^ [Y: poly_poly_a,Z: poly_poly_a] : ( Y = Z ) )
% 0.25/0.55 = ( ^ [P: poly_poly_a,Q: poly_poly_a] :
% 0.25/0.55 ( ( coeffs_poly_a @ P )
% 0.25/0.55 = ( coeffs_poly_a @ Q ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeffs_eq_iff
% 0.25/0.55 thf(fact_3_coeffs__eq__iff,axiom,
% 0.25/0.55 ( ( ^ [Y: poly_a,Z: poly_a] : ( Y = Z ) )
% 0.25/0.55 = ( ^ [P: poly_a,Q: poly_a] :
% 0.25/0.55 ( ( coeffs_a @ P )
% 0.25/0.55 = ( coeffs_a @ Q ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeffs_eq_iff
% 0.25/0.55 thf(fact_4_ys,axiom,
% 0.25/0.55 ( ys
% 0.25/0.55 = ( descar1375166517sums_a @ xs ) ) ).
% 0.25/0.55
% 0.25/0.55 % ys
% 0.25/0.55 thf(fact_5_sign__changes__coeff__sign__changes,axiom,
% 0.25/0.55 ! [Xs: list_poly_a,P2: poly_poly_a] :
% 0.25/0.55 ( ( ( poly_poly_a2 @ Xs )
% 0.25/0.55 = P2 )
% 0.25/0.55 => ( ( descar357075861poly_a @ Xs )
% 0.25/0.55 = ( descar357075861poly_a @ ( coeffs_poly_a @ P2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_coeff_sign_changes
% 0.25/0.55 thf(fact_6_sign__changes__coeff__sign__changes,axiom,
% 0.25/0.55 ! [Xs: list_a,P2: poly_a] :
% 0.25/0.55 ( ( ( poly_a2 @ Xs )
% 0.25/0.55 = P2 )
% 0.25/0.55 => ( ( descar2095969287nges_a @ Xs )
% 0.25/0.55 = ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_coeff_sign_changes
% 0.25/0.55 thf(fact_7_ys__def,axiom,
% 0.25/0.55 ( ys
% 0.25/0.55 = ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ys_def
% 0.25/0.55 thf(fact_8_coeff__sign__changes__reduce__root,axiom,
% 0.25/0.55 ! [A: poly_a,P2: poly_poly_a] :
% 0.25/0.55 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.55 => ( ( descar357075861poly_a @ ( coeffs_poly_a @ ( descar434775507poly_a @ A @ P2 ) ) )
% 0.25/0.55 = ( descar357075861poly_a @ ( coeffs_poly_a @ P2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeff_sign_changes_reduce_root
% 0.25/0.55 thf(fact_9_coeff__sign__changes__reduce__root,axiom,
% 0.25/0.55 ! [A: a,P2: poly_a] :
% 0.25/0.55 ( ( ord_less_a @ zero_zero_a @ A )
% 0.25/0.55 => ( ( descar2095969287nges_a @ ( coeffs_a @ ( descar466059845root_a @ A @ P2 ) ) )
% 0.25/0.55 = ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeff_sign_changes_reduce_root
% 0.25/0.55 thf(fact_10_is__zero__def,axiom,
% 0.25/0.55 ( is_zero_poly_a
% 0.25/0.55 = ( ^ [P: poly_poly_a] : ( null_poly_a @ ( coeffs_poly_a @ P ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % is_zero_def
% 0.25/0.55 thf(fact_11_is__zero__def,axiom,
% 0.25/0.55 ( is_zero_a
% 0.25/0.55 = ( ^ [P: poly_a] : ( null_a @ ( coeffs_a @ P ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % is_zero_def
% 0.25/0.55 thf(fact_12_Poly__coeffs,axiom,
% 0.25/0.55 ! [P2: poly_poly_a] :
% 0.25/0.55 ( ( poly_poly_a2 @ ( coeffs_poly_a @ P2 ) )
% 0.25/0.55 = P2 ) ).
% 0.25/0.55
% 0.25/0.55 % Poly_coeffs
% 0.25/0.55 thf(fact_13_Poly__coeffs,axiom,
% 0.25/0.55 ! [P2: poly_a] :
% 0.25/0.55 ( ( poly_a2 @ ( coeffs_a @ P2 ) )
% 0.25/0.55 = P2 ) ).
% 0.25/0.55
% 0.25/0.55 % Poly_coeffs
% 0.25/0.55 thf(fact_14_sign__changes__Nil,axiom,
% 0.25/0.55 ( ( descar357075861poly_a @ nil_poly_a )
% 0.25/0.55 = zero_zero_nat ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_Nil
% 0.25/0.55 thf(fact_15_sign__changes__Nil,axiom,
% 0.25/0.55 ( ( descar2095969287nges_a @ nil_a )
% 0.25/0.55 = zero_zero_nat ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_Nil
% 0.25/0.55 thf(fact_16_xs__def,axiom,
% 0.25/0.55 ( xs
% 0.25/0.55 = ( coeffs_a @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % xs_def
% 0.25/0.55 thf(fact_17_coeff__sign__changes__smult,axiom,
% 0.25/0.55 ! [A: a,P2: poly_a] :
% 0.25/0.55 ( ( ord_less_a @ zero_zero_a @ A )
% 0.25/0.55 => ( ( descar2095969287nges_a @ ( coeffs_a @ ( smult_a @ A @ P2 ) ) )
% 0.25/0.55 = ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeff_sign_changes_smult
% 0.25/0.55 thf(fact_18_coeff__sign__changes__smult,axiom,
% 0.25/0.55 ! [A: poly_a,P2: poly_poly_a] :
% 0.25/0.55 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.55 => ( ( descar357075861poly_a @ ( coeffs_poly_a @ ( smult_poly_a @ A @ P2 ) ) )
% 0.25/0.55 = ( descar357075861poly_a @ ( coeffs_poly_a @ P2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeff_sign_changes_smult
% 0.25/0.55 thf(fact_19_sign__changes__0__Cons,axiom,
% 0.25/0.55 ! [Xs: list_a] :
% 0.25/0.55 ( ( descar2095969287nges_a @ ( cons_a @ zero_zero_a @ Xs ) )
% 0.25/0.55 = ( descar2095969287nges_a @ Xs ) ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_0_Cons
% 0.25/0.55 thf(fact_20_sign__changes__0__Cons,axiom,
% 0.25/0.55 ! [Xs: list_poly_a] :
% 0.25/0.55 ( ( descar357075861poly_a @ ( cons_poly_a @ zero_zero_poly_a @ Xs ) )
% 0.25/0.55 = ( descar357075861poly_a @ Xs ) ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_0_Cons
% 0.25/0.55 thf(fact_21_sign__changes__Cons__Cons__0,axiom,
% 0.25/0.55 ! [X: a,Xs: list_a] :
% 0.25/0.55 ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ zero_zero_a @ Xs ) ) )
% 0.25/0.55 = ( descar2095969287nges_a @ ( cons_a @ X @ Xs ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_Cons_Cons_0
% 0.25/0.55 thf(fact_22_sign__changes__Cons__Cons__0,axiom,
% 0.25/0.55 ! [X: poly_a,Xs: list_poly_a] :
% 0.25/0.55 ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ zero_zero_poly_a @ Xs ) ) )
% 0.25/0.55 = ( descar357075861poly_a @ ( cons_poly_a @ X @ Xs ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_Cons_Cons_0
% 0.25/0.55 thf(fact_23_pCons__eq__iff,axiom,
% 0.25/0.55 ! [A: a,P2: poly_a,B: a,Q2: poly_a] :
% 0.25/0.55 ( ( ( pCons_a @ A @ P2 )
% 0.25/0.55 = ( pCons_a @ B @ Q2 ) )
% 0.25/0.55 = ( ( A = B )
% 0.25/0.55 & ( P2 = Q2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_eq_iff
% 0.25/0.55 thf(fact_24_minus__pCons,axiom,
% 0.25/0.55 ! [A: a,P2: poly_a] :
% 0.25/0.55 ( ( uminus_uminus_poly_a @ ( pCons_a @ A @ P2 ) )
% 0.25/0.55 = ( pCons_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_poly_a @ P2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % minus_pCons
% 0.25/0.55 thf(fact_25_smult__smult,axiom,
% 0.25/0.55 ! [A: poly_a,B: poly_a,P2: poly_poly_a] :
% 0.25/0.55 ( ( smult_poly_a @ A @ ( smult_poly_a @ B @ P2 ) )
% 0.25/0.55 = ( smult_poly_a @ ( times_times_poly_a @ A @ B ) @ P2 ) ) ).
% 0.25/0.55
% 0.25/0.55 % smult_smult
% 0.25/0.55 thf(fact_26_smult__smult,axiom,
% 0.25/0.55 ! [A: nat,B: nat,P2: poly_nat] :
% 0.25/0.55 ( ( smult_nat @ A @ ( smult_nat @ B @ P2 ) )
% 0.25/0.55 = ( smult_nat @ ( times_times_nat @ A @ B ) @ P2 ) ) ).
% 0.25/0.55
% 0.25/0.55 % smult_smult
% 0.25/0.55 thf(fact_27_smult__1__left,axiom,
% 0.25/0.55 ! [P2: poly_a] :
% 0.25/0.55 ( ( smult_a @ one_one_a @ P2 )
% 0.25/0.55 = P2 ) ).
% 0.25/0.55
% 0.25/0.55 % smult_1_left
% 0.25/0.55 thf(fact_28_smult__1__left,axiom,
% 0.25/0.55 ! [P2: poly_nat] :
% 0.25/0.55 ( ( smult_nat @ one_one_nat @ P2 )
% 0.25/0.55 = P2 ) ).
% 0.25/0.55
% 0.25/0.55 % smult_1_left
% 0.25/0.55 thf(fact_29_smult__minus__left,axiom,
% 0.25/0.55 ! [A: a,P2: poly_a] :
% 0.25/0.55 ( ( smult_a @ ( uminus_uminus_a @ A ) @ P2 )
% 0.25/0.55 = ( uminus_uminus_poly_a @ ( smult_a @ A @ P2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % smult_minus_left
% 0.25/0.55 thf(fact_30_smult__0__right,axiom,
% 0.25/0.55 ! [A: a] :
% 0.25/0.55 ( ( smult_a @ A @ zero_zero_poly_a )
% 0.25/0.55 = zero_zero_poly_a ) ).
% 0.25/0.55
% 0.25/0.55 % smult_0_right
% 0.25/0.55 thf(fact_31_mult__smult__left,axiom,
% 0.25/0.55 ! [A: a,P2: poly_a,Q2: poly_a] :
% 0.25/0.55 ( ( times_times_poly_a @ ( smult_a @ A @ P2 ) @ Q2 )
% 0.25/0.55 = ( smult_a @ A @ ( times_times_poly_a @ P2 @ Q2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % mult_smult_left
% 0.25/0.55 thf(fact_32_mult__smult__right,axiom,
% 0.25/0.55 ! [P2: poly_a,A: a,Q2: poly_a] :
% 0.25/0.55 ( ( times_times_poly_a @ P2 @ ( smult_a @ A @ Q2 ) )
% 0.25/0.55 = ( smult_a @ A @ ( times_times_poly_a @ P2 @ Q2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % mult_smult_right
% 0.25/0.55 thf(fact_33_pCons__0__0,axiom,
% 0.25/0.55 ( ( pCons_poly_a @ zero_zero_poly_a @ zero_z2096148049poly_a )
% 0.25/0.55 = zero_z2096148049poly_a ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_0_0
% 0.25/0.55 thf(fact_34_pCons__0__0,axiom,
% 0.25/0.55 ( ( pCons_a @ zero_zero_a @ zero_zero_poly_a )
% 0.25/0.55 = zero_zero_poly_a ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_0_0
% 0.25/0.55 thf(fact_35_pCons__0__0,axiom,
% 0.25/0.55 ( ( pCons_nat @ zero_zero_nat @ zero_zero_poly_nat )
% 0.25/0.55 = zero_zero_poly_nat ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_0_0
% 0.25/0.55 thf(fact_36_pCons__eq__0__iff,axiom,
% 0.25/0.55 ! [A: poly_a,P2: poly_poly_a] :
% 0.25/0.55 ( ( ( pCons_poly_a @ A @ P2 )
% 0.25/0.55 = zero_z2096148049poly_a )
% 0.25/0.55 = ( ( A = zero_zero_poly_a )
% 0.25/0.55 & ( P2 = zero_z2096148049poly_a ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_eq_0_iff
% 0.25/0.55 thf(fact_37_pCons__eq__0__iff,axiom,
% 0.25/0.55 ! [A: nat,P2: poly_nat] :
% 0.25/0.55 ( ( ( pCons_nat @ A @ P2 )
% 0.25/0.55 = zero_zero_poly_nat )
% 0.25/0.55 = ( ( A = zero_zero_nat )
% 0.25/0.55 & ( P2 = zero_zero_poly_nat ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_eq_0_iff
% 0.25/0.55 thf(fact_38_pCons__eq__0__iff,axiom,
% 0.25/0.55 ! [A: a,P2: poly_a] :
% 0.25/0.55 ( ( ( pCons_a @ A @ P2 )
% 0.25/0.55 = zero_zero_poly_a )
% 0.25/0.55 = ( ( A = zero_zero_a )
% 0.25/0.55 & ( P2 = zero_zero_poly_a ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_eq_0_iff
% 0.25/0.55 thf(fact_39_one__poly__eq__simps_I2_J,axiom,
% 0.25/0.55 ( ( pCons_nat @ one_one_nat @ zero_zero_poly_nat )
% 0.25/0.55 = one_one_poly_nat ) ).
% 0.25/0.55
% 0.25/0.55 % one_poly_eq_simps(2)
% 0.25/0.55 thf(fact_40_one__poly__eq__simps_I2_J,axiom,
% 0.25/0.55 ( ( pCons_a @ one_one_a @ zero_zero_poly_a )
% 0.25/0.55 = one_one_poly_a ) ).
% 0.25/0.55
% 0.25/0.55 % one_poly_eq_simps(2)
% 0.25/0.55 thf(fact_41_one__poly__eq__simps_I1_J,axiom,
% 0.25/0.55 ( one_one_poly_nat
% 0.25/0.55 = ( pCons_nat @ one_one_nat @ zero_zero_poly_nat ) ) ).
% 0.25/0.55
% 0.25/0.55 % one_poly_eq_simps(1)
% 0.25/0.55 thf(fact_42_one__poly__eq__simps_I1_J,axiom,
% 0.25/0.55 ( one_one_poly_a
% 0.25/0.55 = ( pCons_a @ one_one_a @ zero_zero_poly_a ) ) ).
% 0.25/0.55
% 0.25/0.55 % one_poly_eq_simps(1)
% 0.25/0.55 thf(fact_43_smult__0__left,axiom,
% 0.25/0.55 ! [P2: poly_poly_a] :
% 0.25/0.55 ( ( smult_poly_a @ zero_zero_poly_a @ P2 )
% 0.25/0.55 = zero_z2096148049poly_a ) ).
% 0.25/0.55
% 0.25/0.55 % smult_0_left
% 0.25/0.55 thf(fact_44_smult__0__left,axiom,
% 0.25/0.55 ! [P2: poly_a] :
% 0.25/0.55 ( ( smult_a @ zero_zero_a @ P2 )
% 0.25/0.55 = zero_zero_poly_a ) ).
% 0.25/0.55
% 0.25/0.55 % smult_0_left
% 0.25/0.55 thf(fact_45_smult__0__left,axiom,
% 0.25/0.55 ! [P2: poly_nat] :
% 0.25/0.55 ( ( smult_nat @ zero_zero_nat @ P2 )
% 0.25/0.55 = zero_zero_poly_nat ) ).
% 0.25/0.55
% 0.25/0.55 % smult_0_left
% 0.25/0.55 thf(fact_46_smult__eq__0__iff,axiom,
% 0.25/0.55 ! [A: poly_a,P2: poly_poly_a] :
% 0.25/0.55 ( ( ( smult_poly_a @ A @ P2 )
% 0.25/0.55 = zero_z2096148049poly_a )
% 0.25/0.55 = ( ( A = zero_zero_poly_a )
% 0.25/0.55 | ( P2 = zero_z2096148049poly_a ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % smult_eq_0_iff
% 0.25/0.55 thf(fact_47_smult__eq__0__iff,axiom,
% 0.25/0.55 ! [A: nat,P2: poly_nat] :
% 0.25/0.55 ( ( ( smult_nat @ A @ P2 )
% 0.25/0.55 = zero_zero_poly_nat )
% 0.25/0.55 = ( ( A = zero_zero_nat )
% 0.25/0.55 | ( P2 = zero_zero_poly_nat ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % smult_eq_0_iff
% 0.25/0.55 thf(fact_48_smult__eq__0__iff,axiom,
% 0.25/0.55 ! [A: a,P2: poly_a] :
% 0.25/0.55 ( ( ( smult_a @ A @ P2 )
% 0.25/0.55 = zero_zero_poly_a )
% 0.25/0.55 = ( ( A = zero_zero_a )
% 0.25/0.55 | ( P2 = zero_zero_poly_a ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % smult_eq_0_iff
% 0.25/0.55 thf(fact_49_smult__pCons,axiom,
% 0.25/0.55 ! [A: a,B: a,P2: poly_a] :
% 0.25/0.55 ( ( smult_a @ A @ ( pCons_a @ B @ P2 ) )
% 0.25/0.55 = ( pCons_a @ ( times_times_a @ A @ B ) @ ( smult_a @ A @ P2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % smult_pCons
% 0.25/0.55 thf(fact_50_smult__pCons,axiom,
% 0.25/0.55 ! [A: poly_a,B: poly_a,P2: poly_poly_a] :
% 0.25/0.55 ( ( smult_poly_a @ A @ ( pCons_poly_a @ B @ P2 ) )
% 0.25/0.55 = ( pCons_poly_a @ ( times_times_poly_a @ A @ B ) @ ( smult_poly_a @ A @ P2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % smult_pCons
% 0.25/0.55 thf(fact_51_smult__pCons,axiom,
% 0.25/0.55 ! [A: nat,B: nat,P2: poly_nat] :
% 0.25/0.55 ( ( smult_nat @ A @ ( pCons_nat @ B @ P2 ) )
% 0.25/0.55 = ( pCons_nat @ ( times_times_nat @ A @ B ) @ ( smult_nat @ A @ P2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % smult_pCons
% 0.25/0.55 thf(fact_52_coeffs__eq__Nil,axiom,
% 0.25/0.55 ! [P2: poly_poly_a] :
% 0.25/0.55 ( ( ( coeffs_poly_a @ P2 )
% 0.25/0.55 = nil_poly_a )
% 0.25/0.55 = ( P2 = zero_z2096148049poly_a ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeffs_eq_Nil
% 0.25/0.55 thf(fact_53_coeffs__eq__Nil,axiom,
% 0.25/0.55 ! [P2: poly_a] :
% 0.25/0.55 ( ( ( coeffs_a @ P2 )
% 0.25/0.55 = nil_a )
% 0.25/0.55 = ( P2 = zero_zero_poly_a ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeffs_eq_Nil
% 0.25/0.55 thf(fact_54_coeffs__0__eq__Nil,axiom,
% 0.25/0.55 ( ( coeffs_poly_a @ zero_z2096148049poly_a )
% 0.25/0.55 = nil_poly_a ) ).
% 0.25/0.55
% 0.25/0.55 % coeffs_0_eq_Nil
% 0.25/0.55 thf(fact_55_coeffs__0__eq__Nil,axiom,
% 0.25/0.55 ( ( coeffs_a @ zero_zero_poly_a )
% 0.25/0.55 = nil_a ) ).
% 0.25/0.55
% 0.25/0.55 % coeffs_0_eq_Nil
% 0.25/0.55 thf(fact_56_psums__0__Cons,axiom,
% 0.25/0.55 ! [Xs: list_poly_a] :
% 0.25/0.55 ( ( descar282223555poly_a @ ( cons_poly_a @ zero_zero_poly_a @ Xs ) )
% 0.25/0.55 = ( cons_poly_a @ zero_zero_poly_a @ ( descar282223555poly_a @ Xs ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % psums_0_Cons
% 0.25/0.55 thf(fact_57_psums__0__Cons,axiom,
% 0.25/0.55 ! [Xs: list_nat] :
% 0.25/0.55 ( ( descar226543321ms_nat @ ( cons_nat @ zero_zero_nat @ Xs ) )
% 0.25/0.55 = ( cons_nat @ zero_zero_nat @ ( descar226543321ms_nat @ Xs ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % psums_0_Cons
% 0.25/0.55 thf(fact_58_psums__0__Cons,axiom,
% 0.25/0.55 ! [Xs: list_a] :
% 0.25/0.55 ( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ Xs ) )
% 0.25/0.55 = ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ Xs ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % psums_0_Cons
% 0.25/0.55 thf(fact_59_coeffs__1__eq,axiom,
% 0.25/0.55 ( ( coeffs_poly_a @ one_one_poly_poly_a )
% 0.25/0.55 = ( cons_poly_a @ one_one_poly_a @ nil_poly_a ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeffs_1_eq
% 0.25/0.55 thf(fact_60_coeffs__1__eq,axiom,
% 0.25/0.55 ( ( coeffs_a @ one_one_poly_a )
% 0.25/0.55 = ( cons_a @ one_one_a @ nil_a ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeffs_1_eq
% 0.25/0.55 thf(fact_61_coeffs__1__eq,axiom,
% 0.25/0.55 ( ( coeffs_nat @ one_one_poly_nat )
% 0.25/0.55 = ( cons_nat @ one_one_nat @ nil_nat ) ) ).
% 0.25/0.55
% 0.25/0.55 % coeffs_1_eq
% 0.25/0.55 thf(fact_62_sign__changes__singleton,axiom,
% 0.25/0.55 ! [X: a] :
% 0.25/0.55 ( ( descar2095969287nges_a @ ( cons_a @ X @ nil_a ) )
% 0.25/0.55 = zero_zero_nat ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_singleton
% 0.25/0.55 thf(fact_63_sign__changes__singleton,axiom,
% 0.25/0.55 ! [X: poly_a] :
% 0.25/0.55 ( ( descar357075861poly_a @ ( cons_poly_a @ X @ nil_poly_a ) )
% 0.25/0.55 = zero_zero_nat ) ).
% 0.25/0.55
% 0.25/0.55 % sign_changes_singleton
% 0.25/0.55 thf(fact_64__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062,axiom,
% 0.25/0.55 ( ( descar2095969287nges_a @ xs )
% 0.25/0.55 = ( v @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % \<open>sign_changes xs = v ([:1::'a, - (1::'a):] * g)\<close>
% 0.25/0.55 thf(fact_65_Poly__snoc__zero,axiom,
% 0.25/0.55 ! [As: list_poly_a] :
% 0.25/0.55 ( ( poly_poly_a2 @ ( append_poly_a @ As @ ( cons_poly_a @ zero_zero_poly_a @ nil_poly_a ) ) )
% 0.25/0.55 = ( poly_poly_a2 @ As ) ) ).
% 0.25/0.55
% 0.25/0.55 % Poly_snoc_zero
% 0.25/0.55 thf(fact_66_Poly__snoc__zero,axiom,
% 0.25/0.55 ! [As: list_a] :
% 0.25/0.55 ( ( poly_a2 @ ( append_a @ As @ ( cons_a @ zero_zero_a @ nil_a ) ) )
% 0.25/0.55 = ( poly_a2 @ As ) ) ).
% 0.25/0.55
% 0.25/0.55 % Poly_snoc_zero
% 0.25/0.55 thf(fact_67_Poly__snoc__zero,axiom,
% 0.25/0.55 ! [As: list_nat] :
% 0.25/0.55 ( ( poly_nat2 @ ( append_nat @ As @ ( cons_nat @ zero_zero_nat @ nil_nat ) ) )
% 0.25/0.55 = ( poly_nat2 @ As ) ) ).
% 0.25/0.55
% 0.25/0.55 % Poly_snoc_zero
% 0.25/0.55 thf(fact_68_Poly_Osimps_I2_J,axiom,
% 0.25/0.55 ! [A: a,As: list_a] :
% 0.25/0.55 ( ( poly_a2 @ ( cons_a @ A @ As ) )
% 0.25/0.55 = ( pCons_a @ A @ ( poly_a2 @ As ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % Poly.simps(2)
% 0.25/0.55 thf(fact_69_Poly_Osimps_I1_J,axiom,
% 0.25/0.55 ( ( poly_a2 @ nil_a )
% 0.25/0.55 = zero_zero_poly_a ) ).
% 0.25/0.55
% 0.25/0.55 % Poly.simps(1)
% 0.25/0.55 thf(fact_70_psums_Osimps_I2_J,axiom,
% 0.25/0.55 ! [X: a] :
% 0.25/0.55 ( ( descar1375166517sums_a @ ( cons_a @ X @ nil_a ) )
% 0.25/0.55 = ( cons_a @ X @ nil_a ) ) ).
% 0.25/0.55
% 0.25/0.55 % psums.simps(2)
% 0.25/0.55 thf(fact_71_psums_Osimps_I1_J,axiom,
% 0.25/0.55 ( ( descar1375166517sums_a @ nil_a )
% 0.25/0.55 = nil_a ) ).
% 0.25/0.55
% 0.25/0.55 % psums.simps(1)
% 0.25/0.55 thf(fact_72_pCons__one,axiom,
% 0.25/0.55 ( ( pCons_nat @ one_one_nat @ zero_zero_poly_nat )
% 0.25/0.55 = one_one_poly_nat ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_one
% 0.25/0.55 thf(fact_73_pCons__one,axiom,
% 0.25/0.55 ( ( pCons_a @ one_one_a @ zero_zero_poly_a )
% 0.25/0.55 = one_one_poly_a ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_one
% 0.25/0.55 thf(fact_74_pCons__cases,axiom,
% 0.25/0.55 ! [P2: poly_a] :
% 0.25/0.55 ~ ! [A2: a,Q3: poly_a] :
% 0.25/0.55 ( P2
% 0.25/0.55 != ( pCons_a @ A2 @ Q3 ) ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_cases
% 0.25/0.55 thf(fact_75_is__zero__null,axiom,
% 0.25/0.55 ( is_zero_a
% 0.25/0.55 = ( ^ [P: poly_a] : ( P = zero_zero_poly_a ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % is_zero_null
% 0.25/0.55 thf(fact_76_pCons__induct,axiom,
% 0.25/0.55 ! [P3: poly_poly_a > $o,P2: poly_poly_a] :
% 0.25/0.55 ( ( P3 @ zero_z2096148049poly_a )
% 0.25/0.55 => ( ! [A2: poly_a,P4: poly_poly_a] :
% 0.25/0.55 ( ( ( A2 != zero_zero_poly_a )
% 0.25/0.55 | ( P4 != zero_z2096148049poly_a ) )
% 0.25/0.55 => ( ( P3 @ P4 )
% 0.25/0.55 => ( P3 @ ( pCons_poly_a @ A2 @ P4 ) ) ) )
% 0.25/0.55 => ( P3 @ P2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_induct
% 0.25/0.55 thf(fact_77_pCons__induct,axiom,
% 0.25/0.55 ! [P3: poly_nat > $o,P2: poly_nat] :
% 0.25/0.55 ( ( P3 @ zero_zero_poly_nat )
% 0.25/0.55 => ( ! [A2: nat,P4: poly_nat] :
% 0.25/0.55 ( ( ( A2 != zero_zero_nat )
% 0.25/0.55 | ( P4 != zero_zero_poly_nat ) )
% 0.25/0.55 => ( ( P3 @ P4 )
% 0.25/0.55 => ( P3 @ ( pCons_nat @ A2 @ P4 ) ) ) )
% 0.25/0.55 => ( P3 @ P2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % pCons_induct
% 0.25/0.55 thf(fact_78_pCons__induct,axiom,
% 0.25/0.55 ! [P3: poly_a > $o,P2: poly_a] :
% 0.25/0.55 ( ( P3 @ zero_zero_poly_a )
% 0.25/0.55 => ( ! [A2: a,P4: poly_a] :
% 0.25/0.55 ( ( ( A2 != zero_zero_a )
% 0.25/0.55 | ( P4 != zero_zero_poly_a ) )
% 0.25/0.56 => ( ( P3 @ P4 )
% 0.25/0.56 => ( P3 @ ( pCons_a @ A2 @ P4 ) ) ) )
% 0.25/0.56 => ( P3 @ P2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % pCons_induct
% 0.25/0.56 thf(fact_79_pderiv_Ocases,axiom,
% 0.25/0.56 ! [X: poly_a] :
% 0.25/0.56 ~ ! [A2: a,P4: poly_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( pCons_a @ A2 @ P4 ) ) ).
% 0.25/0.56
% 0.25/0.56 % pderiv.cases
% 0.25/0.56 thf(fact_80_poly__induct2,axiom,
% 0.25/0.56 ! [P3: poly_a > poly_a > $o,P2: poly_a,Q2: poly_a] :
% 0.25/0.56 ( ( P3 @ zero_zero_poly_a @ zero_zero_poly_a )
% 0.25/0.56 => ( ! [A2: a,P4: poly_a,B2: a,Q3: poly_a] :
% 0.25/0.56 ( ( P3 @ P4 @ Q3 )
% 0.25/0.56 => ( P3 @ ( pCons_a @ A2 @ P4 ) @ ( pCons_a @ B2 @ Q3 ) ) )
% 0.25/0.56 => ( P3 @ P2 @ Q2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % poly_induct2
% 0.25/0.56 thf(fact_81_pderiv_Oinduct,axiom,
% 0.25/0.56 ! [P3: poly_a > $o,A0: poly_a] :
% 0.25/0.56 ( ! [A2: a,P4: poly_a] :
% 0.25/0.56 ( ( ( P4 != zero_zero_poly_a )
% 0.25/0.56 => ( P3 @ P4 ) )
% 0.25/0.56 => ( P3 @ ( pCons_a @ A2 @ P4 ) ) )
% 0.25/0.56 => ( P3 @ A0 ) ) ).
% 0.25/0.56
% 0.25/0.56 % pderiv.induct
% 0.25/0.56 thf(fact_82_mult__poly__0__left,axiom,
% 0.25/0.56 ! [Q2: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ zero_zero_poly_a @ Q2 )
% 0.25/0.56 = zero_zero_poly_a ) ).
% 0.25/0.56
% 0.25/0.56 % mult_poly_0_left
% 0.25/0.56 thf(fact_83_mult__poly__0__right,axiom,
% 0.25/0.56 ! [P2: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ P2 @ zero_zero_poly_a )
% 0.25/0.56 = zero_zero_poly_a ) ).
% 0.25/0.56
% 0.25/0.56 % mult_poly_0_right
% 0.25/0.56 thf(fact_84_plus__coeffs_Oinduct,axiom,
% 0.25/0.56 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.25/0.56 ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
% 0.25/0.56 => ( ! [V: a,Va: list_a] : ( P3 @ nil_a @ ( cons_a @ V @ Va ) )
% 0.25/0.56 => ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 0.25/0.56 ( ( P3 @ Xs2 @ Ys )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
% 0.25/0.56 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % plus_coeffs.induct
% 0.25/0.56 thf(fact_85_not__0__coeffs__not__Nil,axiom,
% 0.25/0.56 ! [P2: poly_poly_a] :
% 0.25/0.56 ( ( P2 != zero_z2096148049poly_a )
% 0.25/0.56 => ( ( coeffs_poly_a @ P2 )
% 0.25/0.56 != nil_poly_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_0_coeffs_not_Nil
% 0.25/0.56 thf(fact_86_not__0__coeffs__not__Nil,axiom,
% 0.25/0.56 ! [P2: poly_a] :
% 0.25/0.56 ( ( P2 != zero_zero_poly_a )
% 0.25/0.56 => ( ( coeffs_a @ P2 )
% 0.25/0.56 != nil_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_0_coeffs_not_Nil
% 0.25/0.56 thf(fact_87_minus__poly__rev__list_Oinduct,axiom,
% 0.25/0.56 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.25/0.56 ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 0.25/0.56 ( ( P3 @ Xs2 @ Ys )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
% 0.25/0.56 => ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
% 0.25/0.56 => ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
% 0.25/0.56 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % minus_poly_rev_list.induct
% 0.25/0.56 thf(fact_88_synthetic__div__unique__lemma,axiom,
% 0.25/0.56 ! [C: a,P2: poly_a,A: a] :
% 0.25/0.56 ( ( ( smult_a @ C @ P2 )
% 0.25/0.56 = ( pCons_a @ A @ P2 ) )
% 0.25/0.56 => ( P2 = zero_zero_poly_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % synthetic_div_unique_lemma
% 0.25/0.56 thf(fact_89_psums_Ocases,axiom,
% 0.25/0.56 ! [X: list_a] :
% 0.25/0.56 ( ( X != nil_a )
% 0.25/0.56 => ( ! [X2: a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( cons_a @ X2 @ nil_a ) )
% 0.25/0.56 => ~ ! [X2: a,Y2: a,Xs2: list_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % psums.cases
% 0.25/0.56 thf(fact_90_reduce__root__pCons,axiom,
% 0.25/0.56 ! [A: a,C: a,P2: poly_a] :
% 0.25/0.56 ( ( descar466059845root_a @ A @ ( pCons_a @ C @ P2 ) )
% 0.25/0.56 = ( pCons_a @ C @ ( smult_a @ A @ ( descar466059845root_a @ A @ P2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % reduce_root_pCons
% 0.25/0.56 thf(fact_91_reduce__root__pCons,axiom,
% 0.25/0.56 ! [A: poly_a,C: poly_a,P2: poly_poly_a] :
% 0.25/0.56 ( ( descar434775507poly_a @ A @ ( pCons_poly_a @ C @ P2 ) )
% 0.25/0.56 = ( pCons_poly_a @ C @ ( smult_poly_a @ A @ ( descar434775507poly_a @ A @ P2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % reduce_root_pCons
% 0.25/0.56 thf(fact_92_reduce__root__nonzero,axiom,
% 0.25/0.56 ! [A: a,P2: poly_a] :
% 0.25/0.56 ( ( A != zero_zero_a )
% 0.25/0.56 => ( ( P2 != zero_zero_poly_a )
% 0.25/0.56 => ( ( descar466059845root_a @ A @ P2 )
% 0.25/0.56 != zero_zero_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % reduce_root_nonzero
% 0.25/0.56 thf(fact_93_reduce__root__nonzero,axiom,
% 0.25/0.56 ! [A: poly_a,P2: poly_poly_a] :
% 0.25/0.56 ( ( A != zero_zero_poly_a )
% 0.25/0.56 => ( ( P2 != zero_z2096148049poly_a )
% 0.25/0.56 => ( ( descar434775507poly_a @ A @ P2 )
% 0.25/0.56 != zero_z2096148049poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % reduce_root_nonzero
% 0.25/0.56 thf(fact_94_sign__changes__Cons__Cons__same,axiom,
% 0.25/0.56 ! [X: a,Y3: a,Xs: list_a] :
% 0.25/0.56 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ X @ Y3 ) )
% 0.25/0.56 => ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ Y3 @ Xs ) ) )
% 0.25/0.56 = ( descar2095969287nges_a @ ( cons_a @ Y3 @ Xs ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % sign_changes_Cons_Cons_same
% 0.25/0.56 thf(fact_95_sign__changes__Cons__Cons__same,axiom,
% 0.25/0.56 ! [X: poly_a,Y3: poly_a,Xs: list_poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ X @ Y3 ) )
% 0.25/0.56 => ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ Y3 @ Xs ) ) )
% 0.25/0.56 = ( descar357075861poly_a @ ( cons_poly_a @ Y3 @ Xs ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % sign_changes_Cons_Cons_same
% 0.25/0.56 thf(fact_96_append1__eq__conv,axiom,
% 0.25/0.56 ! [Xs: list_a,X: a,Ys2: list_a,Y3: a] :
% 0.25/0.56 ( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
% 0.25/0.56 = ( append_a @ Ys2 @ ( cons_a @ Y3 @ nil_a ) ) )
% 0.25/0.56 = ( ( Xs = Ys2 )
% 0.25/0.56 & ( X = Y3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append1_eq_conv
% 0.25/0.56 thf(fact_97_mult__minus1,axiom,
% 0.25/0.56 ! [Z2: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ one_one_poly_a ) @ Z2 )
% 0.25/0.56 = ( uminus_uminus_poly_a @ Z2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_minus1
% 0.25/0.56 thf(fact_98_mult__minus1,axiom,
% 0.25/0.56 ! [Z2: a] :
% 0.25/0.56 ( ( times_times_a @ ( uminus_uminus_a @ one_one_a ) @ Z2 )
% 0.25/0.56 = ( uminus_uminus_a @ Z2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_minus1
% 0.25/0.56 thf(fact_99_mult__minus1__right,axiom,
% 0.25/0.56 ! [Z2: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ Z2 @ ( uminus_uminus_poly_a @ one_one_poly_a ) )
% 0.25/0.56 = ( uminus_uminus_poly_a @ Z2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_minus1_right
% 0.25/0.56 thf(fact_100_mult__minus1__right,axiom,
% 0.25/0.56 ! [Z2: a] :
% 0.25/0.56 ( ( times_times_a @ Z2 @ ( uminus_uminus_a @ one_one_a ) )
% 0.25/0.56 = ( uminus_uminus_a @ Z2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_minus1_right
% 0.25/0.56 thf(fact_101_less__neg__neg,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ A ) )
% 0.25/0.56 = ( ord_less_poly_a @ A @ zero_zero_poly_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_neg_neg
% 0.25/0.56 thf(fact_102_less__neg__neg,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( ord_less_a @ A @ ( uminus_uminus_a @ A ) )
% 0.25/0.56 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_neg_neg
% 0.25/0.56 thf(fact_103_neg__less__pos,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ A )
% 0.25/0.56 = ( ord_less_poly_a @ zero_zero_poly_a @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_less_pos
% 0.25/0.56 thf(fact_104_neg__less__pos,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ A )
% 0.25/0.56 = ( ord_less_a @ zero_zero_a @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_less_pos
% 0.25/0.56 thf(fact_105_neg__0__less__iff__less,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( uminus_uminus_poly_a @ A ) )
% 0.25/0.56 = ( ord_less_poly_a @ A @ zero_zero_poly_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_0_less_iff_less
% 0.25/0.56 thf(fact_106_neg__0__less__iff__less,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
% 0.25/0.56 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_0_less_iff_less
% 0.25/0.56 thf(fact_107_neg__less__0__iff__less,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ zero_zero_poly_a )
% 0.25/0.56 = ( ord_less_poly_a @ zero_zero_poly_a @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_less_0_iff_less
% 0.25/0.56 thf(fact_108_neg__less__0__iff__less,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
% 0.25/0.56 = ( ord_less_a @ zero_zero_a @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_less_0_iff_less
% 0.25/0.56 thf(fact_109_mult__cancel__left1,axiom,
% 0.25/0.56 ! [C: a,B: a] :
% 0.25/0.56 ( ( C
% 0.25/0.56 = ( times_times_a @ C @ B ) )
% 0.25/0.56 = ( ( C = zero_zero_a )
% 0.25/0.56 | ( B = one_one_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_left1
% 0.25/0.56 thf(fact_110_mult__cancel__left1,axiom,
% 0.25/0.56 ! [C: poly_a,B: poly_a] :
% 0.25/0.56 ( ( C
% 0.25/0.56 = ( times_times_poly_a @ C @ B ) )
% 0.25/0.56 = ( ( C = zero_zero_poly_a )
% 0.25/0.56 | ( B = one_one_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_left1
% 0.25/0.56 thf(fact_111_mult__cancel__left2,axiom,
% 0.25/0.56 ! [C: a,A: a] :
% 0.25/0.56 ( ( ( times_times_a @ C @ A )
% 0.25/0.56 = C )
% 0.25/0.56 = ( ( C = zero_zero_a )
% 0.25/0.56 | ( A = one_one_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_left2
% 0.25/0.56 thf(fact_112_mult__cancel__left2,axiom,
% 0.25/0.56 ! [C: poly_a,A: poly_a] :
% 0.25/0.56 ( ( ( times_times_poly_a @ C @ A )
% 0.25/0.56 = C )
% 0.25/0.56 = ( ( C = zero_zero_poly_a )
% 0.25/0.56 | ( A = one_one_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_left2
% 0.25/0.56 thf(fact_113_mult__cancel__right1,axiom,
% 0.25/0.56 ! [C: a,B: a] :
% 0.25/0.56 ( ( C
% 0.25/0.56 = ( times_times_a @ B @ C ) )
% 0.25/0.56 = ( ( C = zero_zero_a )
% 0.25/0.56 | ( B = one_one_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_right1
% 0.25/0.56 thf(fact_114_mult__cancel__right1,axiom,
% 0.25/0.56 ! [C: poly_a,B: poly_a] :
% 0.25/0.56 ( ( C
% 0.25/0.56 = ( times_times_poly_a @ B @ C ) )
% 0.25/0.56 = ( ( C = zero_zero_poly_a )
% 0.25/0.56 | ( B = one_one_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_right1
% 0.25/0.56 thf(fact_115_mult__cancel__right2,axiom,
% 0.25/0.56 ! [A: a,C: a] :
% 0.25/0.56 ( ( ( times_times_a @ A @ C )
% 0.25/0.56 = C )
% 0.25/0.56 = ( ( C = zero_zero_a )
% 0.25/0.56 | ( A = one_one_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_right2
% 0.25/0.56 thf(fact_116_mult__cancel__right2,axiom,
% 0.25/0.56 ! [A: poly_a,C: poly_a] :
% 0.25/0.56 ( ( ( times_times_poly_a @ A @ C )
% 0.25/0.56 = C )
% 0.25/0.56 = ( ( C = zero_zero_poly_a )
% 0.25/0.56 | ( A = one_one_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_right2
% 0.25/0.56 thf(fact_117_neg__equal__iff__equal,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ( uminus_uminus_a @ A )
% 0.25/0.56 = ( uminus_uminus_a @ B ) )
% 0.25/0.56 = ( A = B ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_equal_iff_equal
% 0.25/0.56 thf(fact_118_add_Oinverse__inverse,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % add.inverse_inverse
% 0.25/0.56 thf(fact_119_list_Oinject,axiom,
% 0.25/0.56 ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
% 0.25/0.56 ( ( ( cons_a @ X21 @ X22 )
% 0.25/0.56 = ( cons_a @ Y21 @ Y22 ) )
% 0.25/0.56 = ( ( X21 = Y21 )
% 0.25/0.56 & ( X22 = Y22 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.inject
% 0.25/0.56 thf(fact_120_same__append__eq,axiom,
% 0.25/0.56 ! [Xs: list_a,Ys2: list_a,Zs: list_a] :
% 0.25/0.56 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.56 = ( append_a @ Xs @ Zs ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % same_append_eq
% 0.25/0.56 thf(fact_121_append__same__eq,axiom,
% 0.25/0.56 ! [Ys2: list_a,Xs: list_a,Zs: list_a] :
% 0.25/0.56 ( ( ( append_a @ Ys2 @ Xs )
% 0.25/0.56 = ( append_a @ Zs @ Xs ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_same_eq
% 0.25/0.56 thf(fact_122_append__assoc,axiom,
% 0.25/0.56 ! [Xs: list_a,Ys2: list_a,Zs: list_a] :
% 0.25/0.56 ( ( append_a @ ( append_a @ Xs @ Ys2 ) @ Zs )
% 0.25/0.56 = ( append_a @ Xs @ ( append_a @ Ys2 @ Zs ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_assoc
% 0.25/0.56 thf(fact_123_append_Oassoc,axiom,
% 0.25/0.56 ! [A: list_a,B: list_a,C: list_a] :
% 0.25/0.56 ( ( append_a @ ( append_a @ A @ B ) @ C )
% 0.25/0.56 = ( append_a @ A @ ( append_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append.assoc
% 0.25/0.56 thf(fact_124_not__gr__zero,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.25/0.56 = ( N = zero_zero_nat ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_gr_zero
% 0.25/0.56 thf(fact_125_mult__cancel__right,axiom,
% 0.25/0.56 ! [A: a,C: a,B: a] :
% 0.25/0.56 ( ( ( times_times_a @ A @ C )
% 0.25/0.56 = ( times_times_a @ B @ C ) )
% 0.25/0.56 = ( ( C = zero_zero_a )
% 0.25/0.56 | ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_right
% 0.25/0.56 thf(fact_126_mult__cancel__right,axiom,
% 0.25/0.56 ! [A: poly_a,C: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ( times_times_poly_a @ A @ C )
% 0.25/0.56 = ( times_times_poly_a @ B @ C ) )
% 0.25/0.56 = ( ( C = zero_zero_poly_a )
% 0.25/0.56 | ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_right
% 0.25/0.56 thf(fact_127_mult__cancel__right,axiom,
% 0.25/0.56 ! [A: nat,C: nat,B: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ A @ C )
% 0.25/0.56 = ( times_times_nat @ B @ C ) )
% 0.25/0.56 = ( ( C = zero_zero_nat )
% 0.25/0.56 | ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_right
% 0.25/0.56 thf(fact_128_mult__cancel__left,axiom,
% 0.25/0.56 ! [C: a,A: a,B: a] :
% 0.25/0.56 ( ( ( times_times_a @ C @ A )
% 0.25/0.56 = ( times_times_a @ C @ B ) )
% 0.25/0.56 = ( ( C = zero_zero_a )
% 0.25/0.56 | ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_left
% 0.25/0.56 thf(fact_129_mult__cancel__left,axiom,
% 0.25/0.56 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ( times_times_poly_a @ C @ A )
% 0.25/0.56 = ( times_times_poly_a @ C @ B ) )
% 0.25/0.56 = ( ( C = zero_zero_poly_a )
% 0.25/0.56 | ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_left
% 0.25/0.56 thf(fact_130_mult__cancel__left,axiom,
% 0.25/0.56 ! [C: nat,A: nat,B: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ C @ A )
% 0.25/0.56 = ( times_times_nat @ C @ B ) )
% 0.25/0.56 = ( ( C = zero_zero_nat )
% 0.25/0.56 | ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel_left
% 0.25/0.56 thf(fact_131_mult__eq__0__iff,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ( times_times_a @ A @ B )
% 0.25/0.56 = zero_zero_a )
% 0.25/0.56 = ( ( A = zero_zero_a )
% 0.25/0.56 | ( B = zero_zero_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_eq_0_iff
% 0.25/0.56 thf(fact_132_mult__eq__0__iff,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ( times_times_poly_a @ A @ B )
% 0.25/0.56 = zero_zero_poly_a )
% 0.25/0.56 = ( ( A = zero_zero_poly_a )
% 0.25/0.56 | ( B = zero_zero_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_eq_0_iff
% 0.25/0.56 thf(fact_133_mult__eq__0__iff,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ A @ B )
% 0.25/0.56 = zero_zero_nat )
% 0.25/0.56 = ( ( A = zero_zero_nat )
% 0.25/0.56 | ( B = zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_eq_0_iff
% 0.25/0.56 thf(fact_134_mult__zero__right,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( times_times_a @ A @ zero_zero_a )
% 0.25/0.56 = zero_zero_a ) ).
% 0.25/0.56
% 0.25/0.56 % mult_zero_right
% 0.25/0.56 thf(fact_135_mult__zero__right,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ A @ zero_zero_poly_a )
% 0.25/0.56 = zero_zero_poly_a ) ).
% 0.25/0.56
% 0.25/0.56 % mult_zero_right
% 0.25/0.56 thf(fact_136_mult__zero__right,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ( ( times_times_nat @ A @ zero_zero_nat )
% 0.25/0.56 = zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % mult_zero_right
% 0.25/0.56 thf(fact_137_mult__zero__left,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( times_times_a @ zero_zero_a @ A )
% 0.25/0.56 = zero_zero_a ) ).
% 0.25/0.56
% 0.25/0.56 % mult_zero_left
% 0.25/0.56 thf(fact_138_mult__zero__left,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.56 = zero_zero_poly_a ) ).
% 0.25/0.56
% 0.25/0.56 % mult_zero_left
% 0.25/0.56 thf(fact_139_mult__zero__left,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ( ( times_times_nat @ zero_zero_nat @ A )
% 0.25/0.56 = zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % mult_zero_left
% 0.25/0.56 thf(fact_140_neg__equal__zero,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( ( uminus_uminus_poly_a @ A )
% 0.25/0.56 = A )
% 0.25/0.56 = ( A = zero_zero_poly_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_equal_zero
% 0.25/0.56 thf(fact_141_neg__equal__zero,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( ( uminus_uminus_a @ A )
% 0.25/0.56 = A )
% 0.25/0.56 = ( A = zero_zero_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_equal_zero
% 0.25/0.56 thf(fact_142_equal__neg__zero,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( uminus_uminus_poly_a @ A ) )
% 0.25/0.56 = ( A = zero_zero_poly_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % equal_neg_zero
% 0.25/0.56 thf(fact_143_equal__neg__zero,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( uminus_uminus_a @ A ) )
% 0.25/0.56 = ( A = zero_zero_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % equal_neg_zero
% 0.25/0.56 thf(fact_144_neg__equal__0__iff__equal,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( ( uminus_uminus_poly_a @ A )
% 0.25/0.56 = zero_zero_poly_a )
% 0.25/0.56 = ( A = zero_zero_poly_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_equal_0_iff_equal
% 0.25/0.56 thf(fact_145_neg__equal__0__iff__equal,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( ( uminus_uminus_a @ A )
% 0.25/0.56 = zero_zero_a )
% 0.25/0.56 = ( A = zero_zero_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_equal_0_iff_equal
% 0.25/0.56 thf(fact_146_neg__0__equal__iff__equal,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( zero_zero_poly_a
% 0.25/0.56 = ( uminus_uminus_poly_a @ A ) )
% 0.25/0.56 = ( zero_zero_poly_a = A ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_0_equal_iff_equal
% 0.25/0.56 thf(fact_147_neg__0__equal__iff__equal,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( zero_zero_a
% 0.25/0.56 = ( uminus_uminus_a @ A ) )
% 0.25/0.56 = ( zero_zero_a = A ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_0_equal_iff_equal
% 0.25/0.56 thf(fact_148_add_Oinverse__neutral,axiom,
% 0.25/0.56 ( ( uminus_uminus_poly_a @ zero_zero_poly_a )
% 0.25/0.56 = zero_zero_poly_a ) ).
% 0.25/0.56
% 0.25/0.56 % add.inverse_neutral
% 0.25/0.56 thf(fact_149_add_Oinverse__neutral,axiom,
% 0.25/0.56 ( ( uminus_uminus_a @ zero_zero_a )
% 0.25/0.56 = zero_zero_a ) ).
% 0.25/0.56
% 0.25/0.56 % add.inverse_neutral
% 0.25/0.56 thf(fact_150_mult_Oright__neutral,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( times_times_a @ A @ one_one_a )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % mult.right_neutral
% 0.25/0.56 thf(fact_151_mult_Oright__neutral,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ A @ one_one_poly_a )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % mult.right_neutral
% 0.25/0.56 thf(fact_152_mult_Oright__neutral,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ( ( times_times_nat @ A @ one_one_nat )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % mult.right_neutral
% 0.25/0.56 thf(fact_153_mult_Oleft__neutral,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( times_times_a @ one_one_a @ A )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % mult.left_neutral
% 0.25/0.56 thf(fact_154_mult_Oleft__neutral,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ one_one_poly_a @ A )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % mult.left_neutral
% 0.25/0.56 thf(fact_155_mult_Oleft__neutral,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ( ( times_times_nat @ one_one_nat @ A )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % mult.left_neutral
% 0.25/0.56 thf(fact_156_neg__less__iff__less,axiom,
% 0.25/0.56 ! [B: poly_a,A: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ B ) @ ( uminus_uminus_poly_a @ A ) )
% 0.25/0.56 = ( ord_less_poly_a @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_less_iff_less
% 0.25/0.56 thf(fact_157_neg__less__iff__less,axiom,
% 0.25/0.56 ! [B: a,A: a] :
% 0.25/0.56 ( ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) )
% 0.25/0.56 = ( ord_less_a @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % neg_less_iff_less
% 0.25/0.56 thf(fact_158_mult__minus__right,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
% 0.25/0.56 = ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_minus_right
% 0.25/0.56 thf(fact_159_mult__minus__right,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( times_times_a @ A @ ( uminus_uminus_a @ B ) )
% 0.25/0.56 = ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_minus_right
% 0.25/0.56 thf(fact_160_minus__mult__minus,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ ( uminus_uminus_poly_a @ B ) )
% 0.25/0.56 = ( times_times_poly_a @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % minus_mult_minus
% 0.25/0.56 thf(fact_161_minus__mult__minus,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( times_times_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
% 0.25/0.56 = ( times_times_a @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % minus_mult_minus
% 0.25/0.56 thf(fact_162_mult__minus__left,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
% 0.25/0.56 = ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_minus_left
% 0.25/0.56 thf(fact_163_mult__minus__left,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
% 0.25/0.56 = ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_minus_left
% 0.25/0.56 thf(fact_164_append_Oright__neutral,axiom,
% 0.25/0.56 ! [A: list_a] :
% 0.25/0.56 ( ( append_a @ A @ nil_a )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % append.right_neutral
% 0.25/0.56 thf(fact_165_append__is__Nil__conv,axiom,
% 0.25/0.56 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.56 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.56 = nil_a )
% 0.25/0.56 = ( ( Xs = nil_a )
% 0.25/0.56 & ( Ys2 = nil_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_is_Nil_conv
% 0.25/0.56 thf(fact_166_Nil__is__append__conv,axiom,
% 0.25/0.56 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.56 ( ( nil_a
% 0.25/0.56 = ( append_a @ Xs @ Ys2 ) )
% 0.25/0.56 = ( ( Xs = nil_a )
% 0.25/0.56 & ( Ys2 = nil_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Nil_is_append_conv
% 0.25/0.56 thf(fact_167_self__append__conv2,axiom,
% 0.25/0.56 ! [Ys2: list_a,Xs: list_a] :
% 0.25/0.56 ( ( Ys2
% 0.25/0.56 = ( append_a @ Xs @ Ys2 ) )
% 0.25/0.56 = ( Xs = nil_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % self_append_conv2
% 0.25/0.56 thf(fact_168_append__self__conv2,axiom,
% 0.25/0.56 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.56 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.56 = Ys2 )
% 0.25/0.56 = ( Xs = nil_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_self_conv2
% 0.25/0.56 thf(fact_169_self__append__conv,axiom,
% 0.25/0.56 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.56 ( ( Xs
% 0.25/0.56 = ( append_a @ Xs @ Ys2 ) )
% 0.25/0.56 = ( Ys2 = nil_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % self_append_conv
% 0.25/0.56 thf(fact_170_append__self__conv,axiom,
% 0.25/0.56 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.56 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.56 = Xs )
% 0.25/0.56 = ( Ys2 = nil_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_self_conv
% 0.25/0.56 thf(fact_171_append__Nil2,axiom,
% 0.25/0.56 ! [Xs: list_a] :
% 0.25/0.56 ( ( append_a @ Xs @ nil_a )
% 0.25/0.56 = Xs ) ).
% 0.25/0.56
% 0.25/0.56 % append_Nil2
% 0.25/0.56 thf(fact_172_smult__one,axiom,
% 0.25/0.56 ! [C: a] :
% 0.25/0.56 ( ( smult_a @ C @ one_one_poly_a )
% 0.25/0.56 = ( pCons_a @ C @ zero_zero_poly_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % smult_one
% 0.25/0.56 thf(fact_173_zero__reorient,axiom,
% 0.25/0.56 ! [X: poly_a] :
% 0.25/0.56 ( ( zero_zero_poly_a = X )
% 0.25/0.56 = ( X = zero_zero_poly_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_reorient
% 0.25/0.56 thf(fact_174_zero__reorient,axiom,
% 0.25/0.56 ! [X: a] :
% 0.25/0.56 ( ( zero_zero_a = X )
% 0.25/0.56 = ( X = zero_zero_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_reorient
% 0.25/0.56 thf(fact_175_zero__reorient,axiom,
% 0.25/0.56 ! [X: nat] :
% 0.25/0.56 ( ( zero_zero_nat = X )
% 0.25/0.56 = ( X = zero_zero_nat ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_reorient
% 0.25/0.56 thf(fact_176_linorder__neqE__linordered__idom,axiom,
% 0.25/0.56 ! [X: a,Y3: a] :
% 0.25/0.56 ( ( X != Y3 )
% 0.25/0.56 => ( ~ ( ord_less_a @ X @ Y3 )
% 0.25/0.56 => ( ord_less_a @ Y3 @ X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_neqE_linordered_idom
% 0.25/0.56 thf(fact_177_linorder__neqE__linordered__idom,axiom,
% 0.25/0.56 ! [X: poly_a,Y3: poly_a] :
% 0.25/0.56 ( ( X != Y3 )
% 0.25/0.56 => ( ~ ( ord_less_poly_a @ X @ Y3 )
% 0.25/0.56 => ( ord_less_poly_a @ Y3 @ X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_neqE_linordered_idom
% 0.25/0.56 thf(fact_178_mult_Oleft__commute,axiom,
% 0.25/0.56 ! [B: poly_a,A: poly_a,C: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ B @ ( times_times_poly_a @ A @ C ) )
% 0.25/0.56 = ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult.left_commute
% 0.25/0.56 thf(fact_179_mult_Oleft__commute,axiom,
% 0.25/0.56 ! [B: nat,A: nat,C: nat] :
% 0.25/0.56 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.25/0.56 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult.left_commute
% 0.25/0.56 thf(fact_180_mult_Ocommute,axiom,
% 0.25/0.56 ( times_times_poly_a
% 0.25/0.56 = ( ^ [A3: poly_a,B3: poly_a] : ( times_times_poly_a @ B3 @ A3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult.commute
% 0.25/0.56 thf(fact_181_mult_Ocommute,axiom,
% 0.25/0.56 ( times_times_nat
% 0.25/0.56 = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult.commute
% 0.25/0.56 thf(fact_182_mult_Oassoc,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
% 0.25/0.56 = ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult.assoc
% 0.25/0.56 thf(fact_183_mult_Oassoc,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C: nat] :
% 0.25/0.56 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.56 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult.assoc
% 0.25/0.56 thf(fact_184_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
% 0.25/0.56 = ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ab_semigroup_mult_class.mult_ac(1)
% 0.25/0.56 thf(fact_185_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C: nat] :
% 0.25/0.56 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.56 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ab_semigroup_mult_class.mult_ac(1)
% 0.25/0.56 thf(fact_186_one__reorient,axiom,
% 0.25/0.56 ! [X: a] :
% 0.25/0.56 ( ( one_one_a = X )
% 0.25/0.56 = ( X = one_one_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % one_reorient
% 0.25/0.56 thf(fact_187_one__reorient,axiom,
% 0.25/0.56 ! [X: nat] :
% 0.25/0.56 ( ( one_one_nat = X )
% 0.25/0.56 = ( X = one_one_nat ) ) ).
% 0.25/0.56
% 0.25/0.56 % one_reorient
% 0.25/0.56 thf(fact_188_minus__equation__iff,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ( uminus_uminus_a @ A )
% 0.25/0.56 = B )
% 0.25/0.56 = ( ( uminus_uminus_a @ B )
% 0.25/0.56 = A ) ) ).
% 0.25/0.56
% 0.25/0.56 % minus_equation_iff
% 0.25/0.56 thf(fact_189_equation__minus__iff,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( uminus_uminus_a @ B ) )
% 0.25/0.56 = ( B
% 0.25/0.56 = ( uminus_uminus_a @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % equation_minus_iff
% 0.25/0.56 thf(fact_190_not__Cons__self2,axiom,
% 0.25/0.56 ! [X: a,Xs: list_a] :
% 0.25/0.56 ( ( cons_a @ X @ Xs )
% 0.25/0.56 != Xs ) ).
% 0.25/0.56
% 0.25/0.56 % not_Cons_self2
% 0.25/0.56 thf(fact_191_append__eq__append__conv2,axiom,
% 0.25/0.56 ! [Xs: list_a,Ys2: list_a,Zs: list_a,Ts: list_a] :
% 0.25/0.56 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.56 = ( append_a @ Zs @ Ts ) )
% 0.25/0.56 = ( ? [Us: list_a] :
% 0.25/0.56 ( ( ( Xs
% 0.25/0.56 = ( append_a @ Zs @ Us ) )
% 0.25/0.56 & ( ( append_a @ Us @ Ys2 )
% 0.25/0.56 = Ts ) )
% 0.25/0.56 | ( ( ( append_a @ Xs @ Us )
% 0.25/0.56 = Zs )
% 0.25/0.56 & ( Ys2
% 0.25/0.56 = ( append_a @ Us @ Ts ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_eq_append_conv2
% 0.25/0.56 thf(fact_192_append__eq__appendI,axiom,
% 0.25/0.56 ! [Xs: list_a,Xs1: list_a,Zs: list_a,Ys2: list_a,Us2: list_a] :
% 0.25/0.56 ( ( ( append_a @ Xs @ Xs1 )
% 0.25/0.56 = Zs )
% 0.25/0.56 => ( ( Ys2
% 0.25/0.56 = ( append_a @ Xs1 @ Us2 ) )
% 0.25/0.56 => ( ( append_a @ Xs @ Ys2 )
% 0.25/0.56 = ( append_a @ Zs @ Us2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_eq_appendI
% 0.25/0.56 thf(fact_193_sign__changes__two,axiom,
% 0.25/0.56 ! [X: a,Y3: a] :
% 0.25/0.56 ( ( ( ( ( ord_less_a @ zero_zero_a @ X )
% 0.25/0.56 & ( ord_less_a @ Y3 @ zero_zero_a ) )
% 0.25/0.56 | ( ( ord_less_a @ X @ zero_zero_a )
% 0.25/0.56 & ( ord_less_a @ zero_zero_a @ Y3 ) ) )
% 0.25/0.56 => ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ Y3 @ nil_a ) ) )
% 0.25/0.56 = one_one_nat ) )
% 0.25/0.56 & ( ~ ( ( ( ord_less_a @ zero_zero_a @ X )
% 0.25/0.56 & ( ord_less_a @ Y3 @ zero_zero_a ) )
% 0.25/0.56 | ( ( ord_less_a @ X @ zero_zero_a )
% 0.25/0.56 & ( ord_less_a @ zero_zero_a @ Y3 ) ) )
% 0.25/0.56 => ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ Y3 @ nil_a ) ) )
% 0.25/0.56 = zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % sign_changes_two
% 0.25/0.56 thf(fact_194_sign__changes__two,axiom,
% 0.25/0.56 ! [X: poly_a,Y3: poly_a] :
% 0.25/0.56 ( ( ( ( ( ord_less_poly_a @ zero_zero_poly_a @ X )
% 0.25/0.56 & ( ord_less_poly_a @ Y3 @ zero_zero_poly_a ) )
% 0.25/0.56 | ( ( ord_less_poly_a @ X @ zero_zero_poly_a )
% 0.25/0.56 & ( ord_less_poly_a @ zero_zero_poly_a @ Y3 ) ) )
% 0.25/0.56 => ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ Y3 @ nil_poly_a ) ) )
% 0.25/0.56 = one_one_nat ) )
% 0.25/0.56 & ( ~ ( ( ( ord_less_poly_a @ zero_zero_poly_a @ X )
% 0.25/0.56 & ( ord_less_poly_a @ Y3 @ zero_zero_poly_a ) )
% 0.25/0.56 | ( ( ord_less_poly_a @ X @ zero_zero_poly_a )
% 0.25/0.56 & ( ord_less_poly_a @ zero_zero_poly_a @ Y3 ) ) )
% 0.25/0.56 => ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ Y3 @ nil_poly_a ) ) )
% 0.25/0.56 = zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % sign_changes_two
% 0.25/0.56 thf(fact_195_zero__less__iff__neq__zero,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.25/0.56 = ( N != zero_zero_nat ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_less_iff_neq_zero
% 0.25/0.56 thf(fact_196_gr__implies__not__zero,axiom,
% 0.25/0.56 ! [M: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ M @ N )
% 0.25/0.56 => ( N != zero_zero_nat ) ) ).
% 0.25/0.56
% 0.25/0.56 % gr_implies_not_zero
% 0.25/0.56 thf(fact_197_not__less__zero,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % not_less_zero
% 0.25/0.56 thf(fact_198_gr__zeroI,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( N != zero_zero_nat )
% 0.25/0.56 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % gr_zeroI
% 0.25/0.56 thf(fact_199_less__numeral__extra_I3_J,axiom,
% 0.25/0.56 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(3)
% 0.25/0.56 thf(fact_200_less__numeral__extra_I3_J,axiom,
% 0.25/0.56 ~ ( ord_less_a @ zero_zero_a @ zero_zero_a ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(3)
% 0.25/0.56 thf(fact_201_less__numeral__extra_I3_J,axiom,
% 0.25/0.56 ~ ( ord_less_poly_a @ zero_zero_poly_a @ zero_zero_poly_a ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(3)
% 0.25/0.56 thf(fact_202_mult__right__cancel,axiom,
% 0.25/0.56 ! [C: a,A: a,B: a] :
% 0.25/0.56 ( ( C != zero_zero_a )
% 0.25/0.56 => ( ( ( times_times_a @ A @ C )
% 0.25/0.56 = ( times_times_a @ B @ C ) )
% 0.25/0.56 = ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_right_cancel
% 0.25/0.56 thf(fact_203_mult__right__cancel,axiom,
% 0.25/0.56 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( C != zero_zero_poly_a )
% 0.25/0.56 => ( ( ( times_times_poly_a @ A @ C )
% 0.25/0.56 = ( times_times_poly_a @ B @ C ) )
% 0.25/0.56 = ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_right_cancel
% 0.25/0.56 thf(fact_204_mult__right__cancel,axiom,
% 0.25/0.56 ! [C: nat,A: nat,B: nat] :
% 0.25/0.56 ( ( C != zero_zero_nat )
% 0.25/0.56 => ( ( ( times_times_nat @ A @ C )
% 0.25/0.56 = ( times_times_nat @ B @ C ) )
% 0.25/0.56 = ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_right_cancel
% 0.25/0.56 thf(fact_205_mult__left__cancel,axiom,
% 0.25/0.56 ! [C: a,A: a,B: a] :
% 0.25/0.56 ( ( C != zero_zero_a )
% 0.25/0.56 => ( ( ( times_times_a @ C @ A )
% 0.25/0.56 = ( times_times_a @ C @ B ) )
% 0.25/0.56 = ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_left_cancel
% 0.25/0.56 thf(fact_206_mult__left__cancel,axiom,
% 0.25/0.56 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( C != zero_zero_poly_a )
% 0.25/0.56 => ( ( ( times_times_poly_a @ C @ A )
% 0.25/0.56 = ( times_times_poly_a @ C @ B ) )
% 0.25/0.56 = ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_left_cancel
% 0.25/0.56 thf(fact_207_mult__left__cancel,axiom,
% 0.25/0.56 ! [C: nat,A: nat,B: nat] :
% 0.25/0.56 ( ( C != zero_zero_nat )
% 0.25/0.56 => ( ( ( times_times_nat @ C @ A )
% 0.25/0.56 = ( times_times_nat @ C @ B ) )
% 0.25/0.56 = ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_left_cancel
% 0.25/0.56 thf(fact_208_no__zero__divisors,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( A != zero_zero_a )
% 0.25/0.56 => ( ( B != zero_zero_a )
% 0.25/0.56 => ( ( times_times_a @ A @ B )
% 0.25/0.56 != zero_zero_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % no_zero_divisors
% 0.25/0.56 thf(fact_209_no__zero__divisors,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( A != zero_zero_poly_a )
% 0.25/0.56 => ( ( B != zero_zero_poly_a )
% 0.25/0.56 => ( ( times_times_poly_a @ A @ B )
% 0.25/0.56 != zero_zero_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % no_zero_divisors
% 0.25/0.56 thf(fact_210_no__zero__divisors,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( A != zero_zero_nat )
% 0.25/0.56 => ( ( B != zero_zero_nat )
% 0.25/0.56 => ( ( times_times_nat @ A @ B )
% 0.25/0.56 != zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % no_zero_divisors
% 0.25/0.56 thf(fact_211_divisors__zero,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ( times_times_a @ A @ B )
% 0.25/0.56 = zero_zero_a )
% 0.25/0.56 => ( ( A = zero_zero_a )
% 0.25/0.56 | ( B = zero_zero_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % divisors_zero
% 0.25/0.56 thf(fact_212_divisors__zero,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ( times_times_poly_a @ A @ B )
% 0.25/0.56 = zero_zero_poly_a )
% 0.25/0.56 => ( ( A = zero_zero_poly_a )
% 0.25/0.56 | ( B = zero_zero_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % divisors_zero
% 0.25/0.56 thf(fact_213_divisors__zero,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ A @ B )
% 0.25/0.56 = zero_zero_nat )
% 0.25/0.56 => ( ( A = zero_zero_nat )
% 0.25/0.56 | ( B = zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % divisors_zero
% 0.25/0.56 thf(fact_214_mult__not__zero,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ( times_times_a @ A @ B )
% 0.25/0.56 != zero_zero_a )
% 0.25/0.56 => ( ( A != zero_zero_a )
% 0.25/0.56 & ( B != zero_zero_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_not_zero
% 0.25/0.56 thf(fact_215_mult__not__zero,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ( times_times_poly_a @ A @ B )
% 0.25/0.56 != zero_zero_poly_a )
% 0.25/0.56 => ( ( A != zero_zero_poly_a )
% 0.25/0.56 & ( B != zero_zero_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_not_zero
% 0.25/0.56 thf(fact_216_mult__not__zero,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ A @ B )
% 0.25/0.56 != zero_zero_nat )
% 0.25/0.56 => ( ( A != zero_zero_nat )
% 0.25/0.56 & ( B != zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_not_zero
% 0.25/0.56 thf(fact_217_zero__neq__one,axiom,
% 0.25/0.56 zero_zero_poly_a != one_one_poly_a ).
% 0.25/0.56
% 0.25/0.56 % zero_neq_one
% 0.25/0.56 thf(fact_218_zero__neq__one,axiom,
% 0.25/0.56 zero_zero_a != one_one_a ).
% 0.25/0.56
% 0.25/0.56 % zero_neq_one
% 0.25/0.56 thf(fact_219_zero__neq__one,axiom,
% 0.25/0.56 zero_zero_nat != one_one_nat ).
% 0.25/0.56
% 0.25/0.56 % zero_neq_one
% 0.25/0.56 thf(fact_220_less__numeral__extra_I4_J,axiom,
% 0.25/0.56 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(4)
% 0.25/0.56 thf(fact_221_less__numeral__extra_I4_J,axiom,
% 0.25/0.56 ~ ( ord_less_a @ one_one_a @ one_one_a ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(4)
% 0.25/0.56 thf(fact_222_less__numeral__extra_I4_J,axiom,
% 0.25/0.56 ~ ( ord_less_poly_a @ one_one_poly_a @ one_one_poly_a ) ).
% 0.25/0.56
% 0.25/0.56 % less_numeral_extra(4)
% 0.25/0.56 thf(fact_223_mult_Ocomm__neutral,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( times_times_a @ A @ one_one_a )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % mult.comm_neutral
% 0.25/0.56 thf(fact_224_mult_Ocomm__neutral,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ A @ one_one_poly_a )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % mult.comm_neutral
% 0.25/0.56 thf(fact_225_mult_Ocomm__neutral,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ( ( times_times_nat @ A @ one_one_nat )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % mult.comm_neutral
% 0.25/0.56 thf(fact_226_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.56 ! [A: a] :
% 0.25/0.56 ( ( times_times_a @ one_one_a @ A )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % comm_monoid_mult_class.mult_1
% 0.25/0.56 thf(fact_227_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.56 ! [A: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ one_one_poly_a @ A )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % comm_monoid_mult_class.mult_1
% 0.25/0.56 thf(fact_228_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ( ( times_times_nat @ one_one_nat @ A )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % comm_monoid_mult_class.mult_1
% 0.25/0.56 thf(fact_229_minus__less__iff,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
% 0.25/0.56 = ( ord_less_poly_a @ ( uminus_uminus_poly_a @ B ) @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % minus_less_iff
% 0.25/0.56 thf(fact_230_minus__less__iff,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
% 0.25/0.56 = ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % minus_less_iff
% 0.25/0.56 thf(fact_231_less__minus__iff,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
% 0.25/0.56 = ( ord_less_poly_a @ B @ ( uminus_uminus_poly_a @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_minus_iff
% 0.25/0.56 thf(fact_232_less__minus__iff,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
% 0.25/0.56 = ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_minus_iff
% 0.25/0.56 thf(fact_233_minus__mult__commute,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
% 0.25/0.56 = ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % minus_mult_commute
% 0.25/0.56 thf(fact_234_minus__mult__commute,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
% 0.25/0.56 = ( times_times_a @ A @ ( uminus_uminus_a @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % minus_mult_commute
% 0.25/0.56 thf(fact_235_square__eq__iff,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ( times_times_poly_a @ A @ A )
% 0.25/0.56 = ( times_times_poly_a @ B @ B ) )
% 0.25/0.56 = ( ( A = B )
% 0.25/0.56 | ( A
% 0.25/0.56 = ( uminus_uminus_poly_a @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % square_eq_iff
% 0.25/0.56 thf(fact_236_square__eq__iff,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ( times_times_a @ A @ A )
% 0.25/0.56 = ( times_times_a @ B @ B ) )
% 0.25/0.56 = ( ( A = B )
% 0.25/0.56 | ( A
% 0.25/0.56 = ( uminus_uminus_a @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % square_eq_iff
% 0.25/0.56 thf(fact_237_one__neq__neg__one,axiom,
% 0.25/0.56 ( one_one_a
% 0.25/0.56 != ( uminus_uminus_a @ one_one_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % one_neq_neg_one
% 0.25/0.56 thf(fact_238_strict__sorted_Oinduct,axiom,
% 0.25/0.56 ! [P3: list_a > $o,A0: list_a] :
% 0.25/0.56 ( ( P3 @ nil_a )
% 0.25/0.56 => ( ! [X2: a,Ys: list_a] :
% 0.25/0.56 ( ( P3 @ Ys )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ Ys ) ) )
% 0.25/0.56 => ( P3 @ A0 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % strict_sorted.induct
% 0.25/0.56 thf(fact_239_strict__sorted_Ocases,axiom,
% 0.25/0.56 ! [X: list_a] :
% 0.25/0.56 ( ( X != nil_a )
% 0.25/0.56 => ~ ! [X2: a,Ys: list_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( cons_a @ X2 @ Ys ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % strict_sorted.cases
% 0.25/0.56 thf(fact_240_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.56 ! [P3: ( a > a ) > list_a > list_a > $o,A0: a > a,A1: list_a,A22: list_a] :
% 0.25/0.56 ( ! [F2: a > a,X_1: list_a] : ( P3 @ F2 @ nil_a @ X_1 )
% 0.25/0.56 => ( ! [F2: a > a,A2: a,As2: list_a,Bs: list_a] :
% 0.25/0.56 ( ( P3 @ F2 @ As2 @ ( cons_a @ ( F2 @ A2 ) @ Bs ) )
% 0.25/0.56 => ( P3 @ F2 @ ( cons_a @ A2 @ As2 ) @ Bs ) )
% 0.25/0.56 => ( P3 @ A0 @ A1 @ A22 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % map_tailrec_rev.induct
% 0.25/0.56 thf(fact_241_list__nonempty__induct,axiom,
% 0.25/0.56 ! [Xs: list_a,P3: list_a > $o] :
% 0.25/0.56 ( ( Xs != nil_a )
% 0.25/0.56 => ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
% 0.25/0.56 => ( ! [X2: a,Xs2: list_a] :
% 0.25/0.56 ( ( Xs2 != nil_a )
% 0.25/0.56 => ( ( P3 @ Xs2 )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ Xs2 ) ) ) )
% 0.25/0.56 => ( P3 @ Xs ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list_nonempty_induct
% 0.25/0.56 thf(fact_242_successively_Oinduct,axiom,
% 0.25/0.56 ! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.25/0.56 ( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
% 0.25/0.56 => ( ! [P5: a > a > $o,X2: a] : ( P3 @ P5 @ ( cons_a @ X2 @ nil_a ) )
% 0.25/0.56 => ( ! [P5: a > a > $o,X2: a,Y2: a,Xs2: list_a] :
% 0.25/0.56 ( ( P3 @ P5 @ ( cons_a @ Y2 @ Xs2 ) )
% 0.25/0.56 => ( P3 @ P5 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) )
% 0.25/0.56 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % successively.induct
% 0.25/0.56 thf(fact_243_remdups__adj_Oinduct,axiom,
% 0.25/0.56 ! [P3: list_a > $o,A0: list_a] :
% 0.25/0.56 ( ( P3 @ nil_a )
% 0.25/0.56 => ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
% 0.25/0.56 => ( ! [X2: a,Y2: a,Xs2: list_a] :
% 0.25/0.56 ( ( ( X2 = Y2 )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
% 0.25/0.56 => ( ( ( X2 != Y2 )
% 0.25/0.56 => ( P3 @ ( cons_a @ Y2 @ Xs2 ) ) )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) )
% 0.25/0.56 => ( P3 @ A0 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % remdups_adj.induct
% 0.25/0.56 thf(fact_244_sorted__wrt_Oinduct,axiom,
% 0.25/0.56 ! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.25/0.56 ( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
% 0.25/0.56 => ( ! [P5: a > a > $o,X2: a,Ys: list_a] :
% 0.25/0.56 ( ( P3 @ P5 @ Ys )
% 0.25/0.56 => ( P3 @ P5 @ ( cons_a @ X2 @ Ys ) ) )
% 0.25/0.56 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % sorted_wrt.induct
% 0.25/0.56 thf(fact_245_remdups__adj_Ocases,axiom,
% 0.25/0.56 ! [X: list_a] :
% 0.25/0.56 ( ( X != nil_a )
% 0.25/0.56 => ( ! [X2: a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( cons_a @ X2 @ nil_a ) )
% 0.25/0.56 => ~ ! [X2: a,Y2: a,Xs2: list_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % remdups_adj.cases
% 0.25/0.56 thf(fact_246_transpose_Ocases,axiom,
% 0.25/0.56 ! [X: list_list_a] :
% 0.25/0.56 ( ( X != nil_list_a )
% 0.25/0.56 => ( ! [Xss: list_list_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( cons_list_a @ nil_a @ Xss ) )
% 0.25/0.56 => ~ ! [X2: a,Xs2: list_a,Xss: list_list_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( cons_list_a @ ( cons_a @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % transpose.cases
% 0.25/0.56 thf(fact_247_shuffles_Oinduct,axiom,
% 0.25/0.56 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.25/0.56 ( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
% 0.25/0.56 => ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
% 0.25/0.56 => ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 0.25/0.56 ( ( P3 @ Xs2 @ ( cons_a @ Y2 @ Ys ) )
% 0.25/0.56 => ( ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) ) )
% 0.25/0.56 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % shuffles.induct
% 0.25/0.56 thf(fact_248_min__list_Oinduct,axiom,
% 0.25/0.56 ! [P3: list_a > $o,A0: list_a] :
% 0.25/0.56 ( ! [X2: a,Xs2: list_a] :
% 0.25/0.56 ( ! [X212: a,X222: list_a] :
% 0.25/0.56 ( ( Xs2
% 0.25/0.56 = ( cons_a @ X212 @ X222 ) )
% 0.25/0.56 => ( P3 @ Xs2 ) )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
% 0.25/0.56 => ( ( P3 @ nil_a )
% 0.25/0.56 => ( P3 @ A0 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % min_list.induct
% 0.25/0.56 thf(fact_249_min__list_Ocases,axiom,
% 0.25/0.56 ! [X: list_a] :
% 0.25/0.56 ( ! [X2: a,Xs2: list_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( cons_a @ X2 @ Xs2 ) )
% 0.25/0.56 => ( X = nil_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % min_list.cases
% 0.25/0.56 thf(fact_250_induct__list012,axiom,
% 0.25/0.56 ! [P3: list_a > $o,Xs: list_a] :
% 0.25/0.56 ( ( P3 @ nil_a )
% 0.25/0.56 => ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
% 0.25/0.56 => ( ! [X2: a,Y2: a,Zs2: list_a] :
% 0.25/0.56 ( ( P3 @ Zs2 )
% 0.25/0.56 => ( ( P3 @ ( cons_a @ Y2 @ Zs2 ) )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Zs2 ) ) ) ) )
% 0.25/0.56 => ( P3 @ Xs ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % induct_list012
% 0.25/0.56 thf(fact_251_splice_Oinduct,axiom,
% 0.25/0.56 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.25/0.56 ( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
% 0.25/0.56 => ( ! [X2: a,Xs2: list_a,Ys: list_a] :
% 0.25/0.56 ( ( P3 @ Ys @ Xs2 )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys ) )
% 0.25/0.56 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % splice.induct
% 0.25/0.56 thf(fact_252_list__induct2_H,axiom,
% 0.25/0.56 ! [P3: list_a > list_a > $o,Xs: list_a,Ys2: list_a] :
% 0.25/0.56 ( ( P3 @ nil_a @ nil_a )
% 0.25/0.56 => ( ! [X2: a,Xs2: list_a] : ( P3 @ ( cons_a @ X2 @ Xs2 ) @ nil_a )
% 0.25/0.56 => ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
% 0.25/0.56 => ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 0.25/0.56 ( ( P3 @ Xs2 @ Ys )
% 0.25/0.56 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
% 0.25/0.56 => ( P3 @ Xs @ Ys2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list_induct2'
% 0.25/0.56 thf(fact_253_neq__Nil__conv,axiom,
% 0.25/0.56 ! [Xs: list_a] :
% 0.25/0.56 ( ( Xs != nil_a )
% 0.25/0.56 = ( ? [Y4: a,Ys3: list_a] :
% 0.25/0.56 ( Xs
% 0.25/0.56 = ( cons_a @ Y4 @ Ys3 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % neq_Nil_conv
% 0.25/0.56 thf(fact_254_list_Oinducts,axiom,
% 0.25/0.56 ! [P3: list_a > $o,List: list_a] :
% 0.25/0.56 ( ( P3 @ nil_a )
% 0.25/0.56 => ( ! [X1: a,X23: list_a] :
% 0.25/0.56 ( ( P3 @ X23 )
% 0.25/0.56 => ( P3 @ ( cons_a @ X1 @ X23 ) ) )
% 0.25/0.56 => ( P3 @ List ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.inducts
% 0.25/0.56 thf(fact_255_list_Oexhaust,axiom,
% 0.25/0.56 ! [Y3: list_a] :
% 0.25/0.56 ( ( Y3 != nil_a )
% 0.25/0.56 => ~ ! [X213: a,X223: list_a] :
% 0.25/0.56 ( Y3
% 0.25/0.56 != ( cons_a @ X213 @ X223 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.exhaust
% 0.25/0.56 thf(fact_256_list_OdiscI,axiom,
% 0.25/0.56 ! [List: list_a,X21: a,X22: list_a] :
% 0.25/0.56 ( ( List
% 0.25/0.56 = ( cons_a @ X21 @ X22 ) )
% 0.25/0.56 => ( List != nil_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.discI
% 0.25/0.56 thf(fact_257_list_Odistinct_I1_J,axiom,
% 0.25/0.56 ! [X21: a,X22: list_a] :
% 0.25/0.56 ( nil_a
% 0.25/0.56 != ( cons_a @ X21 @ X22 ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.distinct(1)
% 0.25/0.56 thf(fact_258_append__Cons,axiom,
% 0.25/0.56 ! [X: a,Xs: list_a,Ys2: list_a] :
% 0.25/0.56 ( ( append_a @ ( cons_a @ X @ Xs ) @ Ys2 )
% 0.25/0.56 = ( cons_a @ X @ ( append_a @ Xs @ Ys2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_Cons
% 0.25/0.56 thf(fact_259_Cons__eq__appendI,axiom,
% 0.25/0.56 ! [X: a,Xs1: list_a,Ys2: list_a,Xs: list_a,Zs: list_a] :
% 0.25/0.56 ( ( ( cons_a @ X @ Xs1 )
% 0.25/0.56 = Ys2 )
% 0.25/0.56 => ( ( Xs
% 0.25/0.56 = ( append_a @ Xs1 @ Zs ) )
% 0.25/0.56 => ( ( cons_a @ X @ Xs )
% 0.25/0.56 = ( append_a @ Ys2 @ Zs ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Cons_eq_appendI
% 0.25/0.56 thf(fact_260_append_Oleft__neutral,axiom,
% 0.25/0.56 ! [A: list_a] :
% 0.25/0.56 ( ( append_a @ nil_a @ A )
% 0.25/0.56 = A ) ).
% 0.25/0.56
% 0.25/0.56 % append.left_neutral
% 0.25/0.56 thf(fact_261_append__Nil,axiom,
% 0.25/0.56 ! [Ys2: list_a] :
% 0.25/0.56 ( ( append_a @ nil_a @ Ys2 )
% 0.25/0.56 = Ys2 ) ).
% 0.25/0.56
% 0.25/0.56 % append_Nil
% 0.25/0.56 thf(fact_262_eq__Nil__appendI,axiom,
% 0.25/0.56 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.56 ( ( Xs = Ys2 )
% 0.25/0.56 => ( Xs
% 0.25/0.56 = ( append_a @ nil_a @ Ys2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_Nil_appendI
% 0.25/0.56 thf(fact_263_null__rec_I1_J,axiom,
% 0.25/0.56 ! [X: a,Xs: list_a] :
% 0.25/0.56 ~ ( null_a @ ( cons_a @ X @ Xs ) ) ).
% 0.25/0.56
% 0.25/0.56 % null_rec(1)
% 0.25/0.56 thf(fact_264_eq__Nil__null,axiom,
% 0.25/0.56 ! [Xs: list_a] :
% 0.25/0.56 ( ( Xs = nil_a )
% 0.25/0.56 = ( null_a @ Xs ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_Nil_null
% 0.25/0.56 thf(fact_265_null__rec_I2_J,axiom,
% 0.25/0.56 null_a @ nil_a ).
% 0.25/0.56
% 0.25/0.56 % null_rec(2)
% 0.25/0.56 thf(fact_266_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.56 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.25/0.56 thf(fact_267_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.25/0.56 ! [A: a,B: a,C: a] :
% 0.25/0.56 ( ( ord_less_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_a @ zero_zero_a @ C )
% 0.25/0.56 => ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.25/0.56 thf(fact_268_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.25/0.56 => ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.25/0.56 thf(fact_269_mult__less__cancel__right__disj,axiom,
% 0.25/0.56 ! [A: a,C: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) )
% 0.25/0.56 = ( ( ( ord_less_a @ zero_zero_a @ C )
% 0.25/0.56 & ( ord_less_a @ A @ B ) )
% 0.25/0.56 | ( ( ord_less_a @ C @ zero_zero_a )
% 0.25/0.56 & ( ord_less_a @ B @ A ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_cancel_right_disj
% 0.25/0.56 thf(fact_270_mult__less__cancel__right__disj,axiom,
% 0.25/0.56 ! [A: poly_a,C: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) )
% 0.25/0.56 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.25/0.56 & ( ord_less_poly_a @ A @ B ) )
% 0.25/0.56 | ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.25/0.56 & ( ord_less_poly_a @ B @ A ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_cancel_right_disj
% 0.25/0.56 thf(fact_271_mult__strict__right__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.56 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_right_mono
% 0.25/0.56 thf(fact_272_mult__strict__right__mono,axiom,
% 0.25/0.56 ! [A: a,B: a,C: a] :
% 0.25/0.56 ( ( ord_less_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_a @ zero_zero_a @ C )
% 0.25/0.56 => ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_right_mono
% 0.25/0.56 thf(fact_273_mult__strict__right__mono,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.25/0.56 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_right_mono
% 0.25/0.56 thf(fact_274_mult__strict__right__mono__neg,axiom,
% 0.25/0.56 ! [B: a,A: a,C: a] :
% 0.25/0.56 ( ( ord_less_a @ B @ A )
% 0.25/0.56 => ( ( ord_less_a @ C @ zero_zero_a )
% 0.25/0.56 => ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_right_mono_neg
% 0.25/0.56 thf(fact_275_mult__strict__right__mono__neg,axiom,
% 0.25/0.56 ! [B: poly_a,A: poly_a,C: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ B @ A )
% 0.25/0.56 => ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.25/0.56 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_right_mono_neg
% 0.25/0.56 thf(fact_276_mult__less__cancel__left__disj,axiom,
% 0.25/0.56 ! [C: a,A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) )
% 0.25/0.56 = ( ( ( ord_less_a @ zero_zero_a @ C )
% 0.25/0.56 & ( ord_less_a @ A @ B ) )
% 0.25/0.56 | ( ( ord_less_a @ C @ zero_zero_a )
% 0.25/0.56 & ( ord_less_a @ B @ A ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_cancel_left_disj
% 0.25/0.56 thf(fact_277_mult__less__cancel__left__disj,axiom,
% 0.25/0.56 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) )
% 0.25/0.56 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.25/0.56 & ( ord_less_poly_a @ A @ B ) )
% 0.25/0.56 | ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.25/0.56 & ( ord_less_poly_a @ B @ A ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_cancel_left_disj
% 0.25/0.56 thf(fact_278_mult__strict__left__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.56 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_left_mono
% 0.25/0.56 thf(fact_279_mult__strict__left__mono,axiom,
% 0.25/0.56 ! [A: a,B: a,C: a] :
% 0.25/0.56 ( ( ord_less_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_a @ zero_zero_a @ C )
% 0.25/0.56 => ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_left_mono
% 0.25/0.56 thf(fact_280_mult__strict__left__mono,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.25/0.56 => ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_left_mono
% 0.25/0.56 thf(fact_281_mult__strict__left__mono__neg,axiom,
% 0.25/0.56 ! [B: a,A: a,C: a] :
% 0.25/0.56 ( ( ord_less_a @ B @ A )
% 0.25/0.56 => ( ( ord_less_a @ C @ zero_zero_a )
% 0.25/0.56 => ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_left_mono_neg
% 0.25/0.56 thf(fact_282_mult__strict__left__mono__neg,axiom,
% 0.25/0.56 ! [B: poly_a,A: poly_a,C: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ B @ A )
% 0.25/0.56 => ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.25/0.56 => ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_strict_left_mono_neg
% 0.25/0.56 thf(fact_283_mult__less__cancel__left__pos,axiom,
% 0.25/0.56 ! [C: a,A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ zero_zero_a @ C )
% 0.25/0.56 => ( ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) )
% 0.25/0.56 = ( ord_less_a @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_cancel_left_pos
% 0.25/0.56 thf(fact_284_mult__less__cancel__left__pos,axiom,
% 0.25/0.56 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.25/0.56 => ( ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) )
% 0.25/0.56 = ( ord_less_poly_a @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_cancel_left_pos
% 0.25/0.56 thf(fact_285_mult__less__cancel__left__neg,axiom,
% 0.25/0.56 ! [C: a,A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ C @ zero_zero_a )
% 0.25/0.56 => ( ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) )
% 0.25/0.56 = ( ord_less_a @ B @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_cancel_left_neg
% 0.25/0.56 thf(fact_286_mult__less__cancel__left__neg,axiom,
% 0.25/0.56 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.25/0.56 => ( ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) )
% 0.25/0.56 = ( ord_less_poly_a @ B @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_cancel_left_neg
% 0.25/0.56 thf(fact_287_zero__less__mult__pos2,axiom,
% 0.25/0.56 ! [B: nat,A: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.25/0.56 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.56 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_less_mult_pos2
% 0.25/0.56 thf(fact_288_zero__less__mult__pos2,axiom,
% 0.25/0.56 ! [B: a,A: a] :
% 0.25/0.56 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ B @ A ) )
% 0.25/0.56 => ( ( ord_less_a @ zero_zero_a @ A )
% 0.25/0.56 => ( ord_less_a @ zero_zero_a @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_less_mult_pos2
% 0.25/0.56 thf(fact_289_zero__less__mult__pos2,axiom,
% 0.25/0.56 ! [B: poly_a,A: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ B @ A ) )
% 0.25/0.56 => ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.56 => ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_less_mult_pos2
% 0.25/0.56 thf(fact_290_zero__less__mult__pos,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.25/0.56 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.56 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_less_mult_pos
% 0.25/0.56 thf(fact_291_zero__less__mult__pos,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
% 0.25/0.56 => ( ( ord_less_a @ zero_zero_a @ A )
% 0.25/0.56 => ( ord_less_a @ zero_zero_a @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_less_mult_pos
% 0.25/0.56 thf(fact_292_zero__less__mult__pos,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
% 0.25/0.56 => ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.56 => ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_less_mult_pos
% 0.25/0.56 thf(fact_293_zero__less__mult__iff,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
% 0.25/0.56 = ( ( ( ord_less_a @ zero_zero_a @ A )
% 0.25/0.56 & ( ord_less_a @ zero_zero_a @ B ) )
% 0.25/0.56 | ( ( ord_less_a @ A @ zero_zero_a )
% 0.25/0.56 & ( ord_less_a @ B @ zero_zero_a ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_less_mult_iff
% 0.25/0.56 thf(fact_294_zero__less__mult__iff,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
% 0.25/0.56 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.56 & ( ord_less_poly_a @ zero_zero_poly_a @ B ) )
% 0.25/0.56 | ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
% 0.25/0.56 & ( ord_less_poly_a @ B @ zero_zero_poly_a ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % zero_less_mult_iff
% 0.25/0.56 thf(fact_295_mult__pos__neg2,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.56 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.25/0.56 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_pos_neg2
% 0.25/0.56 thf(fact_296_mult__pos__neg2,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ zero_zero_a @ A )
% 0.25/0.56 => ( ( ord_less_a @ B @ zero_zero_a )
% 0.25/0.56 => ( ord_less_a @ ( times_times_a @ B @ A ) @ zero_zero_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_pos_neg2
% 0.25/0.56 thf(fact_297_mult__pos__neg2,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.56 => ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
% 0.25/0.56 => ( ord_less_poly_a @ ( times_times_poly_a @ B @ A ) @ zero_zero_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_pos_neg2
% 0.25/0.56 thf(fact_298_mult__pos__pos,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.56 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.56 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_pos_pos
% 0.25/0.56 thf(fact_299_mult__pos__pos,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ zero_zero_a @ A )
% 0.25/0.56 => ( ( ord_less_a @ zero_zero_a @ B )
% 0.25/0.56 => ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_pos_pos
% 0.25/0.56 thf(fact_300_mult__pos__pos,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.56 => ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
% 0.25/0.56 => ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_pos_pos
% 0.25/0.56 thf(fact_301_mult__pos__neg,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.56 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.25/0.56 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_pos_neg
% 0.25/0.56 thf(fact_302_mult__pos__neg,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ zero_zero_a @ A )
% 0.25/0.56 => ( ( ord_less_a @ B @ zero_zero_a )
% 0.25/0.56 => ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_pos_neg
% 0.25/0.56 thf(fact_303_mult__pos__neg,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.56 => ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
% 0.25/0.56 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_pos_neg
% 0.25/0.56 thf(fact_304_mult__neg__pos,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.25/0.56 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.56 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_neg_pos
% 0.25/0.56 thf(fact_305_mult__neg__pos,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ A @ zero_zero_a )
% 0.25/0.56 => ( ( ord_less_a @ zero_zero_a @ B )
% 0.25/0.56 => ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_neg_pos
% 0.25/0.56 thf(fact_306_mult__neg__pos,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
% 0.25/0.56 => ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
% 0.25/0.56 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_neg_pos
% 0.25/0.56 thf(fact_307_mult__less__0__iff,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a )
% 0.25/0.56 = ( ( ( ord_less_a @ zero_zero_a @ A )
% 0.25/0.56 & ( ord_less_a @ B @ zero_zero_a ) )
% 0.25/0.56 | ( ( ord_less_a @ A @ zero_zero_a )
% 0.25/0.56 & ( ord_less_a @ zero_zero_a @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_0_iff
% 0.25/0.56 thf(fact_308_mult__less__0__iff,axiom,
% 0.25/0.56 ! [A: poly_a,B: poly_a] :
% 0.25/0.56 ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a )
% 0.25/0.56 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.25/0.56 & ( ord_less_poly_a @ B @ zero_zero_poly_a ) )
% 0.25/0.56 | ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
% 0.25/0.56 & ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_0_iff
% 0.25/0.56 thf(fact_309_nat__mult__less__cancel__disj,axiom,
% 0.25/0.56 ! [K: nat,M: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.25/0.56 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.56 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_mult_less_cancel_disj
% 0.25/0.56 thf(fact_310_nat__0__less__mult__iff,axiom,
% 0.25/0.56 ! [M: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.25/0.56 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.56 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_0_less_mult_iff
% 0.25/0.56 thf(fact_311_mult__less__cancel2,axiom,
% 0.25/0.56 ! [M: nat,K: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.25/0.56 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.56 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_cancel2
% 0.25/0.56 thf(fact_312_mult__cancel2,axiom,
% 0.25/0.56 ! [M: nat,K: nat,N: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ M @ K )
% 0.25/0.56 = ( times_times_nat @ N @ K ) )
% 0.25/0.56 = ( ( M = N )
% 0.25/0.56 | ( K = zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel2
% 0.25/0.56 thf(fact_313_neq0__conv,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( N != zero_zero_nat )
% 0.25/0.56 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % neq0_conv
% 0.25/0.56 thf(fact_314_less__nat__zero__code,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % less_nat_zero_code
% 0.25/0.56 thf(fact_315_bot__nat__0_Onot__eq__extremum,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ( ( A != zero_zero_nat )
% 0.25/0.56 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % bot_nat_0.not_eq_extremum
% 0.25/0.56 thf(fact_316_mult__is__0,axiom,
% 0.25/0.56 ! [M: nat,N: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ M @ N )
% 0.25/0.56 = zero_zero_nat )
% 0.25/0.56 = ( ( M = zero_zero_nat )
% 0.25/0.56 | ( N = zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_is_0
% 0.25/0.56 thf(fact_317_mult__0__right,axiom,
% 0.25/0.56 ! [M: nat] :
% 0.25/0.56 ( ( times_times_nat @ M @ zero_zero_nat )
% 0.25/0.56 = zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % mult_0_right
% 0.25/0.56 thf(fact_318_mult__cancel1,axiom,
% 0.25/0.56 ! [K: nat,M: nat,N: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ K @ M )
% 0.25/0.56 = ( times_times_nat @ K @ N ) )
% 0.25/0.56 = ( ( M = N )
% 0.25/0.56 | ( K = zero_zero_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_cancel1
% 0.25/0.56 thf(fact_319_nat__1__eq__mult__iff,axiom,
% 0.25/0.56 ! [M: nat,N: nat] :
% 0.25/0.56 ( ( one_one_nat
% 0.25/0.56 = ( times_times_nat @ M @ N ) )
% 0.25/0.56 = ( ( M = one_one_nat )
% 0.25/0.56 & ( N = one_one_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_1_eq_mult_iff
% 0.25/0.56 thf(fact_320_nat__mult__eq__1__iff,axiom,
% 0.25/0.56 ! [M: nat,N: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ M @ N )
% 0.25/0.56 = one_one_nat )
% 0.25/0.56 = ( ( M = one_one_nat )
% 0.25/0.56 & ( N = one_one_nat ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_mult_eq_1_iff
% 0.25/0.56 thf(fact_321_less__one,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ N @ one_one_nat )
% 0.25/0.56 = ( N = zero_zero_nat ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_one
% 0.25/0.56 thf(fact_322_nat__mult__1,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( times_times_nat @ one_one_nat @ N )
% 0.25/0.56 = N ) ).
% 0.25/0.56
% 0.25/0.56 % nat_mult_1
% 0.25/0.56 thf(fact_323_nat__mult__1__right,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( times_times_nat @ N @ one_one_nat )
% 0.25/0.56 = N ) ).
% 0.25/0.56
% 0.25/0.56 % nat_mult_1_right
% 0.25/0.56 thf(fact_324_linorder__neqE__nat,axiom,
% 0.25/0.56 ! [X: nat,Y3: nat] :
% 0.25/0.56 ( ( X != Y3 )
% 0.25/0.56 => ( ~ ( ord_less_nat @ X @ Y3 )
% 0.25/0.56 => ( ord_less_nat @ Y3 @ X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_neqE_nat
% 0.25/0.56 thf(fact_325_infinite__descent,axiom,
% 0.25/0.56 ! [P3: nat > $o,N: nat] :
% 0.25/0.56 ( ! [N2: nat] :
% 0.25/0.56 ( ~ ( P3 @ N2 )
% 0.25/0.56 => ? [M2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ M2 @ N2 )
% 0.25/0.56 & ~ ( P3 @ M2 ) ) )
% 0.25/0.56 => ( P3 @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % infinite_descent
% 0.25/0.56 thf(fact_326_nat__less__induct,axiom,
% 0.25/0.56 ! [P3: nat > $o,N: nat] :
% 0.25/0.56 ( ! [N2: nat] :
% 0.25/0.56 ( ! [M2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ M2 @ N2 )
% 0.25/0.56 => ( P3 @ M2 ) )
% 0.25/0.56 => ( P3 @ N2 ) )
% 0.25/0.56 => ( P3 @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_less_induct
% 0.25/0.56 thf(fact_327_less__irrefl__nat,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ N @ N ) ).
% 0.25/0.56
% 0.25/0.56 % less_irrefl_nat
% 0.25/0.56 thf(fact_328_less__not__refl3,axiom,
% 0.25/0.56 ! [S: nat,T: nat] :
% 0.25/0.56 ( ( ord_less_nat @ S @ T )
% 0.25/0.56 => ( S != T ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_not_refl3
% 0.25/0.56 thf(fact_329_less__not__refl2,axiom,
% 0.25/0.56 ! [N: nat,M: nat] :
% 0.25/0.56 ( ( ord_less_nat @ N @ M )
% 0.25/0.56 => ( M != N ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_not_refl2
% 0.25/0.56 thf(fact_330_less__not__refl,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ N @ N ) ).
% 0.25/0.56
% 0.25/0.56 % less_not_refl
% 0.25/0.56 thf(fact_331_nat__neq__iff,axiom,
% 0.25/0.56 ! [M: nat,N: nat] :
% 0.25/0.56 ( ( M != N )
% 0.25/0.56 = ( ( ord_less_nat @ M @ N )
% 0.25/0.56 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_neq_iff
% 0.25/0.56 thf(fact_332_gr0I,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( N != zero_zero_nat )
% 0.25/0.56 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % gr0I
% 0.25/0.56 thf(fact_333_not__gr0,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.25/0.56 = ( N = zero_zero_nat ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_gr0
% 0.25/0.56 thf(fact_334_not__less0,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % not_less0
% 0.25/0.56 thf(fact_335_less__zeroE,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % less_zeroE
% 0.25/0.56 thf(fact_336_gr__implies__not0,axiom,
% 0.25/0.56 ! [M: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ M @ N )
% 0.25/0.56 => ( N != zero_zero_nat ) ) ).
% 0.25/0.56
% 0.25/0.56 % gr_implies_not0
% 0.25/0.56 thf(fact_337_infinite__descent0,axiom,
% 0.25/0.56 ! [P3: nat > $o,N: nat] :
% 0.25/0.56 ( ( P3 @ zero_zero_nat )
% 0.25/0.56 => ( ! [N2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.56 => ( ~ ( P3 @ N2 )
% 0.25/0.56 => ? [M2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ M2 @ N2 )
% 0.25/0.56 & ~ ( P3 @ M2 ) ) ) )
% 0.25/0.56 => ( P3 @ N ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % infinite_descent0
% 0.25/0.56 thf(fact_338_bot__nat__0_Oextremum__strict,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % bot_nat_0.extremum_strict
% 0.25/0.56 thf(fact_339_mult__less__mono1,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat] :
% 0.25/0.56 ( ( ord_less_nat @ I @ J )
% 0.25/0.56 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.56 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_mono1
% 0.25/0.56 thf(fact_340_mult__less__mono2,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat] :
% 0.25/0.56 ( ( ord_less_nat @ I @ J )
% 0.25/0.56 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.56 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mult_less_mono2
% 0.25/0.56 thf(fact_341_mult__0,axiom,
% 0.25/0.56 ! [N: nat] :
% 0.25/0.56 ( ( times_times_nat @ zero_zero_nat @ N )
% 0.25/0.56 = zero_zero_nat ) ).
% 0.25/0.56
% 0.25/0.56 % mult_0
% 0.25/0.56 thf(fact_342_nat__mult__eq__cancel1,axiom,
% 0.25/0.56 ! [K: nat,M: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.56 => ( ( ( times_times_nat @ K @ M )
% 0.25/0.56 = ( times_times_nat @ K @ N ) )
% 0.25/0.56 = ( M = N ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_mult_eq_cancel1
% 0.25/0.56 thf(fact_343_nat__mult__less__cancel1,axiom,
% 0.25/0.56 ! [K: nat,M: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.56 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.25/0.56 = ( ord_less_nat @ M @ N ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_mult_less_cancel1
% 0.25/0.56 thf(fact_344_nat__mult__eq__cancel__disj,axiom,
% 0.25/0.56 ! [K: nat,M: nat,N: nat] :
% 0.25/0.56 ( ( ( times_times_nat @ K @ M )
% 0.25/0.56 = ( times_times_nat @ K @ N ) )
% 0.25/0.62 = ( ( K = zero_zero_nat )
% 0.25/0.62 | ( M = N ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % nat_mult_eq_cancel_disj
% 0.25/0.62 thf(fact_345_mult__eq__self__implies__10,axiom,
% 0.25/0.62 ! [M: nat,N: nat] :
% 0.25/0.62 ( ( M
% 0.25/0.62 = ( times_times_nat @ M @ N ) )
% 0.25/0.62 => ( ( N = one_one_nat )
% 0.25/0.62 | ( M = zero_zero_nat ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % mult_eq_self_implies_10
% 0.25/0.62
% 0.25/0.62 % Conjectures (1)
% 0.25/0.62 thf(conj_0,conjecture,
% 0.25/0.62 ( ( descar2095969287nges_a @ ys )
% 0.25/0.62 = ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ) ).
% 0.25/0.62
% 0.25/0.62 %------------------------------------------------------------------------------
% 0.25/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.hQkXClTMlU/cvc5---1.0.5_26230.p...
% 0.25/0.62 (declare-sort $$unsorted 0)
% 0.25/0.62 (declare-sort tptp.poly_poly_a 0)
% 0.25/0.62 (declare-sort tptp.list_poly_a 0)
% 0.25/0.62 (declare-sort tptp.list_list_a 0)
% 0.25/0.62 (declare-sort tptp.poly_nat 0)
% 0.25/0.62 (declare-sort tptp.list_nat 0)
% 0.25/0.62 (declare-sort tptp.poly_a 0)
% 0.25/0.62 (declare-sort tptp.list_a 0)
% 0.25/0.62 (declare-sort tptp.nat 0)
% 0.25/0.62 (declare-sort tptp.a 0)
% 0.25/0.62 (declare-fun tptp.descar226543321ms_nat (tptp.list_nat) tptp.list_nat)
% 0.25/0.62 (declare-fun tptp.descar282223555poly_a (tptp.list_poly_a) tptp.list_poly_a)
% 0.25/0.62 (declare-fun tptp.descar1375166517sums_a (tptp.list_a) tptp.list_a)
% 0.25/0.62 (declare-fun tptp.descar434775507poly_a (tptp.poly_a tptp.poly_poly_a) tptp.poly_poly_a)
% 0.25/0.62 (declare-fun tptp.descar466059845root_a (tptp.a tptp.poly_a) tptp.poly_a)
% 0.25/0.62 (declare-fun tptp.descar357075861poly_a (tptp.list_poly_a) tptp.nat)
% 0.25/0.62 (declare-fun tptp.descar2095969287nges_a (tptp.list_a) tptp.nat)
% 0.25/0.62 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.25/0.62 (declare-fun tptp.one_one_poly_nat () tptp.poly_nat)
% 0.25/0.62 (declare-fun tptp.one_one_poly_poly_a () tptp.poly_poly_a)
% 0.25/0.62 (declare-fun tptp.one_one_poly_a () tptp.poly_a)
% 0.25/0.62 (declare-fun tptp.one_one_a () tptp.a)
% 0.25/0.62 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 0.25/0.62 (declare-fun tptp.times_times_poly_a (tptp.poly_a tptp.poly_a) tptp.poly_a)
% 0.25/0.62 (declare-fun tptp.times_times_a (tptp.a tptp.a) tptp.a)
% 0.25/0.62 (declare-fun tptp.uminus_uminus_poly_a (tptp.poly_a) tptp.poly_a)
% 0.25/0.62 (declare-fun tptp.uminus_uminus_a (tptp.a) tptp.a)
% 0.25/0.62 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.25/0.62 (declare-fun tptp.zero_zero_poly_nat () tptp.poly_nat)
% 0.25/0.62 (declare-fun tptp.zero_z2096148049poly_a () tptp.poly_poly_a)
% 0.25/0.62 (declare-fun tptp.zero_zero_poly_a () tptp.poly_a)
% 0.25/0.62 (declare-fun tptp.zero_zero_a () tptp.a)
% 0.25/0.62 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 0.25/0.62 (declare-fun tptp.append_poly_a (tptp.list_poly_a tptp.list_poly_a) tptp.list_poly_a)
% 0.25/0.62 (declare-fun tptp.append_a (tptp.list_a tptp.list_a) tptp.list_a)
% 0.25/0.62 (declare-fun tptp.cons_list_a (tptp.list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.62 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 0.25/0.62 (declare-fun tptp.cons_poly_a (tptp.poly_a tptp.list_poly_a) tptp.list_poly_a)
% 0.25/0.62 (declare-fun tptp.cons_a (tptp.a tptp.list_a) tptp.list_a)
% 0.25/0.62 (declare-fun tptp.nil_list_a () tptp.list_list_a)
% 0.25/0.62 (declare-fun tptp.nil_nat () tptp.list_nat)
% 0.25/0.62 (declare-fun tptp.nil_poly_a () tptp.list_poly_a)
% 0.25/0.62 (declare-fun tptp.nil_a () tptp.list_a)
% 0.25/0.62 (declare-fun tptp.null_poly_a (tptp.list_poly_a) Bool)
% 0.25/0.62 (declare-fun tptp.null_a (tptp.list_a) Bool)
% 0.25/0.62 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.62 (declare-fun tptp.ord_less_poly_a (tptp.poly_a tptp.poly_a) Bool)
% 0.25/0.62 (declare-fun tptp.ord_less_a (tptp.a tptp.a) Bool)
% 0.25/0.62 (declare-fun tptp.poly_nat2 (tptp.list_nat) tptp.poly_nat)
% 0.25/0.62 (declare-fun tptp.poly_poly_a2 (tptp.list_poly_a) tptp.poly_poly_a)
% 0.25/0.62 (declare-fun tptp.poly_a2 (tptp.list_a) tptp.poly_a)
% 0.25/0.62 (declare-fun tptp.coeffs_nat (tptp.poly_nat) tptp.list_nat)
% 0.25/0.62 (declare-fun tptp.coeffs_poly_a (tptp.poly_poly_a) tptp.list_poly_a)
% 0.25/0.62 (declare-fun tptp.coeffs_a (tptp.poly_a) tptp.list_a)
% 0.25/0.62 (declare-fun tptp.is_zero_poly_a (tptp.poly_poly_a) Bool)
% 0.25/0.62 (declare-fun tptp.is_zero_a (tptp.poly_a) Bool)
% 0.25/0.62 (declare-fun tptp.pCons_nat (tptp.nat tptp.poly_nat) tptp.poly_nat)
% 0.25/0.62 (declare-fun tptp.pCons_poly_a (tptp.poly_a tptp.poly_poly_a) tptp.poly_poly_a)
% 0.25/0.62 (declare-fun tptp.pCons_a (tptp.a tptp.poly_a) tptp.poly_a)
% 0.25/0.62 (declare-fun tptp.smult_nat (tptp.nat tptp.poly_nat) tptp.poly_nat)
% 0.25/0.62 (declare-fun tptp.smult_poly_a (tptp.poly_a tptp.poly_poly_a) tptp.poly_poly_a)
% 0.25/0.62 (declare-fun tptp.smult_a (tptp.a tptp.poly_a) tptp.poly_a)
% 0.25/0.62 (declare-fun tptp.g () tptp.poly_a)
% 0.25/0.62 (declare-fun tptp.v (tptp.poly_a) tptp.nat)
% 0.25/0.62 (declare-fun tptp.xs () tptp.list_a)
% 0.25/0.62 (declare-fun tptp.ys () tptp.list_a)
% 0.25/0.62 (assert (= tptp.v (lambda ((F tptp.poly_a)) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a F)))))
% 0.25/0.62 (assert (not (= tptp.g tptp.zero_zero_poly_a)))
% 0.25/0.62 (assert (= (lambda ((Y tptp.poly_poly_a) (Z tptp.poly_poly_a)) (= Y Z)) (lambda ((P tptp.poly_poly_a) (Q tptp.poly_poly_a)) (= (@ tptp.coeffs_poly_a P) (@ tptp.coeffs_poly_a Q)))))
% 0.25/0.62 (assert (= (lambda ((Y tptp.poly_a) (Z tptp.poly_a)) (= Y Z)) (lambda ((P tptp.poly_a) (Q tptp.poly_a)) (= (@ tptp.coeffs_a P) (@ tptp.coeffs_a Q)))))
% 0.25/0.62 (assert (= tptp.ys (@ tptp.descar1375166517sums_a tptp.xs)))
% 0.25/0.62 (assert (forall ((Xs tptp.list_poly_a) (P2 tptp.poly_poly_a)) (=> (= (@ tptp.poly_poly_a2 Xs) P2) (= (@ tptp.descar357075861poly_a Xs) (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a P2))))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (P2 tptp.poly_a)) (=> (= (@ tptp.poly_a2 Xs) P2) (= (@ tptp.descar2095969287nges_a Xs) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a P2))))))
% 0.25/0.62 (assert (= tptp.ys (@ (@ tptp.append_a (@ tptp.coeffs_a tptp.g)) (@ (@ tptp.cons_a tptp.zero_zero_a) tptp.nil_a))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A) (= (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a (@ (@ tptp.descar434775507poly_a A) P2))) (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a P2))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (P2 tptp.poly_a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (= (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a (@ (@ tptp.descar466059845root_a A) P2))) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a P2))))))
% 0.25/0.62 (assert (= tptp.is_zero_poly_a (lambda ((P tptp.poly_poly_a)) (@ tptp.null_poly_a (@ tptp.coeffs_poly_a P)))))
% 0.25/0.62 (assert (= tptp.is_zero_a (lambda ((P tptp.poly_a)) (@ tptp.null_a (@ tptp.coeffs_a P)))))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_poly_a)) (= (@ tptp.poly_poly_a2 (@ tptp.coeffs_poly_a P2)) P2)))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_a)) (= (@ tptp.poly_a2 (@ tptp.coeffs_a P2)) P2)))
% 0.25/0.62 (assert (= (@ tptp.descar357075861poly_a tptp.nil_poly_a) tptp.zero_zero_nat))
% 0.25/0.62 (assert (= (@ tptp.descar2095969287nges_a tptp.nil_a) tptp.zero_zero_nat))
% 0.25/0.62 (assert (= tptp.xs (@ tptp.coeffs_a (@ (@ tptp.times_times_poly_a (@ (@ tptp.pCons_a tptp.one_one_a) (@ (@ tptp.pCons_a (@ tptp.uminus_uminus_a tptp.one_one_a)) tptp.zero_zero_poly_a))) tptp.g))))
% 0.25/0.62 (assert (forall ((A tptp.a) (P2 tptp.poly_a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (= (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a (@ (@ tptp.smult_a A) P2))) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a P2))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A) (= (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a (@ (@ tptp.smult_poly_a A) P2))) (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a P2))))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.descar2095969287nges_a (@ (@ tptp.cons_a tptp.zero_zero_a) Xs)) (@ tptp.descar2095969287nges_a Xs))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_poly_a)) (= (@ tptp.descar357075861poly_a (@ (@ tptp.cons_poly_a tptp.zero_zero_poly_a) Xs)) (@ tptp.descar357075861poly_a Xs))))
% 0.25/0.62 (assert (forall ((X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (= (@ tptp.descar2095969287nges_a (@ _let_1 (@ (@ tptp.cons_a tptp.zero_zero_a) Xs))) (@ tptp.descar2095969287nges_a (@ _let_1 Xs))))))
% 0.25/0.62 (assert (forall ((X tptp.poly_a) (Xs tptp.list_poly_a)) (let ((_let_1 (@ tptp.cons_poly_a X))) (= (@ tptp.descar357075861poly_a (@ _let_1 (@ (@ tptp.cons_poly_a tptp.zero_zero_poly_a) Xs))) (@ tptp.descar357075861poly_a (@ _let_1 Xs))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (P2 tptp.poly_a) (B tptp.a) (Q2 tptp.poly_a)) (= (= (@ (@ tptp.pCons_a A) P2) (@ (@ tptp.pCons_a B) Q2)) (and (= A B) (= P2 Q2)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (P2 tptp.poly_a)) (= (@ tptp.uminus_uminus_poly_a (@ (@ tptp.pCons_a A) P2)) (@ (@ tptp.pCons_a (@ tptp.uminus_uminus_a A)) (@ tptp.uminus_uminus_poly_a P2)))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a) (P2 tptp.poly_poly_a)) (= (@ (@ tptp.smult_poly_a A) (@ (@ tptp.smult_poly_a B) P2)) (@ (@ tptp.smult_poly_a (@ (@ tptp.times_times_poly_a A) B)) P2))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (P2 tptp.poly_nat)) (= (@ (@ tptp.smult_nat A) (@ (@ tptp.smult_nat B) P2)) (@ (@ tptp.smult_nat (@ (@ tptp.times_times_nat A) B)) P2))))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_a)) (= (@ (@ tptp.smult_a tptp.one_one_a) P2) P2)))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_nat)) (= (@ (@ tptp.smult_nat tptp.one_one_nat) P2) P2)))
% 0.25/0.62 (assert (forall ((A tptp.a) (P2 tptp.poly_a)) (= (@ (@ tptp.smult_a (@ tptp.uminus_uminus_a A)) P2) (@ tptp.uminus_uminus_poly_a (@ (@ tptp.smult_a A) P2)))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.smult_a A) tptp.zero_zero_poly_a) tptp.zero_zero_poly_a)))
% 0.25/0.62 (assert (forall ((A tptp.a) (P2 tptp.poly_a) (Q2 tptp.poly_a)) (let ((_let_1 (@ tptp.smult_a A))) (= (@ (@ tptp.times_times_poly_a (@ _let_1 P2)) Q2) (@ _let_1 (@ (@ tptp.times_times_poly_a P2) Q2))))))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_a) (A tptp.a) (Q2 tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a P2))) (let ((_let_2 (@ tptp.smult_a A))) (= (@ _let_1 (@ _let_2 Q2)) (@ _let_2 (@ _let_1 Q2)))))))
% 0.25/0.62 (assert (= (@ (@ tptp.pCons_poly_a tptp.zero_zero_poly_a) tptp.zero_z2096148049poly_a) tptp.zero_z2096148049poly_a))
% 0.25/0.62 (assert (= (@ (@ tptp.pCons_a tptp.zero_zero_a) tptp.zero_zero_poly_a) tptp.zero_zero_poly_a))
% 0.25/0.62 (assert (= (@ (@ tptp.pCons_nat tptp.zero_zero_nat) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (= (= (@ (@ tptp.pCons_poly_a A) P2) tptp.zero_z2096148049poly_a) (and (= A tptp.zero_zero_poly_a) (= P2 tptp.zero_z2096148049poly_a)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (P2 tptp.poly_nat)) (= (= (@ (@ tptp.pCons_nat A) P2) tptp.zero_zero_poly_nat) (and (= A tptp.zero_zero_nat) (= P2 tptp.zero_zero_poly_nat)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (P2 tptp.poly_a)) (= (= (@ (@ tptp.pCons_a A) P2) tptp.zero_zero_poly_a) (and (= A tptp.zero_zero_a) (= P2 tptp.zero_zero_poly_a)))))
% 0.25/0.62 (assert (= (@ (@ tptp.pCons_nat tptp.one_one_nat) tptp.zero_zero_poly_nat) tptp.one_one_poly_nat))
% 0.25/0.62 (assert (= (@ (@ tptp.pCons_a tptp.one_one_a) tptp.zero_zero_poly_a) tptp.one_one_poly_a))
% 0.25/0.62 (assert (= tptp.one_one_poly_nat (@ (@ tptp.pCons_nat tptp.one_one_nat) tptp.zero_zero_poly_nat)))
% 0.25/0.62 (assert (= tptp.one_one_poly_a (@ (@ tptp.pCons_a tptp.one_one_a) tptp.zero_zero_poly_a)))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_poly_a)) (= (@ (@ tptp.smult_poly_a tptp.zero_zero_poly_a) P2) tptp.zero_z2096148049poly_a)))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_a)) (= (@ (@ tptp.smult_a tptp.zero_zero_a) P2) tptp.zero_zero_poly_a)))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_nat)) (= (@ (@ tptp.smult_nat tptp.zero_zero_nat) P2) tptp.zero_zero_poly_nat)))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (= (= (@ (@ tptp.smult_poly_a A) P2) tptp.zero_z2096148049poly_a) (or (= A tptp.zero_zero_poly_a) (= P2 tptp.zero_z2096148049poly_a)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (P2 tptp.poly_nat)) (= (= (@ (@ tptp.smult_nat A) P2) tptp.zero_zero_poly_nat) (or (= A tptp.zero_zero_nat) (= P2 tptp.zero_zero_poly_nat)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (P2 tptp.poly_a)) (= (= (@ (@ tptp.smult_a A) P2) tptp.zero_zero_poly_a) (or (= A tptp.zero_zero_a) (= P2 tptp.zero_zero_poly_a)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a) (P2 tptp.poly_a)) (let ((_let_1 (@ tptp.smult_a A))) (= (@ _let_1 (@ (@ tptp.pCons_a B) P2)) (@ (@ tptp.pCons_a (@ (@ tptp.times_times_a A) B)) (@ _let_1 P2))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a) (P2 tptp.poly_poly_a)) (let ((_let_1 (@ tptp.smult_poly_a A))) (= (@ _let_1 (@ (@ tptp.pCons_poly_a B) P2)) (@ (@ tptp.pCons_poly_a (@ (@ tptp.times_times_poly_a A) B)) (@ _let_1 P2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (P2 tptp.poly_nat)) (let ((_let_1 (@ tptp.smult_nat A))) (= (@ _let_1 (@ (@ tptp.pCons_nat B) P2)) (@ (@ tptp.pCons_nat (@ (@ tptp.times_times_nat A) B)) (@ _let_1 P2))))))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_poly_a)) (= (= (@ tptp.coeffs_poly_a P2) tptp.nil_poly_a) (= P2 tptp.zero_z2096148049poly_a))))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_a)) (= (= (@ tptp.coeffs_a P2) tptp.nil_a) (= P2 tptp.zero_zero_poly_a))))
% 0.25/0.62 (assert (= (@ tptp.coeffs_poly_a tptp.zero_z2096148049poly_a) tptp.nil_poly_a))
% 0.25/0.62 (assert (= (@ tptp.coeffs_a tptp.zero_zero_poly_a) tptp.nil_a))
% 0.25/0.62 (assert (forall ((Xs tptp.list_poly_a)) (let ((_let_1 (@ tptp.cons_poly_a tptp.zero_zero_poly_a))) (= (@ tptp.descar282223555poly_a (@ _let_1 Xs)) (@ _let_1 (@ tptp.descar282223555poly_a Xs))))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat tptp.zero_zero_nat))) (= (@ tptp.descar226543321ms_nat (@ _let_1 Xs)) (@ _let_1 (@ tptp.descar226543321ms_nat Xs))))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a tptp.zero_zero_a))) (= (@ tptp.descar1375166517sums_a (@ _let_1 Xs)) (@ _let_1 (@ tptp.descar1375166517sums_a Xs))))))
% 0.25/0.62 (assert (= (@ tptp.coeffs_poly_a tptp.one_one_poly_poly_a) (@ (@ tptp.cons_poly_a tptp.one_one_poly_a) tptp.nil_poly_a)))
% 0.25/0.62 (assert (= (@ tptp.coeffs_a tptp.one_one_poly_a) (@ (@ tptp.cons_a tptp.one_one_a) tptp.nil_a)))
% 0.25/0.62 (assert (= (@ tptp.coeffs_nat tptp.one_one_poly_nat) (@ (@ tptp.cons_nat tptp.one_one_nat) tptp.nil_nat)))
% 0.25/0.62 (assert (forall ((X tptp.a)) (= (@ tptp.descar2095969287nges_a (@ (@ tptp.cons_a X) tptp.nil_a)) tptp.zero_zero_nat)))
% 0.25/0.62 (assert (forall ((X tptp.poly_a)) (= (@ tptp.descar357075861poly_a (@ (@ tptp.cons_poly_a X) tptp.nil_poly_a)) tptp.zero_zero_nat)))
% 0.25/0.62 (assert (= (@ tptp.descar2095969287nges_a tptp.xs) (@ tptp.v (@ (@ tptp.times_times_poly_a (@ (@ tptp.pCons_a tptp.one_one_a) (@ (@ tptp.pCons_a (@ tptp.uminus_uminus_a tptp.one_one_a)) tptp.zero_zero_poly_a))) tptp.g))))
% 0.25/0.62 (assert (forall ((As tptp.list_poly_a)) (= (@ tptp.poly_poly_a2 (@ (@ tptp.append_poly_a As) (@ (@ tptp.cons_poly_a tptp.zero_zero_poly_a) tptp.nil_poly_a))) (@ tptp.poly_poly_a2 As))))
% 0.25/0.62 (assert (forall ((As tptp.list_a)) (= (@ tptp.poly_a2 (@ (@ tptp.append_a As) (@ (@ tptp.cons_a tptp.zero_zero_a) tptp.nil_a))) (@ tptp.poly_a2 As))))
% 0.25/0.62 (assert (forall ((As tptp.list_nat)) (= (@ tptp.poly_nat2 (@ (@ tptp.append_nat As) (@ (@ tptp.cons_nat tptp.zero_zero_nat) tptp.nil_nat))) (@ tptp.poly_nat2 As))))
% 0.25/0.62 (assert (forall ((A tptp.a) (As tptp.list_a)) (= (@ tptp.poly_a2 (@ (@ tptp.cons_a A) As)) (@ (@ tptp.pCons_a A) (@ tptp.poly_a2 As)))))
% 0.25/0.62 (assert (= (@ tptp.poly_a2 tptp.nil_a) tptp.zero_zero_poly_a))
% 0.25/0.62 (assert (forall ((X tptp.a)) (let ((_let_1 (@ (@ tptp.cons_a X) tptp.nil_a))) (= (@ tptp.descar1375166517sums_a _let_1) _let_1))))
% 0.25/0.62 (assert (= (@ tptp.descar1375166517sums_a tptp.nil_a) tptp.nil_a))
% 0.25/0.62 (assert (= (@ (@ tptp.pCons_nat tptp.one_one_nat) tptp.zero_zero_poly_nat) tptp.one_one_poly_nat))
% 0.25/0.62 (assert (= (@ (@ tptp.pCons_a tptp.one_one_a) tptp.zero_zero_poly_a) tptp.one_one_poly_a))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_a)) (not (forall ((A2 tptp.a) (Q3 tptp.poly_a)) (not (= P2 (@ (@ tptp.pCons_a A2) Q3)))))))
% 0.25/0.62 (assert (= tptp.is_zero_a (lambda ((P tptp.poly_a)) (= P tptp.zero_zero_poly_a))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.poly_poly_a Bool)) (P2 tptp.poly_poly_a)) (=> (@ P3 tptp.zero_z2096148049poly_a) (=> (forall ((A2 tptp.poly_a) (P4 tptp.poly_poly_a)) (=> (or (not (= A2 tptp.zero_zero_poly_a)) (not (= P4 tptp.zero_z2096148049poly_a))) (=> (@ P3 P4) (@ P3 (@ (@ tptp.pCons_poly_a A2) P4))))) (@ P3 P2)))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.poly_nat Bool)) (P2 tptp.poly_nat)) (=> (@ P3 tptp.zero_zero_poly_nat) (=> (forall ((A2 tptp.nat) (P4 tptp.poly_nat)) (=> (or (not (= A2 tptp.zero_zero_nat)) (not (= P4 tptp.zero_zero_poly_nat))) (=> (@ P3 P4) (@ P3 (@ (@ tptp.pCons_nat A2) P4))))) (@ P3 P2)))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.poly_a Bool)) (P2 tptp.poly_a)) (=> (@ P3 tptp.zero_zero_poly_a) (=> (forall ((A2 tptp.a) (P4 tptp.poly_a)) (=> (or (not (= A2 tptp.zero_zero_a)) (not (= P4 tptp.zero_zero_poly_a))) (=> (@ P3 P4) (@ P3 (@ (@ tptp.pCons_a A2) P4))))) (@ P3 P2)))))
% 0.25/0.62 (assert (forall ((X tptp.poly_a)) (not (forall ((A2 tptp.a) (P4 tptp.poly_a)) (not (= X (@ (@ tptp.pCons_a A2) P4)))))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.poly_a tptp.poly_a Bool)) (P2 tptp.poly_a) (Q2 tptp.poly_a)) (=> (@ (@ P3 tptp.zero_zero_poly_a) tptp.zero_zero_poly_a) (=> (forall ((A2 tptp.a) (P4 tptp.poly_a) (B2 tptp.a) (Q3 tptp.poly_a)) (=> (@ (@ P3 P4) Q3) (@ (@ P3 (@ (@ tptp.pCons_a A2) P4)) (@ (@ tptp.pCons_a B2) Q3)))) (@ (@ P3 P2) Q2)))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.poly_a Bool)) (A0 tptp.poly_a)) (=> (forall ((A2 tptp.a) (P4 tptp.poly_a)) (=> (=> (not (= P4 tptp.zero_zero_poly_a)) (@ P3 P4)) (@ P3 (@ (@ tptp.pCons_a A2) P4)))) (@ P3 A0))))
% 0.25/0.62 (assert (forall ((Q2 tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a tptp.zero_zero_poly_a) Q2) tptp.zero_zero_poly_a)))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a P2) tptp.zero_zero_poly_a) tptp.zero_zero_poly_a)))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((Xs2 tptp.list_a)) (@ (@ P3 Xs2) tptp.nil_a)) (=> (forall ((V tptp.a) (Va tptp.list_a)) (@ (@ P3 tptp.nil_a) (@ (@ tptp.cons_a V) Va))) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Y2 tptp.a) (Ys tptp.list_a)) (=> (@ (@ P3 Xs2) Ys) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) (@ (@ tptp.cons_a Y2) Ys)))) (@ (@ P3 A0) A1))))))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_poly_a)) (=> (not (= P2 tptp.zero_z2096148049poly_a)) (not (= (@ tptp.coeffs_poly_a P2) tptp.nil_poly_a)))))
% 0.25/0.62 (assert (forall ((P2 tptp.poly_a)) (=> (not (= P2 tptp.zero_zero_poly_a)) (not (= (@ tptp.coeffs_a P2) tptp.nil_a)))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Y2 tptp.a) (Ys tptp.list_a)) (=> (@ (@ P3 Xs2) Ys) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) (@ (@ tptp.cons_a Y2) Ys)))) (=> (forall ((Xs2 tptp.list_a)) (@ (@ P3 Xs2) tptp.nil_a)) (=> (forall ((Y2 tptp.a) (Ys tptp.list_a)) (@ (@ P3 tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys))) (@ (@ P3 A0) A1))))))
% 0.25/0.62 (assert (forall ((C tptp.a) (P2 tptp.poly_a) (A tptp.a)) (=> (= (@ (@ tptp.smult_a C) P2) (@ (@ tptp.pCons_a A) P2)) (= P2 tptp.zero_zero_poly_a))))
% 0.25/0.62 (assert (forall ((X tptp.list_a)) (=> (not (= X tptp.nil_a)) (=> (forall ((X2 tptp.a)) (not (= X (@ (@ tptp.cons_a X2) tptp.nil_a)))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs2 tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) (@ (@ tptp.cons_a Y2) Xs2))))))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (C tptp.a) (P2 tptp.poly_a)) (let ((_let_1 (@ tptp.descar466059845root_a A))) (let ((_let_2 (@ tptp.pCons_a C))) (= (@ _let_1 (@ _let_2 P2)) (@ _let_2 (@ (@ tptp.smult_a A) (@ _let_1 P2))))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (C tptp.poly_a) (P2 tptp.poly_poly_a)) (let ((_let_1 (@ tptp.descar434775507poly_a A))) (let ((_let_2 (@ tptp.pCons_poly_a C))) (= (@ _let_1 (@ _let_2 P2)) (@ _let_2 (@ (@ tptp.smult_poly_a A) (@ _let_1 P2))))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (P2 tptp.poly_a)) (=> (not (= A tptp.zero_zero_a)) (=> (not (= P2 tptp.zero_zero_poly_a)) (not (= (@ (@ tptp.descar466059845root_a A) P2) tptp.zero_zero_poly_a))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (=> (not (= A tptp.zero_zero_poly_a)) (=> (not (= P2 tptp.zero_z2096148049poly_a)) (not (= (@ (@ tptp.descar434775507poly_a A) P2) tptp.zero_z2096148049poly_a))))))
% 0.25/0.62 (assert (forall ((X tptp.a) (Y3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs))) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) (@ (@ tptp.times_times_a X) Y3)) (= (@ tptp.descar2095969287nges_a (@ (@ tptp.cons_a X) _let_1)) (@ tptp.descar2095969287nges_a _let_1))))))
% 0.25/0.62 (assert (forall ((X tptp.poly_a) (Y3 tptp.poly_a) (Xs tptp.list_poly_a)) (let ((_let_1 (@ (@ tptp.cons_poly_a Y3) Xs))) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) (@ (@ tptp.times_times_poly_a X) Y3)) (= (@ tptp.descar357075861poly_a (@ (@ tptp.cons_poly_a X) _let_1)) (@ tptp.descar357075861poly_a _let_1))))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (X tptp.a) (Ys2 tptp.list_a) (Y3 tptp.a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X) tptp.nil_a)) (@ (@ tptp.append_a Ys2) (@ (@ tptp.cons_a Y3) tptp.nil_a))) (and (= Xs Ys2) (= X Y3)))))
% 0.25/0.62 (assert (forall ((Z2 tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a (@ tptp.uminus_uminus_poly_a tptp.one_one_poly_a)) Z2) (@ tptp.uminus_uminus_poly_a Z2))))
% 0.25/0.62 (assert (forall ((Z2 tptp.a)) (= (@ (@ tptp.times_times_a (@ tptp.uminus_uminus_a tptp.one_one_a)) Z2) (@ tptp.uminus_uminus_a Z2))))
% 0.25/0.62 (assert (forall ((Z2 tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a Z2) (@ tptp.uminus_uminus_poly_a tptp.one_one_poly_a)) (@ tptp.uminus_uminus_poly_a Z2))))
% 0.25/0.62 (assert (forall ((Z2 tptp.a)) (= (@ (@ tptp.times_times_a Z2) (@ tptp.uminus_uminus_a tptp.one_one_a)) (@ tptp.uminus_uminus_a Z2))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a A))) (= (@ _let_1 (@ tptp.uminus_uminus_poly_a A)) (@ _let_1 tptp.zero_zero_poly_a)))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (let ((_let_1 (@ tptp.ord_less_a A))) (= (@ _let_1 (@ tptp.uminus_uminus_a A)) (@ _let_1 tptp.zero_zero_a)))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a A)) A) (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) A) (@ (@ tptp.ord_less_a tptp.zero_zero_a) A))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) (@ tptp.uminus_uminus_poly_a A)) (@ (@ tptp.ord_less_poly_a A) tptp.zero_zero_poly_a))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a tptp.zero_zero_a) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_a A) tptp.zero_zero_a))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a A)) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) tptp.zero_zero_a) (@ (@ tptp.ord_less_a tptp.zero_zero_a) A))))
% 0.25/0.62 (assert (forall ((C tptp.a) (B tptp.a)) (= (= C (@ (@ tptp.times_times_a C) B)) (or (= C tptp.zero_zero_a) (= B tptp.one_one_a)))))
% 0.25/0.62 (assert (forall ((C tptp.poly_a) (B tptp.poly_a)) (= (= C (@ (@ tptp.times_times_poly_a C) B)) (or (= C tptp.zero_zero_poly_a) (= B tptp.one_one_poly_a)))))
% 0.25/0.62 (assert (forall ((C tptp.a) (A tptp.a)) (= (= (@ (@ tptp.times_times_a C) A) C) (or (= C tptp.zero_zero_a) (= A tptp.one_one_a)))))
% 0.25/0.62 (assert (forall ((C tptp.poly_a) (A tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a C) A) C) (or (= C tptp.zero_zero_poly_a) (= A tptp.one_one_poly_a)))))
% 0.25/0.62 (assert (forall ((C tptp.a) (B tptp.a)) (= (= C (@ (@ tptp.times_times_a B) C)) (or (= C tptp.zero_zero_a) (= B tptp.one_one_a)))))
% 0.25/0.62 (assert (forall ((C tptp.poly_a) (B tptp.poly_a)) (= (= C (@ (@ tptp.times_times_poly_a B) C)) (or (= C tptp.zero_zero_poly_a) (= B tptp.one_one_poly_a)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (C tptp.a)) (= (= (@ (@ tptp.times_times_a A) C) C) (or (= C tptp.zero_zero_a) (= A tptp.one_one_a)))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (C tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) C) C) (or (= C tptp.zero_zero_poly_a) (= A tptp.one_one_poly_a)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (= (@ tptp.uminus_uminus_a A) (@ tptp.uminus_uminus_a B)) (= A B))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ tptp.uminus_uminus_a (@ tptp.uminus_uminus_a A)) A)))
% 0.25/0.62 (assert (forall ((X21 tptp.a) (X22 tptp.list_a) (Y21 tptp.a) (Y22 tptp.list_a)) (= (= (@ (@ tptp.cons_a X21) X22) (@ (@ tptp.cons_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs)) (= Ys2 Zs)))))
% 0.25/0.62 (assert (forall ((Ys2 tptp.list_a) (Xs tptp.list_a) (Zs tptp.list_a)) (= (= (@ (@ tptp.append_a Ys2) Xs) (@ (@ tptp.append_a Zs) Xs)) (= Ys2 Zs))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (@ (@ tptp.append_a (@ _let_1 Ys2)) Zs) (@ _let_1 (@ (@ tptp.append_a Ys2) Zs))))))
% 0.25/0.62 (assert (forall ((A tptp.list_a) (B tptp.list_a) (C tptp.list_a)) (let ((_let_1 (@ tptp.append_a A))) (= (@ (@ tptp.append_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_a B) C))))))
% 0.25/0.62 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.25/0.62 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (= (= (@ (@ tptp.times_times_a A) C) (@ (@ tptp.times_times_a B) C)) (or (= C tptp.zero_zero_a) (= A B)))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (C tptp.poly_a) (B tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) C) (@ (@ tptp.times_times_poly_a B) C)) (or (= C tptp.zero_zero_poly_a) (= A B)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 0.25/0.62 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_a) (= A B))))))
% 0.25/0.62 (assert (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_poly_a) (= A B))))))
% 0.25/0.62 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (= (@ (@ tptp.times_times_a A) B) tptp.zero_zero_a) (or (= A tptp.zero_zero_a) (= B tptp.zero_zero_a)))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) B) tptp.zero_zero_poly_a) (or (= A tptp.zero_zero_poly_a) (= B tptp.zero_zero_poly_a)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a A) tptp.zero_zero_a) tptp.zero_zero_a)))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a A) tptp.zero_zero_poly_a) tptp.zero_zero_poly_a)))
% 0.25/0.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a tptp.zero_zero_a) A) tptp.zero_zero_a)))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a tptp.zero_zero_poly_a) A) tptp.zero_zero_poly_a)))
% 0.25/0.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (= (@ tptp.uminus_uminus_poly_a A) A) (= A tptp.zero_zero_poly_a))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (= (@ tptp.uminus_uminus_a A) A) (= A tptp.zero_zero_a))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (= A (@ tptp.uminus_uminus_poly_a A)) (= A tptp.zero_zero_poly_a))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (= A (@ tptp.uminus_uminus_a A)) (= A tptp.zero_zero_a))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (= (@ tptp.uminus_uminus_poly_a A) tptp.zero_zero_poly_a) (= A tptp.zero_zero_poly_a))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (= (@ tptp.uminus_uminus_a A) tptp.zero_zero_a) (= A tptp.zero_zero_a))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (= tptp.zero_zero_poly_a (@ tptp.uminus_uminus_poly_a A)) (= tptp.zero_zero_poly_a A))))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (= tptp.zero_zero_a (@ tptp.uminus_uminus_a A)) (= tptp.zero_zero_a A))))
% 0.25/0.62 (assert (= (@ tptp.uminus_uminus_poly_a tptp.zero_zero_poly_a) tptp.zero_zero_poly_a))
% 0.25/0.62 (assert (= (@ tptp.uminus_uminus_a tptp.zero_zero_a) tptp.zero_zero_a))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a A) tptp.one_one_a) A)))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a A) tptp.one_one_poly_a) A)))
% 0.25/0.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a tptp.one_one_a) A) A)))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a tptp.one_one_poly_a) A) A)))
% 0.25/0.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 0.25/0.62 (assert (forall ((B tptp.poly_a) (A tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a B)) (@ tptp.uminus_uminus_poly_a A)) (@ (@ tptp.ord_less_poly_a A) B))))
% 0.25/0.62 (assert (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a B)) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_a A) B))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a A))) (= (@ _let_1 (@ tptp.uminus_uminus_poly_a B)) (@ tptp.uminus_uminus_poly_a (@ _let_1 B))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a A))) (= (@ _let_1 (@ tptp.uminus_uminus_a B)) (@ tptp.uminus_uminus_a (@ _let_1 B))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a (@ tptp.uminus_uminus_poly_a A)) (@ tptp.uminus_uminus_poly_a B)) (@ (@ tptp.times_times_poly_a A) B))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.times_times_a (@ tptp.uminus_uminus_a A)) (@ tptp.uminus_uminus_a B)) (@ (@ tptp.times_times_a A) B))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a (@ tptp.uminus_uminus_poly_a A)) B) (@ tptp.uminus_uminus_poly_a (@ (@ tptp.times_times_poly_a A) B)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.times_times_a (@ tptp.uminus_uminus_a A)) B) (@ tptp.uminus_uminus_a (@ (@ tptp.times_times_a A) B)))))
% 0.25/0.62 (assert (forall ((A tptp.list_a)) (= (@ (@ tptp.append_a A) tptp.nil_a) A)))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) tptp.nil_a) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= tptp.nil_a (@ (@ tptp.append_a Xs) Ys2)) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))))
% 0.25/0.62 (assert (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (= (= Ys2 (@ (@ tptp.append_a Xs) Ys2)) (= Xs tptp.nil_a))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) Ys2) (= Xs tptp.nil_a))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= Xs (@ (@ tptp.append_a Xs) Ys2)) (= Ys2 tptp.nil_a))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) Xs) (= Ys2 tptp.nil_a))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a)) (= (@ (@ tptp.append_a Xs) tptp.nil_a) Xs)))
% 0.25/0.62 (assert (forall ((C tptp.a)) (= (@ (@ tptp.smult_a C) tptp.one_one_poly_a) (@ (@ tptp.pCons_a C) tptp.zero_zero_poly_a))))
% 0.25/0.62 (assert (forall ((X tptp.poly_a)) (= (= tptp.zero_zero_poly_a X) (= X tptp.zero_zero_poly_a))))
% 0.25/0.62 (assert (forall ((X tptp.a)) (= (= tptp.zero_zero_a X) (= X tptp.zero_zero_a))))
% 0.25/0.62 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 0.25/0.62 (assert (forall ((X tptp.a) (Y3 tptp.a)) (=> (not (= X Y3)) (=> (not (@ (@ tptp.ord_less_a X) Y3)) (@ (@ tptp.ord_less_a Y3) X)))))
% 0.25/0.62 (assert (forall ((X tptp.poly_a) (Y3 tptp.poly_a)) (=> (not (= X Y3)) (=> (not (@ (@ tptp.ord_less_poly_a X) Y3)) (@ (@ tptp.ord_less_poly_a Y3) X)))))
% 0.25/0.62 (assert (forall ((B tptp.poly_a) (A tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a B))) (let ((_let_2 (@ tptp.times_times_poly_a A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.25/0.62 (assert (= tptp.times_times_poly_a (lambda ((A3 tptp.poly_a) (B3 tptp.poly_a)) (@ (@ tptp.times_times_poly_a B3) A3))))
% 0.25/0.62 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A3))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a A))) (= (@ (@ tptp.times_times_poly_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_poly_a B) C))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a A))) (= (@ (@ tptp.times_times_poly_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_poly_a B) C))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 0.25/0.62 (assert (forall ((X tptp.a)) (= (= tptp.one_one_a X) (= X tptp.one_one_a))))
% 0.25/0.62 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (= (@ tptp.uminus_uminus_a A) B) (= (@ tptp.uminus_uminus_a B) A))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (= A (@ tptp.uminus_uminus_a B)) (= B (@ tptp.uminus_uminus_a A)))))
% 0.25/0.62 (assert (forall ((X tptp.a) (Xs tptp.list_a)) (not (= (@ (@ tptp.cons_a X) Xs) Xs))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a) (Ts tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) (@ (@ tptp.append_a Zs) Ts)) (exists ((Us tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (or (and (= Xs (@ (@ tptp.append_a Zs) Us)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append_a Xs) Us) Zs) (= Ys2 (@ _let_1 Ts)))))))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Xs1 tptp.list_a) (Zs tptp.list_a) (Ys2 tptp.list_a) (Us2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys2 (@ (@ tptp.append_a Xs1) Us2)) (= (@ _let_1 Ys2) (@ (@ tptp.append_a Zs) Us2)))))))
% 0.25/0.62 (assert (forall ((X tptp.a) (Y3 tptp.a)) (let ((_let_1 (@ tptp.descar2095969287nges_a (@ (@ tptp.cons_a X) (@ (@ tptp.cons_a Y3) tptp.nil_a))))) (let ((_let_2 (@ tptp.ord_less_a tptp.zero_zero_a))) (let ((_let_3 (or (and (@ _let_2 X) (@ (@ tptp.ord_less_a Y3) tptp.zero_zero_a)) (and (@ (@ tptp.ord_less_a X) tptp.zero_zero_a) (@ _let_2 Y3))))) (and (=> _let_3 (= _let_1 tptp.one_one_nat)) (=> (not _let_3) (= _let_1 tptp.zero_zero_nat))))))))
% 0.25/0.62 (assert (forall ((X tptp.poly_a) (Y3 tptp.poly_a)) (let ((_let_1 (@ tptp.descar357075861poly_a (@ (@ tptp.cons_poly_a X) (@ (@ tptp.cons_poly_a Y3) tptp.nil_poly_a))))) (let ((_let_2 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (let ((_let_3 (or (and (@ _let_2 X) (@ (@ tptp.ord_less_poly_a Y3) tptp.zero_zero_poly_a)) (and (@ (@ tptp.ord_less_poly_a X) tptp.zero_zero_poly_a) (@ _let_2 Y3))))) (and (=> _let_3 (= _let_1 tptp.one_one_nat)) (=> (not _let_3) (= _let_1 tptp.zero_zero_nat))))))))
% 0.25/0.62 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.25/0.62 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.25/0.62 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.25/0.62 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.25/0.62 (assert (not (@ (@ tptp.ord_less_a tptp.zero_zero_a) tptp.zero_zero_a)))
% 0.25/0.62 (assert (not (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) tptp.zero_zero_poly_a)))
% 0.25/0.62 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (=> (not (= C tptp.zero_zero_a)) (= (= (@ (@ tptp.times_times_a A) C) (@ (@ tptp.times_times_a B) C)) (= A B)))))
% 0.25/0.62 (assert (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (=> (not (= C tptp.zero_zero_poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) C) (@ (@ tptp.times_times_poly_a B) C)) (= A B)))))
% 0.25/0.62 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 0.25/0.62 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (not (= C tptp.zero_zero_a)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 0.25/0.62 (assert (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (not (= C tptp.zero_zero_poly_a)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 0.25/0.62 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (=> (not (= A tptp.zero_zero_a)) (=> (not (= B tptp.zero_zero_a)) (not (= (@ (@ tptp.times_times_a A) B) tptp.zero_zero_a))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (not (= A tptp.zero_zero_poly_a)) (=> (not (= B tptp.zero_zero_poly_a)) (not (= (@ (@ tptp.times_times_poly_a A) B) tptp.zero_zero_poly_a))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (=> (= (@ (@ tptp.times_times_a A) B) tptp.zero_zero_a) (or (= A tptp.zero_zero_a) (= B tptp.zero_zero_a)))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (= (@ (@ tptp.times_times_poly_a A) B) tptp.zero_zero_poly_a) (or (= A tptp.zero_zero_poly_a) (= B tptp.zero_zero_poly_a)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (=> (not (= (@ (@ tptp.times_times_a A) B) tptp.zero_zero_a)) (and (not (= A tptp.zero_zero_a)) (not (= B tptp.zero_zero_a))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (not (= (@ (@ tptp.times_times_poly_a A) B) tptp.zero_zero_poly_a)) (and (not (= A tptp.zero_zero_poly_a)) (not (= B tptp.zero_zero_poly_a))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 0.25/0.62 (assert (not (= tptp.zero_zero_poly_a tptp.one_one_poly_a)))
% 0.25/0.62 (assert (not (= tptp.zero_zero_a tptp.one_one_a)))
% 0.25/0.62 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 0.25/0.62 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 0.25/0.62 (assert (not (@ (@ tptp.ord_less_a tptp.one_one_a) tptp.one_one_a)))
% 0.25/0.62 (assert (not (@ (@ tptp.ord_less_poly_a tptp.one_one_poly_a) tptp.one_one_poly_a)))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a A) tptp.one_one_a) A)))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a A) tptp.one_one_poly_a) A)))
% 0.25/0.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 0.25/0.62 (assert (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a tptp.one_one_a) A) A)))
% 0.25/0.62 (assert (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a tptp.one_one_poly_a) A) A)))
% 0.25/0.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a A)) B) (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a B)) A))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) B) (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a B)) A))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a A) (@ tptp.uminus_uminus_poly_a B)) (@ (@ tptp.ord_less_poly_a B) (@ tptp.uminus_uminus_poly_a A)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a A) (@ tptp.uminus_uminus_a B)) (@ (@ tptp.ord_less_a B) (@ tptp.uminus_uminus_a A)))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a (@ tptp.uminus_uminus_poly_a A)) B) (@ (@ tptp.times_times_poly_a A) (@ tptp.uminus_uminus_poly_a B)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.times_times_a (@ tptp.uminus_uminus_a A)) B) (@ (@ tptp.times_times_a A) (@ tptp.uminus_uminus_a B)))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) A) (@ (@ tptp.times_times_poly_a B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_poly_a B))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (= (= (@ (@ tptp.times_times_a A) A) (@ (@ tptp.times_times_a B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_a B))))))
% 0.25/0.62 (assert (not (= tptp.one_one_a (@ tptp.uminus_uminus_a tptp.one_one_a))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (@ P3 tptp.nil_a) (=> (forall ((X2 tptp.a) (Ys tptp.list_a)) (=> (@ P3 Ys) (@ P3 (@ (@ tptp.cons_a X2) Ys)))) (@ P3 A0)))))
% 0.25/0.62 (assert (forall ((X tptp.list_a)) (=> (not (= X tptp.nil_a)) (not (forall ((X2 tptp.a) (Ys tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) Ys))))))))
% 0.25/0.62 (assert (forall ((P3 (-> (-> tptp.a tptp.a) tptp.list_a tptp.list_a Bool)) (A0 (-> tptp.a tptp.a)) (A1 tptp.list_a) (A22 tptp.list_a)) (=> (forall ((F2 (-> tptp.a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P3 F2) tptp.nil_a) X_1)) (=> (forall ((F2 (-> tptp.a tptp.a)) (A2 tptp.a) (As2 tptp.list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P3 F2))) (=> (@ (@ _let_1 As2) (@ (@ tptp.cons_a (@ F2 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A2) As2)) Bs)))) (@ (@ (@ P3 A0) A1) A22)))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (P3 (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X2 tptp.a)) (@ P3 (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a)) (=> (not (= Xs2 tptp.nil_a)) (=> (@ P3 Xs2) (@ P3 (@ (@ tptp.cons_a X2) Xs2))))) (@ P3 Xs))))))
% 0.25/0.62 (assert (forall ((P3 (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P5 (-> tptp.a tptp.a Bool))) (@ (@ P3 P5) tptp.nil_a)) (=> (forall ((P5 (-> tptp.a tptp.a Bool)) (X2 tptp.a)) (@ (@ P3 P5) (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((P5 (-> tptp.a tptp.a Bool)) (X2 tptp.a) (Y2 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Xs2))) (let ((_let_2 (@ P3 P5))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_a X2) _let_1)))))) (@ (@ P3 A0) A1))))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (@ P3 tptp.nil_a) (=> (forall ((X2 tptp.a)) (@ P3 (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Xs2))) (let ((_let_2 (@ tptp.cons_a X2))) (let ((_let_3 (= X2 Y2))) (=> (=> _let_3 (@ P3 (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P3 _let_1)) (@ P3 (@ _let_2 _let_1)))))))) (@ P3 A0))))))
% 0.25/0.62 (assert (forall ((P3 (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P5 (-> tptp.a tptp.a Bool))) (@ (@ P3 P5) tptp.nil_a)) (=> (forall ((P5 (-> tptp.a tptp.a Bool)) (X2 tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ P3 P5))) (=> (@ _let_1 Ys) (@ _let_1 (@ (@ tptp.cons_a X2) Ys))))) (@ (@ P3 A0) A1)))))
% 0.25/0.62 (assert (forall ((X tptp.list_a)) (=> (not (= X tptp.nil_a)) (=> (forall ((X2 tptp.a)) (not (= X (@ (@ tptp.cons_a X2) tptp.nil_a)))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs2 tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) (@ (@ tptp.cons_a Y2) Xs2))))))))))
% 0.25/0.62 (assert (forall ((X tptp.list_list_a)) (=> (not (= X tptp.nil_list_a)) (=> (forall ((Xss tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a tptp.nil_a) Xss)))) (not (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Xss tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a (@ (@ tptp.cons_a X2) Xs2)) Xss)))))))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P3 tptp.nil_a) X_1)) (=> (forall ((Xs2 tptp.list_a)) (@ (@ P3 Xs2) tptp.nil_a)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Y2 tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Ys))) (let ((_let_2 (@ P3 (@ (@ tptp.cons_a X2) Xs2)))) (=> (@ (@ P3 Xs2) _let_1) (=> (@ _let_2 Ys) (@ _let_2 _let_1)))))) (@ (@ P3 A0) A1))))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a)) (=> (forall ((X212 tptp.a) (X222 tptp.list_a)) (=> (= Xs2 (@ (@ tptp.cons_a X212) X222)) (@ P3 Xs2))) (@ P3 (@ (@ tptp.cons_a X2) Xs2)))) (=> (@ P3 tptp.nil_a) (@ P3 A0)))))
% 0.25/0.62 (assert (forall ((X tptp.list_a)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) Xs2)))) (= X tptp.nil_a))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P3 tptp.nil_a) (=> (forall ((X2 tptp.a)) (@ P3 (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Zs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Zs2))) (=> (@ P3 Zs2) (=> (@ P3 _let_1) (@ P3 (@ (@ tptp.cons_a X2) _let_1)))))) (@ P3 Xs))))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P3 tptp.nil_a) X_1)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ P3 Ys) Xs2) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) Ys))) (@ (@ P3 A0) A1)))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ P3 tptp.nil_a) tptp.nil_a) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a)) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) tptp.nil_a)) (=> (forall ((Y2 tptp.a) (Ys tptp.list_a)) (@ (@ P3 tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys))) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Y2 tptp.a) (Ys tptp.list_a)) (=> (@ (@ P3 Xs2) Ys) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) (@ (@ tptp.cons_a Y2) Ys)))) (@ (@ P3 Xs) Ys2)))))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a)) (= (not (= Xs tptp.nil_a)) (exists ((Y4 tptp.a) (Ys3 tptp.list_a)) (= Xs (@ (@ tptp.cons_a Y4) Ys3))))))
% 0.25/0.62 (assert (forall ((P3 (-> tptp.list_a Bool)) (List tptp.list_a)) (=> (@ P3 tptp.nil_a) (=> (forall ((X1 tptp.a) (X23 tptp.list_a)) (=> (@ P3 X23) (@ P3 (@ (@ tptp.cons_a X1) X23)))) (@ P3 List)))))
% 0.25/0.62 (assert (forall ((Y3 tptp.list_a)) (=> (not (= Y3 tptp.nil_a)) (not (forall ((X213 tptp.a) (X223 tptp.list_a)) (not (= Y3 (@ (@ tptp.cons_a X213) X223))))))))
% 0.25/0.62 (assert (forall ((List tptp.list_a) (X21 tptp.a) (X22 tptp.list_a)) (=> (= List (@ (@ tptp.cons_a X21) X22)) (not (= List tptp.nil_a)))))
% 0.25/0.62 (assert (forall ((X21 tptp.a) (X22 tptp.list_a)) (not (= tptp.nil_a (@ (@ tptp.cons_a X21) X22)))))
% 0.25/0.62 (assert (forall ((X tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (= (@ (@ tptp.append_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.append_a Xs) Ys2))))))
% 0.25/0.62 (assert (forall ((X tptp.a) (Xs1 tptp.list_a) (Ys2 tptp.list_a) (Xs tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs (@ (@ tptp.append_a Xs1) Zs)) (= (@ _let_1 Xs) (@ (@ tptp.append_a Ys2) Zs)))))))
% 0.25/0.62 (assert (forall ((A tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) A) A)))
% 0.25/0.62 (assert (forall ((Ys2 tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) Ys2) Ys2)))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append_a tptp.nil_a) Ys2)))))
% 0.25/0.62 (assert (forall ((X tptp.a) (Xs tptp.list_a)) (not (@ tptp.null_a (@ (@ tptp.cons_a X) Xs)))))
% 0.25/0.62 (assert (forall ((Xs tptp.list_a)) (= (= Xs tptp.nil_a) (@ tptp.null_a Xs))))
% 0.25/0.62 (assert (@ tptp.null_a tptp.nil_a))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a A) B) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a A) B) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) C)) (@ (@ tptp.times_times_a B) C)) (or (and (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a A) B)) (and (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (@ (@ tptp.ord_less_a B) A))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (C tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) C)) (@ (@ tptp.times_times_poly_a B) C)) (or (and (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a A) B)) (and (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a B) A))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (@ (@ tptp.ord_less_a A) B) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) C)) (@ (@ tptp.times_times_a B) C))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a A) B) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) C)) (@ (@ tptp.times_times_poly_a B) C))))))
% 0.25/0.62 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (=> (@ (@ tptp.ord_less_a B) A) (=> (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) C)) (@ (@ tptp.times_times_a B) C))))))
% 0.25/0.62 (assert (forall ((B tptp.poly_a) (A tptp.poly_a) (C tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a B) A) (=> (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) C)) (@ (@ tptp.times_times_poly_a B) C))))))
% 0.25/0.62 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (= (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a A) B)) (and (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (@ (@ tptp.ord_less_a B) A)))))))
% 0.25/0.62 (assert (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (= (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a A) B)) (and (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a B) A)))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a A) B) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a A) B) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)))))))
% 0.25/0.62 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a B) A) (=> (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)))))))
% 0.25/0.62 (assert (forall ((B tptp.poly_a) (A tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a B) A) (=> (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)))))))
% 0.25/0.62 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (= (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_a A) B))))))
% 0.25/0.62 (assert (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (= (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_poly_a A) B))))))
% 0.25/0.62 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (= (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_a B) A))))))
% 0.25/0.62 (assert (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (= (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_poly_a B) A))))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.25/0.62 (assert (forall ((B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ _let_1 (@ (@ tptp.times_times_a B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.25/0.62 (assert (forall ((B tptp.poly_a) (A tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (=> (@ _let_1 (@ (@ tptp.times_times_poly_a B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ _let_1 (@ (@ tptp.times_times_a A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (=> (@ _let_1 (@ (@ tptp.times_times_poly_a A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (= (@ _let_1 (@ (@ tptp.times_times_a A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_a A) tptp.zero_zero_a) (@ (@ tptp.ord_less_a B) tptp.zero_zero_a)))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (= (@ _let_1 (@ (@ tptp.times_times_poly_a A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_poly_a A) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a B) tptp.zero_zero_poly_a)))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (=> (@ (@ tptp.ord_less_a B) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a B) A)) tptp.zero_zero_a)))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A) (=> (@ (@ tptp.ord_less_poly_a B) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a B) A)) tptp.zero_zero_poly_a)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 0.25/0.62 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_a A) B)))))))
% 0.25/0.62 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_poly_a A) B)))))))
% 0.25/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (=> (@ (@ tptp.ord_less_a B) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) B)) tptp.zero_zero_a)))))
% 0.25/0.63 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A) (=> (@ (@ tptp.ord_less_poly_a B) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) B)) tptp.zero_zero_poly_a)))))
% 0.25/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_a A) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) B) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) B)) tptp.zero_zero_a)))))
% 0.25/0.63 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a A) tptp.zero_zero_poly_a) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) B) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) B)) tptp.zero_zero_poly_a)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (= (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) B)) tptp.zero_zero_a) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_a B) tptp.zero_zero_a)) (and (@ (@ tptp.ord_less_a A) tptp.zero_zero_a) (@ _let_1 B)))))))
% 0.25/0.63 (assert (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (= (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) B)) tptp.zero_zero_poly_a) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_poly_a B) tptp.zero_zero_poly_a)) (and (@ (@ tptp.ord_less_poly_a A) tptp.zero_zero_poly_a) (@ _let_1 B)))))))
% 0.25/0.63 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))))
% 0.25/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 0.25/0.63 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))))
% 0.25/0.63 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.25/0.63 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 0.25/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 0.25/0.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.25/0.63 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))))
% 0.25/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 0.25/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 0.25/0.63 (assert (forall ((X tptp.nat) (Y3 tptp.nat)) (=> (not (= X Y3)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (@ (@ tptp.ord_less_nat Y3) X)))))
% 0.25/0.63 (assert (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P3 N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P3 M2)))))) (@ P3 N))))
% 0.25/0.63 (assert (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P3 M2))) (@ P3 N2))) (@ P3 N))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.25/0.63 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.25/0.63 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.25/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.25/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.25/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.25/0.63 (assert (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P3 tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P3 N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P3 M2))))))) (@ P3 N)))))
% 0.25/0.63 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 0.25/0.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K))))))
% 0.65/0.91 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))
% 0.65/0.91 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.65/0.91 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 0.65/0.91 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 0.65/0.91 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))))
% 0.65/0.91 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 0.65/0.91 (assert (not (= (@ tptp.descar2095969287nges_a tptp.ys) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a tptp.g)))))
% 0.65/0.91 (set-info :filename cvc5---1.0.5_26230)
% 0.65/0.91 (check-sat-assuming ( true ))
% 0.65/0.91 ------- get file name : TPTP file name is ITP044^1
% 0.65/0.91 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26230.smt2...
% 0.65/0.91 --- Run --ho-elim --full-saturate-quant at 10...
% 0.65/0.91 % SZS status Theorem for ITP044^1
% 0.65/0.91 % SZS output start Proof for ITP044^1
% 0.65/0.91 (
% 0.65/0.91 (let ((_let_1 (@ tptp.coeffs_a tptp.g))) (let ((_let_2 (@ tptp.descar2095969287nges_a _let_1))) (let ((_let_3 (not (= (@ tptp.descar2095969287nges_a tptp.ys) _let_2)))) (let ((_let_4 (@ tptp.uminus_uminus_a tptp.one_one_a))) (let ((_let_5 (@ tptp.pCons_a tptp.one_one_a))) (let ((_let_6 (@ _let_5 tptp.zero_zero_poly_a))) (let ((_let_7 (= _let_6 tptp.one_one_poly_a))) (let ((_let_8 (@ (@ tptp.pCons_nat tptp.one_one_nat) tptp.zero_zero_poly_nat))) (let ((_let_9 (= _let_8 tptp.one_one_poly_nat))) (let ((_let_10 (forall ((As tptp.list_a)) (= (@ tptp.poly_a2 (@ (@ tptp.append_a As) (@ (@ tptp.cons_a tptp.zero_zero_a) tptp.nil_a))) (@ tptp.poly_a2 As))))) (let ((_let_11 (@ (@ tptp.times_times_poly_a (@ _let_5 (@ (@ tptp.pCons_a _let_4) tptp.zero_zero_poly_a))) tptp.g))) (let ((_let_12 (@ tptp.coeffs_a tptp.zero_zero_poly_a))) (let ((_let_13 (= _let_12 tptp.nil_a))) (let ((_let_14 (= (@ tptp.coeffs_poly_a tptp.zero_z2096148049poly_a) tptp.nil_poly_a))) (let ((_let_15 (= tptp.one_one_poly_a _let_6))) (let ((_let_16 (= tptp.one_one_poly_nat _let_8))) (let ((_let_17 (@ tptp.coeffs_a _let_11))) (let ((_let_18 (= tptp.xs _let_17))) (let ((_let_19 (= (@ tptp.descar357075861poly_a tptp.nil_poly_a) tptp.zero_zero_nat))) (let ((_let_20 (forall ((P2 tptp.poly_a)) (= (@ tptp.poly_a2 (@ tptp.coeffs_a P2)) P2)))) (let ((_let_21 (= tptp.is_zero_a (lambda ((P tptp.poly_a)) (@ tptp.null_a (@ tptp.coeffs_a P)))))) (let ((_let_22 (= tptp.is_zero_poly_a (lambda ((P tptp.poly_poly_a)) (@ tptp.null_poly_a (@ tptp.coeffs_poly_a P)))))) (let ((_let_23 (@ tptp.cons_a tptp.zero_zero_a))) (let ((_let_24 (@ tptp.append_a _let_1))) (let ((_let_25 (= tptp.ys (@ _let_24 (@ _let_23 tptp.nil_a))))) (let ((_let_26 (forall ((Xs tptp.list_a) (P2 tptp.poly_a)) (=> (= (@ tptp.poly_a2 Xs) P2) (= (@ tptp.descar2095969287nges_a Xs) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a P2))))))) (let ((_let_27 (= tptp.ys (@ tptp.descar1375166517sums_a tptp.xs)))) (let ((_let_28 (= tptp.v (lambda ((F tptp.poly_a)) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a F)))))) (let ((_let_29 (ho_44 k_51 (ho_21 k_20 (ho_16 (ho_15 k_17 (ho_16 (ho_50 k_49 tptp.one_one_a) (ho_16 (ho_50 k_49 (ho_48 k_47 tptp.one_one_a)) tptp.zero_zero_poly_a))) tptp.g))))) (let ((_let_30 (ho_21 k_20 tptp.g))) (let ((_let_31 (ho_44 (ho_46 k_45 _let_30) (ho_44 (ho_43 k_42 tptp.zero_zero_a) (ho_21 k_20 tptp.zero_zero_poly_a))))) (let ((_let_32 (= _let_31 _let_29))) (let ((_let_33 (= (ho_41 k_40 _let_29) (ho_41 k_40 _let_30)))) (let ((_let_34 (ho_39 k_38 _let_30))) (let ((_let_35 (= tptp.g _let_34))) (let ((_let_36 (ho_39 k_38 _let_31))) (let ((_let_37 (= _let_34 _let_36))) (let ((_let_38 (= (ho_41 k_40 (ho_21 k_20 _let_36)) (ho_41 k_40 _let_31)))) (let ((_let_39 (@ tptp.descar1375166517sums_a _let_17))) (let ((_let_40 (AND_INTRO (SYMM (ASSUME :args (_let_13))) (SYMM (ASSUME :args (_let_14))) (ASSUME :args (_let_15)) (ASSUME :args (_let_16)) (ASSUME :args (_let_18)) (SYMM (ASSUME :args (_let_19))) (ASSUME :args (_let_21)) (ASSUME :args (_let_22)) (ASSUME :args (_let_27)) (ASSUME :args (_let_28))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_25)) (TRANS (MACRO_SR_EQ_INTRO _let_40 :args (_let_25 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_39 (@ _let_24 (@ _let_23 _let_12))) _let_32))))))) (let ((_let_42 (not _let_33))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_40 :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (= _let_2 (@ tptp.descar2095969287nges_a _let_39))) _let_42))))))) (let ((_let_44 (forall ((P2 tptp.poly_a)) (= P2 (ho_39 k_38 (ho_21 k_20 P2)))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_20)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((P2 tptp.poly_a)) (= P2 (@ tptp.poly_a2 (@ tptp.coeffs_a P2)))) _let_44))))))) (let ((_let_46 (forall ((As tptp.list_a)) (= (ho_39 k_38 (ho_44 (ho_46 k_45 As) (ho_44 (ho_43 k_42 tptp.zero_zero_a) (ho_21 k_20 tptp.zero_zero_poly_a)))) (ho_39 k_38 As))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO _let_40 :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((As tptp.list_a)) (= (@ tptp.poly_a2 As) (@ tptp.poly_a2 (@ (@ tptp.append_a As) (@ (@ tptp.cons_a tptp.zero_zero_a) (@ tptp.coeffs_a tptp.zero_zero_poly_a)))))) _let_46))))))) (let ((_let_48 (forall ((Xs tptp.list_a)) (= (ho_41 k_40 (ho_21 k_20 (ho_39 k_38 Xs))) (ho_41 k_40 Xs))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_26)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xs tptp.list_a)) (= (@ tptp.descar2095969287nges_a Xs) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a (@ tptp.poly_a2 Xs))))) _let_48))))))) (let ((_let_50 (not _let_38))) (let ((_let_51 (not _let_37))) (let ((_let_52 (not _let_35))) (let ((_let_53 (not _let_32))) (let ((_let_54 (_let_50))) (let ((_let_55 (ASSUME :args (_let_38)))) (let ((_let_56 (APPLY_UF ho_41))) (let ((_let_57 (ASSUME :args (_let_35)))) (let ((_let_58 (ASSUME :args (_let_37)))) (let ((_let_59 (REFL :args (k_40)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_55 (MODUS_PONENS (AND_INTRO _let_41 _let_43 _let_57 _let_58) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (CONG _let_59 (SYMM (SYMM _let_41)) :args _let_56) (CONG _let_59 (CONG (REFL :args (k_20)) (TRANS (SYMM _let_58) (SYMM _let_57)) :args (APPLY_UF ho_21)) :args _let_56) :args (=)) (FALSE_INTRO _let_43)) :args ((= _let_38 false)))) :args (_let_32 _let_42 _let_35 _let_37)))) :args (_let_32 _let_42 _let_35 _let_37 _let_38)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_54))) (TRUE_INTRO (SYMM (SYMM _let_55))))) :args (_let_38 _let_50)) :args ((not (and _let_32 _let_42 _let_35 _let_37 _let_38)) SB_LITERAL))) (CONG (REFL :args (_let_53)) (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_33))) (REFL :args (_let_52)) (REFL :args (_let_51)) (REFL :args _let_54) :args (or))) :args ((or _let_33 _let_53 _let_52 _let_51 _let_50))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_31 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_48))) _let_49 :args (_let_38 false _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_30 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_46 k_45 As)))) :args (_let_46)))) _let_47 :args (_let_37 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (tptp.g QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_21 k_20 P2)))) :args (_let_44))) _let_45 :args (_let_35 false _let_44)) _let_43 _let_41 :args (false false _let_38 false _let_37 false _let_35 true _let_33 false _let_32)) :args (_let_28 (not (= tptp.g tptp.zero_zero_poly_a)) (= (lambda ((Y tptp.poly_poly_a) (Z tptp.poly_poly_a)) (= Y Z)) (lambda ((P tptp.poly_poly_a) (Q tptp.poly_poly_a)) (= (@ tptp.coeffs_poly_a P) (@ tptp.coeffs_poly_a Q)))) (= (lambda ((Y tptp.poly_a) (Z tptp.poly_a)) (= Y Z)) (lambda ((P tptp.poly_a) (Q tptp.poly_a)) (= (@ tptp.coeffs_a P) (@ tptp.coeffs_a Q)))) _let_27 (forall ((Xs tptp.list_poly_a) (P2 tptp.poly_poly_a)) (=> (= (@ tptp.poly_poly_a2 Xs) P2) (= (@ tptp.descar357075861poly_a Xs) (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a P2))))) _let_26 _let_25 (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A) (= (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a (@ (@ tptp.descar434775507poly_a A) P2))) (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a P2))))) (forall ((A tptp.a) (P2 tptp.poly_a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (= (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a (@ (@ tptp.descar466059845root_a A) P2))) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a P2))))) _let_22 _let_21 (forall ((P2 tptp.poly_poly_a)) (= (@ tptp.poly_poly_a2 (@ tptp.coeffs_poly_a P2)) P2)) _let_20 _let_19 (= (@ tptp.descar2095969287nges_a tptp.nil_a) tptp.zero_zero_nat) _let_18 (forall ((A tptp.a) (P2 tptp.poly_a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (= (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a (@ (@ tptp.smult_a A) P2))) (@ tptp.descar2095969287nges_a (@ tptp.coeffs_a P2))))) (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A) (= (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a (@ (@ tptp.smult_poly_a A) P2))) (@ tptp.descar357075861poly_a (@ tptp.coeffs_poly_a P2))))) (forall ((Xs tptp.list_a)) (= (@ tptp.descar2095969287nges_a (@ (@ tptp.cons_a tptp.zero_zero_a) Xs)) (@ tptp.descar2095969287nges_a Xs))) (forall ((Xs tptp.list_poly_a)) (= (@ tptp.descar357075861poly_a (@ (@ tptp.cons_poly_a tptp.zero_zero_poly_a) Xs)) (@ tptp.descar357075861poly_a Xs))) (forall ((X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (= (@ tptp.descar2095969287nges_a (@ _let_1 (@ (@ tptp.cons_a tptp.zero_zero_a) Xs))) (@ tptp.descar2095969287nges_a (@ _let_1 Xs))))) (forall ((X tptp.poly_a) (Xs tptp.list_poly_a)) (let ((_let_1 (@ tptp.cons_poly_a X))) (= (@ tptp.descar357075861poly_a (@ _let_1 (@ (@ tptp.cons_poly_a tptp.zero_zero_poly_a) Xs))) (@ tptp.descar357075861poly_a (@ _let_1 Xs))))) (forall ((A tptp.a) (P2 tptp.poly_a) (B tptp.a) (Q2 tptp.poly_a)) (= (= (@ (@ tptp.pCons_a A) P2) (@ (@ tptp.pCons_a B) Q2)) (and (= A B) (= P2 Q2)))) (forall ((A tptp.a) (P2 tptp.poly_a)) (= (@ tptp.uminus_uminus_poly_a (@ (@ tptp.pCons_a A) P2)) (@ (@ tptp.pCons_a (@ tptp.uminus_uminus_a A)) (@ tptp.uminus_uminus_poly_a P2)))) (forall ((A tptp.poly_a) (B tptp.poly_a) (P2 tptp.poly_poly_a)) (= (@ (@ tptp.smult_poly_a A) (@ (@ tptp.smult_poly_a B) P2)) (@ (@ tptp.smult_poly_a (@ (@ tptp.times_times_poly_a A) B)) P2))) (forall ((A tptp.nat) (B tptp.nat) (P2 tptp.poly_nat)) (= (@ (@ tptp.smult_nat A) (@ (@ tptp.smult_nat B) P2)) (@ (@ tptp.smult_nat (@ (@ tptp.times_times_nat A) B)) P2))) (forall ((P2 tptp.poly_a)) (= (@ (@ tptp.smult_a tptp.one_one_a) P2) P2)) (forall ((P2 tptp.poly_nat)) (= (@ (@ tptp.smult_nat tptp.one_one_nat) P2) P2)) (forall ((A tptp.a) (P2 tptp.poly_a)) (= (@ (@ tptp.smult_a (@ tptp.uminus_uminus_a A)) P2) (@ tptp.uminus_uminus_poly_a (@ (@ tptp.smult_a A) P2)))) (forall ((A tptp.a)) (= (@ (@ tptp.smult_a A) tptp.zero_zero_poly_a) tptp.zero_zero_poly_a)) (forall ((A tptp.a) (P2 tptp.poly_a) (Q2 tptp.poly_a)) (let ((_let_1 (@ tptp.smult_a A))) (= (@ (@ tptp.times_times_poly_a (@ _let_1 P2)) Q2) (@ _let_1 (@ (@ tptp.times_times_poly_a P2) Q2))))) (forall ((P2 tptp.poly_a) (A tptp.a) (Q2 tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a P2))) (let ((_let_2 (@ tptp.smult_a A))) (= (@ _let_1 (@ _let_2 Q2)) (@ _let_2 (@ _let_1 Q2)))))) (= (@ (@ tptp.pCons_poly_a tptp.zero_zero_poly_a) tptp.zero_z2096148049poly_a) tptp.zero_z2096148049poly_a) (= (@ (@ tptp.pCons_a tptp.zero_zero_a) tptp.zero_zero_poly_a) tptp.zero_zero_poly_a) (= (@ (@ tptp.pCons_nat tptp.zero_zero_nat) tptp.zero_zero_poly_nat) tptp.zero_zero_poly_nat) (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (= (= (@ (@ tptp.pCons_poly_a A) P2) tptp.zero_z2096148049poly_a) (and (= A tptp.zero_zero_poly_a) (= P2 tptp.zero_z2096148049poly_a)))) (forall ((A tptp.nat) (P2 tptp.poly_nat)) (= (= (@ (@ tptp.pCons_nat A) P2) tptp.zero_zero_poly_nat) (and (= A tptp.zero_zero_nat) (= P2 tptp.zero_zero_poly_nat)))) (forall ((A tptp.a) (P2 tptp.poly_a)) (= (= (@ (@ tptp.pCons_a A) P2) tptp.zero_zero_poly_a) (and (= A tptp.zero_zero_a) (= P2 tptp.zero_zero_poly_a)))) _let_9 _let_7 _let_16 _let_15 (forall ((P2 tptp.poly_poly_a)) (= (@ (@ tptp.smult_poly_a tptp.zero_zero_poly_a) P2) tptp.zero_z2096148049poly_a)) (forall ((P2 tptp.poly_a)) (= (@ (@ tptp.smult_a tptp.zero_zero_a) P2) tptp.zero_zero_poly_a)) (forall ((P2 tptp.poly_nat)) (= (@ (@ tptp.smult_nat tptp.zero_zero_nat) P2) tptp.zero_zero_poly_nat)) (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (= (= (@ (@ tptp.smult_poly_a A) P2) tptp.zero_z2096148049poly_a) (or (= A tptp.zero_zero_poly_a) (= P2 tptp.zero_z2096148049poly_a)))) (forall ((A tptp.nat) (P2 tptp.poly_nat)) (= (= (@ (@ tptp.smult_nat A) P2) tptp.zero_zero_poly_nat) (or (= A tptp.zero_zero_nat) (= P2 tptp.zero_zero_poly_nat)))) (forall ((A tptp.a) (P2 tptp.poly_a)) (= (= (@ (@ tptp.smult_a A) P2) tptp.zero_zero_poly_a) (or (= A tptp.zero_zero_a) (= P2 tptp.zero_zero_poly_a)))) (forall ((A tptp.a) (B tptp.a) (P2 tptp.poly_a)) (let ((_let_1 (@ tptp.smult_a A))) (= (@ _let_1 (@ (@ tptp.pCons_a B) P2)) (@ (@ tptp.pCons_a (@ (@ tptp.times_times_a A) B)) (@ _let_1 P2))))) (forall ((A tptp.poly_a) (B tptp.poly_a) (P2 tptp.poly_poly_a)) (let ((_let_1 (@ tptp.smult_poly_a A))) (= (@ _let_1 (@ (@ tptp.pCons_poly_a B) P2)) (@ (@ tptp.pCons_poly_a (@ (@ tptp.times_times_poly_a A) B)) (@ _let_1 P2))))) (forall ((A tptp.nat) (B tptp.nat) (P2 tptp.poly_nat)) (let ((_let_1 (@ tptp.smult_nat A))) (= (@ _let_1 (@ (@ tptp.pCons_nat B) P2)) (@ (@ tptp.pCons_nat (@ (@ tptp.times_times_nat A) B)) (@ _let_1 P2))))) (forall ((P2 tptp.poly_poly_a)) (= (= (@ tptp.coeffs_poly_a P2) tptp.nil_poly_a) (= P2 tptp.zero_z2096148049poly_a))) (forall ((P2 tptp.poly_a)) (= (= (@ tptp.coeffs_a P2) tptp.nil_a) (= P2 tptp.zero_zero_poly_a))) _let_14 _let_13 (forall ((Xs tptp.list_poly_a)) (let ((_let_1 (@ tptp.cons_poly_a tptp.zero_zero_poly_a))) (= (@ tptp.descar282223555poly_a (@ _let_1 Xs)) (@ _let_1 (@ tptp.descar282223555poly_a Xs))))) (forall ((Xs tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat tptp.zero_zero_nat))) (= (@ tptp.descar226543321ms_nat (@ _let_1 Xs)) (@ _let_1 (@ tptp.descar226543321ms_nat Xs))))) (forall ((Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a tptp.zero_zero_a))) (= (@ tptp.descar1375166517sums_a (@ _let_1 Xs)) (@ _let_1 (@ tptp.descar1375166517sums_a Xs))))) (= (@ tptp.coeffs_poly_a tptp.one_one_poly_poly_a) (@ (@ tptp.cons_poly_a tptp.one_one_poly_a) tptp.nil_poly_a)) (= (@ tptp.coeffs_a tptp.one_one_poly_a) (@ (@ tptp.cons_a tptp.one_one_a) tptp.nil_a)) (= (@ tptp.coeffs_nat tptp.one_one_poly_nat) (@ (@ tptp.cons_nat tptp.one_one_nat) tptp.nil_nat)) (forall ((X tptp.a)) (= (@ tptp.descar2095969287nges_a (@ (@ tptp.cons_a X) tptp.nil_a)) tptp.zero_zero_nat)) (forall ((X tptp.poly_a)) (= (@ tptp.descar357075861poly_a (@ (@ tptp.cons_poly_a X) tptp.nil_poly_a)) tptp.zero_zero_nat)) (= (@ tptp.descar2095969287nges_a tptp.xs) (@ tptp.v _let_11)) (forall ((As tptp.list_poly_a)) (= (@ tptp.poly_poly_a2 (@ (@ tptp.append_poly_a As) (@ (@ tptp.cons_poly_a tptp.zero_zero_poly_a) tptp.nil_poly_a))) (@ tptp.poly_poly_a2 As))) _let_10 (forall ((As tptp.list_nat)) (= (@ tptp.poly_nat2 (@ (@ tptp.append_nat As) (@ (@ tptp.cons_nat tptp.zero_zero_nat) tptp.nil_nat))) (@ tptp.poly_nat2 As))) (forall ((A tptp.a) (As tptp.list_a)) (= (@ tptp.poly_a2 (@ (@ tptp.cons_a A) As)) (@ (@ tptp.pCons_a A) (@ tptp.poly_a2 As)))) (= (@ tptp.poly_a2 tptp.nil_a) tptp.zero_zero_poly_a) (forall ((X tptp.a)) (let ((_let_1 (@ (@ tptp.cons_a X) tptp.nil_a))) (= (@ tptp.descar1375166517sums_a _let_1) _let_1))) (= (@ tptp.descar1375166517sums_a tptp.nil_a) tptp.nil_a) _let_9 _let_7 (forall ((P2 tptp.poly_a)) (not (forall ((A2 tptp.a) (Q3 tptp.poly_a)) (not (= P2 (@ (@ tptp.pCons_a A2) Q3)))))) (= tptp.is_zero_a (lambda ((P tptp.poly_a)) (= P tptp.zero_zero_poly_a))) (forall ((P3 (-> tptp.poly_poly_a Bool)) (P2 tptp.poly_poly_a)) (=> (@ P3 tptp.zero_z2096148049poly_a) (=> (forall ((A2 tptp.poly_a) (P4 tptp.poly_poly_a)) (=> (or (not (= A2 tptp.zero_zero_poly_a)) (not (= P4 tptp.zero_z2096148049poly_a))) (=> (@ P3 P4) (@ P3 (@ (@ tptp.pCons_poly_a A2) P4))))) (@ P3 P2)))) (forall ((P3 (-> tptp.poly_nat Bool)) (P2 tptp.poly_nat)) (=> (@ P3 tptp.zero_zero_poly_nat) (=> (forall ((A2 tptp.nat) (P4 tptp.poly_nat)) (=> (or (not (= A2 tptp.zero_zero_nat)) (not (= P4 tptp.zero_zero_poly_nat))) (=> (@ P3 P4) (@ P3 (@ (@ tptp.pCons_nat A2) P4))))) (@ P3 P2)))) (forall ((P3 (-> tptp.poly_a Bool)) (P2 tptp.poly_a)) (=> (@ P3 tptp.zero_zero_poly_a) (=> (forall ((A2 tptp.a) (P4 tptp.poly_a)) (=> (or (not (= A2 tptp.zero_zero_a)) (not (= P4 tptp.zero_zero_poly_a))) (=> (@ P3 P4) (@ P3 (@ (@ tptp.pCons_a A2) P4))))) (@ P3 P2)))) (forall ((X tptp.poly_a)) (not (forall ((A2 tptp.a) (P4 tptp.poly_a)) (not (= X (@ (@ tptp.pCons_a A2) P4)))))) (forall ((P3 (-> tptp.poly_a tptp.poly_a Bool)) (P2 tptp.poly_a) (Q2 tptp.poly_a)) (=> (@ (@ P3 tptp.zero_zero_poly_a) tptp.zero_zero_poly_a) (=> (forall ((A2 tptp.a) (P4 tptp.poly_a) (B2 tptp.a) (Q3 tptp.poly_a)) (=> (@ (@ P3 P4) Q3) (@ (@ P3 (@ (@ tptp.pCons_a A2) P4)) (@ (@ tptp.pCons_a B2) Q3)))) (@ (@ P3 P2) Q2)))) (forall ((P3 (-> tptp.poly_a Bool)) (A0 tptp.poly_a)) (=> (forall ((A2 tptp.a) (P4 tptp.poly_a)) (=> (=> (not (= P4 tptp.zero_zero_poly_a)) (@ P3 P4)) (@ P3 (@ (@ tptp.pCons_a A2) P4)))) (@ P3 A0))) (forall ((Q2 tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a tptp.zero_zero_poly_a) Q2) tptp.zero_zero_poly_a)) (forall ((P2 tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a P2) tptp.zero_zero_poly_a) tptp.zero_zero_poly_a)) (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((Xs2 tptp.list_a)) (@ (@ P3 Xs2) tptp.nil_a)) (=> (forall ((V tptp.a) (Va tptp.list_a)) (@ (@ P3 tptp.nil_a) (@ (@ tptp.cons_a V) Va))) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Y2 tptp.a) (Ys tptp.list_a)) (=> (@ (@ P3 Xs2) Ys) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) (@ (@ tptp.cons_a Y2) Ys)))) (@ (@ P3 A0) A1))))) (forall ((P2 tptp.poly_poly_a)) (=> (not (= P2 tptp.zero_z2096148049poly_a)) (not (= (@ tptp.coeffs_poly_a P2) tptp.nil_poly_a)))) (forall ((P2 tptp.poly_a)) (=> (not (= P2 tptp.zero_zero_poly_a)) (not (= (@ tptp.coeffs_a P2) tptp.nil_a)))) (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Y2 tptp.a) (Ys tptp.list_a)) (=> (@ (@ P3 Xs2) Ys) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) (@ (@ tptp.cons_a Y2) Ys)))) (=> (forall ((Xs2 tptp.list_a)) (@ (@ P3 Xs2) tptp.nil_a)) (=> (forall ((Y2 tptp.a) (Ys tptp.list_a)) (@ (@ P3 tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys))) (@ (@ P3 A0) A1))))) (forall ((C tptp.a) (P2 tptp.poly_a) (A tptp.a)) (=> (= (@ (@ tptp.smult_a C) P2) (@ (@ tptp.pCons_a A) P2)) (= P2 tptp.zero_zero_poly_a))) (forall ((X tptp.list_a)) (=> (not (= X tptp.nil_a)) (=> (forall ((X2 tptp.a)) (not (= X (@ (@ tptp.cons_a X2) tptp.nil_a)))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs2 tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) (@ (@ tptp.cons_a Y2) Xs2))))))))) (forall ((A tptp.a) (C tptp.a) (P2 tptp.poly_a)) (let ((_let_1 (@ tptp.descar466059845root_a A))) (let ((_let_2 (@ tptp.pCons_a C))) (= (@ _let_1 (@ _let_2 P2)) (@ _let_2 (@ (@ tptp.smult_a A) (@ _let_1 P2))))))) (forall ((A tptp.poly_a) (C tptp.poly_a) (P2 tptp.poly_poly_a)) (let ((_let_1 (@ tptp.descar434775507poly_a A))) (let ((_let_2 (@ tptp.pCons_poly_a C))) (= (@ _let_1 (@ _let_2 P2)) (@ _let_2 (@ (@ tptp.smult_poly_a A) (@ _let_1 P2))))))) (forall ((A tptp.a) (P2 tptp.poly_a)) (=> (not (= A tptp.zero_zero_a)) (=> (not (= P2 tptp.zero_zero_poly_a)) (not (= (@ (@ tptp.descar466059845root_a A) P2) tptp.zero_zero_poly_a))))) (forall ((A tptp.poly_a) (P2 tptp.poly_poly_a)) (=> (not (= A tptp.zero_zero_poly_a)) (=> (not (= P2 tptp.zero_z2096148049poly_a)) (not (= (@ (@ tptp.descar434775507poly_a A) P2) tptp.zero_z2096148049poly_a))))) (forall ((X tptp.a) (Y3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs))) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) (@ (@ tptp.times_times_a X) Y3)) (= (@ tptp.descar2095969287nges_a (@ (@ tptp.cons_a X) _let_1)) (@ tptp.descar2095969287nges_a _let_1))))) (forall ((X tptp.poly_a) (Y3 tptp.poly_a) (Xs tptp.list_poly_a)) (let ((_let_1 (@ (@ tptp.cons_poly_a Y3) Xs))) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) (@ (@ tptp.times_times_poly_a X) Y3)) (= (@ tptp.descar357075861poly_a (@ (@ tptp.cons_poly_a X) _let_1)) (@ tptp.descar357075861poly_a _let_1))))) (forall ((Xs tptp.list_a) (X tptp.a) (Ys2 tptp.list_a) (Y3 tptp.a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X) tptp.nil_a)) (@ (@ tptp.append_a Ys2) (@ (@ tptp.cons_a Y3) tptp.nil_a))) (and (= Xs Ys2) (= X Y3)))) (forall ((Z2 tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a (@ tptp.uminus_uminus_poly_a tptp.one_one_poly_a)) Z2) (@ tptp.uminus_uminus_poly_a Z2))) (forall ((Z2 tptp.a)) (= (@ (@ tptp.times_times_a (@ tptp.uminus_uminus_a tptp.one_one_a)) Z2) (@ tptp.uminus_uminus_a Z2))) (forall ((Z2 tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a Z2) (@ tptp.uminus_uminus_poly_a tptp.one_one_poly_a)) (@ tptp.uminus_uminus_poly_a Z2))) (forall ((Z2 tptp.a)) (= (@ (@ tptp.times_times_a Z2) (@ tptp.uminus_uminus_a tptp.one_one_a)) (@ tptp.uminus_uminus_a Z2))) (forall ((A tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a A))) (= (@ _let_1 (@ tptp.uminus_uminus_poly_a A)) (@ _let_1 tptp.zero_zero_poly_a)))) (forall ((A tptp.a)) (let ((_let_1 (@ tptp.ord_less_a A))) (= (@ _let_1 (@ tptp.uminus_uminus_a A)) (@ _let_1 tptp.zero_zero_a)))) (forall ((A tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a A)) A) (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) A) (@ (@ tptp.ord_less_a tptp.zero_zero_a) A))) (forall ((A tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) (@ tptp.uminus_uminus_poly_a A)) (@ (@ tptp.ord_less_poly_a A) tptp.zero_zero_poly_a))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a tptp.zero_zero_a) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_a A) tptp.zero_zero_a))) (forall ((A tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a A)) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) tptp.zero_zero_a) (@ (@ tptp.ord_less_a tptp.zero_zero_a) A))) (forall ((C tptp.a) (B tptp.a)) (= (= C (@ (@ tptp.times_times_a C) B)) (or (= C tptp.zero_zero_a) (= B tptp.one_one_a)))) (forall ((C tptp.poly_a) (B tptp.poly_a)) (= (= C (@ (@ tptp.times_times_poly_a C) B)) (or (= C tptp.zero_zero_poly_a) (= B tptp.one_one_poly_a)))) (forall ((C tptp.a) (A tptp.a)) (= (= (@ (@ tptp.times_times_a C) A) C) (or (= C tptp.zero_zero_a) (= A tptp.one_one_a)))) (forall ((C tptp.poly_a) (A tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a C) A) C) (or (= C tptp.zero_zero_poly_a) (= A tptp.one_one_poly_a)))) (forall ((C tptp.a) (B tptp.a)) (= (= C (@ (@ tptp.times_times_a B) C)) (or (= C tptp.zero_zero_a) (= B tptp.one_one_a)))) (forall ((C tptp.poly_a) (B tptp.poly_a)) (= (= C (@ (@ tptp.times_times_poly_a B) C)) (or (= C tptp.zero_zero_poly_a) (= B tptp.one_one_poly_a)))) (forall ((A tptp.a) (C tptp.a)) (= (= (@ (@ tptp.times_times_a A) C) C) (or (= C tptp.zero_zero_a) (= A tptp.one_one_a)))) (forall ((A tptp.poly_a) (C tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) C) C) (or (= C tptp.zero_zero_poly_a) (= A tptp.one_one_poly_a)))) (forall ((A tptp.a) (B tptp.a)) (= (= (@ tptp.uminus_uminus_a A) (@ tptp.uminus_uminus_a B)) (= A B))) (forall ((A tptp.a)) (= (@ tptp.uminus_uminus_a (@ tptp.uminus_uminus_a A)) A)) (forall ((X21 tptp.a) (X22 tptp.list_a) (Y21 tptp.a) (Y22 tptp.list_a)) (= (= (@ (@ tptp.cons_a X21) X22) (@ (@ tptp.cons_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs)) (= Ys2 Zs)))) (forall ((Ys2 tptp.list_a) (Xs tptp.list_a) (Zs tptp.list_a)) (= (= (@ (@ tptp.append_a Ys2) Xs) (@ (@ tptp.append_a Zs) Xs)) (= Ys2 Zs))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (@ (@ tptp.append_a (@ _let_1 Ys2)) Zs) (@ _let_1 (@ (@ tptp.append_a Ys2) Zs))))) (forall ((A tptp.list_a) (B tptp.list_a) (C tptp.list_a)) (let ((_let_1 (@ tptp.append_a A))) (= (@ (@ tptp.append_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_a B) C))))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (= (= (@ (@ tptp.times_times_a A) C) (@ (@ tptp.times_times_a B) C)) (or (= C tptp.zero_zero_a) (= A B)))) (forall ((A tptp.poly_a) (C tptp.poly_a) (B tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) C) (@ (@ tptp.times_times_poly_a B) C)) (or (= C tptp.zero_zero_poly_a) (= A B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_a) (= A B))))) (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_poly_a) (= A B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))) (forall ((A tptp.a) (B tptp.a)) (= (= (@ (@ tptp.times_times_a A) B) tptp.zero_zero_a) (or (= A tptp.zero_zero_a) (= B tptp.zero_zero_a)))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) B) tptp.zero_zero_poly_a) (or (= A tptp.zero_zero_poly_a) (= B tptp.zero_zero_poly_a)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a A) tptp.zero_zero_a) tptp.zero_zero_a)) (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a A) tptp.zero_zero_poly_a) tptp.zero_zero_poly_a)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a tptp.zero_zero_a) A) tptp.zero_zero_a)) (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a tptp.zero_zero_poly_a) A) tptp.zero_zero_poly_a)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.poly_a)) (= (= (@ tptp.uminus_uminus_poly_a A) A) (= A tptp.zero_zero_poly_a))) (forall ((A tptp.a)) (= (= (@ tptp.uminus_uminus_a A) A) (= A tptp.zero_zero_a))) (forall ((A tptp.poly_a)) (= (= A (@ tptp.uminus_uminus_poly_a A)) (= A tptp.zero_zero_poly_a))) (forall ((A tptp.a)) (= (= A (@ tptp.uminus_uminus_a A)) (= A tptp.zero_zero_a))) (forall ((A tptp.poly_a)) (= (= (@ tptp.uminus_uminus_poly_a A) tptp.zero_zero_poly_a) (= A tptp.zero_zero_poly_a))) (forall ((A tptp.a)) (= (= (@ tptp.uminus_uminus_a A) tptp.zero_zero_a) (= A tptp.zero_zero_a))) (forall ((A tptp.poly_a)) (= (= tptp.zero_zero_poly_a (@ tptp.uminus_uminus_poly_a A)) (= tptp.zero_zero_poly_a A))) (forall ((A tptp.a)) (= (= tptp.zero_zero_a (@ tptp.uminus_uminus_a A)) (= tptp.zero_zero_a A))) (= (@ tptp.uminus_uminus_poly_a tptp.zero_zero_poly_a) tptp.zero_zero_poly_a) (= (@ tptp.uminus_uminus_a tptp.zero_zero_a) tptp.zero_zero_a) (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a A) tptp.one_one_a) A)) (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a A) tptp.one_one_poly_a) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a tptp.one_one_a) A) A)) (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a tptp.one_one_poly_a) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((B tptp.poly_a) (A tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a B)) (@ tptp.uminus_uminus_poly_a A)) (@ (@ tptp.ord_less_poly_a A) B))) (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a B)) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_a A) B))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a A))) (= (@ _let_1 (@ tptp.uminus_uminus_poly_a B)) (@ tptp.uminus_uminus_poly_a (@ _let_1 B))))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a A))) (= (@ _let_1 (@ tptp.uminus_uminus_a B)) (@ tptp.uminus_uminus_a (@ _let_1 B))))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a (@ tptp.uminus_uminus_poly_a A)) (@ tptp.uminus_uminus_poly_a B)) (@ (@ tptp.times_times_poly_a A) B))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.times_times_a (@ tptp.uminus_uminus_a A)) (@ tptp.uminus_uminus_a B)) (@ (@ tptp.times_times_a A) B))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a (@ tptp.uminus_uminus_poly_a A)) B) (@ tptp.uminus_uminus_poly_a (@ (@ tptp.times_times_poly_a A) B)))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.times_times_a (@ tptp.uminus_uminus_a A)) B) (@ tptp.uminus_uminus_a (@ (@ tptp.times_times_a A) B)))) (forall ((A tptp.list_a)) (= (@ (@ tptp.append_a A) tptp.nil_a) A)) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) tptp.nil_a) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= tptp.nil_a (@ (@ tptp.append_a Xs) Ys2)) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))) (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (= (= Ys2 (@ (@ tptp.append_a Xs) Ys2)) (= Xs tptp.nil_a))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) Ys2) (= Xs tptp.nil_a))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= Xs (@ (@ tptp.append_a Xs) Ys2)) (= Ys2 tptp.nil_a))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) Xs) (= Ys2 tptp.nil_a))) (forall ((Xs tptp.list_a)) (= (@ (@ tptp.append_a Xs) tptp.nil_a) Xs)) (forall ((C tptp.a)) (= (@ (@ tptp.smult_a C) tptp.one_one_poly_a) (@ (@ tptp.pCons_a C) tptp.zero_zero_poly_a))) (forall ((X tptp.poly_a)) (= (= tptp.zero_zero_poly_a X) (= X tptp.zero_zero_poly_a))) (forall ((X tptp.a)) (= (= tptp.zero_zero_a X) (= X tptp.zero_zero_a))) (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))) (forall ((X tptp.a) (Y3 tptp.a)) (=> (not (= X Y3)) (=> (not (@ (@ tptp.ord_less_a X) Y3)) (@ (@ tptp.ord_less_a Y3) X)))) (forall ((X tptp.poly_a) (Y3 tptp.poly_a)) (=> (not (= X Y3)) (=> (not (@ (@ tptp.ord_less_poly_a X) Y3)) (@ (@ tptp.ord_less_poly_a Y3) X)))) (forall ((B tptp.poly_a) (A tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a B))) (let ((_let_2 (@ tptp.times_times_poly_a 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.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.times_times_poly_a (lambda ((A3 tptp.poly_a) (B3 tptp.poly_a)) (@ (@ tptp.times_times_poly_a B3) A3))) (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A3))) (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a A))) (= (@ (@ tptp.times_times_poly_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_poly_a B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))) (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a A))) (= (@ (@ tptp.times_times_poly_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_poly_a B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))) (forall ((X tptp.a)) (= (= tptp.one_one_a X) (= X tptp.one_one_a))) (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))) (forall ((A tptp.a) (B tptp.a)) (= (= (@ tptp.uminus_uminus_a A) B) (= (@ tptp.uminus_uminus_a B) A))) (forall ((A tptp.a) (B tptp.a)) (= (= A (@ tptp.uminus_uminus_a B)) (= B (@ tptp.uminus_uminus_a A)))) (forall ((X tptp.a) (Xs tptp.list_a)) (not (= (@ (@ tptp.cons_a X) Xs) Xs))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a) (Ts tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) (@ (@ tptp.append_a Zs) Ts)) (exists ((Us tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (or (and (= Xs (@ (@ tptp.append_a Zs) Us)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append_a Xs) Us) Zs) (= Ys2 (@ _let_1 Ts)))))))) (forall ((Xs tptp.list_a) (Xs1 tptp.list_a) (Zs tptp.list_a) (Ys2 tptp.list_a) (Us2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys2 (@ (@ tptp.append_a Xs1) Us2)) (= (@ _let_1 Ys2) (@ (@ tptp.append_a Zs) Us2)))))) (forall ((X tptp.a) (Y3 tptp.a)) (let ((_let_1 (@ tptp.descar2095969287nges_a (@ (@ tptp.cons_a X) (@ (@ tptp.cons_a Y3) tptp.nil_a))))) (let ((_let_2 (@ tptp.ord_less_a tptp.zero_zero_a))) (let ((_let_3 (or (and (@ _let_2 X) (@ (@ tptp.ord_less_a Y3) tptp.zero_zero_a)) (and (@ (@ tptp.ord_less_a X) tptp.zero_zero_a) (@ _let_2 Y3))))) (and (=> _let_3 (= _let_1 tptp.one_one_nat)) (=> (not _let_3) (= _let_1 tptp.zero_zero_nat))))))) (forall ((X tptp.poly_a) (Y3 tptp.poly_a)) (let ((_let_1 (@ tptp.descar357075861poly_a (@ (@ tptp.cons_poly_a X) (@ (@ tptp.cons_poly_a Y3) tptp.nil_poly_a))))) (let ((_let_2 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (let ((_let_3 (or (and (@ _let_2 X) (@ (@ tptp.ord_less_poly_a Y3) tptp.zero_zero_poly_a)) (and (@ (@ tptp.ord_less_poly_a X) tptp.zero_zero_poly_a) (@ _let_2 Y3))))) (and (=> _let_3 (= _let_1 tptp.one_one_nat)) (=> (not _let_3) (= _let_1 tptp.zero_zero_nat))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= 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)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) (not (@ (@ tptp.ord_less_a tptp.zero_zero_a) tptp.zero_zero_a)) (not (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) tptp.zero_zero_poly_a)) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (=> (not (= C tptp.zero_zero_a)) (= (= (@ (@ tptp.times_times_a A) C) (@ (@ tptp.times_times_a B) C)) (= A B)))) (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (=> (not (= C tptp.zero_zero_poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) C) (@ (@ tptp.times_times_poly_a B) C)) (= A B)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (not (= C tptp.zero_zero_a)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (not (= C tptp.zero_zero_poly_a)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (forall ((A tptp.a) (B tptp.a)) (=> (not (= A tptp.zero_zero_a)) (=> (not (= B tptp.zero_zero_a)) (not (= (@ (@ tptp.times_times_a A) B) tptp.zero_zero_a))))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (not (= A tptp.zero_zero_poly_a)) (=> (not (= B tptp.zero_zero_poly_a)) (not (= (@ (@ tptp.times_times_poly_a A) B) tptp.zero_zero_poly_a))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))) (forall ((A tptp.a) (B tptp.a)) (=> (= (@ (@ tptp.times_times_a A) B) tptp.zero_zero_a) (or (= A tptp.zero_zero_a) (= B tptp.zero_zero_a)))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (= (@ (@ tptp.times_times_poly_a A) B) tptp.zero_zero_poly_a) (or (= A tptp.zero_zero_poly_a) (= B tptp.zero_zero_poly_a)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.a) (B tptp.a)) (=> (not (= (@ (@ tptp.times_times_a A) B) tptp.zero_zero_a)) (and (not (= A tptp.zero_zero_a)) (not (= B tptp.zero_zero_a))))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (not (= (@ (@ tptp.times_times_poly_a A) B) tptp.zero_zero_poly_a)) (and (not (= A tptp.zero_zero_poly_a)) (not (= B tptp.zero_zero_poly_a))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))) (not (= tptp.zero_zero_poly_a tptp.one_one_poly_a)) (not (= tptp.zero_zero_a tptp.one_one_a)) (not (= tptp.zero_zero_nat tptp.one_one_nat)) (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)) (not (@ (@ tptp.ord_less_a tptp.one_one_a) tptp.one_one_a)) (not (@ (@ tptp.ord_less_poly_a tptp.one_one_poly_a) tptp.one_one_poly_a)) (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a A) tptp.one_one_a) A)) (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a A) tptp.one_one_poly_a) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.a)) (= (@ (@ tptp.times_times_a tptp.one_one_a) A) A)) (forall ((A tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a tptp.one_one_poly_a) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a A)) B) (@ (@ tptp.ord_less_poly_a (@ tptp.uminus_uminus_poly_a B)) A))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) B) (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a B)) A))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a A) (@ tptp.uminus_uminus_poly_a B)) (@ (@ tptp.ord_less_poly_a B) (@ tptp.uminus_uminus_poly_a A)))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a A) (@ tptp.uminus_uminus_a B)) (@ (@ tptp.ord_less_a B) (@ tptp.uminus_uminus_a A)))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.times_times_poly_a (@ tptp.uminus_uminus_poly_a A)) B) (@ (@ tptp.times_times_poly_a A) (@ tptp.uminus_uminus_poly_a B)))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.times_times_a (@ tptp.uminus_uminus_a A)) B) (@ (@ tptp.times_times_a A) (@ tptp.uminus_uminus_a B)))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (= (= (@ (@ tptp.times_times_poly_a A) A) (@ (@ tptp.times_times_poly_a B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_poly_a B))))) (forall ((A tptp.a) (B tptp.a)) (= (= (@ (@ tptp.times_times_a A) A) (@ (@ tptp.times_times_a B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_a B))))) (not (= tptp.one_one_a _let_4)) (forall ((P3 (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (@ P3 tptp.nil_a) (=> (forall ((X2 tptp.a) (Ys tptp.list_a)) (=> (@ P3 Ys) (@ P3 (@ (@ tptp.cons_a X2) Ys)))) (@ P3 A0)))) (forall ((X tptp.list_a)) (=> (not (= X tptp.nil_a)) (not (forall ((X2 tptp.a) (Ys tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) Ys))))))) (forall ((P3 (-> (-> tptp.a tptp.a) tptp.list_a tptp.list_a Bool)) (A0 (-> tptp.a tptp.a)) (A1 tptp.list_a) (A22 tptp.list_a)) (=> (forall ((F2 (-> tptp.a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P3 F2) tptp.nil_a) X_1)) (=> (forall ((F2 (-> tptp.a tptp.a)) (A2 tptp.a) (As2 tptp.list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P3 F2))) (=> (@ (@ _let_1 As2) (@ (@ tptp.cons_a (@ F2 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A2) As2)) Bs)))) (@ (@ (@ P3 A0) A1) A22)))) (forall ((Xs tptp.list_a) (P3 (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X2 tptp.a)) (@ P3 (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a)) (=> (not (= Xs2 tptp.nil_a)) (=> (@ P3 Xs2) (@ P3 (@ (@ tptp.cons_a X2) Xs2))))) (@ P3 Xs))))) (forall ((P3 (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P5 (-> tptp.a tptp.a Bool))) (@ (@ P3 P5) tptp.nil_a)) (=> (forall ((P5 (-> tptp.a tptp.a Bool)) (X2 tptp.a)) (@ (@ P3 P5) (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((P5 (-> tptp.a tptp.a Bool)) (X2 tptp.a) (Y2 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Xs2))) (let ((_let_2 (@ P3 P5))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_a X2) _let_1)))))) (@ (@ P3 A0) A1))))) (forall ((P3 (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (@ P3 tptp.nil_a) (=> (forall ((X2 tptp.a)) (@ P3 (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Xs2))) (let ((_let_2 (@ tptp.cons_a X2))) (let ((_let_3 (= X2 Y2))) (=> (=> _let_3 (@ P3 (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P3 _let_1)) (@ P3 (@ _let_2 _let_1)))))))) (@ P3 A0))))) (forall ((P3 (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P5 (-> tptp.a tptp.a Bool))) (@ (@ P3 P5) tptp.nil_a)) (=> (forall ((P5 (-> tptp.a tptp.a Bool)) (X2 tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ P3 P5))) (=> (@ _let_1 Ys) (@ _let_1 (@ (@ tptp.cons_a X2) Ys))))) (@ (@ P3 A0) A1)))) (forall ((X tptp.list_a)) (=> (not (= X tptp.nil_a)) (=> (forall ((X2 tptp.a)) (not (= X (@ (@ tptp.cons_a X2) tptp.nil_a)))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs2 tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) (@ (@ tptp.cons_a Y2) Xs2))))))))) (forall ((X tptp.list_list_a)) (=> (not (= X tptp.nil_list_a)) (=> (forall ((Xss tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a tptp.nil_a) Xss)))) (not (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Xss tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a (@ (@ tptp.cons_a X2) Xs2)) Xss)))))))) (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P3 tptp.nil_a) X_1)) (=> (forall ((Xs2 tptp.list_a)) (@ (@ P3 Xs2) tptp.nil_a)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Y2 tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Ys))) (let ((_let_2 (@ P3 (@ (@ tptp.cons_a X2) Xs2)))) (=> (@ (@ P3 Xs2) _let_1) (=> (@ _let_2 Ys) (@ _let_2 _let_1)))))) (@ (@ P3 A0) A1))))) (forall ((P3 (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a)) (=> (forall ((X212 tptp.a) (X222 tptp.list_a)) (=> (= Xs2 (@ (@ tptp.cons_a X212) X222)) (@ P3 Xs2))) (@ P3 (@ (@ tptp.cons_a X2) Xs2)))) (=> (@ P3 tptp.nil_a) (@ P3 A0)))) (forall ((X tptp.list_a)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) Xs2)))) (= X tptp.nil_a))) (forall ((P3 (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P3 tptp.nil_a) (=> (forall ((X2 tptp.a)) (@ P3 (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Zs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Zs2))) (=> (@ P3 Zs2) (=> (@ P3 _let_1) (@ P3 (@ (@ tptp.cons_a X2) _let_1)))))) (@ P3 Xs))))) (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P3 tptp.nil_a) X_1)) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ P3 Ys) Xs2) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) Ys))) (@ (@ P3 A0) A1)))) (forall ((P3 (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ P3 tptp.nil_a) tptp.nil_a) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a)) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) tptp.nil_a)) (=> (forall ((Y2 tptp.a) (Ys tptp.list_a)) (@ (@ P3 tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys))) (=> (forall ((X2 tptp.a) (Xs2 tptp.list_a) (Y2 tptp.a) (Ys tptp.list_a)) (=> (@ (@ P3 Xs2) Ys) (@ (@ P3 (@ (@ tptp.cons_a X2) Xs2)) (@ (@ tptp.cons_a Y2) Ys)))) (@ (@ P3 Xs) Ys2)))))) (forall ((Xs tptp.list_a)) (= (not (= Xs tptp.nil_a)) (exists ((Y4 tptp.a) (Ys3 tptp.list_a)) (= Xs (@ (@ tptp.cons_a Y4) Ys3))))) (forall ((P3 (-> tptp.list_a Bool)) (List tptp.list_a)) (=> (@ P3 tptp.nil_a) (=> (forall ((X1 tptp.a) (X23 tptp.list_a)) (=> (@ P3 X23) (@ P3 (@ (@ tptp.cons_a X1) X23)))) (@ P3 List)))) (forall ((Y3 tptp.list_a)) (=> (not (= Y3 tptp.nil_a)) (not (forall ((X213 tptp.a) (X223 tptp.list_a)) (not (= Y3 (@ (@ tptp.cons_a X213) X223))))))) (forall ((List tptp.list_a) (X21 tptp.a) (X22 tptp.list_a)) (=> (= List (@ (@ tptp.cons_a X21) X22)) (not (= List tptp.nil_a)))) (forall ((X21 tptp.a) (X22 tptp.list_a)) (not (= tptp.nil_a (@ (@ tptp.cons_a X21) X22)))) (forall ((X tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (= (@ (@ tptp.append_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.append_a Xs) Ys2))))) (forall ((X tptp.a) (Xs1 tptp.list_a) (Ys2 tptp.list_a) (Xs tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs (@ (@ tptp.append_a Xs1) Zs)) (= (@ _let_1 Xs) (@ (@ tptp.append_a Ys2) Zs)))))) (forall ((A tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) A) A)) (forall ((Ys2 tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) Ys2) Ys2)) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append_a tptp.nil_a) Ys2)))) (forall ((X tptp.a) (Xs tptp.list_a)) (not (@ tptp.null_a (@ (@ tptp.cons_a X) Xs)))) (forall ((Xs tptp.list_a)) (= (= Xs tptp.nil_a) (@ tptp.null_a Xs))) (@ tptp.null_a tptp.nil_a) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a A) B) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a A) B) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) C)) (@ (@ tptp.times_times_a B) C)) (or (and (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a A) B)) (and (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (@ (@ tptp.ord_less_a B) A))))) (forall ((A tptp.poly_a) (C tptp.poly_a) (B tptp.poly_a)) (= (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) C)) (@ (@ tptp.times_times_poly_a B) C)) (or (and (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a A) B)) (and (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a B) A))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (@ (@ tptp.ord_less_a A) B) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) C)) (@ (@ tptp.times_times_a B) C))))) (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a A) B) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) C)) (@ (@ tptp.times_times_poly_a B) C))))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (=> (@ (@ tptp.ord_less_a B) A) (=> (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) C)) (@ (@ tptp.times_times_a B) C))))) (forall ((B tptp.poly_a) (A tptp.poly_a) (C tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a B) A) (=> (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) C)) (@ (@ tptp.times_times_poly_a B) C))))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (= (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a A) B)) (and (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (@ (@ tptp.ord_less_a B) A)))))) (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (= (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a A) B)) (and (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a B) A)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a A) B) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.poly_a) (B tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a A) B) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)))))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a B) A) (=> (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)))))) (forall ((B tptp.poly_a) (A tptp.poly_a) (C tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a B) A) (=> (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)))))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) C) (= (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_a A) B))))) (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) C) (= (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_poly_a A) B))))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.times_times_a C))) (=> (@ (@ tptp.ord_less_a C) tptp.zero_zero_a) (= (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_a B) A))))) (forall ((C tptp.poly_a) (A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.times_times_poly_a C))) (=> (@ (@ tptp.ord_less_poly_a C) tptp.zero_zero_poly_a) (= (@ (@ tptp.ord_less_poly_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_poly_a B) A))))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ _let_1 (@ (@ tptp.times_times_a B) A)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((B tptp.poly_a) (A tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (=> (@ _let_1 (@ (@ tptp.times_times_poly_a B) A)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ _let_1 (@ (@ tptp.times_times_a A) B)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (=> (@ _let_1 (@ (@ tptp.times_times_poly_a A) B)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (= (@ _let_1 (@ (@ tptp.times_times_a A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_a A) tptp.zero_zero_a) (@ (@ tptp.ord_less_a B) tptp.zero_zero_a)))))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (= (@ _let_1 (@ (@ tptp.times_times_poly_a A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_poly_a A) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a B) tptp.zero_zero_poly_a)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (=> (@ (@ tptp.ord_less_a B) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a B) A)) tptp.zero_zero_a)))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A) (=> (@ (@ tptp.ord_less_poly_a B) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a B) A)) tptp.zero_zero_poly_a)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_a A) B)))))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_poly_a A) B)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (=> (@ (@ tptp.ord_less_a B) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) B)) tptp.zero_zero_a)))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) A) (=> (@ (@ tptp.ord_less_poly_a B) tptp.zero_zero_poly_a) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) B)) tptp.zero_zero_poly_a)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_a A) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) B) (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) B)) tptp.zero_zero_a)))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (=> (@ (@ tptp.ord_less_poly_a A) tptp.zero_zero_poly_a) (=> (@ (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a) B) (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) B)) tptp.zero_zero_poly_a)))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (= (@ (@ tptp.ord_less_a (@ (@ tptp.times_times_a A) B)) tptp.zero_zero_a) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_a B) tptp.zero_zero_a)) (and (@ (@ tptp.ord_less_a A) tptp.zero_zero_a) (@ _let_1 B)))))) (forall ((A tptp.poly_a) (B tptp.poly_a)) (let ((_let_1 (@ tptp.ord_less_poly_a tptp.zero_zero_poly_a))) (= (@ (@ tptp.ord_less_poly_a (@ (@ tptp.times_times_poly_a A) B)) tptp.zero_zero_poly_a) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_poly_a B) tptp.zero_zero_poly_a)) (and (@ (@ tptp.ord_less_poly_a A) tptp.zero_zero_poly_a) (@ _let_1 B)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K 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)) (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 ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((X tptp.nat) (Y3 tptp.nat)) (=> (not (= X Y3)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (@ (@ tptp.ord_less_nat Y3) X)))) (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P3 N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P3 M2)))))) (@ P3 N))) (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P3 M2))) (@ P3 N2))) (@ P3 N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S 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 ((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 tptp.zero_zero_nat) N)) (= 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 ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))) (forall ((P3 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P3 tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P3 N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P3 M2))))))) (@ P3 N)))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))) _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.75/0.92 )
% 0.75/0.92 % SZS output end Proof for ITP044^1
% 0.75/0.92 % cvc5---1.0.5 exiting
% 0.75/0.92 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------