TSTP Solution File: ITP026^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP026^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 03:17:34 EDT 2023
% Result : Theorem 1.45s 1.76s
% Output : Proof 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.19 % Problem : ITP026^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.20 % Command : do_cvc5 %s %d
% 0.19/0.40 % Computer : n001.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.41 % CPULimit : 300
% 0.19/0.41 % WCLimit : 300
% 0.19/0.41 % DateTime : Sun Aug 27 12:07:03 EDT 2023
% 0.19/0.41 % CPUTime :
% 0.26/0.60 %----Proving TH0
% 0.26/0.60 %------------------------------------------------------------------------------
% 0.26/0.60 % File : ITP026^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.60 % Domain : Interactive Theorem Proving
% 0.26/0.60 % Problem : Sledgehammer Algebra8 problem prob_1404__6432666_1
% 0.26/0.60 % Version : Especial.
% 0.26/0.60 % English :
% 0.26/0.60
% 0.26/0.60 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.60 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.60 % Source : [Des21]
% 0.26/0.60 % Names : Algebra8/prob_1404__6432666_1 [Des21]
% 0.26/0.60
% 0.26/0.60 % Status : Theorem
% 0.26/0.60 % Rating : 0.31 v8.1.0, 0.36 v7.5.0
% 0.26/0.60 % Syntax : Number of formulae : 493 ( 128 unt; 122 typ; 0 def)
% 0.26/0.60 % Number of atoms : 1156 ( 221 equ; 0 cnn)
% 0.26/0.60 % Maximal formula atoms : 12 ( 3 avg)
% 0.26/0.60 % Number of connectives : 4133 ( 74 ~; 13 |; 56 &;3386 @)
% 0.26/0.60 % ( 0 <=>; 604 =>; 0 <=; 0 <~>)
% 0.26/0.60 % Maximal formula depth : 21 ( 8 avg)
% 0.26/0.60 % Number of types : 20 ( 19 usr)
% 0.26/0.60 % Number of type conns : 375 ( 375 >; 0 *; 0 +; 0 <<)
% 0.26/0.60 % Number of symbols : 105 ( 103 usr; 16 con; 0-5 aty)
% 0.26/0.60 % Number of variables : 1109 ( 166 ^; 904 !; 39 ?;1109 :)
% 0.26/0.60 % SPC : TH0_THM_EQU_NAR
% 0.26/0.60
% 0.26/0.60 % Comments : This file was generated by Sledgehammer 2021-02-23 15:46:47.396
% 0.26/0.60 %------------------------------------------------------------------------------
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% 0.26/0.60 misomo1282343797_c_a_c: carrie1950868226xt_b_d > carrie722926983_a_b_c > carrie722926983_a_b_c > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__a_001tf__c_001tf__e_001tf__f,type,
% 0.26/0.60 misomo298454132_c_e_f: carrie1950868226xt_b_d > carrie722926983_a_b_c > carrie1821755406_e_b_f > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__e_001tf__f_001tf__a_001t__Product____Type__Ounit,type,
% 0.26/0.60 misomo368157697t_unit: carrie1950868226xt_b_d > carrie1821755406_e_b_f > carrie1963041556t_unit > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__e_001tf__f_001tf__a_001tf__c,type,
% 0.26/0.60 misomo1752826100_f_a_c: carrie1950868226xt_b_d > carrie1821755406_e_b_f > carrie722926983_a_b_c > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__e_001tf__f_001tf__e_001tf__f,type,
% 0.26/0.60 misomo768936435_f_e_f: carrie1950868226xt_b_d > carrie1821755406_e_b_f > carrie1821755406_e_b_f > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Oquotient__of__submodules_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit,type,
% 0.26/0.60 quotie1196826005t_unit: carrie1950868226xt_b_d > carrie1963041556t_unit > set_a > set_a > set_b ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Oquotient__of__submodules_001tf__b_001tf__d_001tf__a_001tf__c,type,
% 0.26/0.60 quotie1153752712_d_a_c: carrie1950868226xt_b_d > carrie722926983_a_b_c > set_a > set_a > set_b ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Oquotient__of__submodules_001tf__b_001tf__d_001tf__e_001tf__f,type,
% 0.26/0.60 quotie169863047_d_e_f: carrie1950868226xt_b_d > carrie1821755406_e_b_f > set_e > set_e > set_b ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Osmodule__ideal__coeff_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit,type,
% 0.26/0.60 smodul132175289t_unit: carrie1950868226xt_b_d > carrie1963041556t_unit > set_b > set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Osmodule__ideal__coeff_001tf__b_001tf__d_001tf__a_001tf__c,type,
% 0.26/0.60 smodul818989740_d_a_c: carrie1950868226xt_b_d > carrie722926983_a_b_c > set_b > set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Osmodule__ideal__coeff_001tf__b_001tf__d_001tf__e_001tf__f,type,
% 0.26/0.60 smodul1982583723_d_e_f: carrie1950868226xt_b_d > carrie1821755406_e_b_f > set_b > set_e ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Osubmodule_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit,type,
% 0.26/0.60 submod903911234t_unit: carrie1950868226xt_b_d > carrie1963041556t_unit > set_a > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Osubmodule_001tf__b_001tf__d_001tf__a_001tf__c,type,
% 0.26/0.60 submodule_b_d_a_c: carrie1950868226xt_b_d > carrie722926983_a_b_c > set_a > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra7_Osubmodule_001tf__b_001tf__d_001tf__e_001tf__f,type,
% 0.26/0.60 submodule_b_d_e_f: carrie1950868226xt_b_d > carrie1821755406_e_b_f > set_e > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra8__Mirabelle__tltoludslr_Ofgs_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit,type,
% 0.26/0.60 algebr1039611956t_unit: carrie1950868226xt_b_d > carrie1963041556t_unit > set_a > set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra8__Mirabelle__tltoludslr_Ofgs_001tf__b_001tf__d_001tf__a_001tf__c,type,
% 0.26/0.60 algebr1152250919_d_a_c: carrie1950868226xt_b_d > carrie722926983_a_b_c > set_a > set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Algebra8__Mirabelle__tltoludslr_Ofgs_001tf__b_001tf__d_001tf__e_001tf__f,type,
% 0.26/0.60 algebr168361254_d_e_f: carrie1950868226xt_b_d > carrie1821755406_e_b_f > set_e > set_e ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_FuncSet_OPi_001t__Nat__Onat_001tf__a,type,
% 0.26/0.60 pi_nat_a: set_nat > ( nat > set_a ) > set_nat_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_FuncSet_OPi_001t__Nat__Onat_001tf__b,type,
% 0.26/0.60 pi_nat_b: set_nat > ( nat > set_b ) > set_nat_b ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_FuncSet_OPi_001t__Nat__Onat_001tf__e,type,
% 0.26/0.60 pi_nat_e: set_nat > ( nat > set_e ) > set_nat_e ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.26/0.60 minus_minus_nat: nat > nat > nat ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__a_J_J,type,
% 0.26/0.60 minus_1788767276_nat_a: set_nat_a > set_nat_a > set_nat_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__b_J_J,type,
% 0.26/0.60 minus_780847917_nat_b: set_nat_b > set_nat_b > set_nat_b ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.60 minus_minus_set_a: set_a > set_a > set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.26/0.60 zero_zero_nat: nat ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Nat_OSuc,type,
% 0.26/0.60 suc: nat > nat ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__a_J_J,type,
% 0.26/0.60 bot_bot_set_nat_a: set_nat_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__b_J_J,type,
% 0.26/0.60 bot_bot_set_nat_b: set_nat_b ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.60 bot_bot_set_nat: set_nat ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.60 bot_bot_set_a: set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__e_J,type,
% 0.26/0.60 bot_bot_set_e: set_e ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.26/0.60 ord_less_nat: nat > nat > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.60 ord_less_set_a: set_a > set_a > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.26/0.60 ord_less_eq_nat: nat > nat > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__a_J_J,type,
% 0.26/0.60 ord_le157368549_nat_a: set_nat_a > set_nat_a > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__b_J_J,type,
% 0.26/0.60 ord_le1296932838_nat_b: set_nat_b > set_nat_b > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.60 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__e_J,type,
% 0.26/0.60 ord_less_eq_set_e: set_e > set_e > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Set_OCollect_001_062_It__Nat__Onat_Mtf__a_J,type,
% 0.26/0.60 collect_nat_a: ( ( nat > a ) > $o ) > set_nat_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Set_OCollect_001_062_It__Nat__Onat_Mtf__b_J,type,
% 0.26/0.60 collect_nat_b: ( ( nat > b ) > $o ) > set_nat_b ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.26/0.60 collect_nat: ( nat > $o ) > set_nat ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.26/0.60 collect_a: ( a > $o ) > set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Set_Oinsert_001_062_It__Nat__Onat_Mtf__a_J,type,
% 0.26/0.60 insert_nat_a: ( nat > a ) > set_nat_a > set_nat_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Set_Oinsert_001_062_It__Nat__Onat_Mtf__b_J,type,
% 0.26/0.60 insert_nat_b: ( nat > b ) > set_nat_b > set_nat_b ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.26/0.60 insert_a: a > set_a > set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_member_001_062_It__Nat__Onat_Mtf__a_J,type,
% 0.26/0.60 member_nat_a: ( nat > a ) > set_nat_a > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_member_001_062_It__Nat__Onat_Mtf__b_J,type,
% 0.26/0.60 member_nat_b: ( nat > b ) > set_nat_b > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_member_001_062_It__Nat__Onat_Mtf__e_J,type,
% 0.26/0.60 member_nat_e: ( nat > e ) > set_nat_e > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_member_001t__Nat__Onat,type,
% 0.26/0.60 member_nat: nat > set_nat > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_member_001tf__a,type,
% 0.26/0.60 member_a: a > set_a > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_c_member_001tf__e,type,
% 0.26/0.60 member_e: e > set_e > $o ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_H,type,
% 0.26/0.60 h: set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_H1,type,
% 0.26/0.60 h1: set_a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_M,type,
% 0.26/0.60 m: carrie722926983_a_b_c ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_N,type,
% 0.26/0.60 n: carrie1821755406_e_b_f ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_R,type,
% 0.26/0.60 r: carrie1950868226xt_b_d ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_g,type,
% 0.26/0.60 g: nat > a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_h,type,
% 0.26/0.60 h2: a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_m,type,
% 0.26/0.60 m2: nat ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_t,type,
% 0.26/0.60 t: nat > b ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_x,type,
% 0.26/0.60 x: a ).
% 0.26/0.60
% 0.26/0.60 thf(sy_v_xa,type,
% 0.26/0.60 xa: nat ).
% 0.26/0.60
% 0.26/0.60 % Relevant facts (349)
% 0.26/0.60 thf(fact_0_sc__Ring,axiom,
% 0.26/0.60 ring_b_d @ r ).
% 0.26/0.60
% 0.26/0.60 % sc_Ring
% 0.26/0.60 thf(fact_1_submodule__subset1,axiom,
% 0.26/0.60 ! [H: set_a,H2: a] :
% 0.26/0.60 ( ( submodule_b_d_a_c @ r @ m @ H )
% 0.26/0.60 => ( ( member_a @ H2 @ H )
% 0.26/0.60 => ( member_a @ H2 @ ( carrie2021454486_a_b_c @ m ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % submodule_subset1
% 0.26/0.60 thf(fact_2_submodule__whole,axiom,
% 0.26/0.60 submodule_b_d_a_c @ r @ m @ ( carrie2021454486_a_b_c @ m ) ).
% 0.26/0.60
% 0.26/0.60 % submodule_whole
% 0.26/0.60 thf(fact_3_submodule__subset,axiom,
% 0.26/0.60 ! [H: set_a] :
% 0.26/0.60 ( ( submodule_b_d_a_c @ r @ m @ H )
% 0.26/0.60 => ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % submodule_subset
% 0.26/0.60 thf(fact_4_free__generator__sub,axiom,
% 0.26/0.60 ! [H: set_a] :
% 0.26/0.60 ( ( free_g1087686480_d_a_c @ r @ m @ H )
% 0.26/0.60 => ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % free_generator_sub
% 0.26/0.60 thf(fact_5_elem__fgs,axiom,
% 0.26/0.60 ! [A: set_a,X: a] :
% 0.26/0.60 ( ( ord_less_eq_set_a @ A @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.60 => ( ( member_a @ X @ A )
% 0.26/0.60 => ( member_a @ X @ ( algebr1152250919_d_a_c @ r @ m @ A ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % elem_fgs
% 0.26/0.60 thf(fact_6_fgs__sub__carrier,axiom,
% 0.26/0.60 ! [A: set_a] :
% 0.26/0.60 ( ( ord_less_eq_set_a @ A @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.60 => ( ord_less_eq_set_a @ ( algebr1152250919_d_a_c @ r @ m @ A ) @ ( carrie2021454486_a_b_c @ m ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % fgs_sub_carrier
% 0.26/0.60 thf(fact_7_fgs__mono,axiom,
% 0.26/0.60 ! [H: set_a,J: set_a,K: set_a] :
% 0.26/0.60 ( ( free_g1087686480_d_a_c @ r @ m @ H )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ J @ K )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ K @ H )
% 0.26/0.60 => ( ord_less_eq_set_a @ ( algebr1152250919_d_a_c @ r @ m @ J ) @ ( algebr1152250919_d_a_c @ r @ m @ K ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % fgs_mono
% 0.26/0.60 thf(fact_8_fgs__submodule,axiom,
% 0.26/0.60 ! [A: set_a] :
% 0.26/0.60 ( ( ord_less_eq_set_a @ A @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.60 => ( submodule_b_d_a_c @ r @ m @ ( algebr1152250919_d_a_c @ r @ m @ A ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % fgs_submodule
% 0.26/0.60 thf(fact_9_linear__comb__eq,axiom,
% 0.26/0.60 ! [H: set_a,S: nat > b,N: nat,F: nat > a,G: nat > a] :
% 0.26/0.60 ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.60 => ( ( member_nat_b @ S
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ r ) ) )
% 0.26/0.60 => ( ( member_nat_a @ F
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( ( member_nat_a @ G
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( ! [X2: nat] :
% 0.26/0.60 ( ( member_nat @ X2
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) ) )
% 0.26/0.60 => ( ( F @ X2 )
% 0.26/0.60 = ( G @ X2 ) ) )
% 0.26/0.60 => ( ( l_comb_b_d_a_c @ r @ m @ N @ S @ F )
% 0.26/0.60 = ( l_comb_b_d_a_c @ r @ m @ N @ S @ G ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % linear_comb_eq
% 0.26/0.60 thf(fact_10_linear__comb__eqTr,axiom,
% 0.26/0.60 ! [H: set_a,S: nat > b,N: nat,F: nat > a,G: nat > a] :
% 0.26/0.60 ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.60 => ( ( ( member_nat_b @ S
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ r ) ) )
% 0.26/0.60 & ( member_nat_a @ F
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 & ( member_nat_a @ G
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 & ! [X2: nat] :
% 0.26/0.60 ( ( member_nat @ X2
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) ) )
% 0.26/0.60 => ( ( F @ X2 )
% 0.26/0.60 = ( G @ X2 ) ) ) )
% 0.26/0.60 => ( ( l_comb_b_d_a_c @ r @ m @ N @ S @ F )
% 0.26/0.60 = ( l_comb_b_d_a_c @ r @ m @ N @ S @ G ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % linear_comb_eqTr
% 0.26/0.60 thf(fact_11_l__comb__mem,axiom,
% 0.26/0.60 ! [A2: set_b,H: set_a,S: nat > b,N: nat,M: nat > a] :
% 0.26/0.60 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.60 => ( ( member_nat_b @ S
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.60 => ( ( member_nat_a @ M
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( member_a @ ( l_comb_b_d_a_c @ r @ m @ N @ S @ M ) @ ( carrie2021454486_a_b_c @ m ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % l_comb_mem
% 0.26/0.60 thf(fact_12_liear__comb__memTr,axiom,
% 0.26/0.60 ! [A2: set_b,H: set_a,N: nat] :
% 0.26/0.60 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.60 => ! [S2: nat > b,M2: nat > a] :
% 0.26/0.60 ( ( ( member_nat_b @ S2
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.60 & ( member_nat_a @ M2
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) ) )
% 0.26/0.60 => ( member_a @ ( l_comb_b_d_a_c @ r @ m @ N @ S2 @ M2 ) @ ( carrie2021454486_a_b_c @ m ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % liear_comb_memTr
% 0.26/0.60 thf(fact_13_Ann__is__ideal,axiom,
% 0.26/0.60 ideal_b_d @ r @ ( annihilator_b_d_a_c @ r @ m ) ).
% 0.26/0.60
% 0.26/0.60 % Ann_is_ideal
% 0.26/0.60 thf(fact_14_mem__fgs__l__comb,axiom,
% 0.26/0.60 ! [K: set_a,X: a] :
% 0.26/0.60 ( ( K != bot_bot_set_a )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ K @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.60 => ( ( member_a @ X @ ( algebr1152250919_d_a_c @ r @ m @ K ) )
% 0.26/0.60 => ? [N2: nat,X2: nat > a] :
% 0.26/0.60 ( ( member_nat_a @ X2
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : K ) )
% 0.26/0.60 & ? [Xa: nat > b] :
% 0.26/0.60 ( ( member_nat_b @ Xa
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ r ) ) )
% 0.26/0.60 & ( X
% 0.26/0.60 = ( l_comb_b_d_a_c @ r @ m @ N2 @ Xa @ X2 ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % mem_fgs_l_comb
% 0.26/0.60 thf(fact_15_Module__axioms,axiom,
% 0.26/0.60 module_a_b_c_d @ m @ r ).
% 0.26/0.60
% 0.26/0.60 % Module_axioms
% 0.26/0.60 thf(fact_16_quotient__of__submodules__is__ideal,axiom,
% 0.26/0.60 ! [P: set_a,Q: set_a] :
% 0.26/0.60 ( ( submodule_b_d_a_c @ r @ m @ P )
% 0.26/0.60 => ( ( submodule_b_d_a_c @ r @ m @ Q )
% 0.26/0.60 => ( ideal_b_d @ r @ ( quotie1153752712_d_a_c @ r @ m @ P @ Q ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % quotient_of_submodules_is_ideal
% 0.26/0.60 thf(fact_17_smodule__ideal__coeff__is__Submodule,axiom,
% 0.26/0.60 ! [A2: set_b] :
% 0.26/0.60 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.60 => ( submodule_b_d_a_c @ r @ m @ ( smodul818989740_d_a_c @ r @ m @ A2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % smodule_ideal_coeff_is_Submodule
% 0.26/0.60 thf(fact_18_mem__smodule__ideal__coeff,axiom,
% 0.26/0.60 ! [A2: set_b,X: a] :
% 0.26/0.60 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.60 => ( ( member_a @ X @ ( smodul818989740_d_a_c @ r @ m @ A2 ) )
% 0.26/0.60 => ? [N2: nat,X2: nat > b] :
% 0.26/0.60 ( ( member_nat_b @ X2
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.60 & ? [Xa: nat > a] :
% 0.26/0.60 ( ( member_nat_a @ Xa
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : ( carrie2021454486_a_b_c @ m ) ) )
% 0.26/0.60 & ( X
% 0.26/0.60 = ( l_comb_b_d_a_c @ r @ m @ N2 @ X2 @ Xa ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % mem_smodule_ideal_coeff
% 0.26/0.60 thf(fact_19_Module_Oelem__fgs,axiom,
% 0.26/0.60 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,A: set_e,X: e] :
% 0.26/0.60 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_e @ A @ ( carrie730238621_e_b_f @ M3 ) )
% 0.26/0.60 => ( ( member_e @ X @ A )
% 0.26/0.60 => ( member_e @ X @ ( algebr168361254_d_e_f @ R @ M3 @ A ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.elem_fgs
% 0.26/0.60 thf(fact_20_Module_Oelem__fgs,axiom,
% 0.26/0.60 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,A: set_a,X: a] :
% 0.26/0.60 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ A @ ( carrie1074654371t_unit @ M3 ) )
% 0.26/0.60 => ( ( member_a @ X @ A )
% 0.26/0.60 => ( member_a @ X @ ( algebr1039611956t_unit @ R @ M3 @ A ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.elem_fgs
% 0.26/0.60 thf(fact_21_Module_Oelem__fgs,axiom,
% 0.26/0.60 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,A: set_a,X: a] :
% 0.26/0.60 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ A @ ( carrie2021454486_a_b_c @ M3 ) )
% 0.26/0.60 => ( ( member_a @ X @ A )
% 0.26/0.60 => ( member_a @ X @ ( algebr1152250919_d_a_c @ R @ M3 @ A ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.elem_fgs
% 0.26/0.60 thf(fact_22_Module_Ofgs__mono,axiom,
% 0.26/0.60 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,H: set_e,J: set_e,K: set_e] :
% 0.26/0.60 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.60 => ( ( free_g103796815_d_e_f @ R @ M3 @ H )
% 0.26/0.60 => ( ( ord_less_eq_set_e @ J @ K )
% 0.26/0.60 => ( ( ord_less_eq_set_e @ K @ H )
% 0.26/0.60 => ( ord_less_eq_set_e @ ( algebr168361254_d_e_f @ R @ M3 @ J ) @ ( algebr168361254_d_e_f @ R @ M3 @ K ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.fgs_mono
% 0.26/0.60 thf(fact_23_Module_Ofgs__mono,axiom,
% 0.26/0.60 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,H: set_a,J: set_a,K: set_a] :
% 0.26/0.60 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.60 => ( ( free_g637607517t_unit @ R @ M3 @ H )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ J @ K )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ K @ H )
% 0.26/0.60 => ( ord_less_eq_set_a @ ( algebr1039611956t_unit @ R @ M3 @ J ) @ ( algebr1039611956t_unit @ R @ M3 @ K ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.fgs_mono
% 0.26/0.60 thf(fact_24_Module_Ofgs__mono,axiom,
% 0.26/0.60 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,H: set_a,J: set_a,K: set_a] :
% 0.26/0.60 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.60 => ( ( free_g1087686480_d_a_c @ R @ M3 @ H )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ J @ K )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ K @ H )
% 0.26/0.60 => ( ord_less_eq_set_a @ ( algebr1152250919_d_a_c @ R @ M3 @ J ) @ ( algebr1152250919_d_a_c @ R @ M3 @ K ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.fgs_mono
% 0.26/0.60 thf(fact_25_Module_Ofgs__submodule,axiom,
% 0.26/0.60 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,A: set_e] :
% 0.26/0.60 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_e @ A @ ( carrie730238621_e_b_f @ M3 ) )
% 0.26/0.60 => ( submodule_b_d_e_f @ R @ M3 @ ( algebr168361254_d_e_f @ R @ M3 @ A ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.fgs_submodule
% 0.26/0.60 thf(fact_26_Module_Ofgs__submodule,axiom,
% 0.26/0.60 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,A: set_a] :
% 0.26/0.60 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ A @ ( carrie1074654371t_unit @ M3 ) )
% 0.26/0.60 => ( submod903911234t_unit @ R @ M3 @ ( algebr1039611956t_unit @ R @ M3 @ A ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.fgs_submodule
% 0.26/0.60 thf(fact_27_Module_Ofgs__submodule,axiom,
% 0.26/0.60 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,A: set_a] :
% 0.26/0.60 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ A @ ( carrie2021454486_a_b_c @ M3 ) )
% 0.26/0.60 => ( submodule_b_d_a_c @ R @ M3 @ ( algebr1152250919_d_a_c @ R @ M3 @ A ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.fgs_submodule
% 0.26/0.60 thf(fact_28_Module_Omem__fgs__l__comb,axiom,
% 0.26/0.60 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,K: set_e,X: e] :
% 0.26/0.60 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.60 => ( ( K != bot_bot_set_e )
% 0.26/0.60 => ( ( ord_less_eq_set_e @ K @ ( carrie730238621_e_b_f @ M3 ) )
% 0.26/0.60 => ( ( member_e @ X @ ( algebr168361254_d_e_f @ R @ M3 @ K ) )
% 0.26/0.60 => ? [N2: nat,X2: nat > e] :
% 0.26/0.60 ( ( member_nat_e @ X2
% 0.26/0.60 @ ( pi_nat_e
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : K ) )
% 0.26/0.60 & ? [Xa: nat > b] :
% 0.26/0.60 ( ( member_nat_b @ Xa
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ R ) ) )
% 0.26/0.60 & ( X
% 0.26/0.60 = ( l_comb_b_d_e_f @ R @ M3 @ N2 @ Xa @ X2 ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.mem_fgs_l_comb
% 0.26/0.60 thf(fact_29_Module_Omem__fgs__l__comb,axiom,
% 0.26/0.60 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,K: set_a,X: a] :
% 0.26/0.60 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.60 => ( ( K != bot_bot_set_a )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ K @ ( carrie1074654371t_unit @ M3 ) )
% 0.26/0.60 => ( ( member_a @ X @ ( algebr1039611956t_unit @ R @ M3 @ K ) )
% 0.26/0.60 => ? [N2: nat,X2: nat > a] :
% 0.26/0.60 ( ( member_nat_a @ X2
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : K ) )
% 0.26/0.60 & ? [Xa: nat > b] :
% 0.26/0.60 ( ( member_nat_b @ Xa
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ R ) ) )
% 0.26/0.60 & ( X
% 0.26/0.60 = ( l_comb1138968323t_unit @ R @ M3 @ N2 @ Xa @ X2 ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.mem_fgs_l_comb
% 0.26/0.60 thf(fact_30_Module_Omem__fgs__l__comb,axiom,
% 0.26/0.60 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,K: set_a,X: a] :
% 0.26/0.60 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.60 => ( ( K != bot_bot_set_a )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ K @ ( carrie2021454486_a_b_c @ M3 ) )
% 0.26/0.60 => ( ( member_a @ X @ ( algebr1152250919_d_a_c @ R @ M3 @ K ) )
% 0.26/0.60 => ? [N2: nat,X2: nat > a] :
% 0.26/0.60 ( ( member_nat_a @ X2
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : K ) )
% 0.26/0.60 & ? [Xa: nat > b] :
% 0.26/0.60 ( ( member_nat_b @ Xa
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.60 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ R ) ) )
% 0.26/0.60 & ( X
% 0.26/0.60 = ( l_comb_b_d_a_c @ R @ M3 @ N2 @ Xa @ X2 ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.mem_fgs_l_comb
% 0.26/0.60 thf(fact_31_Module_Ofgs__sub__carrier,axiom,
% 0.26/0.60 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,A: set_e] :
% 0.26/0.60 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_e @ A @ ( carrie730238621_e_b_f @ M3 ) )
% 0.26/0.60 => ( ord_less_eq_set_e @ ( algebr168361254_d_e_f @ R @ M3 @ A ) @ ( carrie730238621_e_b_f @ M3 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.fgs_sub_carrier
% 0.26/0.60 thf(fact_32_Module_Ofgs__sub__carrier,axiom,
% 0.26/0.60 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,A: set_a] :
% 0.26/0.60 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ A @ ( carrie1074654371t_unit @ M3 ) )
% 0.26/0.60 => ( ord_less_eq_set_a @ ( algebr1039611956t_unit @ R @ M3 @ A ) @ ( carrie1074654371t_unit @ M3 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.fgs_sub_carrier
% 0.26/0.60 thf(fact_33_Module_Ofgs__sub__carrier,axiom,
% 0.26/0.60 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,A: set_a] :
% 0.26/0.60 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ A @ ( carrie2021454486_a_b_c @ M3 ) )
% 0.26/0.60 => ( ord_less_eq_set_a @ ( algebr1152250919_d_a_c @ R @ M3 @ A ) @ ( carrie2021454486_a_b_c @ M3 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.fgs_sub_carrier
% 0.26/0.60 thf(fact_34_misom__self,axiom,
% 0.26/0.60 misomo1282343797_c_a_c @ r @ m @ m ).
% 0.26/0.60
% 0.26/0.60 % misom_self
% 0.26/0.60 thf(fact_35_HOM__is__module,axiom,
% 0.26/0.60 ! [N3: carrie1821755406_e_b_f] :
% 0.26/0.60 ( ( module_e_b_f_d @ N3 @ r )
% 0.26/0.60 => ( module1648870817unit_d @ ( hOM_b_d_a_c_e_f @ r @ m @ N3 ) @ r ) ) ).
% 0.26/0.60
% 0.26/0.60 % HOM_is_module
% 0.26/0.60 thf(fact_36_HOM__is__module,axiom,
% 0.26/0.60 ! [N3: carrie722926983_a_b_c] :
% 0.26/0.60 ( ( module_a_b_c_d @ N3 @ r )
% 0.26/0.60 => ( module589927589unit_d @ ( hOM_b_d_a_c_a_c @ r @ m @ N3 ) @ r ) ) ).
% 0.26/0.60
% 0.26/0.60 % HOM_is_module
% 0.26/0.60 thf(fact_37_HOM__is__module,axiom,
% 0.26/0.60 ! [N3: carrie1963041556t_unit] :
% 0.26/0.60 ( ( module1821517916unit_d @ N3 @ r )
% 0.26/0.60 => ( module589927589unit_d @ ( hOM_b_717364638t_unit @ r @ m @ N3 ) @ r ) ) ).
% 0.26/0.60
% 0.26/0.60 % HOM_is_module
% 0.26/0.60 thf(fact_38_Suc__pred,axiom,
% 0.26/0.60 ! [N: nat] :
% 0.26/0.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.60 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.26/0.60 = N ) ) ).
% 0.26/0.60
% 0.26/0.60 % Suc_pred
% 0.26/0.60 thf(fact_39_generator__sub__carrier,axiom,
% 0.26/0.60 ! [H: set_a] :
% 0.26/0.60 ( ( generator_b_d_a_c @ r @ m @ H )
% 0.26/0.60 => ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % generator_sub_carrier
% 0.26/0.60 thf(fact_40_free__generator__generator,axiom,
% 0.26/0.60 ! [H: set_a] :
% 0.26/0.60 ( ( free_g1087686480_d_a_c @ r @ m @ H )
% 0.26/0.60 => ( generator_b_d_a_c @ r @ m @ H ) ) ).
% 0.26/0.60
% 0.26/0.60 % free_generator_generator
% 0.26/0.60 thf(fact_41_Module_Ol__comb__mem,axiom,
% 0.26/0.60 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,A2: set_b,H: set_e,S: nat > b,N: nat,M: nat > e] :
% 0.26/0.60 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.60 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.60 => ( ( ord_less_eq_set_e @ H @ ( carrie730238621_e_b_f @ M3 ) )
% 0.26/0.60 => ( ( member_nat_b @ S
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.60 => ( ( member_nat_e @ M
% 0.26/0.60 @ ( pi_nat_e
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( member_e @ ( l_comb_b_d_e_f @ R @ M3 @ N @ S @ M ) @ ( carrie730238621_e_b_f @ M3 ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.l_comb_mem
% 0.26/0.60 thf(fact_42_Module_Ol__comb__mem,axiom,
% 0.26/0.60 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,A2: set_b,H: set_a,S: nat > b,N: nat,M: nat > a] :
% 0.26/0.60 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.60 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ M3 ) )
% 0.26/0.60 => ( ( member_nat_b @ S
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.60 => ( ( member_nat_a @ M
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( member_a @ ( l_comb_b_d_a_c @ R @ M3 @ N @ S @ M ) @ ( carrie2021454486_a_b_c @ M3 ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.l_comb_mem
% 0.26/0.60 thf(fact_43_Module_Ol__comb__mem,axiom,
% 0.26/0.60 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,A2: set_b,H: set_a,S: nat > b,N: nat,M: nat > a] :
% 0.26/0.60 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.60 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ H @ ( carrie1074654371t_unit @ M3 ) )
% 0.26/0.60 => ( ( member_nat_b @ S
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.60 => ( ( member_nat_a @ M
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( member_a @ ( l_comb1138968323t_unit @ R @ M3 @ N @ S @ M ) @ ( carrie1074654371t_unit @ M3 ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.l_comb_mem
% 0.26/0.60 thf(fact_44_Module_Oliear__comb__memTr,axiom,
% 0.26/0.60 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,A2: set_b,H: set_e,N: nat] :
% 0.26/0.60 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.60 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.60 => ( ( ord_less_eq_set_e @ H @ ( carrie730238621_e_b_f @ M3 ) )
% 0.26/0.60 => ! [S2: nat > b,M2: nat > e] :
% 0.26/0.60 ( ( ( member_nat_b @ S2
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.60 & ( member_nat_e @ M2
% 0.26/0.60 @ ( pi_nat_e
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) ) )
% 0.26/0.60 => ( member_e @ ( l_comb_b_d_e_f @ R @ M3 @ N @ S2 @ M2 ) @ ( carrie730238621_e_b_f @ M3 ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.liear_comb_memTr
% 0.26/0.60 thf(fact_45_Module_Oliear__comb__memTr,axiom,
% 0.26/0.60 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,A2: set_b,H: set_a,N: nat] :
% 0.26/0.60 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.60 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ M3 ) )
% 0.26/0.60 => ! [S2: nat > b,M2: nat > a] :
% 0.26/0.60 ( ( ( member_nat_b @ S2
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.60 & ( member_nat_a @ M2
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) ) )
% 0.26/0.60 => ( member_a @ ( l_comb_b_d_a_c @ R @ M3 @ N @ S2 @ M2 ) @ ( carrie2021454486_a_b_c @ M3 ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.liear_comb_memTr
% 0.26/0.60 thf(fact_46_Module_Oliear__comb__memTr,axiom,
% 0.26/0.60 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,A2: set_b,H: set_a,N: nat] :
% 0.26/0.60 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.60 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ H @ ( carrie1074654371t_unit @ M3 ) )
% 0.26/0.60 => ! [S2: nat > b,M2: nat > a] :
% 0.26/0.60 ( ( ( member_nat_b @ S2
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.60 & ( member_nat_a @ M2
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) ) )
% 0.26/0.60 => ( member_a @ ( l_comb1138968323t_unit @ R @ M3 @ N @ S2 @ M2 ) @ ( carrie1074654371t_unit @ M3 ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.liear_comb_memTr
% 0.26/0.60 thf(fact_47_zero__less__diff,axiom,
% 0.26/0.60 ! [N: nat,M: nat] :
% 0.26/0.60 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.26/0.60 = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.60
% 0.26/0.60 % zero_less_diff
% 0.26/0.60 thf(fact_48_Module_Olinear__comb__eq,axiom,
% 0.26/0.60 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,H: set_e,S: nat > b,N: nat,F: nat > e,G: nat > e] :
% 0.26/0.60 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_e @ H @ ( carrie730238621_e_b_f @ M3 ) )
% 0.26/0.60 => ( ( member_nat_b @ S
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ R ) ) )
% 0.26/0.60 => ( ( member_nat_e @ F
% 0.26/0.60 @ ( pi_nat_e
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( ( member_nat_e @ G
% 0.26/0.60 @ ( pi_nat_e
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( ! [X2: nat] :
% 0.26/0.60 ( ( member_nat @ X2
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) ) )
% 0.26/0.60 => ( ( F @ X2 )
% 0.26/0.60 = ( G @ X2 ) ) )
% 0.26/0.60 => ( ( l_comb_b_d_e_f @ R @ M3 @ N @ S @ F )
% 0.26/0.60 = ( l_comb_b_d_e_f @ R @ M3 @ N @ S @ G ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.linear_comb_eq
% 0.26/0.60 thf(fact_49_Module_Olinear__comb__eq,axiom,
% 0.26/0.60 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,H: set_a,S: nat > b,N: nat,F: nat > a,G: nat > a] :
% 0.26/0.60 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.60 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ M3 ) )
% 0.26/0.60 => ( ( member_nat_b @ S
% 0.26/0.60 @ ( pi_nat_b
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ R ) ) )
% 0.26/0.60 => ( ( member_nat_a @ F
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( ( member_nat_a @ G
% 0.26/0.60 @ ( pi_nat_a
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.60 @ ^ [Uu: nat] : H ) )
% 0.26/0.60 => ( ! [X2: nat] :
% 0.26/0.60 ( ( member_nat @ X2
% 0.26/0.60 @ ( collect_nat
% 0.26/0.60 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) ) )
% 0.26/0.60 => ( ( F @ X2 )
% 0.26/0.60 = ( G @ X2 ) ) )
% 0.26/0.60 => ( ( l_comb_b_d_a_c @ R @ M3 @ N @ S @ F )
% 0.26/0.60 = ( l_comb_b_d_a_c @ R @ M3 @ N @ S @ G ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Module.linear_comb_eq
% 0.26/0.60 thf(fact_50_Module_Olinear__comb__eq,axiom,
% 0.26/0.60 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,H: set_a,S: nat > b,N: nat,F: nat > a,G: nat > a] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie1074654371t_unit @ M3 ) )
% 0.26/0.61 => ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ R ) ) )
% 0.26/0.61 => ( ( member_nat_a @ F
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : H ) )
% 0.26/0.61 => ( ( member_nat_a @ G
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : H ) )
% 0.26/0.61 => ( ! [X2: nat] :
% 0.26/0.61 ( ( member_nat @ X2
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) ) )
% 0.26/0.61 => ( ( F @ X2 )
% 0.26/0.61 = ( G @ X2 ) ) )
% 0.26/0.61 => ( ( l_comb1138968323t_unit @ R @ M3 @ N @ S @ F )
% 0.26/0.61 = ( l_comb1138968323t_unit @ R @ M3 @ N @ S @ G ) ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.linear_comb_eq
% 0.26/0.61 thf(fact_51_Module_Olinear__comb__eqTr,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,H: set_e,S: nat > b,N: nat,F: nat > e,G: nat > e] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( ord_less_eq_set_e @ H @ ( carrie730238621_e_b_f @ M3 ) )
% 0.26/0.61 => ( ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ R ) ) )
% 0.26/0.61 & ( member_nat_e @ F
% 0.26/0.61 @ ( pi_nat_e
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : H ) )
% 0.26/0.61 & ( member_nat_e @ G
% 0.26/0.61 @ ( pi_nat_e
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : H ) )
% 0.26/0.61 & ! [X2: nat] :
% 0.26/0.61 ( ( member_nat @ X2
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) ) )
% 0.26/0.61 => ( ( F @ X2 )
% 0.26/0.61 = ( G @ X2 ) ) ) )
% 0.26/0.61 => ( ( l_comb_b_d_e_f @ R @ M3 @ N @ S @ F )
% 0.26/0.61 = ( l_comb_b_d_e_f @ R @ M3 @ N @ S @ G ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.linear_comb_eqTr
% 0.26/0.61 thf(fact_52_Module_Olinear__comb__eqTr,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,H: set_a,S: nat > b,N: nat,F: nat > a,G: nat > a] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ M3 ) )
% 0.26/0.61 => ( ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ R ) ) )
% 0.26/0.61 & ( member_nat_a @ F
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : H ) )
% 0.26/0.61 & ( member_nat_a @ G
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : H ) )
% 0.26/0.61 & ! [X2: nat] :
% 0.26/0.61 ( ( member_nat @ X2
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) ) )
% 0.26/0.61 => ( ( F @ X2 )
% 0.26/0.61 = ( G @ X2 ) ) ) )
% 0.26/0.61 => ( ( l_comb_b_d_a_c @ R @ M3 @ N @ S @ F )
% 0.26/0.61 = ( l_comb_b_d_a_c @ R @ M3 @ N @ S @ G ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.linear_comb_eqTr
% 0.26/0.61 thf(fact_53_Module_Olinear__comb__eqTr,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,H: set_a,S: nat > b,N: nat,F: nat > a,G: nat > a] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie1074654371t_unit @ M3 ) )
% 0.26/0.61 => ( ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ R ) ) )
% 0.26/0.61 & ( member_nat_a @ F
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : H ) )
% 0.26/0.61 & ( member_nat_a @ G
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : H ) )
% 0.26/0.61 & ! [X2: nat] :
% 0.26/0.61 ( ( member_nat @ X2
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) ) )
% 0.26/0.61 => ( ( F @ X2 )
% 0.26/0.61 = ( G @ X2 ) ) ) )
% 0.26/0.61 => ( ( l_comb1138968323t_unit @ R @ M3 @ N @ S @ F )
% 0.26/0.61 = ( l_comb1138968323t_unit @ R @ M3 @ N @ S @ G ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.linear_comb_eqTr
% 0.26/0.61 thf(fact_54_diff__is__0__eq,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ( minus_minus_nat @ M @ N )
% 0.26/0.61 = zero_zero_nat )
% 0.26/0.61 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_is_0_eq
% 0.26/0.61 thf(fact_55_diff__is__0__eq_H,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ( minus_minus_nat @ M @ N )
% 0.26/0.61 = zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_is_0_eq'
% 0.26/0.61 thf(fact_56_old_Onat_Oinject,axiom,
% 0.26/0.61 ! [Nat: nat,Nat2: nat] :
% 0.26/0.61 ( ( ( suc @ Nat )
% 0.26/0.61 = ( suc @ Nat2 ) )
% 0.26/0.61 = ( Nat = Nat2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.nat.inject
% 0.26/0.61 thf(fact_57_nat_Oinject,axiom,
% 0.26/0.61 ! [X22: nat,Y2: nat] :
% 0.26/0.61 ( ( ( suc @ X22 )
% 0.26/0.61 = ( suc @ Y2 ) )
% 0.26/0.61 = ( X22 = Y2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % nat.inject
% 0.26/0.61 thf(fact_58_misom__sym,axiom,
% 0.26/0.61 ! [N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_e_b_f_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo298454132_c_e_f @ r @ m @ N3 )
% 0.26/0.61 => ( misomo1752826100_f_a_c @ r @ N3 @ m ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_sym
% 0.26/0.61 thf(fact_59_misom__sym,axiom,
% 0.26/0.61 ! [N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module1821517916unit_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1857159554t_unit @ r @ m @ N3 )
% 0.26/0.61 => ( misomo1935876354it_a_c @ r @ N3 @ m ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_sym
% 0.26/0.61 thf(fact_60_misom__sym,axiom,
% 0.26/0.61 ! [N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module_a_b_c_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1282343797_c_a_c @ r @ m @ N3 )
% 0.26/0.61 => ( misomo1282343797_c_a_c @ r @ N3 @ m ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_sym
% 0.26/0.61 thf(fact_61_Suc__le__mono,axiom,
% 0.26/0.61 ! [N: nat,M: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.26/0.61 = ( ord_less_eq_nat @ N @ M ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_le_mono
% 0.26/0.61 thf(fact_62_bot__nat__0_Oextremum,axiom,
% 0.26/0.61 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.26/0.61
% 0.26/0.61 % bot_nat_0.extremum
% 0.26/0.61 thf(fact_63_le0,axiom,
% 0.26/0.61 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.26/0.61
% 0.26/0.61 % le0
% 0.26/0.61 thf(fact_64_Suc__less__eq,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.61 = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_less_eq
% 0.26/0.61 thf(fact_65_Suc__mono,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ N )
% 0.26/0.61 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_mono
% 0.26/0.61 thf(fact_66_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: nat > a,P: ( nat > a ) > $o] :
% 0.26/0.61 ( ( member_nat_a @ A @ ( collect_nat_a @ P ) )
% 0.26/0.61 = ( P @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_67_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: nat > b,P: ( nat > b ) > $o] :
% 0.26/0.61 ( ( member_nat_b @ A @ ( collect_nat_b @ P ) )
% 0.26/0.61 = ( P @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_68_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: a,P: a > $o] :
% 0.26/0.61 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.26/0.61 = ( P @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_69_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: nat,P: nat > $o] :
% 0.26/0.61 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.26/0.61 = ( P @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_70_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A2: set_nat_a] :
% 0.26/0.61 ( ( collect_nat_a
% 0.26/0.61 @ ^ [X3: nat > a] : ( member_nat_a @ X3 @ A2 ) )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_71_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A2: set_nat_b] :
% 0.26/0.61 ( ( collect_nat_b
% 0.26/0.61 @ ^ [X3: nat > b] : ( member_nat_b @ X3 @ A2 ) )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_72_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A2: set_a] :
% 0.26/0.61 ( ( collect_a
% 0.26/0.61 @ ^ [X3: a] : ( member_a @ X3 @ A2 ) )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_73_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A2: set_nat] :
% 0.26/0.61 ( ( collect_nat
% 0.26/0.61 @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_74_Collect__cong,axiom,
% 0.26/0.61 ! [P: nat > $o,Q: nat > $o] :
% 0.26/0.61 ( ! [X2: nat] :
% 0.26/0.61 ( ( P @ X2 )
% 0.26/0.61 = ( Q @ X2 ) )
% 0.26/0.61 => ( ( collect_nat @ P )
% 0.26/0.61 = ( collect_nat @ Q ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_cong
% 0.26/0.61 thf(fact_75_bot__nat__0_Onot__eq__extremum,axiom,
% 0.26/0.61 ! [A: nat] :
% 0.26/0.61 ( ( A != zero_zero_nat )
% 0.26/0.61 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % bot_nat_0.not_eq_extremum
% 0.26/0.61 thf(fact_76_less__nat__zero__code,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % less_nat_zero_code
% 0.26/0.61 thf(fact_77_neq0__conv,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( N != zero_zero_nat )
% 0.26/0.61 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % neq0_conv
% 0.26/0.61 thf(fact_78_diff__diff__cancel,axiom,
% 0.26/0.61 ! [I: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ I @ N )
% 0.26/0.61 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.26/0.61 = I ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_diff_cancel
% 0.26/0.61 thf(fact_79_Suc__diff__diff,axiom,
% 0.26/0.61 ! [M: nat,N: nat,K2: nat] :
% 0.26/0.61 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K2 ) )
% 0.26/0.61 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_diff_diff
% 0.26/0.61 thf(fact_80_diff__Suc__Suc,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.61 = ( minus_minus_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_Suc_Suc
% 0.26/0.61 thf(fact_81_diff__self__eq__0,axiom,
% 0.26/0.61 ! [M: nat] :
% 0.26/0.61 ( ( minus_minus_nat @ M @ M )
% 0.26/0.61 = zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % diff_self_eq_0
% 0.26/0.61 thf(fact_82_diff__0__eq__0,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.26/0.61 = zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % diff_0_eq_0
% 0.26/0.61 thf(fact_83_misom__trans,axiom,
% 0.26/0.61 ! [L: carrie1821755406_e_b_f,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_e_b_f_d @ L @ r )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1752826100_f_a_c @ r @ L @ m )
% 0.26/0.61 => ( ( misomo298454132_c_e_f @ r @ m @ N3 )
% 0.26/0.61 => ( misomo768936435_f_e_f @ r @ L @ N3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_trans
% 0.26/0.61 thf(fact_84_misom__trans,axiom,
% 0.26/0.61 ! [L: carrie1821755406_e_b_f,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_e_b_f_d @ L @ r )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1752826100_f_a_c @ r @ L @ m )
% 0.26/0.61 => ( ( misomo1857159554t_unit @ r @ m @ N3 )
% 0.26/0.61 => ( misomo368157697t_unit @ r @ L @ N3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_trans
% 0.26/0.61 thf(fact_85_misom__trans,axiom,
% 0.26/0.61 ! [L: carrie1963041556t_unit,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module1821517916unit_d @ L @ r )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1935876354it_a_c @ r @ L @ m )
% 0.26/0.61 => ( ( misomo298454132_c_e_f @ r @ m @ N3 )
% 0.26/0.61 => ( misomo951986689it_e_f @ r @ L @ N3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_trans
% 0.26/0.61 thf(fact_86_misom__trans,axiom,
% 0.26/0.61 ! [L: carrie1963041556t_unit,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module1821517916unit_d @ L @ r )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1935876354it_a_c @ r @ L @ m )
% 0.26/0.61 => ( ( misomo1857159554t_unit @ r @ m @ N3 )
% 0.26/0.61 => ( misomo493403663t_unit @ r @ L @ N3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_trans
% 0.26/0.61 thf(fact_87_misom__trans,axiom,
% 0.26/0.61 ! [L: carrie1821755406_e_b_f,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module_e_b_f_d @ L @ r )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1752826100_f_a_c @ r @ L @ m )
% 0.26/0.61 => ( ( misomo1282343797_c_a_c @ r @ m @ N3 )
% 0.26/0.61 => ( misomo1752826100_f_a_c @ r @ L @ N3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_trans
% 0.26/0.61 thf(fact_88_misom__trans,axiom,
% 0.26/0.61 ! [L: carrie1963041556t_unit,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module1821517916unit_d @ L @ r )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1935876354it_a_c @ r @ L @ m )
% 0.26/0.61 => ( ( misomo1282343797_c_a_c @ r @ m @ N3 )
% 0.26/0.61 => ( misomo1935876354it_a_c @ r @ L @ N3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_trans
% 0.26/0.61 thf(fact_89_misom__trans,axiom,
% 0.26/0.61 ! [L: carrie722926983_a_b_c,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_a_b_c_d @ L @ r )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1282343797_c_a_c @ r @ L @ m )
% 0.26/0.61 => ( ( misomo298454132_c_e_f @ r @ m @ N3 )
% 0.26/0.61 => ( misomo298454132_c_e_f @ r @ L @ N3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_trans
% 0.26/0.61 thf(fact_90_misom__trans,axiom,
% 0.26/0.61 ! [L: carrie722926983_a_b_c,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_a_b_c_d @ L @ r )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1282343797_c_a_c @ r @ L @ m )
% 0.26/0.61 => ( ( misomo1857159554t_unit @ r @ m @ N3 )
% 0.26/0.61 => ( misomo1857159554t_unit @ r @ L @ N3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_trans
% 0.26/0.61 thf(fact_91_misom__trans,axiom,
% 0.26/0.61 ! [L: carrie722926983_a_b_c,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module_a_b_c_d @ L @ r )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ r )
% 0.26/0.61 => ( ( misomo1282343797_c_a_c @ r @ L @ m )
% 0.26/0.61 => ( ( misomo1282343797_c_a_c @ r @ m @ N3 )
% 0.26/0.61 => ( misomo1282343797_c_a_c @ r @ L @ N3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % misom_trans
% 0.26/0.61 thf(fact_92_zero__less__Suc,axiom,
% 0.26/0.61 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % zero_less_Suc
% 0.26/0.61 thf(fact_93_less__Suc0,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.26/0.61 = ( N = zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_Suc0
% 0.26/0.61 thf(fact_94_Module_OHOM__is__module,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( module241733029unit_d @ ( hOM_b_d_e_f_e_f @ R @ M3 @ N3 ) @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.HOM_is_module
% 0.26/0.61 thf(fact_95_Module_OHOM__is__module,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ R )
% 0.26/0.61 => ( module1330273449unit_d @ ( hOM_b_d_e_f_a_c @ R @ M3 @ N3 ) @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.HOM_is_module
% 0.26/0.61 thf(fact_96_Module_OHOM__is__module,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( module1330273449unit_d @ ( hOM_b_1375846429t_unit @ R @ M3 @ N3 ) @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.HOM_is_module
% 0.26/0.61 thf(fact_97_Module_OHOM__is__module,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( module1648870817unit_d @ ( hOM_b_d_a_c_e_f @ R @ M3 @ N3 ) @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.HOM_is_module
% 0.26/0.61 thf(fact_98_Module_OHOM__is__module,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ R )
% 0.26/0.61 => ( module589927589unit_d @ ( hOM_b_d_a_c_a_c @ R @ M3 @ N3 ) @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.HOM_is_module
% 0.26/0.61 thf(fact_99_Module_OHOM__is__module,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( module589927589unit_d @ ( hOM_b_717364638t_unit @ R @ M3 @ N3 ) @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.HOM_is_module
% 0.26/0.61 thf(fact_100_Module_OHOM__is__module,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( module1648870817unit_d @ ( hOM_b_1959675421it_e_f @ R @ M3 @ N3 ) @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.HOM_is_module
% 0.26/0.61 thf(fact_101_Module_OHOM__is__module,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ R )
% 0.26/0.61 => ( module589927589unit_d @ ( hOM_b_796081438it_a_c @ R @ M3 @ N3 ) @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.HOM_is_module
% 0.26/0.61 thf(fact_102_Module_OHOM__is__module,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( module589927589unit_d @ ( hOM_b_1103679019t_unit @ R @ M3 @ N3 ) @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.HOM_is_module
% 0.26/0.61 thf(fact_103_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,L: carrie1821755406_e_b_f,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ L @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo768936435_f_e_f @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo768936435_f_e_f @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo768936435_f_e_f @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_104_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,L: carrie1821755406_e_b_f,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ L @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo768936435_f_e_f @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo1752826100_f_a_c @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo1752826100_f_a_c @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_105_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,L: carrie1821755406_e_b_f,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ L @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo768936435_f_e_f @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo368157697t_unit @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo368157697t_unit @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_106_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,L: carrie722926983_a_b_c,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ L @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo298454132_c_e_f @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo768936435_f_e_f @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo298454132_c_e_f @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_107_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,L: carrie722926983_a_b_c,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ L @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo298454132_c_e_f @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo368157697t_unit @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo1857159554t_unit @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_108_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,L: carrie1963041556t_unit,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ L @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo951986689it_e_f @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo768936435_f_e_f @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo951986689it_e_f @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_109_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,L: carrie1963041556t_unit,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ L @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo951986689it_e_f @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo1752826100_f_a_c @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo1935876354it_a_c @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_110_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,L: carrie1963041556t_unit,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ L @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo951986689it_e_f @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo368157697t_unit @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo493403663t_unit @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_111_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,L: carrie1821755406_e_b_f,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ L @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo1752826100_f_a_c @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo298454132_c_e_f @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo768936435_f_e_f @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_112_Module_Omisom__trans,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,L: carrie1821755406_e_b_f,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ L @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo1752826100_f_a_c @ R @ L @ M3 )
% 0.26/0.61 => ( ( misomo1857159554t_unit @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo368157697t_unit @ R @ L @ N3 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_trans
% 0.26/0.61 thf(fact_113_Module_Omisom__self,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( misomo768936435_f_e_f @ R @ M3 @ M3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_self
% 0.26/0.61 thf(fact_114_Module_Omisom__self,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( misomo493403663t_unit @ R @ M3 @ M3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_self
% 0.26/0.61 thf(fact_115_Module_Omisom__self,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( misomo1282343797_c_a_c @ R @ M3 @ M3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_self
% 0.26/0.61 thf(fact_116_Module_Omisom__sym,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo768936435_f_e_f @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo768936435_f_e_f @ R @ N3 @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_sym
% 0.26/0.61 thf(fact_117_Module_Omisom__sym,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo1752826100_f_a_c @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo298454132_c_e_f @ R @ N3 @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_sym
% 0.26/0.61 thf(fact_118_Module_Omisom__sym,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo368157697t_unit @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo951986689it_e_f @ R @ N3 @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_sym
% 0.26/0.61 thf(fact_119_Module_Omisom__sym,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo298454132_c_e_f @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo1752826100_f_a_c @ R @ N3 @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_sym
% 0.26/0.61 thf(fact_120_Module_Omisom__sym,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo1857159554t_unit @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo1935876354it_a_c @ R @ N3 @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_sym
% 0.26/0.61 thf(fact_121_Module_Omisom__sym,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,N3: carrie1821755406_e_b_f] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( module_e_b_f_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo951986689it_e_f @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo368157697t_unit @ R @ N3 @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_sym
% 0.26/0.61 thf(fact_122_Module_Omisom__sym,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo1935876354it_a_c @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo1857159554t_unit @ R @ N3 @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_sym
% 0.26/0.61 thf(fact_123_Module_Omisom__sym,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,N3: carrie1963041556t_unit] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( module1821517916unit_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo493403663t_unit @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo493403663t_unit @ R @ N3 @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_sym
% 0.26/0.61 thf(fact_124_Module_Omisom__sym,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,N3: carrie722926983_a_b_c] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( module_a_b_c_d @ N3 @ R )
% 0.26/0.61 => ( ( misomo1282343797_c_a_c @ R @ M3 @ N3 )
% 0.26/0.61 => ( misomo1282343797_c_a_c @ R @ N3 @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.misom_sym
% 0.26/0.61 thf(fact_125_Module_Ofree__generator__generator,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,H: set_e] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( free_g103796815_d_e_f @ R @ M3 @ H )
% 0.26/0.61 => ( generator_b_d_e_f @ R @ M3 @ H ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.free_generator_generator
% 0.26/0.61 thf(fact_126_Module_Ofree__generator__generator,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,H: set_a] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( free_g637607517t_unit @ R @ M3 @ H )
% 0.26/0.61 => ( genera1692266857t_unit @ R @ M3 @ H ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.free_generator_generator
% 0.26/0.61 thf(fact_127_Module_Ofree__generator__generator,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,H: set_a] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( free_g1087686480_d_a_c @ R @ M3 @ H )
% 0.26/0.61 => ( generator_b_d_a_c @ R @ M3 @ H ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.free_generator_generator
% 0.26/0.61 thf(fact_128_Module_Ogenerator__sub__carrier,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,H: set_e] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( generator_b_d_e_f @ R @ M3 @ H )
% 0.26/0.61 => ( ord_less_eq_set_e @ H @ ( carrie730238621_e_b_f @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.generator_sub_carrier
% 0.26/0.61 thf(fact_129_Module_Ogenerator__sub__carrier,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,H: set_a] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( generator_b_d_a_c @ R @ M3 @ H )
% 0.26/0.61 => ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.generator_sub_carrier
% 0.26/0.61 thf(fact_130_Module_Ogenerator__sub__carrier,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,H: set_a] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( genera1692266857t_unit @ R @ M3 @ H )
% 0.26/0.61 => ( ord_less_eq_set_a @ H @ ( carrie1074654371t_unit @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.generator_sub_carrier
% 0.26/0.61 thf(fact_131_Module_OAnn__is__ideal,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ideal_b_d @ R @ ( annihilator_b_d_e_f @ R @ M3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.Ann_is_ideal
% 0.26/0.61 thf(fact_132_Module_OAnn__is__ideal,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ideal_b_d @ R @ ( annihi259882159t_unit @ R @ M3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.Ann_is_ideal
% 0.26/0.61 thf(fact_133_Module_OAnn__is__ideal,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ideal_b_d @ R @ ( annihilator_b_d_a_c @ R @ M3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.Ann_is_ideal
% 0.26/0.61 thf(fact_134_Nat_Oex__has__greatest__nat,axiom,
% 0.26/0.61 ! [P: nat > $o,K2: nat,B: nat] :
% 0.26/0.61 ( ( P @ K2 )
% 0.26/0.61 => ( ! [Y: nat] :
% 0.26/0.61 ( ( P @ Y )
% 0.26/0.61 => ( ord_less_eq_nat @ Y @ B ) )
% 0.26/0.61 => ? [X2: nat] :
% 0.26/0.61 ( ( P @ X2 )
% 0.26/0.61 & ! [Y3: nat] :
% 0.26/0.61 ( ( P @ Y3 )
% 0.26/0.61 => ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Nat.ex_has_greatest_nat
% 0.26/0.61 thf(fact_135_nat__le__linear,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.26/0.61
% 0.26/0.61 % nat_le_linear
% 0.26/0.61 thf(fact_136_le__antisym,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.61 => ( M = N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_antisym
% 0.26/0.61 thf(fact_137_le__trans,axiom,
% 0.26/0.61 ! [I: nat,J3: nat,K2: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ I @ J3 )
% 0.26/0.61 => ( ( ord_less_eq_nat @ J3 @ K2 )
% 0.26/0.61 => ( ord_less_eq_nat @ I @ K2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_trans
% 0.26/0.61 thf(fact_138_n__not__Suc__n,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( N
% 0.26/0.61 != ( suc @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % n_not_Suc_n
% 0.26/0.61 thf(fact_139_Suc__inject,axiom,
% 0.26/0.61 ! [X: nat,Y4: nat] :
% 0.26/0.61 ( ( ( suc @ X )
% 0.26/0.61 = ( suc @ Y4 ) )
% 0.26/0.61 => ( X = Y4 ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_inject
% 0.26/0.61 thf(fact_140_linorder__neqE__nat,axiom,
% 0.26/0.61 ! [X: nat,Y4: nat] :
% 0.26/0.61 ( ( X != Y4 )
% 0.26/0.61 => ( ~ ( ord_less_nat @ X @ Y4 )
% 0.26/0.61 => ( ord_less_nat @ Y4 @ X ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % linorder_neqE_nat
% 0.26/0.61 thf(fact_141_infinite__descent,axiom,
% 0.26/0.61 ! [P: nat > $o,N: nat] :
% 0.26/0.61 ( ! [N2: nat] :
% 0.26/0.61 ( ~ ( P @ N2 )
% 0.26/0.61 => ? [M2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M2 @ N2 )
% 0.26/0.61 & ~ ( P @ M2 ) ) )
% 0.26/0.61 => ( P @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_descent
% 0.26/0.61 thf(fact_142_nat__less__induct,axiom,
% 0.26/0.61 ! [P: nat > $o,N: nat] :
% 0.26/0.61 ( ! [N2: nat] :
% 0.26/0.61 ( ! [M2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M2 @ N2 )
% 0.26/0.61 => ( P @ M2 ) )
% 0.26/0.61 => ( P @ N2 ) )
% 0.26/0.61 => ( P @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % nat_less_induct
% 0.26/0.61 thf(fact_143_less__irrefl__nat,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ~ ( ord_less_nat @ N @ N ) ).
% 0.26/0.61
% 0.26/0.61 % less_irrefl_nat
% 0.26/0.61 thf(fact_144_less__not__refl3,axiom,
% 0.26/0.61 ! [S: nat,T: nat] :
% 0.26/0.61 ( ( ord_less_nat @ S @ T )
% 0.26/0.61 => ( S != T ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_not_refl3
% 0.26/0.61 thf(fact_145_less__not__refl2,axiom,
% 0.26/0.61 ! [N: nat,M: nat] :
% 0.26/0.61 ( ( ord_less_nat @ N @ M )
% 0.26/0.61 => ( M != N ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_not_refl2
% 0.26/0.61 thf(fact_146_less__not__refl,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ~ ( ord_less_nat @ N @ N ) ).
% 0.26/0.61
% 0.26/0.61 % less_not_refl
% 0.26/0.61 thf(fact_147_nat__neq__iff,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( M != N )
% 0.26/0.61 = ( ( ord_less_nat @ M @ N )
% 0.26/0.61 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nat_neq_iff
% 0.26/0.61 thf(fact_148_diff__commute,axiom,
% 0.26/0.61 ! [I: nat,J3: nat,K2: nat] :
% 0.26/0.61 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J3 ) @ K2 )
% 0.26/0.61 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K2 ) @ J3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_commute
% 0.26/0.61 thf(fact_149_Module_Osmodule__ideal__coeff__is__Submodule,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,A2: set_b] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.61 => ( submodule_b_d_e_f @ R @ M3 @ ( smodul1982583723_d_e_f @ R @ M3 @ A2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.smodule_ideal_coeff_is_Submodule
% 0.26/0.61 thf(fact_150_Module_Osmodule__ideal__coeff__is__Submodule,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,A2: set_b] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.61 => ( submod903911234t_unit @ R @ M3 @ ( smodul132175289t_unit @ R @ M3 @ A2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.smodule_ideal_coeff_is_Submodule
% 0.26/0.61 thf(fact_151_Module_Osmodule__ideal__coeff__is__Submodule,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,A2: set_b] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.61 => ( submodule_b_d_a_c @ R @ M3 @ ( smodul818989740_d_a_c @ R @ M3 @ A2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.smodule_ideal_coeff_is_Submodule
% 0.26/0.61 thf(fact_152_Module_Oquotient__of__submodules__is__ideal,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,P: set_e,Q: set_e] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( submodule_b_d_e_f @ R @ M3 @ P )
% 0.26/0.61 => ( ( submodule_b_d_e_f @ R @ M3 @ Q )
% 0.26/0.61 => ( ideal_b_d @ R @ ( quotie169863047_d_e_f @ R @ M3 @ P @ Q ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.quotient_of_submodules_is_ideal
% 0.26/0.61 thf(fact_153_Module_Oquotient__of__submodules__is__ideal,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,P: set_a,Q: set_a] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( submod903911234t_unit @ R @ M3 @ P )
% 0.26/0.61 => ( ( submod903911234t_unit @ R @ M3 @ Q )
% 0.26/0.61 => ( ideal_b_d @ R @ ( quotie1196826005t_unit @ R @ M3 @ P @ Q ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.quotient_of_submodules_is_ideal
% 0.26/0.61 thf(fact_154_Module_Oquotient__of__submodules__is__ideal,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,P: set_a,Q: set_a] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( submodule_b_d_a_c @ R @ M3 @ P )
% 0.26/0.61 => ( ( submodule_b_d_a_c @ R @ M3 @ Q )
% 0.26/0.61 => ( ideal_b_d @ R @ ( quotie1153752712_d_a_c @ R @ M3 @ P @ Q ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.quotient_of_submodules_is_ideal
% 0.26/0.61 thf(fact_155_transitive__stepwise__le,axiom,
% 0.26/0.61 ! [M: nat,N: nat,R: nat > nat > $o] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ! [X2: nat] : ( R @ X2 @ X2 )
% 0.26/0.61 => ( ! [X2: nat,Y: nat,Z: nat] :
% 0.26/0.61 ( ( R @ X2 @ Y )
% 0.26/0.61 => ( ( R @ Y @ Z )
% 0.26/0.61 => ( R @ X2 @ Z ) ) )
% 0.26/0.61 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 0.26/0.61 => ( R @ M @ N ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % transitive_stepwise_le
% 0.26/0.61 thf(fact_156_nat__induct__at__least,axiom,
% 0.26/0.61 ! [M: nat,N: nat,P: nat > $o] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ( P @ M )
% 0.26/0.61 => ( ! [N2: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N2 )
% 0.26/0.61 => ( ( P @ N2 )
% 0.26/0.61 => ( P @ ( suc @ N2 ) ) ) )
% 0.26/0.61 => ( P @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nat_induct_at_least
% 0.26/0.61 thf(fact_157_full__nat__induct,axiom,
% 0.26/0.61 ! [P: nat > $o,N: nat] :
% 0.26/0.61 ( ! [N2: nat] :
% 0.26/0.61 ( ! [M2: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 0.26/0.61 => ( P @ M2 ) )
% 0.26/0.61 => ( P @ N2 ) )
% 0.26/0.61 => ( P @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % full_nat_induct
% 0.26/0.61 thf(fact_158_not__less__eq__eq,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 0.26/0.61 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.26/0.61
% 0.26/0.61 % not_less_eq_eq
% 0.26/0.61 thf(fact_159_Suc__n__not__le__n,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_n_not_le_n
% 0.26/0.61 thf(fact_160_le__Suc__eq,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.61 = ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 | ( M
% 0.26/0.61 = ( suc @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_Suc_eq
% 0.26/0.61 thf(fact_161_Suc__le__D,axiom,
% 0.26/0.61 ! [N: nat,M4: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 0.26/0.61 => ? [M5: nat] :
% 0.26/0.61 ( M4
% 0.26/0.61 = ( suc @ M5 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_le_D
% 0.26/0.61 thf(fact_162_le__SucI,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_SucI
% 0.26/0.61 thf(fact_163_le__SucE,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.26/0.61 => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( M
% 0.26/0.61 = ( suc @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_SucE
% 0.26/0.61 thf(fact_164_Suc__leD,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.26/0.61 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_leD
% 0.26/0.61 thf(fact_165_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.26/0.61 ! [A: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.61 => ( A = zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % bot_nat_0.extremum_uniqueI
% 0.26/0.61 thf(fact_166_bot__nat__0_Oextremum__unique,axiom,
% 0.26/0.61 ! [A: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.61 = ( A = zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % bot_nat_0.extremum_unique
% 0.26/0.61 thf(fact_167_le__0__eq,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.26/0.61 = ( N = zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_0_eq
% 0.26/0.61 thf(fact_168_less__eq__nat_Osimps_I1_J,axiom,
% 0.26/0.61 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.26/0.61
% 0.26/0.61 % less_eq_nat.simps(1)
% 0.26/0.61 thf(fact_169_not0__implies__Suc,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( N != zero_zero_nat )
% 0.26/0.61 => ? [M5: nat] :
% 0.26/0.61 ( N
% 0.26/0.61 = ( suc @ M5 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % not0_implies_Suc
% 0.26/0.61 thf(fact_170_old_Onat_Oinducts,axiom,
% 0.26/0.61 ! [P: nat > $o,Nat: nat] :
% 0.26/0.61 ( ( P @ zero_zero_nat )
% 0.26/0.61 => ( ! [Nat3: nat] :
% 0.26/0.61 ( ( P @ Nat3 )
% 0.26/0.61 => ( P @ ( suc @ Nat3 ) ) )
% 0.26/0.61 => ( P @ Nat ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.nat.inducts
% 0.26/0.61 thf(fact_171_old_Onat_Oexhaust,axiom,
% 0.26/0.61 ! [Y4: nat] :
% 0.26/0.61 ( ( Y4 != zero_zero_nat )
% 0.26/0.61 => ~ ! [Nat3: nat] :
% 0.26/0.61 ( Y4
% 0.26/0.61 != ( suc @ Nat3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.nat.exhaust
% 0.26/0.61 thf(fact_172_Zero__not__Suc,axiom,
% 0.26/0.61 ! [M: nat] :
% 0.26/0.61 ( zero_zero_nat
% 0.26/0.61 != ( suc @ M ) ) ).
% 0.26/0.61
% 0.26/0.61 % Zero_not_Suc
% 0.26/0.61 thf(fact_173_Zero__neq__Suc,axiom,
% 0.26/0.61 ! [M: nat] :
% 0.26/0.61 ( zero_zero_nat
% 0.26/0.61 != ( suc @ M ) ) ).
% 0.26/0.61
% 0.26/0.61 % Zero_neq_Suc
% 0.26/0.61 thf(fact_174_Suc__neq__Zero,axiom,
% 0.26/0.61 ! [M: nat] :
% 0.26/0.61 ( ( suc @ M )
% 0.26/0.61 != zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_neq_Zero
% 0.26/0.61 thf(fact_175_zero__induct,axiom,
% 0.26/0.61 ! [P: nat > $o,K2: nat] :
% 0.26/0.61 ( ( P @ K2 )
% 0.26/0.61 => ( ! [N2: nat] :
% 0.26/0.61 ( ( P @ ( suc @ N2 ) )
% 0.26/0.61 => ( P @ N2 ) )
% 0.26/0.61 => ( P @ zero_zero_nat ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % zero_induct
% 0.26/0.61 thf(fact_176_diff__induct,axiom,
% 0.26/0.61 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.26/0.61 ( ! [X2: nat] : ( P @ X2 @ zero_zero_nat )
% 0.26/0.61 => ( ! [Y: nat] : ( P @ zero_zero_nat @ ( suc @ Y ) )
% 0.26/0.61 => ( ! [X2: nat,Y: nat] :
% 0.26/0.61 ( ( P @ X2 @ Y )
% 0.26/0.61 => ( P @ ( suc @ X2 ) @ ( suc @ Y ) ) )
% 0.26/0.61 => ( P @ M @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_induct
% 0.26/0.61 thf(fact_177_nat__induct,axiom,
% 0.26/0.61 ! [P: nat > $o,N: nat] :
% 0.26/0.61 ( ( P @ zero_zero_nat )
% 0.26/0.61 => ( ! [N2: nat] :
% 0.26/0.61 ( ( P @ N2 )
% 0.26/0.61 => ( P @ ( suc @ N2 ) ) )
% 0.26/0.61 => ( P @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nat_induct
% 0.26/0.61 thf(fact_178_nat_OdiscI,axiom,
% 0.26/0.61 ! [Nat: nat,X22: nat] :
% 0.26/0.61 ( ( Nat
% 0.26/0.61 = ( suc @ X22 ) )
% 0.26/0.61 => ( Nat != zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % nat.discI
% 0.26/0.61 thf(fact_179_old_Onat_Odistinct_I1_J,axiom,
% 0.26/0.61 ! [Nat2: nat] :
% 0.26/0.61 ( zero_zero_nat
% 0.26/0.61 != ( suc @ Nat2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.nat.distinct(1)
% 0.26/0.61 thf(fact_180_old_Onat_Odistinct_I2_J,axiom,
% 0.26/0.61 ! [Nat2: nat] :
% 0.26/0.61 ( ( suc @ Nat2 )
% 0.26/0.61 != zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % old.nat.distinct(2)
% 0.26/0.61 thf(fact_181_nat_Odistinct_I1_J,axiom,
% 0.26/0.61 ! [X22: nat] :
% 0.26/0.61 ( zero_zero_nat
% 0.26/0.61 != ( suc @ X22 ) ) ).
% 0.26/0.61
% 0.26/0.61 % nat.distinct(1)
% 0.26/0.61 thf(fact_182_less__mono__imp__le__mono,axiom,
% 0.26/0.61 ! [F: nat > nat,I: nat,J3: nat] :
% 0.26/0.61 ( ! [I2: nat,J4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ J4 )
% 0.26/0.61 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J4 ) ) )
% 0.26/0.61 => ( ( ord_less_eq_nat @ I @ J3 )
% 0.26/0.61 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_mono_imp_le_mono
% 0.26/0.61 thf(fact_183_le__neq__implies__less,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ( M != N )
% 0.26/0.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_neq_implies_less
% 0.26/0.61 thf(fact_184_less__or__eq__imp__le,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ( ord_less_nat @ M @ N )
% 0.26/0.61 | ( M = N ) )
% 0.26/0.61 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_or_eq_imp_le
% 0.26/0.61 thf(fact_185_le__eq__less__or__eq,axiom,
% 0.26/0.61 ( ord_less_eq_nat
% 0.26/0.61 = ( ^ [M6: nat,N4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M6 @ N4 )
% 0.26/0.61 | ( M6 = N4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_eq_less_or_eq
% 0.26/0.61 thf(fact_186_less__imp__le__nat,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ N )
% 0.26/0.61 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_imp_le_nat
% 0.26/0.61 thf(fact_187_nat__less__le,axiom,
% 0.26/0.61 ( ord_less_nat
% 0.26/0.61 = ( ^ [M6: nat,N4: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M6 @ N4 )
% 0.26/0.61 & ( M6 != N4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nat_less_le
% 0.26/0.61 thf(fact_188_not__less__less__Suc__eq,axiom,
% 0.26/0.61 ! [N: nat,M: nat] :
% 0.26/0.61 ( ~ ( ord_less_nat @ N @ M )
% 0.26/0.61 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.26/0.61 = ( N = M ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % not_less_less_Suc_eq
% 0.26/0.61 thf(fact_189_strict__inc__induct,axiom,
% 0.26/0.61 ! [I: nat,J3: nat,P: nat > $o] :
% 0.26/0.61 ( ( ord_less_nat @ I @ J3 )
% 0.26/0.61 => ( ! [I2: nat] :
% 0.26/0.61 ( ( J3
% 0.26/0.61 = ( suc @ I2 ) )
% 0.26/0.61 => ( P @ I2 ) )
% 0.26/0.61 => ( ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ J3 )
% 0.26/0.61 => ( ( P @ ( suc @ I2 ) )
% 0.26/0.61 => ( P @ I2 ) ) )
% 0.26/0.61 => ( P @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % strict_inc_induct
% 0.26/0.61 thf(fact_190_less__Suc__induct,axiom,
% 0.26/0.61 ! [I: nat,J3: nat,P: nat > nat > $o] :
% 0.26/0.61 ( ( ord_less_nat @ I @ J3 )
% 0.26/0.61 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 0.26/0.61 => ( ! [I2: nat,J4: nat,K3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ J4 )
% 0.26/0.61 => ( ( ord_less_nat @ J4 @ K3 )
% 0.26/0.61 => ( ( P @ I2 @ J4 )
% 0.26/0.61 => ( ( P @ J4 @ K3 )
% 0.26/0.61 => ( P @ I2 @ K3 ) ) ) ) )
% 0.26/0.61 => ( P @ I @ J3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_Suc_induct
% 0.26/0.61 thf(fact_191_less__trans__Suc,axiom,
% 0.26/0.61 ! [I: nat,J3: nat,K2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I @ J3 )
% 0.26/0.61 => ( ( ord_less_nat @ J3 @ K2 )
% 0.26/0.61 => ( ord_less_nat @ ( suc @ I ) @ K2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_trans_Suc
% 0.26/0.61 thf(fact_192_Suc__less__SucD,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.26/0.61 => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_less_SucD
% 0.26/0.61 thf(fact_193_less__antisym,axiom,
% 0.26/0.61 ! [N: nat,M: nat] :
% 0.26/0.61 ( ~ ( ord_less_nat @ N @ M )
% 0.26/0.61 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.26/0.61 => ( M = N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_antisym
% 0.26/0.61 thf(fact_194_Suc__less__eq2,axiom,
% 0.26/0.61 ! [N: nat,M: nat] :
% 0.26/0.61 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.26/0.61 = ( ? [M7: nat] :
% 0.26/0.61 ( ( M
% 0.26/0.61 = ( suc @ M7 ) )
% 0.26/0.61 & ( ord_less_nat @ N @ M7 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_less_eq2
% 0.26/0.61 thf(fact_195_All__less__Suc,axiom,
% 0.26/0.61 ! [N: nat,P: nat > $o] :
% 0.26/0.61 ( ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.26/0.61 => ( P @ I3 ) ) )
% 0.26/0.61 = ( ( P @ N )
% 0.26/0.61 & ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ N )
% 0.26/0.61 => ( P @ I3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % All_less_Suc
% 0.26/0.61 thf(fact_196_not__less__eq,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.26/0.61 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % not_less_eq
% 0.26/0.61 thf(fact_197_less__Suc__eq,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.61 = ( ( ord_less_nat @ M @ N )
% 0.26/0.61 | ( M = N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_Suc_eq
% 0.26/0.61 thf(fact_198_Ex__less__Suc,axiom,
% 0.26/0.61 ! [N: nat,P: nat > $o] :
% 0.26/0.61 ( ( ? [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.26/0.61 & ( P @ I3 ) ) )
% 0.26/0.61 = ( ( P @ N )
% 0.26/0.61 | ? [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ N )
% 0.26/0.61 & ( P @ I3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Ex_less_Suc
% 0.26/0.61 thf(fact_199_less__SucI,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ N )
% 0.26/0.61 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_SucI
% 0.26/0.61 thf(fact_200_less__SucE,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.61 => ( ~ ( ord_less_nat @ M @ N )
% 0.26/0.61 => ( M = N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_SucE
% 0.26/0.61 thf(fact_201_Suc__lessI,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ N )
% 0.26/0.61 => ( ( ( suc @ M )
% 0.26/0.61 != N )
% 0.26/0.61 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_lessI
% 0.26/0.61 thf(fact_202_Suc__lessE,axiom,
% 0.26/0.61 ! [I: nat,K2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ ( suc @ I ) @ K2 )
% 0.26/0.61 => ~ ! [J4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I @ J4 )
% 0.26/0.61 => ( K2
% 0.26/0.61 != ( suc @ J4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_lessE
% 0.26/0.61 thf(fact_203_Suc__lessD,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.26/0.61 => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_lessD
% 0.26/0.61 thf(fact_204_Nat_OlessE,axiom,
% 0.26/0.61 ! [I: nat,K2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I @ K2 )
% 0.26/0.61 => ( ( K2
% 0.26/0.61 != ( suc @ I ) )
% 0.26/0.61 => ~ ! [J4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I @ J4 )
% 0.26/0.61 => ( K2
% 0.26/0.61 != ( suc @ J4 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Nat.lessE
% 0.26/0.61 thf(fact_205_bot__nat__0_Oextremum__strict,axiom,
% 0.26/0.61 ! [A: nat] :
% 0.26/0.61 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % bot_nat_0.extremum_strict
% 0.26/0.61 thf(fact_206_infinite__descent0,axiom,
% 0.26/0.61 ! [P: nat > $o,N: nat] :
% 0.26/0.61 ( ( P @ zero_zero_nat )
% 0.26/0.61 => ( ! [N2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.26/0.61 => ( ~ ( P @ N2 )
% 0.26/0.61 => ? [M2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M2 @ N2 )
% 0.26/0.61 & ~ ( P @ M2 ) ) ) )
% 0.26/0.61 => ( P @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_descent0
% 0.26/0.61 thf(fact_207_gr__implies__not0,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ N )
% 0.26/0.61 => ( N != zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % gr_implies_not0
% 0.26/0.61 thf(fact_208_less__zeroE,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % less_zeroE
% 0.26/0.61 thf(fact_209_not__less0,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % not_less0
% 0.26/0.61 thf(fact_210_not__gr0,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.26/0.61 = ( N = zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % not_gr0
% 0.26/0.61 thf(fact_211_gr0I,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( N != zero_zero_nat )
% 0.26/0.61 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % gr0I
% 0.26/0.61 thf(fact_212_diff__le__mono2,axiom,
% 0.26/0.61 ! [M: nat,N: nat,L2: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_le_mono2
% 0.26/0.61 thf(fact_213_le__diff__iff_H,axiom,
% 0.26/0.61 ! [A: nat,C: nat,B: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ A @ C )
% 0.26/0.61 => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.61 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.26/0.61 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_diff_iff'
% 0.26/0.61 thf(fact_214_diff__le__self,axiom,
% 0.26/0.61 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.26/0.61
% 0.26/0.61 % diff_le_self
% 0.26/0.61 thf(fact_215_diff__le__mono,axiom,
% 0.26/0.61 ! [M: nat,N: nat,L2: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_le_mono
% 0.26/0.61 thf(fact_216_Nat_Odiff__diff__eq,axiom,
% 0.26/0.61 ! [K2: nat,M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ K2 @ M )
% 0.26/0.61 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.26/0.61 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 0.26/0.61 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Nat.diff_diff_eq
% 0.26/0.61 thf(fact_217_le__diff__iff,axiom,
% 0.26/0.61 ! [K2: nat,M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ K2 @ M )
% 0.26/0.61 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.26/0.61 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 0.26/0.61 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_diff_iff
% 0.26/0.61 thf(fact_218_eq__diff__iff,axiom,
% 0.26/0.61 ! [K2: nat,M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ K2 @ M )
% 0.26/0.61 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.26/0.61 => ( ( ( minus_minus_nat @ M @ K2 )
% 0.26/0.61 = ( minus_minus_nat @ N @ K2 ) )
% 0.26/0.61 = ( M = N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % eq_diff_iff
% 0.26/0.61 thf(fact_219_zero__induct__lemma,axiom,
% 0.26/0.61 ! [P: nat > $o,K2: nat,I: nat] :
% 0.26/0.61 ( ( P @ K2 )
% 0.26/0.61 => ( ! [N2: nat] :
% 0.26/0.61 ( ( P @ ( suc @ N2 ) )
% 0.26/0.61 => ( P @ N2 ) )
% 0.26/0.61 => ( P @ ( minus_minus_nat @ K2 @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % zero_induct_lemma
% 0.26/0.61 thf(fact_220_minus__nat_Odiff__0,axiom,
% 0.26/0.61 ! [M: nat] :
% 0.26/0.61 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.26/0.61 = M ) ).
% 0.26/0.61
% 0.26/0.61 % minus_nat.diff_0
% 0.26/0.61 thf(fact_221_diffs0__imp__equal,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ( minus_minus_nat @ M @ N )
% 0.26/0.61 = zero_zero_nat )
% 0.26/0.61 => ( ( ( minus_minus_nat @ N @ M )
% 0.26/0.61 = zero_zero_nat )
% 0.26/0.61 => ( M = N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % diffs0_imp_equal
% 0.26/0.61 thf(fact_222_less__imp__diff__less,axiom,
% 0.26/0.61 ! [J3: nat,K2: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ J3 @ K2 )
% 0.26/0.61 => ( ord_less_nat @ ( minus_minus_nat @ J3 @ N ) @ K2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_imp_diff_less
% 0.26/0.61 thf(fact_223_diff__less__mono2,axiom,
% 0.26/0.61 ! [M: nat,N: nat,L2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ N )
% 0.26/0.61 => ( ( ord_less_nat @ M @ L2 )
% 0.26/0.61 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_less_mono2
% 0.26/0.61 thf(fact_224_Module_Osc__Ring,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ring_b_d @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.sc_Ring
% 0.26/0.61 thf(fact_225_Module_Osc__Ring,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ring_b_d @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.sc_Ring
% 0.26/0.61 thf(fact_226_Module_Osc__Ring,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ring_b_d @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.sc_Ring
% 0.26/0.61 thf(fact_227_Module_Omem__smodule__ideal__coeff,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,A2: set_b,X: e] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.61 => ( ( member_e @ X @ ( smodul1982583723_d_e_f @ R @ M3 @ A2 ) )
% 0.26/0.61 => ? [N2: nat,X2: nat > b] :
% 0.26/0.61 ( ( member_nat_b @ X2
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.61 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.61 & ? [Xa: nat > e] :
% 0.26/0.61 ( ( member_nat_e @ Xa
% 0.26/0.61 @ ( pi_nat_e
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie730238621_e_b_f @ M3 ) ) )
% 0.26/0.61 & ( X
% 0.26/0.61 = ( l_comb_b_d_e_f @ R @ M3 @ N2 @ X2 @ Xa ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.mem_smodule_ideal_coeff
% 0.26/0.61 thf(fact_228_Module_Omem__smodule__ideal__coeff,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,A2: set_b,X: a] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.61 => ( ( member_a @ X @ ( smodul132175289t_unit @ R @ M3 @ A2 ) )
% 0.26/0.61 => ? [N2: nat,X2: nat > b] :
% 0.26/0.61 ( ( member_nat_b @ X2
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.61 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.61 & ? [Xa: nat > a] :
% 0.26/0.61 ( ( member_nat_a @ Xa
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie1074654371t_unit @ M3 ) ) )
% 0.26/0.61 & ( X
% 0.26/0.61 = ( l_comb1138968323t_unit @ R @ M3 @ N2 @ X2 @ Xa ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.mem_smodule_ideal_coeff
% 0.26/0.61 thf(fact_229_Module_Omem__smodule__ideal__coeff,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,A2: set_b,X: a] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( ideal_b_d @ R @ A2 )
% 0.26/0.61 => ( ( member_a @ X @ ( smodul818989740_d_a_c @ R @ M3 @ A2 ) )
% 0.26/0.61 => ? [N2: nat,X2: nat > b] :
% 0.26/0.61 ( ( member_nat_b @ X2
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.61 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.61 & ? [Xa: nat > a] :
% 0.26/0.61 ( ( member_nat_a @ Xa
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N2 ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie2021454486_a_b_c @ M3 ) ) )
% 0.26/0.61 & ( X
% 0.26/0.61 = ( l_comb_b_d_a_c @ R @ M3 @ N2 @ X2 @ Xa ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.mem_smodule_ideal_coeff
% 0.26/0.61 thf(fact_230_lift__Suc__antimono__le,axiom,
% 0.26/0.61 ! [F: nat > nat,N: nat,N5: nat] :
% 0.26/0.61 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.26/0.61 => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.61 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % lift_Suc_antimono_le
% 0.26/0.61 thf(fact_231_lift__Suc__antimono__le,axiom,
% 0.26/0.61 ! [F: nat > set_a,N: nat,N5: nat] :
% 0.26/0.61 ( ! [N2: nat] : ( ord_less_eq_set_a @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.26/0.61 => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.61 => ( ord_less_eq_set_a @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % lift_Suc_antimono_le
% 0.26/0.61 thf(fact_232_lift__Suc__mono__le,axiom,
% 0.26/0.61 ! [F: nat > nat,N: nat,N5: nat] :
% 0.26/0.61 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.61 => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.61 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % lift_Suc_mono_le
% 0.26/0.61 thf(fact_233_lift__Suc__mono__le,axiom,
% 0.26/0.61 ! [F: nat > set_a,N: nat,N5: nat] :
% 0.26/0.61 ( ! [N2: nat] : ( ord_less_eq_set_a @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.61 => ( ( ord_less_eq_nat @ N @ N5 )
% 0.26/0.61 => ( ord_less_eq_set_a @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % lift_Suc_mono_le
% 0.26/0.61 thf(fact_234_lift__Suc__mono__less__iff,axiom,
% 0.26/0.61 ! [F: nat > nat,N: nat,M: nat] :
% 0.26/0.61 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.61 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.26/0.61 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % lift_Suc_mono_less_iff
% 0.26/0.61 thf(fact_235_lift__Suc__mono__less,axiom,
% 0.26/0.61 ! [F: nat > nat,N: nat,N5: nat] :
% 0.26/0.61 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.26/0.61 => ( ( ord_less_nat @ N @ N5 )
% 0.26/0.61 => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % lift_Suc_mono_less
% 0.26/0.61 thf(fact_236_le__imp__less__Suc,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_imp_less_Suc
% 0.26/0.61 thf(fact_237_less__eq__Suc__le,axiom,
% 0.26/0.61 ( ord_less_nat
% 0.26/0.61 = ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_eq_Suc_le
% 0.26/0.61 thf(fact_238_less__Suc__eq__le,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.61 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_Suc_eq_le
% 0.26/0.61 thf(fact_239_le__less__Suc__eq,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.61 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.26/0.61 = ( N = M ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_less_Suc_eq
% 0.26/0.61 thf(fact_240_Suc__le__lessD,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.26/0.61 => ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_le_lessD
% 0.26/0.61 thf(fact_241_inc__induct,axiom,
% 0.26/0.61 ! [I: nat,J3: nat,P: nat > $o] :
% 0.26/0.61 ( ( ord_less_eq_nat @ I @ J3 )
% 0.26/0.61 => ( ( P @ J3 )
% 0.26/0.61 => ( ! [N2: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ I @ N2 )
% 0.26/0.61 => ( ( ord_less_nat @ N2 @ J3 )
% 0.26/0.61 => ( ( P @ ( suc @ N2 ) )
% 0.26/0.61 => ( P @ N2 ) ) ) )
% 0.26/0.61 => ( P @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % inc_induct
% 0.26/0.61 thf(fact_242_dec__induct,axiom,
% 0.26/0.61 ! [I: nat,J3: nat,P: nat > $o] :
% 0.26/0.61 ( ( ord_less_eq_nat @ I @ J3 )
% 0.26/0.61 => ( ( P @ I )
% 0.26/0.61 => ( ! [N2: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ I @ N2 )
% 0.26/0.61 => ( ( ord_less_nat @ N2 @ J3 )
% 0.26/0.61 => ( ( P @ N2 )
% 0.26/0.61 => ( P @ ( suc @ N2 ) ) ) ) )
% 0.26/0.61 => ( P @ J3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % dec_induct
% 0.26/0.61 thf(fact_243_Suc__le__eq,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.26/0.61 = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_le_eq
% 0.26/0.61 thf(fact_244_Suc__leI,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ N )
% 0.26/0.61 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_leI
% 0.26/0.61 thf(fact_245_ex__least__nat__le,axiom,
% 0.26/0.61 ! [P: nat > $o,N: nat] :
% 0.26/0.61 ( ( P @ N )
% 0.26/0.61 => ( ~ ( P @ zero_zero_nat )
% 0.26/0.61 => ? [K3: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ K3 @ N )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K3 )
% 0.26/0.61 => ~ ( P @ I4 ) )
% 0.26/0.61 & ( P @ K3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ex_least_nat_le
% 0.26/0.61 thf(fact_246_less__Suc__eq__0__disj,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.26/0.61 = ( ( M = zero_zero_nat )
% 0.26/0.61 | ? [J2: nat] :
% 0.26/0.61 ( ( M
% 0.26/0.61 = ( suc @ J2 ) )
% 0.26/0.61 & ( ord_less_nat @ J2 @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_Suc_eq_0_disj
% 0.26/0.61 thf(fact_247_gr0__implies__Suc,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.61 => ? [M5: nat] :
% 0.26/0.61 ( N
% 0.26/0.61 = ( suc @ M5 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % gr0_implies_Suc
% 0.26/0.61 thf(fact_248_All__less__Suc2,axiom,
% 0.26/0.61 ! [N: nat,P: nat > $o] :
% 0.26/0.61 ( ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.26/0.61 => ( P @ I3 ) ) )
% 0.26/0.61 = ( ( P @ zero_zero_nat )
% 0.26/0.61 & ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ N )
% 0.26/0.61 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % All_less_Suc2
% 0.26/0.61 thf(fact_249_gr0__conv__Suc,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.61 = ( ? [M6: nat] :
% 0.26/0.61 ( N
% 0.26/0.61 = ( suc @ M6 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % gr0_conv_Suc
% 0.26/0.61 thf(fact_250_Ex__less__Suc2,axiom,
% 0.26/0.61 ! [N: nat,P: nat > $o] :
% 0.26/0.61 ( ( ? [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.26/0.61 & ( P @ I3 ) ) )
% 0.26/0.61 = ( ( P @ zero_zero_nat )
% 0.26/0.61 | ? [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ N )
% 0.26/0.61 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Ex_less_Suc2
% 0.26/0.61 thf(fact_251_Suc__diff__le,axiom,
% 0.26/0.61 ! [N: nat,M: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.61 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.26/0.61 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_diff_le
% 0.26/0.61 thf(fact_252_diff__less__mono,axiom,
% 0.26/0.61 ! [A: nat,B: nat,C: nat] :
% 0.26/0.61 ( ( ord_less_nat @ A @ B )
% 0.26/0.61 => ( ( ord_less_eq_nat @ C @ A )
% 0.26/0.61 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_less_mono
% 0.26/0.61 thf(fact_253_less__diff__iff,axiom,
% 0.26/0.61 ! [K2: nat,M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ K2 @ M )
% 0.26/0.61 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.26/0.61 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 0.26/0.61 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_diff_iff
% 0.26/0.61 thf(fact_254_diff__less__Suc,axiom,
% 0.26/0.61 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_less_Suc
% 0.26/0.61 thf(fact_255_Suc__diff__Suc,axiom,
% 0.26/0.61 ! [N: nat,M: nat] :
% 0.26/0.61 ( ( ord_less_nat @ N @ M )
% 0.26/0.61 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 0.26/0.61 = ( minus_minus_nat @ M @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Suc_diff_Suc
% 0.26/0.61 thf(fact_256_diff__less,axiom,
% 0.26/0.61 ! [N: nat,M: nat] :
% 0.26/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.61 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.26/0.61 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_less
% 0.26/0.61 thf(fact_257_Module_Osubmodule__subset1,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,H: set_e,H2: e] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( submodule_b_d_e_f @ R @ M3 @ H )
% 0.26/0.61 => ( ( member_e @ H2 @ H )
% 0.26/0.61 => ( member_e @ H2 @ ( carrie730238621_e_b_f @ M3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.submodule_subset1
% 0.26/0.61 thf(fact_258_Module_Osubmodule__subset1,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,H: set_a,H2: a] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( submodule_b_d_a_c @ R @ M3 @ H )
% 0.26/0.61 => ( ( member_a @ H2 @ H )
% 0.26/0.61 => ( member_a @ H2 @ ( carrie2021454486_a_b_c @ M3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.submodule_subset1
% 0.26/0.61 thf(fact_259_Module_Osubmodule__subset1,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,H: set_a,H2: a] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( submod903911234t_unit @ R @ M3 @ H )
% 0.26/0.61 => ( ( member_a @ H2 @ H )
% 0.26/0.61 => ( member_a @ H2 @ ( carrie1074654371t_unit @ M3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.submodule_subset1
% 0.26/0.61 thf(fact_260_Module_Osubmodule__whole,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( submodule_b_d_e_f @ R @ M3 @ ( carrie730238621_e_b_f @ M3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.submodule_whole
% 0.26/0.61 thf(fact_261_Module_Osubmodule__whole,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( submodule_b_d_a_c @ R @ M3 @ ( carrie2021454486_a_b_c @ M3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.submodule_whole
% 0.26/0.61 thf(fact_262_Module_Osubmodule__whole,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( submod903911234t_unit @ R @ M3 @ ( carrie1074654371t_unit @ M3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.submodule_whole
% 0.26/0.61 thf(fact_263_ex__least__nat__less,axiom,
% 0.26/0.61 ! [P: nat > $o,N: nat] :
% 0.26/0.61 ( ( P @ N )
% 0.26/0.61 => ( ~ ( P @ zero_zero_nat )
% 0.26/0.61 => ? [K3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ K3 @ N )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ I4 @ K3 )
% 0.26/0.61 => ~ ( P @ I4 ) )
% 0.26/0.61 & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ex_least_nat_less
% 0.26/0.61 thf(fact_264_diff__Suc__less,axiom,
% 0.26/0.61 ! [N: nat,I: nat] :
% 0.26/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.26/0.61 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % diff_Suc_less
% 0.26/0.61 thf(fact_265_Module_Osubmodule__subset,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,H: set_e] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( submodule_b_d_e_f @ R @ M3 @ H )
% 0.26/0.61 => ( ord_less_eq_set_e @ H @ ( carrie730238621_e_b_f @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.submodule_subset
% 0.26/0.61 thf(fact_266_Module_Osubmodule__subset,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,H: set_a] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( submodule_b_d_a_c @ R @ M3 @ H )
% 0.26/0.61 => ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.submodule_subset
% 0.26/0.61 thf(fact_267_Module_Osubmodule__subset,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,H: set_a] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( submod903911234t_unit @ R @ M3 @ H )
% 0.26/0.61 => ( ord_less_eq_set_a @ H @ ( carrie1074654371t_unit @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.submodule_subset
% 0.26/0.61 thf(fact_268_Module_Ofree__generator__sub,axiom,
% 0.26/0.61 ! [M3: carrie1821755406_e_b_f,R: carrie1950868226xt_b_d,H: set_e] :
% 0.26/0.61 ( ( module_e_b_f_d @ M3 @ R )
% 0.26/0.61 => ( ( free_g103796815_d_e_f @ R @ M3 @ H )
% 0.26/0.61 => ( ord_less_eq_set_e @ H @ ( carrie730238621_e_b_f @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.free_generator_sub
% 0.26/0.61 thf(fact_269_Module_Ofree__generator__sub,axiom,
% 0.26/0.61 ! [M3: carrie722926983_a_b_c,R: carrie1950868226xt_b_d,H: set_a] :
% 0.26/0.61 ( ( module_a_b_c_d @ M3 @ R )
% 0.26/0.61 => ( ( free_g1087686480_d_a_c @ R @ M3 @ H )
% 0.26/0.61 => ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.free_generator_sub
% 0.26/0.61 thf(fact_270_Module_Ofree__generator__sub,axiom,
% 0.26/0.61 ! [M3: carrie1963041556t_unit,R: carrie1950868226xt_b_d,H: set_a] :
% 0.26/0.61 ( ( module1821517916unit_d @ M3 @ R )
% 0.26/0.61 => ( ( free_g637607517t_unit @ R @ M3 @ H )
% 0.26/0.61 => ( ord_less_eq_set_a @ H @ ( carrie1074654371t_unit @ M3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Module.free_generator_sub
% 0.26/0.61 thf(fact_271_eSum__in__SubmoduleTr,axiom,
% 0.26/0.61 ! [H: set_a,K: set_a,F: nat > a,N: nat,S: nat > b] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ K @ H )
% 0.26/0.61 => ( ( ( member_nat_a @ F
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : K ) )
% 0.26/0.61 & ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ r ) ) ) )
% 0.26/0.61 => ( ( l_comb1138968323t_unit @ r @ ( mdl_a_b_c @ m @ ( algebr1152250919_d_a_c @ r @ m @ K ) ) @ N @ S @ F )
% 0.26/0.61 = ( l_comb_b_d_a_c @ r @ m @ N @ S @ F ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % eSum_in_SubmoduleTr
% 0.26/0.61 thf(fact_272_eSum__in__Submodule,axiom,
% 0.26/0.61 ! [H: set_a,K: set_a,F: nat > a,N: nat,S: nat > b] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ K @ H )
% 0.26/0.61 => ( ( member_nat_a @ F
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : K ) )
% 0.26/0.61 => ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ r ) ) )
% 0.26/0.61 => ( ( l_comb1138968323t_unit @ r @ ( mdl_a_b_c @ m @ ( algebr1152250919_d_a_c @ r @ m @ K ) ) @ N @ S @ F )
% 0.26/0.61 = ( l_comb_b_d_a_c @ r @ m @ N @ S @ F ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % eSum_in_Submodule
% 0.26/0.61 thf(fact_273_singleton__insert__inj__eq_H,axiom,
% 0.26/0.61 ! [A: a,A2: set_a,B: a] :
% 0.26/0.61 ( ( ( insert_a @ A @ A2 )
% 0.26/0.61 = ( insert_a @ B @ bot_bot_set_a ) )
% 0.26/0.61 = ( ( A = B )
% 0.26/0.61 & ( ord_less_eq_set_a @ A2 @ ( insert_a @ B @ bot_bot_set_a ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % singleton_insert_inj_eq'
% 0.26/0.61 thf(fact_274_singleton__insert__inj__eq,axiom,
% 0.26/0.61 ! [B: a,A: a,A2: set_a] :
% 0.26/0.61 ( ( ( insert_a @ B @ bot_bot_set_a )
% 0.26/0.61 = ( insert_a @ A @ A2 ) )
% 0.26/0.61 = ( ( A = B )
% 0.26/0.61 & ( ord_less_eq_set_a @ A2 @ ( insert_a @ B @ bot_bot_set_a ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % singleton_insert_inj_eq
% 0.26/0.61 thf(fact_275_l__span__closed2Tr,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a,S: nat > b,N: nat,F: nat > a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.61 & ( member_nat_a @ F
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ H ) ) ) )
% 0.26/0.61 => ( member_a @ ( l_comb_b_d_a_c @ r @ m @ N @ S @ F ) @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_span_closed2Tr
% 0.26/0.61 thf(fact_276_l__span__closed2,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a,S: nat > b,N: nat,F: nat > a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.61 => ( ( member_nat_a @ F
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ H ) ) )
% 0.26/0.61 => ( member_a @ ( l_comb_b_d_a_c @ r @ m @ N @ S @ F ) @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_span_closed2
% 0.26/0.61 thf(fact_277_linear__comb0__2Tr,axiom,
% 0.26/0.61 ! [A2: set_b,S: nat > b,N: nat,M: nat > a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.61 & ( member_nat_a @ M
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( insert_a @ ( zero_a1261444626_a_b_c @ m ) @ bot_bot_set_a ) ) ) )
% 0.26/0.61 => ( ( l_comb_b_d_a_c @ r @ m @ N @ S @ M )
% 0.26/0.61 = ( zero_a1261444626_a_b_c @ m ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % linear_comb0_2Tr
% 0.26/0.61 thf(fact_278_module__inc__zero,axiom,
% 0.26/0.61 member_a @ ( zero_a1261444626_a_b_c @ m ) @ ( carrie2021454486_a_b_c @ m ) ).
% 0.26/0.61
% 0.26/0.61 % module_inc_zero
% 0.26/0.61 thf(fact_279_psubsetI,axiom,
% 0.26/0.61 ! [A2: set_a,B2: set_a] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.26/0.61 => ( ( A2 != B2 )
% 0.26/0.61 => ( ord_less_set_a @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % psubsetI
% 0.26/0.61 thf(fact_280_subsetI,axiom,
% 0.26/0.61 ! [A2: set_nat_a,B2: set_nat_a] :
% 0.26/0.61 ( ! [X2: nat > a] :
% 0.26/0.61 ( ( member_nat_a @ X2 @ A2 )
% 0.26/0.61 => ( member_nat_a @ X2 @ B2 ) )
% 0.26/0.61 => ( ord_le157368549_nat_a @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetI
% 0.26/0.61 thf(fact_281_subsetI,axiom,
% 0.26/0.61 ! [A2: set_nat_b,B2: set_nat_b] :
% 0.26/0.61 ( ! [X2: nat > b] :
% 0.26/0.61 ( ( member_nat_b @ X2 @ A2 )
% 0.26/0.61 => ( member_nat_b @ X2 @ B2 ) )
% 0.26/0.61 => ( ord_le1296932838_nat_b @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetI
% 0.26/0.61 thf(fact_282_subsetI,axiom,
% 0.26/0.61 ! [A2: set_a,B2: set_a] :
% 0.26/0.61 ( ! [X2: a] :
% 0.26/0.61 ( ( member_a @ X2 @ A2 )
% 0.26/0.61 => ( member_a @ X2 @ B2 ) )
% 0.26/0.61 => ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetI
% 0.26/0.61 thf(fact_283_subset__antisym,axiom,
% 0.26/0.61 ! [A2: set_a,B2: set_a] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.26/0.61 => ( A2 = B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_antisym
% 0.26/0.61 thf(fact_284_Diff__empty,axiom,
% 0.26/0.61 ! [A2: set_a] :
% 0.26/0.61 ( ( minus_minus_set_a @ A2 @ bot_bot_set_a )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Diff_empty
% 0.26/0.61 thf(fact_285_empty__Diff,axiom,
% 0.26/0.61 ! [A2: set_a] :
% 0.26/0.61 ( ( minus_minus_set_a @ bot_bot_set_a @ A2 )
% 0.26/0.61 = bot_bot_set_a ) ).
% 0.26/0.61
% 0.26/0.61 % empty_Diff
% 0.26/0.61 thf(fact_286_Diff__cancel,axiom,
% 0.26/0.61 ! [A2: set_a] :
% 0.26/0.61 ( ( minus_minus_set_a @ A2 @ A2 )
% 0.26/0.61 = bot_bot_set_a ) ).
% 0.26/0.61
% 0.26/0.61 % Diff_cancel
% 0.26/0.61 thf(fact_287_empty__iff,axiom,
% 0.26/0.61 ! [C: nat > a] :
% 0.26/0.61 ~ ( member_nat_a @ C @ bot_bot_set_nat_a ) ).
% 0.26/0.61
% 0.26/0.61 % empty_iff
% 0.26/0.61 thf(fact_288_empty__iff,axiom,
% 0.26/0.61 ! [C: nat > b] :
% 0.26/0.61 ~ ( member_nat_b @ C @ bot_bot_set_nat_b ) ).
% 0.26/0.61
% 0.26/0.61 % empty_iff
% 0.26/0.61 thf(fact_289_empty__iff,axiom,
% 0.26/0.61 ! [C: a] :
% 0.26/0.61 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 0.26/0.61
% 0.26/0.61 % empty_iff
% 0.26/0.61 thf(fact_290_all__not__in__conv,axiom,
% 0.26/0.61 ! [A2: set_nat_a] :
% 0.26/0.61 ( ( ! [X3: nat > a] :
% 0.26/0.61 ~ ( member_nat_a @ X3 @ A2 ) )
% 0.26/0.61 = ( A2 = bot_bot_set_nat_a ) ) ).
% 0.26/0.61
% 0.26/0.61 % all_not_in_conv
% 0.26/0.61 thf(fact_291_all__not__in__conv,axiom,
% 0.26/0.61 ! [A2: set_nat_b] :
% 0.26/0.61 ( ( ! [X3: nat > b] :
% 0.26/0.61 ~ ( member_nat_b @ X3 @ A2 ) )
% 0.26/0.61 = ( A2 = bot_bot_set_nat_b ) ) ).
% 0.26/0.61
% 0.26/0.61 % all_not_in_conv
% 0.26/0.61 thf(fact_292_all__not__in__conv,axiom,
% 0.26/0.61 ! [A2: set_a] :
% 0.26/0.61 ( ( ! [X3: a] :
% 0.26/0.61 ~ ( member_a @ X3 @ A2 ) )
% 0.26/0.61 = ( A2 = bot_bot_set_a ) ) ).
% 0.26/0.61
% 0.26/0.61 % all_not_in_conv
% 0.26/0.61 thf(fact_293_Collect__empty__eq,axiom,
% 0.26/0.61 ! [P: nat > $o] :
% 0.26/0.61 ( ( ( collect_nat @ P )
% 0.26/0.61 = bot_bot_set_nat )
% 0.26/0.61 = ( ! [X3: nat] :
% 0.26/0.61 ~ ( P @ X3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_empty_eq
% 0.26/0.61 thf(fact_294_Collect__empty__eq,axiom,
% 0.26/0.61 ! [P: a > $o] :
% 0.26/0.61 ( ( ( collect_a @ P )
% 0.26/0.61 = bot_bot_set_a )
% 0.26/0.61 = ( ! [X3: a] :
% 0.26/0.61 ~ ( P @ X3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_empty_eq
% 0.26/0.61 thf(fact_295_empty__Collect__eq,axiom,
% 0.26/0.61 ! [P: nat > $o] :
% 0.26/0.61 ( ( bot_bot_set_nat
% 0.26/0.61 = ( collect_nat @ P ) )
% 0.26/0.61 = ( ! [X3: nat] :
% 0.26/0.61 ~ ( P @ X3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % empty_Collect_eq
% 0.26/0.61 thf(fact_296_empty__Collect__eq,axiom,
% 0.26/0.61 ! [P: a > $o] :
% 0.26/0.61 ( ( bot_bot_set_a
% 0.26/0.61 = ( collect_a @ P ) )
% 0.26/0.61 = ( ! [X3: a] :
% 0.26/0.61 ~ ( P @ X3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % empty_Collect_eq
% 0.26/0.61 thf(fact_297_Diff__insert0,axiom,
% 0.26/0.61 ! [X: nat > a,A2: set_nat_a,B2: set_nat_a] :
% 0.26/0.61 ( ~ ( member_nat_a @ X @ A2 )
% 0.26/0.61 => ( ( minus_1788767276_nat_a @ A2 @ ( insert_nat_a @ X @ B2 ) )
% 0.26/0.61 = ( minus_1788767276_nat_a @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Diff_insert0
% 0.26/0.61 thf(fact_298_Diff__insert0,axiom,
% 0.26/0.61 ! [X: nat > b,A2: set_nat_b,B2: set_nat_b] :
% 0.26/0.61 ( ~ ( member_nat_b @ X @ A2 )
% 0.26/0.61 => ( ( minus_780847917_nat_b @ A2 @ ( insert_nat_b @ X @ B2 ) )
% 0.26/0.61 = ( minus_780847917_nat_b @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Diff_insert0
% 0.26/0.61 thf(fact_299_Diff__insert0,axiom,
% 0.26/0.61 ! [X: a,A2: set_a,B2: set_a] :
% 0.26/0.61 ( ~ ( member_a @ X @ A2 )
% 0.26/0.61 => ( ( minus_minus_set_a @ A2 @ ( insert_a @ X @ B2 ) )
% 0.26/0.61 = ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Diff_insert0
% 0.26/0.61 thf(fact_300_insert__Diff1,axiom,
% 0.26/0.61 ! [X: nat > a,B2: set_nat_a,A2: set_nat_a] :
% 0.26/0.61 ( ( member_nat_a @ X @ B2 )
% 0.26/0.61 => ( ( minus_1788767276_nat_a @ ( insert_nat_a @ X @ A2 ) @ B2 )
% 0.26/0.61 = ( minus_1788767276_nat_a @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_Diff1
% 0.26/0.61 thf(fact_301_insert__Diff1,axiom,
% 0.26/0.61 ! [X: nat > b,B2: set_nat_b,A2: set_nat_b] :
% 0.26/0.61 ( ( member_nat_b @ X @ B2 )
% 0.26/0.61 => ( ( minus_780847917_nat_b @ ( insert_nat_b @ X @ A2 ) @ B2 )
% 0.26/0.61 = ( minus_780847917_nat_b @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_Diff1
% 0.26/0.61 thf(fact_302_insert__Diff1,axiom,
% 0.26/0.61 ! [X: a,B2: set_a,A2: set_a] :
% 0.26/0.61 ( ( member_a @ X @ B2 )
% 0.26/0.61 => ( ( minus_minus_set_a @ ( insert_a @ X @ A2 ) @ B2 )
% 0.26/0.61 = ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_Diff1
% 0.26/0.61 thf(fact_303_insertCI,axiom,
% 0.26/0.61 ! [A: nat > a,B2: set_nat_a,B: nat > a] :
% 0.26/0.61 ( ( ~ ( member_nat_a @ A @ B2 )
% 0.26/0.61 => ( A = B ) )
% 0.26/0.61 => ( member_nat_a @ A @ ( insert_nat_a @ B @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insertCI
% 0.26/0.61 thf(fact_304_insertCI,axiom,
% 0.26/0.61 ! [A: nat > b,B2: set_nat_b,B: nat > b] :
% 0.26/0.61 ( ( ~ ( member_nat_b @ A @ B2 )
% 0.26/0.61 => ( A = B ) )
% 0.26/0.61 => ( member_nat_b @ A @ ( insert_nat_b @ B @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insertCI
% 0.26/0.61 thf(fact_305_insertCI,axiom,
% 0.26/0.61 ! [A: a,B2: set_a,B: a] :
% 0.26/0.61 ( ( ~ ( member_a @ A @ B2 )
% 0.26/0.61 => ( A = B ) )
% 0.26/0.61 => ( member_a @ A @ ( insert_a @ B @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insertCI
% 0.26/0.61 thf(fact_306_insert__iff,axiom,
% 0.26/0.61 ! [A: nat > a,B: nat > a,A2: set_nat_a] :
% 0.26/0.61 ( ( member_nat_a @ A @ ( insert_nat_a @ B @ A2 ) )
% 0.26/0.61 = ( ( A = B )
% 0.26/0.61 | ( member_nat_a @ A @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_iff
% 0.26/0.61 thf(fact_307_insert__iff,axiom,
% 0.26/0.61 ! [A: nat > b,B: nat > b,A2: set_nat_b] :
% 0.26/0.61 ( ( member_nat_b @ A @ ( insert_nat_b @ B @ A2 ) )
% 0.26/0.61 = ( ( A = B )
% 0.26/0.61 | ( member_nat_b @ A @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_iff
% 0.26/0.61 thf(fact_308_insert__iff,axiom,
% 0.26/0.61 ! [A: a,B: a,A2: set_a] :
% 0.26/0.61 ( ( member_a @ A @ ( insert_a @ B @ A2 ) )
% 0.26/0.61 = ( ( A = B )
% 0.26/0.61 | ( member_a @ A @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_iff
% 0.26/0.61 thf(fact_309_insert__absorb2,axiom,
% 0.26/0.61 ! [X: a,A2: set_a] :
% 0.26/0.61 ( ( insert_a @ X @ ( insert_a @ X @ A2 ) )
% 0.26/0.61 = ( insert_a @ X @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_absorb2
% 0.26/0.61 thf(fact_310_submodule__inc__0,axiom,
% 0.26/0.61 ! [H: set_a] :
% 0.26/0.61 ( ( submodule_b_d_a_c @ r @ m @ H )
% 0.26/0.61 => ( member_a @ ( zero_a1261444626_a_b_c @ m ) @ H ) ) ).
% 0.26/0.61
% 0.26/0.61 % submodule_inc_0
% 0.26/0.61 thf(fact_311_mdl__carrier,axiom,
% 0.26/0.61 ! [H: set_a] :
% 0.26/0.61 ( ( submodule_b_d_a_c @ r @ m @ H )
% 0.26/0.61 => ( ( carrie1074654371t_unit @ ( mdl_a_b_c @ m @ H ) )
% 0.26/0.61 = H ) ) ).
% 0.26/0.61
% 0.26/0.61 % mdl_carrier
% 0.26/0.61 thf(fact_312_mdl__is__module,axiom,
% 0.26/0.61 ! [H: set_a] :
% 0.26/0.61 ( ( submodule_b_d_a_c @ r @ m @ H )
% 0.26/0.61 => ( module1821517916unit_d @ ( mdl_a_b_c @ m @ H ) @ r ) ) ).
% 0.26/0.61
% 0.26/0.61 % mdl_is_module
% 0.26/0.61 thf(fact_313_submodule__of__mdl,axiom,
% 0.26/0.61 ! [H: set_a,N3: set_a] :
% 0.26/0.61 ( ( submodule_b_d_a_c @ r @ m @ H )
% 0.26/0.61 => ( ( submodule_b_d_a_c @ r @ m @ N3 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ N3 )
% 0.26/0.61 => ( submod903911234t_unit @ r @ ( mdl_a_b_c @ m @ N3 ) @ H ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % submodule_of_mdl
% 0.26/0.61 thf(fact_314_h__in__linear__span,axiom,
% 0.26/0.61 ! [H: set_a,H2: a] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( member_a @ H2 @ H )
% 0.26/0.61 => ( member_a @ H2 @ ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ H ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % h_in_linear_span
% 0.26/0.61 thf(fact_315_l__span__cont__H,axiom,
% 0.26/0.61 ! [H: set_a] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ord_less_eq_set_a @ H @ ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ H ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_span_cont_H
% 0.26/0.61 thf(fact_316_l__span__l__span,axiom,
% 0.26/0.61 ! [H: set_a] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ H ) )
% 0.26/0.61 = ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ H ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_span_l_span
% 0.26/0.61 thf(fact_317_l__span__gen__mono,axiom,
% 0.26/0.61 ! [K: set_a,H: set_a,A2: set_b] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ K @ H )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ord_less_eq_set_a @ ( linear_span_b_d_a_c @ r @ m @ A2 @ K ) @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_span_gen_mono
% 0.26/0.61 thf(fact_318_linear__span__sub,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ord_less_eq_set_a @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) @ ( carrie2021454486_a_b_c @ m ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % linear_span_sub
% 0.26/0.61 thf(fact_319_l__span__sub__submodule,axiom,
% 0.26/0.61 ! [A2: set_b,N3: set_a,H: set_a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( submodule_b_d_a_c @ r @ m @ N3 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ N3 )
% 0.26/0.61 => ( ord_less_eq_set_a @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) @ N3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_span_sub_submodule
% 0.26/0.61 thf(fact_320_fgs__generator,axiom,
% 0.26/0.61 ! [H: set_a] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( genera1692266857t_unit @ r @ ( mdl_a_b_c @ m @ ( algebr1152250919_d_a_c @ r @ m @ H ) ) @ H ) ) ).
% 0.26/0.61
% 0.26/0.61 % fgs_generator
% 0.26/0.61 thf(fact_321_submodule__0,axiom,
% 0.26/0.61 submodule_b_d_a_c @ r @ m @ ( insert_a @ ( zero_a1261444626_a_b_c @ m ) @ bot_bot_set_a ) ).
% 0.26/0.61
% 0.26/0.61 % submodule_0
% 0.26/0.61 thf(fact_322_empty__fgs,axiom,
% 0.26/0.61 ( ( algebr1152250919_d_a_c @ r @ m @ bot_bot_set_a )
% 0.26/0.61 = ( insert_a @ ( zero_a1261444626_a_b_c @ m ) @ bot_bot_set_a ) ) ).
% 0.26/0.61
% 0.26/0.61 % empty_fgs
% 0.26/0.61 thf(fact_323_le__zero__eq,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.26/0.61 = ( N = zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_zero_eq
% 0.26/0.61 thf(fact_324_not__gr__zero,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.26/0.61 = ( N = zero_zero_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % not_gr_zero
% 0.26/0.61 thf(fact_325_zero__diff,axiom,
% 0.26/0.61 ! [A: nat] :
% 0.26/0.61 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.26/0.61 = zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % zero_diff
% 0.26/0.61 thf(fact_326_diff__zero,axiom,
% 0.26/0.61 ! [A: nat] :
% 0.26/0.61 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % diff_zero
% 0.26/0.61 thf(fact_327_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.26/0.61 ! [A: nat] :
% 0.26/0.61 ( ( minus_minus_nat @ A @ A )
% 0.26/0.61 = zero_zero_nat ) ).
% 0.26/0.61
% 0.26/0.61 % cancel_comm_monoid_add_class.diff_cancel
% 0.26/0.61 thf(fact_328_Diff__eq__empty__iff,axiom,
% 0.26/0.61 ! [A2: set_a,B2: set_a] :
% 0.26/0.61 ( ( ( minus_minus_set_a @ A2 @ B2 )
% 0.26/0.61 = bot_bot_set_a )
% 0.26/0.61 = ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % Diff_eq_empty_iff
% 0.26/0.61 thf(fact_329_subset__empty,axiom,
% 0.26/0.61 ! [A2: set_a] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
% 0.26/0.61 = ( A2 = bot_bot_set_a ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_empty
% 0.26/0.61 thf(fact_330_empty__subsetI,axiom,
% 0.26/0.61 ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) ).
% 0.26/0.61
% 0.26/0.61 % empty_subsetI
% 0.26/0.61 thf(fact_331_insert__subset,axiom,
% 0.26/0.61 ! [X: nat > a,A2: set_nat_a,B2: set_nat_a] :
% 0.26/0.61 ( ( ord_le157368549_nat_a @ ( insert_nat_a @ X @ A2 ) @ B2 )
% 0.26/0.61 = ( ( member_nat_a @ X @ B2 )
% 0.26/0.61 & ( ord_le157368549_nat_a @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_subset
% 0.26/0.61 thf(fact_332_insert__subset,axiom,
% 0.26/0.61 ! [X: nat > b,A2: set_nat_b,B2: set_nat_b] :
% 0.26/0.61 ( ( ord_le1296932838_nat_b @ ( insert_nat_b @ X @ A2 ) @ B2 )
% 0.26/0.61 = ( ( member_nat_b @ X @ B2 )
% 0.26/0.61 & ( ord_le1296932838_nat_b @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_subset
% 0.26/0.61 thf(fact_333_insert__subset,axiom,
% 0.26/0.61 ! [X: a,A2: set_a,B2: set_a] :
% 0.26/0.61 ( ( ord_less_eq_set_a @ ( insert_a @ X @ A2 ) @ B2 )
% 0.26/0.61 = ( ( member_a @ X @ B2 )
% 0.26/0.61 & ( ord_less_eq_set_a @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_subset
% 0.26/0.61 thf(fact_334_insert__Diff__single,axiom,
% 0.26/0.61 ! [A: a,A2: set_a] :
% 0.26/0.61 ( ( insert_a @ A @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.26/0.61 = ( insert_a @ A @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % insert_Diff_single
% 0.26/0.61 thf(fact_335_singletonI,axiom,
% 0.26/0.61 ! [A: nat > a] : ( member_nat_a @ A @ ( insert_nat_a @ A @ bot_bot_set_nat_a ) ) ).
% 0.26/0.61
% 0.26/0.61 % singletonI
% 0.26/0.61 thf(fact_336_singletonI,axiom,
% 0.26/0.61 ! [A: nat > b] : ( member_nat_b @ A @ ( insert_nat_b @ A @ bot_bot_set_nat_b ) ) ).
% 0.26/0.61
% 0.26/0.61 % singletonI
% 0.26/0.61 thf(fact_337_singletonI,axiom,
% 0.26/0.61 ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.26/0.61
% 0.26/0.61 % singletonI
% 0.26/0.61 thf(fact_338_linear__span__subModule,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( submodule_b_d_a_c @ r @ m @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % linear_span_subModule
% 0.26/0.61 thf(fact_339_l__spanA__l__span,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( linear_span_b_d_a_c @ r @ m @ A2 @ ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ H ) )
% 0.26/0.61 = ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_spanA_l_span
% 0.26/0.61 thf(fact_340_lin__span__coeff__mono,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ord_less_eq_set_a @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) @ ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ H ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % lin_span_coeff_mono
% 0.26/0.61 thf(fact_341_linear__span__inc__0,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( member_a @ ( zero_a1261444626_a_b_c @ m ) @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % linear_span_inc_0
% 0.26/0.61 thf(fact_342_generator__generator,axiom,
% 0.26/0.61 ! [H: set_a,H1: set_a] :
% 0.26/0.61 ( ( generator_b_d_a_c @ r @ m @ H )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H1 @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( linear_span_b_d_a_c @ r @ m @ ( carrie2079586589xt_b_d @ r ) @ H1 ) )
% 0.26/0.61 => ( generator_b_d_a_c @ r @ m @ H1 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % generator_generator
% 0.26/0.61 thf(fact_343_l__span__zero,axiom,
% 0.26/0.61 ! [A2: set_b] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( linear_span_b_d_a_c @ r @ m @ A2 @ ( insert_a @ ( zero_a1261444626_a_b_c @ m ) @ bot_bot_set_a ) )
% 0.26/0.61 = ( insert_a @ ( zero_a1261444626_a_b_c @ m ) @ bot_bot_set_a ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_span_zero
% 0.26/0.61 thf(fact_344_l__span__closed3,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( generator_b_d_a_c @ r @ m @ H )
% 0.26/0.61 => ( ( ( smodul818989740_d_a_c @ r @ m @ A2 )
% 0.26/0.61 = ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( linear_span_b_d_a_c @ r @ m @ A2 @ H )
% 0.26/0.61 = ( carrie2021454486_a_b_c @ m ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_span_closed3
% 0.26/0.61 thf(fact_345_singleton__conv,axiom,
% 0.26/0.61 ! [A: a] :
% 0.26/0.61 ( ( collect_a
% 0.26/0.61 @ ^ [X3: a] : ( X3 = A ) )
% 0.26/0.61 = ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.26/0.61
% 0.26/0.61 % singleton_conv
% 0.26/0.61 thf(fact_346_l__comb__mem__linear__span,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a,S: nat > b,N: nat,F: nat > a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.61 => ( ( member_nat_a @ F
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : H ) )
% 0.26/0.61 => ( member_a @ ( l_comb_b_d_a_c @ r @ m @ N @ S @ F ) @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_comb_mem_linear_span
% 0.26/0.61 thf(fact_347_l__span__closed,axiom,
% 0.26/0.61 ! [A2: set_b,H: set_a,S: nat > b,N: nat,F: nat > a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_a @ H @ ( carrie2021454486_a_b_c @ m ) )
% 0.26/0.61 => ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.61 => ( ( member_nat_a @ F
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) ) )
% 0.26/0.61 => ( member_a @ ( l_comb_b_d_a_c @ r @ m @ N @ S @ F ) @ ( linear_span_b_d_a_c @ r @ m @ A2 @ H ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % l_span_closed
% 0.26/0.61 thf(fact_348_linear__comb0__2,axiom,
% 0.26/0.61 ! [A2: set_b,S: nat > b,N: nat,M: nat > a] :
% 0.26/0.61 ( ( ideal_b_d @ r @ A2 )
% 0.26/0.61 => ( ( member_nat_b @ S
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : A2 ) )
% 0.26/0.61 => ( ( member_nat_a @ M
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [J2: nat] : ( ord_less_eq_nat @ J2 @ N ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( insert_a @ ( zero_a1261444626_a_b_c @ m ) @ bot_bot_set_a ) ) )
% 0.26/0.61 => ( ( l_comb_b_d_a_c @ r @ m @ N @ S @ M )
% 0.26/0.61 = ( zero_a1261444626_a_b_c @ m ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % linear_comb0_2
% 0.26/0.61
% 0.26/0.61 % Conjectures (22)
% 0.26/0.61 thf(conj_0,hypothesis,
% 0.26/0.61 ( member_nat_a @ g
% 0.26/0.61 @ ( pi_nat_a
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [K4: nat] : ( ord_less_eq_nat @ K4 @ m2 ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( insert_a @ h2 @ h1 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 thf(conj_1,hypothesis,
% 0.26/0.61 ! [X4: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ X4 @ m2 )
% 0.26/0.61 => ! [Y3: nat] :
% 0.26/0.61 ( ( ord_less_eq_nat @ Y3 @ m2 )
% 0.26/0.61 => ( ( ( g @ X4 )
% 0.26/0.61 = ( g @ Y3 ) )
% 0.26/0.61 => ( X4 = Y3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 thf(conj_2,hypothesis,
% 0.26/0.61 ( member_nat_b @ t
% 0.26/0.61 @ ( pi_nat_b
% 0.26/0.61 @ ( collect_nat
% 0.26/0.61 @ ^ [K4: nat] : ( ord_less_eq_nat @ K4 @ m2 ) )
% 0.26/0.61 @ ^ [Uu: nat] : ( carrie2079586589xt_b_d @ r ) ) ) ).
% 0.26/0.61
% 0.26/0.61 thf(conj_3,hypothesis,
% 0.26/0.61 ( ( g @ m2 )
% 0.26/0.61 = h2 ) ).
% 0.26/0.61
% 0.26/0.61 thf(conj_4,hypothesis,
% 0.26/0.61 module_e_b_f_d @ n @ r ).
% 0.26/0.61
% 0.26/0.61 thf(conj_5,hypothesis,
% 0.26/0.61 free_g1087686480_d_a_c @ r @ m @ h ).
% 0.26/0.61
% 0.26/0.61 thf(conj_6,hypothesis,
% 0.26/0.61 ord_less_eq_set_a @ h1 @ h ).
% 0.26/0.61
% 0.26/0.61 thf(conj_7,hypothesis,
% 0.26/0.61 $true ).
% 0.26/0.61
% 0.26/0.61 thf(conj_8,hypothesis,
% 0.26/0.61 ideal_b_d @ r @ ( carrie2079586589xt_b_d @ r ) ).
% 0.26/0.61
% 0.26/0.61 thf(conj_9,hypothesis,
% 0.26/0.71 ord_less_eq_set_a @ h @ ( carrie2021454486_a_b_c @ m ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_10,hypothesis,
% 0.26/0.71 ord_less_eq_set_a @ h1 @ ( carrie2021454486_a_b_c @ m ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_11,hypothesis,
% 0.26/0.71 ord_less_eq_set_a @ ( algebr1152250919_d_a_c @ r @ m @ h1 ) @ ( carrie2021454486_a_b_c @ m ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_12,hypothesis,
% 0.26/0.71 member_a @ ( l_comb_b_d_a_c @ r @ m @ m2 @ t @ g ) @ ( algebr1152250919_d_a_c @ r @ m @ ( insert_a @ h2 @ h1 ) ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_13,hypothesis,
% 0.26/0.71 ( x
% 0.26/0.71 = ( l_comb_b_d_a_c @ r @ m @ m2 @ t @ g ) ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_14,hypothesis,
% 0.26/0.71 member_a @ h2 @ h ).
% 0.26/0.71
% 0.26/0.71 thf(conj_15,hypothesis,
% 0.26/0.71 ~ ( member_a @ h2 @ h1 ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_16,hypothesis,
% 0.26/0.71 ord_less_nat @ zero_zero_nat @ m2 ).
% 0.26/0.71
% 0.26/0.71 thf(conj_17,hypothesis,
% 0.26/0.71 member_a @ h2 @ ( carrie2021454486_a_b_c @ m ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_18,hypothesis,
% 0.26/0.71 submodule_b_d_a_c @ r @ m @ ( algebr1152250919_d_a_c @ r @ m @ ( insert_a @ h2 @ bot_bot_set_a ) ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_19,hypothesis,
% 0.26/0.71 ord_less_eq_nat @ xa @ ( minus_minus_nat @ m2 @ ( suc @ zero_zero_nat ) ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_20,hypothesis,
% 0.26/0.71 ( ( ( g @ xa )
% 0.26/0.71 = h2 )
% 0.26/0.71 | ( member_a @ ( g @ xa ) @ h1 ) ) ).
% 0.26/0.71
% 0.26/0.71 thf(conj_21,conjecture,
% 0.26/0.71 member_a @ ( g @ xa ) @ h1 ).
% 0.26/0.71
% 0.26/0.71 %------------------------------------------------------------------------------
% 0.26/0.71 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.1IRBQrwfIT/cvc5---1.0.5_20326.p...
% 0.26/0.71 (declare-sort $$unsorted 0)
% 0.26/0.71 (declare-sort tptp.carrie377329159t_unit 0)
% 0.26/0.71 (declare-sort tptp.carrie292259835t_unit 0)
% 0.26/0.71 (declare-sort tptp.carrie1065537299t_unit 0)
% 0.26/0.71 (declare-sort tptp.carrie980467975t_unit 0)
% 0.26/0.71 (declare-sort tptp.carrie1963041556t_unit 0)
% 0.26/0.71 (declare-sort tptp.carrie1821755406_e_b_f 0)
% 0.26/0.71 (declare-sort tptp.carrie722926983_a_b_c 0)
% 0.26/0.71 (declare-sort tptp.carrie1950868226xt_b_d 0)
% 0.26/0.71 (declare-sort tptp.set_nat_e 0)
% 0.26/0.71 (declare-sort tptp.set_nat_b 0)
% 0.26/0.71 (declare-sort tptp.set_nat_a 0)
% 0.26/0.71 (declare-sort tptp.set_nat 0)
% 0.26/0.71 (declare-sort tptp.set_e 0)
% 0.26/0.71 (declare-sort tptp.set_b 0)
% 0.26/0.71 (declare-sort tptp.set_a 0)
% 0.26/0.71 (declare-sort tptp.nat 0)
% 0.26/0.71 (declare-sort tptp.e 0)
% 0.26/0.71 (declare-sort tptp.b 0)
% 0.26/0.71 (declare-sort tptp.a 0)
% 0.26/0.71 (declare-fun tptp.carrie1074654371t_unit (tptp.carrie1963041556t_unit) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.carrie2021454486_a_b_c (tptp.carrie722926983_a_b_c) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.carrie2079586589xt_b_d (tptp.carrie1950868226xt_b_d) tptp.set_b)
% 0.26/0.71 (declare-fun tptp.carrie730238621_e_b_f (tptp.carrie1821755406_e_b_f) tptp.set_e)
% 0.26/0.71 (declare-fun tptp.ring_b_d (tptp.carrie1950868226xt_b_d) Bool)
% 0.26/0.71 (declare-fun tptp.zero_a1261444626_a_b_c (tptp.carrie722926983_a_b_c) tptp.a)
% 0.26/0.71 (declare-fun tptp.ideal_b_d (tptp.carrie1950868226xt_b_d tptp.set_b) Bool)
% 0.26/0.71 (declare-fun tptp.annihi259882159t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit) tptp.set_b)
% 0.26/0.71 (declare-fun tptp.annihilator_b_d_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c) tptp.set_b)
% 0.26/0.71 (declare-fun tptp.annihilator_b_d_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f) tptp.set_b)
% 0.26/0.71 (declare-fun tptp.hOM_b_1103679019t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.carrie1963041556t_unit) tptp.carrie980467975t_unit)
% 0.26/0.71 (declare-fun tptp.hOM_b_796081438it_a_c (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.carrie722926983_a_b_c) tptp.carrie980467975t_unit)
% 0.26/0.71 (declare-fun tptp.hOM_b_1959675421it_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.carrie1821755406_e_b_f) tptp.carrie1065537299t_unit)
% 0.26/0.71 (declare-fun tptp.hOM_b_717364638t_unit (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.carrie1963041556t_unit) tptp.carrie980467975t_unit)
% 0.26/0.71 (declare-fun tptp.hOM_b_d_a_c_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.carrie722926983_a_b_c) tptp.carrie980467975t_unit)
% 0.26/0.71 (declare-fun tptp.hOM_b_d_a_c_e_f (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.carrie1821755406_e_b_f) tptp.carrie1065537299t_unit)
% 0.26/0.71 (declare-fun tptp.hOM_b_1375846429t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.carrie1963041556t_unit) tptp.carrie292259835t_unit)
% 0.26/0.71 (declare-fun tptp.hOM_b_d_e_f_a_c (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.carrie722926983_a_b_c) tptp.carrie292259835t_unit)
% 0.26/0.71 (declare-fun tptp.hOM_b_d_e_f_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.carrie1821755406_e_b_f) tptp.carrie377329159t_unit)
% 0.26/0.71 (declare-fun tptp.module589927589unit_d (tptp.carrie980467975t_unit tptp.carrie1950868226xt_b_d) Bool)
% 0.26/0.71 (declare-fun tptp.module1648870817unit_d (tptp.carrie1065537299t_unit tptp.carrie1950868226xt_b_d) Bool)
% 0.26/0.71 (declare-fun tptp.module1330273449unit_d (tptp.carrie292259835t_unit tptp.carrie1950868226xt_b_d) Bool)
% 0.26/0.71 (declare-fun tptp.module241733029unit_d (tptp.carrie377329159t_unit tptp.carrie1950868226xt_b_d) Bool)
% 0.26/0.71 (declare-fun tptp.module1821517916unit_d (tptp.carrie1963041556t_unit tptp.carrie1950868226xt_b_d) Bool)
% 0.26/0.71 (declare-fun tptp.module_a_b_c_d (tptp.carrie722926983_a_b_c tptp.carrie1950868226xt_b_d) Bool)
% 0.26/0.71 (declare-fun tptp.module_e_b_f_d (tptp.carrie1821755406_e_b_f tptp.carrie1950868226xt_b_d) Bool)
% 0.26/0.71 (declare-fun tptp.free_g637607517t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.free_g1087686480_d_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.free_g103796815_d_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.set_e) Bool)
% 0.26/0.71 (declare-fun tptp.genera1692266857t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.generator_b_d_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.generator_b_d_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.set_e) Bool)
% 0.26/0.71 (declare-fun tptp.l_comb1138968323t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.nat (-> tptp.nat tptp.b) (-> tptp.nat tptp.a)) tptp.a)
% 0.26/0.71 (declare-fun tptp.l_comb_b_d_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.nat (-> tptp.nat tptp.b) (-> tptp.nat tptp.a)) tptp.a)
% 0.26/0.71 (declare-fun tptp.l_comb_b_d_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.nat (-> tptp.nat tptp.b) (-> tptp.nat tptp.e)) tptp.e)
% 0.26/0.71 (declare-fun tptp.linear_span_b_d_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.set_b tptp.set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.mdl_a_b_c (tptp.carrie722926983_a_b_c tptp.set_a) tptp.carrie1963041556t_unit)
% 0.26/0.71 (declare-fun tptp.misomo493403663t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.carrie1963041556t_unit) Bool)
% 0.26/0.71 (declare-fun tptp.misomo1935876354it_a_c (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.carrie722926983_a_b_c) Bool)
% 0.26/0.71 (declare-fun tptp.misomo951986689it_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.carrie1821755406_e_b_f) Bool)
% 0.26/0.71 (declare-fun tptp.misomo1857159554t_unit (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.carrie1963041556t_unit) Bool)
% 0.26/0.71 (declare-fun tptp.misomo1282343797_c_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.carrie722926983_a_b_c) Bool)
% 0.26/0.71 (declare-fun tptp.misomo298454132_c_e_f (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.carrie1821755406_e_b_f) Bool)
% 0.26/0.71 (declare-fun tptp.misomo368157697t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.carrie1963041556t_unit) Bool)
% 0.26/0.71 (declare-fun tptp.misomo1752826100_f_a_c (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.carrie722926983_a_b_c) Bool)
% 0.26/0.71 (declare-fun tptp.misomo768936435_f_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.carrie1821755406_e_b_f) Bool)
% 0.26/0.71 (declare-fun tptp.quotie1196826005t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.set_a tptp.set_a) tptp.set_b)
% 0.26/0.71 (declare-fun tptp.quotie1153752712_d_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.set_a tptp.set_a) tptp.set_b)
% 0.26/0.71 (declare-fun tptp.quotie169863047_d_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.set_e tptp.set_e) tptp.set_b)
% 0.26/0.71 (declare-fun tptp.smodul132175289t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.set_b) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.smodul818989740_d_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.set_b) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.smodul1982583723_d_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.set_b) tptp.set_e)
% 0.26/0.71 (declare-fun tptp.submod903911234t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.submodule_b_d_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.submodule_b_d_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.set_e) Bool)
% 0.26/0.71 (declare-fun tptp.algebr1039611956t_unit (tptp.carrie1950868226xt_b_d tptp.carrie1963041556t_unit tptp.set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.algebr1152250919_d_a_c (tptp.carrie1950868226xt_b_d tptp.carrie722926983_a_b_c tptp.set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.algebr168361254_d_e_f (tptp.carrie1950868226xt_b_d tptp.carrie1821755406_e_b_f tptp.set_e) tptp.set_e)
% 0.26/0.71 (declare-fun tptp.pi_nat_a (tptp.set_nat (-> tptp.nat tptp.set_a)) tptp.set_nat_a)
% 0.26/0.71 (declare-fun tptp.pi_nat_b (tptp.set_nat (-> tptp.nat tptp.set_b)) tptp.set_nat_b)
% 0.26/0.71 (declare-fun tptp.pi_nat_e (tptp.set_nat (-> tptp.nat tptp.set_e)) tptp.set_nat_e)
% 0.26/0.71 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.26/0.71 (declare-fun tptp.minus_1788767276_nat_a (tptp.set_nat_a tptp.set_nat_a) tptp.set_nat_a)
% 0.26/0.71 (declare-fun tptp.minus_780847917_nat_b (tptp.set_nat_b tptp.set_nat_b) tptp.set_nat_b)
% 0.26/0.71 (declare-fun tptp.minus_minus_set_a (tptp.set_a tptp.set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.26/0.71 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.26/0.71 (declare-fun tptp.bot_bot_set_nat_a () tptp.set_nat_a)
% 0.26/0.71 (declare-fun tptp.bot_bot_set_nat_b () tptp.set_nat_b)
% 0.26/0.71 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 0.26/0.71 (declare-fun tptp.bot_bot_set_a () tptp.set_a)
% 0.26/0.71 (declare-fun tptp.bot_bot_set_e () tptp.set_e)
% 0.26/0.71 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_set_a (tptp.set_a tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le157368549_nat_a (tptp.set_nat_a tptp.set_nat_a) Bool)
% 0.26/0.71 (declare-fun tptp.ord_le1296932838_nat_b (tptp.set_nat_b tptp.set_nat_b) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.ord_less_eq_set_e (tptp.set_e tptp.set_e) Bool)
% 0.26/0.71 (declare-fun tptp.collect_nat_a ((-> (-> tptp.nat tptp.a) Bool)) tptp.set_nat_a)
% 0.26/0.71 (declare-fun tptp.collect_nat_b ((-> (-> tptp.nat tptp.b) Bool)) tptp.set_nat_b)
% 0.26/0.71 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.26/0.71 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.insert_nat_a ((-> tptp.nat tptp.a) tptp.set_nat_a) tptp.set_nat_a)
% 0.26/0.71 (declare-fun tptp.insert_nat_b ((-> tptp.nat tptp.b) tptp.set_nat_b) tptp.set_nat_b)
% 0.26/0.71 (declare-fun tptp.insert_a (tptp.a tptp.set_a) tptp.set_a)
% 0.26/0.71 (declare-fun tptp.member_nat_a ((-> tptp.nat tptp.a) tptp.set_nat_a) Bool)
% 0.26/0.71 (declare-fun tptp.member_nat_b ((-> tptp.nat tptp.b) tptp.set_nat_b) Bool)
% 0.26/0.71 (declare-fun tptp.member_nat_e ((-> tptp.nat tptp.e) tptp.set_nat_e) Bool)
% 0.26/0.71 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.26/0.71 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.26/0.71 (declare-fun tptp.member_e (tptp.e tptp.set_e) Bool)
% 0.26/0.71 (declare-fun tptp.h () tptp.set_a)
% 0.26/0.71 (declare-fun tptp.h1 () tptp.set_a)
% 0.26/0.71 (declare-fun tptp.m () tptp.carrie722926983_a_b_c)
% 0.26/0.71 (declare-fun tptp.n () tptp.carrie1821755406_e_b_f)
% 0.26/0.71 (declare-fun tptp.r () tptp.carrie1950868226xt_b_d)
% 0.26/0.71 (declare-fun tptp.g (tptp.nat) tptp.a)
% 0.26/0.71 (declare-fun tptp.h2 () tptp.a)
% 0.26/0.71 (declare-fun tptp.m2 () tptp.nat)
% 0.26/0.71 (declare-fun tptp.t (tptp.nat) tptp.b)
% 0.26/0.71 (declare-fun tptp.x () tptp.a)
% 0.26/0.71 (declare-fun tptp.xa () tptp.nat)
% 0.26/0.71 (assert (@ tptp.ring_b_d tptp.r))
% 0.26/0.71 (assert (forall ((H tptp.set_a) (H2 tptp.a)) (let ((_let_1 (@ tptp.member_a H2))) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) H) (=> (@ _let_1 H) (@ _let_1 (@ tptp.carrie2021454486_a_b_c tptp.m)))))))
% 0.26/0.71 (assert (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2021454486_a_b_c tptp.m)))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)))))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c tptp.r) tptp.m) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)))))
% 0.26/0.71 (assert (forall ((A tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.ord_less_eq_set_a A) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ _let_1 A) (@ _let_1 (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) A)))))))
% 0.26/0.71 (assert (forall ((A tptp.set_a)) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c tptp.m))) (=> (@ (@ tptp.ord_less_eq_set_a A) _let_1) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) A)) _let_1)))))
% 0.26/0.71 (assert (forall ((H tptp.set_a) (J tptp.set_a) (K tptp.set_a)) (let ((_let_1 (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m))) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c tptp.r) tptp.m) H) (=> (@ (@ tptp.ord_less_eq_set_a J) K) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 J)) (@ _let_1 K))))))))
% 0.26/0.71 (assert (forall ((A tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) A)))))
% 0.26/0.71 (assert (forall ((H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d tptp.r)))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2)))) (= (@ _let_1 F) (@ _let_1 G))))))))))
% 0.26/0.71 (assert (forall ((H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d tptp.r)))) (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2))))) (= (@ _let_1 F) (@ _let_1 G)))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c tptp.m))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) _let_1) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a M) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) M)) _let_1))))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a) (N tptp.nat)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (forall ((S2 (-> tptp.nat tptp.b)) (M2 (-> tptp.nat tptp.a))) (=> (and (@ (@ tptp.member_nat_b S2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_a M2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H)))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S2) M2)) (@ tptp.carrie2021454486_a_b_c tptp.m))))))))
% 0.26/0.71 (assert (@ (@ tptp.ideal_b_d tptp.r) (@ (@ tptp.annihilator_b_d_a_c tptp.r) tptp.m)))
% 0.26/0.71 (assert (forall ((K tptp.set_a) (X tptp.a)) (=> (not (= K tptp.bot_bot_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a K) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) K)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a X2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) K))) (exists ((Xa (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b Xa) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d tptp.r)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N2) Xa) X2)))))))))))
% 0.26/0.71 (assert (@ (@ tptp.module_a_b_c_d tptp.m) tptp.r))
% 0.26/0.71 (assert (forall ((P tptp.set_a) (Q tptp.set_a)) (let ((_let_1 (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m))) (=> (@ _let_1 P) (=> (@ _let_1 Q) (@ (@ tptp.ideal_b_d tptp.r) (@ (@ (@ (@ tptp.quotie1153752712_d_a_c tptp.r) tptp.m) P) Q)))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) (@ (@ (@ tptp.smodul818989740_d_a_c tptp.r) tptp.m) A2)))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (X tptp.a)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.smodul818989740_d_a_c tptp.r) tptp.m) A2)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b X2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) A2))) (exists ((Xa (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a Xa) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2021454486_a_b_c tptp.m)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N2) X2) Xa))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A tptp.set_e) (X tptp.e)) (let ((_let_1 (@ tptp.member_e X))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_e A) (@ tptp.carrie730238621_e_b_f M3)) (=> (@ _let_1 A) (@ _let_1 (@ (@ (@ tptp.algebr168361254_d_e_f R) M3) A))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) (@ tptp.carrie1074654371t_unit M3)) (=> (@ _let_1 A) (@ _let_1 (@ (@ (@ tptp.algebr1039611956t_unit R) M3) A))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) (@ tptp.carrie2021454486_a_b_c M3)) (=> (@ _let_1 A) (@ _let_1 (@ (@ (@ tptp.algebr1152250919_d_a_c R) M3) A))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e) (J tptp.set_e) (K tptp.set_e)) (let ((_let_1 (@ (@ tptp.algebr168361254_d_e_f R) M3))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.free_g103796815_d_e_f R) M3) H) (=> (@ (@ tptp.ord_less_eq_set_e J) K) (=> (@ (@ tptp.ord_less_eq_set_e K) H) (@ (@ tptp.ord_less_eq_set_e (@ _let_1 J)) (@ _let_1 K)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (J tptp.set_a) (K tptp.set_a)) (let ((_let_1 (@ (@ tptp.algebr1039611956t_unit R) M3))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.free_g637607517t_unit R) M3) H) (=> (@ (@ tptp.ord_less_eq_set_a J) K) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 J)) (@ _let_1 K)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (J tptp.set_a) (K tptp.set_a)) (let ((_let_1 (@ (@ tptp.algebr1152250919_d_a_c R) M3))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c R) M3) H) (=> (@ (@ tptp.ord_less_eq_set_a J) K) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 J)) (@ _let_1 K)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_e A) (@ tptp.carrie730238621_e_b_f M3)) (@ (@ (@ tptp.submodule_b_d_e_f R) M3) (@ (@ (@ tptp.algebr168361254_d_e_f R) M3) A))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) (@ tptp.carrie1074654371t_unit M3)) (@ (@ (@ tptp.submod903911234t_unit R) M3) (@ (@ (@ tptp.algebr1039611956t_unit R) M3) A))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) (@ tptp.carrie2021454486_a_b_c M3)) (@ (@ (@ tptp.submodule_b_d_a_c R) M3) (@ (@ (@ tptp.algebr1152250919_d_a_c R) M3) A))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (K tptp.set_e) (X tptp.e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (not (= K tptp.bot_bot_set_e)) (=> (@ (@ tptp.ord_less_eq_set_e K) (@ tptp.carrie730238621_e_b_f M3)) (=> (@ (@ tptp.member_e X) (@ (@ (@ tptp.algebr168361254_d_e_f R) M3) K)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.e))) (and (@ (@ tptp.member_nat_e X2) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) K))) (exists ((Xa (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b Xa) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N2) Xa) X2))))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (K tptp.set_a) (X tptp.a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (not (= K tptp.bot_bot_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a K) (@ tptp.carrie1074654371t_unit M3)) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.algebr1039611956t_unit R) M3) K)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a X2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) K))) (exists ((Xa (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b Xa) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (= X (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N2) Xa) X2))))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (K tptp.set_a) (X tptp.a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (not (= K tptp.bot_bot_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a K) (@ tptp.carrie2021454486_a_b_c M3)) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.algebr1152250919_d_a_c R) M3) K)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a X2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) K))) (exists ((Xa (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b Xa) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N2) Xa) X2))))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A tptp.set_e)) (let ((_let_1 (@ tptp.carrie730238621_e_b_f M3))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_e A) _let_1) (@ (@ tptp.ord_less_eq_set_e (@ (@ (@ tptp.algebr168361254_d_e_f R) M3) A)) _let_1))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a)) (let ((_let_1 (@ tptp.carrie1074654371t_unit M3))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) _let_1) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ tptp.algebr1039611956t_unit R) M3) A)) _let_1))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a)) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c M3))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) _let_1) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ tptp.algebr1152250919_d_a_c R) M3) A)) _let_1))))))
% 0.26/0.71 (assert (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) tptp.m) tptp.m))
% 0.26/0.71 (assert (forall ((N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (@ (@ tptp.module1648870817unit_d (@ (@ (@ tptp.hOM_b_d_a_c_e_f tptp.r) tptp.m) N3)) tptp.r))))
% 0.26/0.71 (assert (forall ((N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_d_a_c_a_c tptp.r) tptp.m) N3)) tptp.r))))
% 0.26/0.71 (assert (forall ((N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_717364638t_unit tptp.r) tptp.m) N3)) tptp.r))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.generator_b_d_a_c tptp.r) tptp.m) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)))))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c tptp.r) tptp.m) H) (@ (@ (@ tptp.generator_b_d_a_c tptp.r) tptp.m) H))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_e) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.e))) (let ((_let_1 (@ tptp.carrie730238621_e_b_f M3))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_e H) _let_1) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_e M) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_e (@ (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N) S) M)) _let_1)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c M3))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) _let_1) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a M) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N) S) M)) _let_1)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.carrie1074654371t_unit M3))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) _let_1) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a M) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N) S) M)) _let_1)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_e) (N tptp.nat)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3)) (forall ((S2 (-> tptp.nat tptp.b)) (M2 (-> tptp.nat tptp.e))) (=> (and (@ (@ tptp.member_nat_b S2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_e M2) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H)))) (@ (@ tptp.member_e (@ (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N) S2) M2)) (@ tptp.carrie730238621_e_b_f M3)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_a) (N tptp.nat)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3)) (forall ((S2 (-> tptp.nat tptp.b)) (M2 (-> tptp.nat tptp.a))) (=> (and (@ (@ tptp.member_nat_b S2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_a M2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H)))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N) S2) M2)) (@ tptp.carrie2021454486_a_b_c M3)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_a) (N tptp.nat)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3)) (forall ((S2 (-> tptp.nat tptp.b)) (M2 (-> tptp.nat tptp.a))) (=> (and (@ (@ tptp.member_nat_b S2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_a M2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H)))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N) S2) M2)) (@ tptp.carrie1074654371t_unit M3)))))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.e)) (G (-> tptp.nat tptp.e))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N) S))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (=> (@ (@ tptp.member_nat_e F) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (@ (@ tptp.member_nat_e G) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2)))) (= (@ _let_1 F) (@ _let_1 G)))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N) S))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2)))) (= (@ _let_1 F) (@ _let_1 G)))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N) S))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2)))) (= (@ _let_1 F) (@ _let_1 G)))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.e)) (G (-> tptp.nat tptp.e))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N) S))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3)) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (@ (@ tptp.member_nat_e F) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_nat_e G) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2))))) (= (@ _let_1 F) (@ _let_1 G))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N) S))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3)) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2))))) (= (@ _let_1 F) (@ _let_1 G))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N) S))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3)) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2))))) (= (@ _let_1 F) (@ _let_1 G))))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 0.26/0.71 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 0.26/0.71 (assert (forall ((N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo298454132_c_e_f tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo1752826100_f_a_c tptp.r) N3) tptp.m)))))
% 0.26/0.71 (assert (forall ((N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1857159554t_unit tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo1935876354it_a_c tptp.r) N3) tptp.m)))))
% 0.26/0.71 (assert (forall ((N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ tptp.misomo1282343797_c_a_c tptp.r))) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (=> (@ (@ _let_1 tptp.m) N3) (@ (@ _let_1 N3) tptp.m))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.26/0.71 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 0.26/0.71 (assert (forall ((A (-> tptp.nat tptp.a)) (P (-> (-> tptp.nat tptp.a) Bool))) (= (@ (@ tptp.member_nat_a A) (@ tptp.collect_nat_a P)) (@ P A))))
% 0.26/0.71 (assert (forall ((A (-> tptp.nat tptp.b)) (P (-> (-> tptp.nat tptp.b) Bool))) (= (@ (@ tptp.member_nat_b A) (@ tptp.collect_nat_b P)) (@ P A))))
% 0.26/0.71 (assert (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))))
% 0.26/0.71 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_nat_a)) (= (@ tptp.collect_nat_a (lambda ((X3 (-> tptp.nat tptp.a))) (@ (@ tptp.member_nat_a X3) A2))) A2)))
% 0.26/0.71 (assert (forall ((A2 tptp.set_nat_b)) (= (@ tptp.collect_nat_b (lambda ((X3 (-> tptp.nat tptp.b))) (@ (@ tptp.member_nat_b X3) A2))) A2)))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X3 tptp.a)) (@ (@ tptp.member_a X3) A2))) A2)))
% 0.26/0.71 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A2))) A2)))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X2 tptp.nat)) (= (@ P X2) (@ Q X2))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 0.26/0.71 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K2))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 0.26/0.71 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.26/0.71 (assert (forall ((L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_e_b_f_d L) tptp.r) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c tptp.r) L) tptp.m) (=> (@ (@ (@ tptp.misomo298454132_c_e_f tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo768936435_f_e_f tptp.r) L) N3)))))))
% 0.26/0.71 (assert (forall ((L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d L) tptp.r) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c tptp.r) L) tptp.m) (=> (@ (@ (@ tptp.misomo1857159554t_unit tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo368157697t_unit tptp.r) L) N3)))))))
% 0.26/0.71 (assert (forall ((L tptp.carrie1963041556t_unit) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module1821517916unit_d L) tptp.r) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1935876354it_a_c tptp.r) L) tptp.m) (=> (@ (@ (@ tptp.misomo298454132_c_e_f tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo951986689it_e_f tptp.r) L) N3)))))))
% 0.26/0.71 (assert (forall ((L tptp.carrie1963041556t_unit) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module1821517916unit_d L) tptp.r) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1935876354it_a_c tptp.r) L) tptp.m) (=> (@ (@ (@ tptp.misomo1857159554t_unit tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo493403663t_unit tptp.r) L) N3)))))))
% 0.26/0.71 (assert (forall ((L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ (@ tptp.misomo1752826100_f_a_c tptp.r) L))) (=> (@ (@ tptp.module_e_b_f_d L) tptp.r) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (=> (@ _let_1 tptp.m) (=> (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) tptp.m) N3) (@ _let_1 N3))))))))
% 0.26/0.71 (assert (forall ((L tptp.carrie1963041556t_unit) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ (@ tptp.misomo1935876354it_a_c tptp.r) L))) (=> (@ (@ tptp.module1821517916unit_d L) tptp.r) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (=> (@ _let_1 tptp.m) (=> (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) tptp.m) N3) (@ _let_1 N3))))))))
% 0.26/0.71 (assert (forall ((L tptp.carrie722926983_a_b_c) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ tptp.misomo298454132_c_e_f tptp.r))) (=> (@ (@ tptp.module_a_b_c_d L) tptp.r) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) L) tptp.m) (=> (@ (@ _let_1 tptp.m) N3) (@ (@ _let_1 L) N3))))))))
% 0.26/0.71 (assert (forall ((L tptp.carrie722926983_a_b_c) (N3 tptp.carrie1963041556t_unit)) (let ((_let_1 (@ tptp.misomo1857159554t_unit tptp.r))) (=> (@ (@ tptp.module_a_b_c_d L) tptp.r) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) L) tptp.m) (=> (@ (@ _let_1 tptp.m) N3) (@ (@ _let_1 L) N3))))))))
% 0.26/0.71 (assert (forall ((L tptp.carrie722926983_a_b_c) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ tptp.misomo1282343797_c_a_c tptp.r))) (let ((_let_2 (@ _let_1 L))) (=> (@ (@ tptp.module_a_b_c_d L) tptp.r) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (=> (@ _let_2 tptp.m) (=> (@ (@ _let_1 tptp.m) N3) (@ _let_2 N3)))))))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (@ (@ tptp.module241733029unit_d (@ (@ (@ tptp.hOM_b_d_e_f_e_f R) M3) N3)) R)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (@ (@ tptp.module1330273449unit_d (@ (@ (@ tptp.hOM_b_d_e_f_a_c R) M3) N3)) R)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (@ (@ tptp.module1330273449unit_d (@ (@ (@ tptp.hOM_b_1375846429t_unit R) M3) N3)) R)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (@ (@ tptp.module1648870817unit_d (@ (@ (@ tptp.hOM_b_d_a_c_e_f R) M3) N3)) R)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_d_a_c_a_c R) M3) N3)) R)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_717364638t_unit R) M3) N3)) R)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (@ (@ tptp.module1648870817unit_d (@ (@ (@ tptp.hOM_b_1959675421it_e_f R) M3) N3)) R)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_796081438it_a_c R) M3) N3)) R)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_1103679019t_unit R) M3) N3)) R)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ tptp.misomo768936435_f_e_f R))) (let ((_let_2 (@ _let_1 L))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ _let_2 M3) (=> (@ (@ _let_1 M3) N3) (@ _let_2 N3))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ tptp.misomo1752826100_f_a_c R))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ (@ tptp.misomo768936435_f_e_f R) L) M3) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 L) N3)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1963041556t_unit)) (let ((_let_1 (@ tptp.misomo368157697t_unit R))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo768936435_f_e_f R) L) M3) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 L) N3)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie722926983_a_b_c) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ (@ tptp.misomo298454132_c_e_f R) L))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_a_b_c_d L) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ _let_1 M3) (=> (@ (@ (@ tptp.misomo768936435_f_e_f R) M3) N3) (@ _let_1 N3)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie722926983_a_b_c) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_a_b_c_d L) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo298454132_c_e_f R) L) M3) (=> (@ (@ (@ tptp.misomo368157697t_unit R) M3) N3) (@ (@ (@ tptp.misomo1857159554t_unit R) L) N3))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1963041556t_unit) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ (@ tptp.misomo951986689it_e_f R) L))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d L) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ _let_1 M3) (=> (@ (@ (@ tptp.misomo768936435_f_e_f R) M3) N3) (@ _let_1 N3)))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1963041556t_unit) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d L) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ (@ tptp.misomo951986689it_e_f R) L) M3) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c R) M3) N3) (@ (@ (@ tptp.misomo1935876354it_a_c R) L) N3))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1963041556t_unit) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d L) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo951986689it_e_f R) L) M3) (=> (@ (@ (@ tptp.misomo368157697t_unit R) M3) N3) (@ (@ (@ tptp.misomo493403663t_unit R) L) N3))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c R) L) M3) (=> (@ (@ (@ tptp.misomo298454132_c_e_f R) M3) N3) (@ (@ (@ tptp.misomo768936435_f_e_f R) L) N3))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c R) L) M3) (=> (@ (@ (@ tptp.misomo1857159554t_unit R) M3) N3) (@ (@ (@ tptp.misomo368157697t_unit R) L) N3))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (@ (@ (@ tptp.misomo768936435_f_e_f R) M3) M3))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (@ (@ (@ tptp.misomo493403663t_unit R) M3) M3))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (@ (@ (@ tptp.misomo1282343797_c_a_c R) M3) M3))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ tptp.misomo768936435_f_e_f R))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 N3) M3)))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c R) M3) N3) (@ (@ (@ tptp.misomo298454132_c_e_f R) N3) M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo368157697t_unit R) M3) N3) (@ (@ (@ tptp.misomo951986689it_e_f R) N3) M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ (@ (@ tptp.misomo298454132_c_e_f R) M3) N3) (@ (@ (@ tptp.misomo1752826100_f_a_c R) N3) M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo1857159554t_unit R) M3) N3) (@ (@ (@ tptp.misomo1935876354it_a_c R) N3) M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ (@ (@ tptp.misomo951986689it_e_f R) M3) N3) (@ (@ (@ tptp.misomo368157697t_unit R) N3) M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ (@ tptp.misomo1935876354it_a_c R) M3) N3) (@ (@ (@ tptp.misomo1857159554t_unit R) N3) M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (let ((_let_1 (@ tptp.misomo493403663t_unit R))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 N3) M3)))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ tptp.misomo1282343797_c_a_c R))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 N3) M3)))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.free_g103796815_d_e_f R) M3) H) (@ (@ (@ tptp.generator_b_d_e_f R) M3) H)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.free_g637607517t_unit R) M3) H) (@ (@ (@ tptp.genera1692266857t_unit R) M3) H)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c R) M3) H) (@ (@ (@ tptp.generator_b_d_a_c R) M3) H)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.generator_b_d_e_f R) M3) H) (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.generator_b_d_a_c R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.genera1692266857t_unit R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (@ (@ tptp.ideal_b_d R) (@ (@ tptp.annihilator_b_d_e_f R) M3)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (@ (@ tptp.ideal_b_d R) (@ (@ tptp.annihi259882159t_unit R) M3)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (@ (@ tptp.ideal_b_d R) (@ (@ tptp.annihilator_b_d_a_c R) M3)))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (K2 tptp.nat) (B tptp.nat)) (=> (@ P K2) (=> (forall ((Y tptp.nat)) (=> (@ P Y) (@ (@ tptp.ord_less_eq_nat Y) B))) (exists ((X2 tptp.nat)) (and (@ P X2) (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) X2)))))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (J3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J3) (=> (@ (@ tptp.ord_less_eq_nat J3) K2) (@ _let_1 K2))))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 0.26/0.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y4)) (= X Y4))))
% 0.26/0.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_nat Y4) X)))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2)))))) (@ P N))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.26/0.71 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (J3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J3)) K2) (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) J3)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (@ (@ (@ tptp.submodule_b_d_e_f R) M3) (@ (@ (@ tptp.smodul1982583723_d_e_f R) M3) A2))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (@ (@ (@ tptp.submod903911234t_unit R) M3) (@ (@ (@ tptp.smodul132175289t_unit R) M3) A2))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (@ (@ (@ tptp.submodule_b_d_a_c R) M3) (@ (@ (@ tptp.smodul818989740_d_a_c R) M3) A2))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (P tptp.set_e) (Q tptp.set_e)) (let ((_let_1 (@ (@ tptp.submodule_b_d_e_f R) M3))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ _let_1 P) (=> (@ _let_1 Q) (@ (@ tptp.ideal_b_d R) (@ (@ (@ (@ tptp.quotie169863047_d_e_f R) M3) P) Q))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (P tptp.set_a) (Q tptp.set_a)) (let ((_let_1 (@ (@ tptp.submod903911234t_unit R) M3))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ _let_1 P) (=> (@ _let_1 Q) (@ (@ tptp.ideal_b_d R) (@ (@ (@ (@ tptp.quotie1196826005t_unit R) M3) P) Q))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (P tptp.set_a) (Q tptp.set_a)) (let ((_let_1 (@ (@ tptp.submodule_b_d_a_c R) M3))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ _let_1 P) (=> (@ _let_1 Q) (@ (@ tptp.ideal_b_d R) (@ (@ (@ (@ tptp.quotie1153752712_d_a_c R) M3) P) Q))))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X2 tptp.nat)) (@ (@ R X2) X2)) (=> (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ R X2))) (=> (@ _let_1 Y) (=> (@ (@ R Y) Z) (@ _let_1 Z))))) (=> (forall ((N2 tptp.nat)) (@ (@ R N2) (@ tptp.suc N2))) (@ (@ R M) N)))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.26/0.71 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (Nat tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((Nat3 tptp.nat)) (=> (@ P Nat3) (@ P (@ tptp.suc Nat3)))) (@ P Nat)))))
% 0.26/0.71 (assert (forall ((Y4 tptp.nat)) (=> (not (= Y4 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y4 (@ tptp.suc Nat3))))))))
% 0.26/0.71 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.26/0.71 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.26/0.71 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (K2 tptp.nat)) (=> (@ P K2) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P tptp.zero_zero_nat)))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X2 tptp.nat)) (@ (@ P X2) tptp.zero_zero_nat)) (=> (forall ((Y tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y))) (=> (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ P X2) Y) (@ (@ P (@ tptp.suc X2)) (@ tptp.suc Y)))) (@ (@ P M) N))))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc N2)))) (@ P N)))))
% 0.26/0.71 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 0.26/0.71 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 0.26/0.71 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 0.26/0.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J3 tptp.nat)) (=> (forall ((I2 tptp.nat) (J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J4) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J4)))) (=> (@ (@ tptp.ord_less_eq_nat I) J3) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J3))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.26/0.71 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N4) (= M6 N4)))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.26/0.71 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N4) (not (= M6 N4))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (J3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J3) (=> (forall ((I2 tptp.nat)) (=> (= J3 (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J3) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I))))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (J3 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J3) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J4 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J4) (=> (@ (@ tptp.ord_less_nat J4) K3) (=> (@ _let_1 J4) (=> (@ (@ P J4) K3) (@ _let_1 K3))))))) (@ (@ P I) J3))))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (J3 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (=> (@ (@ tptp.ord_less_nat J3) K2) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K2)))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M7 tptp.nat)) (and (= M (@ tptp.suc M7)) (@ (@ tptp.ord_less_nat N) M7))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P N) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K2) (not (forall ((J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J4) (not (= K2 (@ tptp.suc J4)))))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (=> (not (= K2 (@ tptp.suc I))) (not (forall ((J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J4) (not (= K2 (@ tptp.suc J4))))))))))
% 0.26/0.71 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2))))))) (@ P N)))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 0.26/0.71 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N) L2)))))
% 0.26/0.71 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ _let_1 N))))))))
% 0.26/0.71 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 0.26/0.71 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K2) (@ (@ tptp.minus_minus_nat N) K2)) (= M N)))))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (K2 tptp.nat) (I tptp.nat)) (=> (@ P K2) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P (@ (@ tptp.minus_minus_nat K2) I))))))
% 0.26/0.71 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 0.26/0.71 (assert (forall ((J3 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) K2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J3) N)) K2))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (@ tptp.ring_b_d R))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (@ tptp.ring_b_d R))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (@ tptp.ring_b_d R))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (X tptp.e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.member_e X) (@ (@ (@ tptp.smodul1982583723_d_e_f R) M3) A2)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b X2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) A2))) (exists ((Xa (-> tptp.nat tptp.e))) (and (@ (@ tptp.member_nat_e Xa) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie730238621_e_b_f M3)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N2) X2) Xa)))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (X tptp.a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.smodul132175289t_unit R) M3) A2)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b X2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) A2))) (exists ((Xa (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a Xa) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie1074654371t_unit M3)))) (= X (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N2) X2) Xa)))))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (X tptp.a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.smodul818989740_d_a_c R) M3) A2)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b X2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) A2))) (exists ((Xa (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a Xa) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2021454486_a_b_c M3)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N2) X2) Xa)))))))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.nat tptp.set_a)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_a (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_a (@ F N5)) (@ F N))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N5))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.nat tptp.set_a)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_a (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_a (@ F N)) (@ F N5))))))
% 0.26/0.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 0.26/0.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N5))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 0.26/0.71 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N4)) __flatten_var_0))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (J3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J3) (=> (@ P J3) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J3) (=> (@ P (@ tptp.suc N2)) (@ P N2))))) (@ P I))))))
% 0.26/0.71 (assert (forall ((I tptp.nat) (J3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J3) (=> (@ P I) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J3) (=> (@ P N2) (@ P (@ tptp.suc N2)))))) (@ P J3))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (not (@ P I4)))) (@ P K3)))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J2 tptp.nat)) (and (= M (@ tptp.suc J2)) (@ (@ tptp.ord_less_nat J2) N)))))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 0.26/0.71 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 0.26/0.71 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.ord_less_nat M) N)))))))
% 0.26/0.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e) (H2 tptp.e)) (let ((_let_1 (@ tptp.member_e H2))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.submodule_b_d_e_f R) M3) H) (=> (@ _let_1 H) (@ _let_1 (@ tptp.carrie730238621_e_b_f M3))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (H2 tptp.a)) (let ((_let_1 (@ tptp.member_a H2))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.submodule_b_d_a_c R) M3) H) (=> (@ _let_1 H) (@ _let_1 (@ tptp.carrie2021454486_a_b_c M3))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (H2 tptp.a)) (let ((_let_1 (@ tptp.member_a H2))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.submod903911234t_unit R) M3) H) (=> (@ _let_1 H) (@ _let_1 (@ tptp.carrie1074654371t_unit M3))))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (@ (@ (@ tptp.submodule_b_d_e_f R) M3) (@ tptp.carrie730238621_e_b_f M3)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (@ (@ (@ tptp.submodule_b_d_a_c R) M3) (@ tptp.carrie2021454486_a_b_c M3)))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (@ (@ (@ tptp.submod903911234t_unit R) M3) (@ tptp.carrie1074654371t_unit M3)))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K3) (not (@ P I4)))) (@ P (@ tptp.suc K3))))))))
% 0.26/0.71 (assert (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.submodule_b_d_e_f R) M3) H) (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.submodule_b_d_a_c R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.submod903911234t_unit R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.free_g103796815_d_e_f R) M3) H) (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3))))))
% 0.26/0.71 (assert (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.free_g637607517t_unit R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3))))))
% 0.26/0.71 (assert (forall ((H tptp.set_a) (K tptp.set_a) (F (-> tptp.nat tptp.a)) (N tptp.nat) (S (-> tptp.nat tptp.b))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (=> (and (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) K))) (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d tptp.r))))) (= (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit tptp.r) (@ (@ tptp.mdl_a_b_c tptp.m) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) K))) N) S) F) (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)))))))
% 0.26/0.71 (assert (forall ((H tptp.set_a) (K tptp.set_a) (F (-> tptp.nat tptp.a)) (N tptp.nat) (S (-> tptp.nat tptp.b))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) K))) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d tptp.r)))) (= (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit tptp.r) (@ (@ tptp.mdl_a_b_c tptp.m) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) K))) N) S) F) (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F))))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (A2 tptp.set_a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.insert_a B) tptp.bot_bot_set_a))) (= (= (@ (@ tptp.insert_a A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_a A2) _let_1))))))
% 0.26/0.71 (assert (forall ((B tptp.a) (A tptp.a) (A2 tptp.set_a)) (let ((_let_1 (@ (@ tptp.insert_a B) tptp.bot_bot_set_a))) (= (= _let_1 (@ (@ tptp.insert_a A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_a A2) _let_1))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H))))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H)))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H)))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_a M) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ tptp.insert_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) tptp.bot_bot_set_a))))) (= (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) M) (@ tptp.zero_a1261444626_a_b_c tptp.m))))))
% 0.26/0.71 (assert (@ (@ tptp.member_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) (@ tptp.carrie2021454486_a_b_c tptp.m)))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_a A2) B2)))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_nat_a) (B2 tptp.set_nat_a)) (=> (forall ((X2 (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.member_nat_a X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le157368549_nat_a A2) B2))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_nat_b) (B2 tptp.set_nat_b)) (=> (forall ((X2 (-> tptp.nat tptp.b))) (let ((_let_1 (@ tptp.member_nat_b X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1296932838_nat_b A2) B2))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (=> (forall ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_a A2) B2))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (@ (@ tptp.ord_less_eq_set_a B2) A2) (= A2 B2)))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a)) (= (@ (@ tptp.minus_minus_set_a A2) tptp.bot_bot_set_a) A2)))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a)) (= (@ (@ tptp.minus_minus_set_a tptp.bot_bot_set_a) A2) tptp.bot_bot_set_a)))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a)) (= (@ (@ tptp.minus_minus_set_a A2) A2) tptp.bot_bot_set_a)))
% 0.26/0.71 (assert (forall ((C (-> tptp.nat tptp.a))) (not (@ (@ tptp.member_nat_a C) tptp.bot_bot_set_nat_a))))
% 0.26/0.71 (assert (forall ((C (-> tptp.nat tptp.b))) (not (@ (@ tptp.member_nat_b C) tptp.bot_bot_set_nat_b))))
% 0.26/0.71 (assert (forall ((C tptp.a)) (not (@ (@ tptp.member_a C) tptp.bot_bot_set_a))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_nat_a)) (= (forall ((X3 (-> tptp.nat tptp.a))) (not (@ (@ tptp.member_nat_a X3) A2))) (= A2 tptp.bot_bot_set_nat_a))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_nat_b)) (= (forall ((X3 (-> tptp.nat tptp.b))) (not (@ (@ tptp.member_nat_b X3) A2))) (= A2 tptp.bot_bot_set_nat_b))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a)) (= (forall ((X3 tptp.a)) (not (@ (@ tptp.member_a X3) A2))) (= A2 tptp.bot_bot_set_a))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X3 tptp.nat)) (not (@ P X3))))))
% 0.26/0.71 (assert (forall ((P (-> tptp.a Bool))) (= (= (@ tptp.collect_a P) tptp.bot_bot_set_a) (forall ((X3 tptp.a)) (not (@ P X3))))))
% 0.26/0.71 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X3 tptp.nat)) (not (@ P X3))))))
% 0.26/0.71 (assert (forall ((P (-> tptp.a Bool))) (= (= tptp.bot_bot_set_a (@ tptp.collect_a P)) (forall ((X3 tptp.a)) (not (@ P X3))))))
% 0.26/0.71 (assert (forall ((X (-> tptp.nat tptp.a)) (A2 tptp.set_nat_a) (B2 tptp.set_nat_a)) (let ((_let_1 (@ tptp.minus_1788767276_nat_a A2))) (=> (not (@ (@ tptp.member_nat_a X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat_a X) B2)) (@ _let_1 B2))))))
% 0.26/0.71 (assert (forall ((X (-> tptp.nat tptp.b)) (A2 tptp.set_nat_b) (B2 tptp.set_nat_b)) (let ((_let_1 (@ tptp.minus_780847917_nat_b A2))) (=> (not (@ (@ tptp.member_nat_b X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat_b X) B2)) (@ _let_1 B2))))))
% 0.26/0.71 (assert (forall ((X tptp.a) (A2 tptp.set_a) (B2 tptp.set_a)) (let ((_let_1 (@ tptp.minus_minus_set_a A2))) (=> (not (@ (@ tptp.member_a X) A2)) (= (@ _let_1 (@ (@ tptp.insert_a X) B2)) (@ _let_1 B2))))))
% 0.26/0.71 (assert (forall ((X (-> tptp.nat tptp.a)) (B2 tptp.set_nat_a) (A2 tptp.set_nat_a)) (=> (@ (@ tptp.member_nat_a X) B2) (= (@ (@ tptp.minus_1788767276_nat_a (@ (@ tptp.insert_nat_a X) A2)) B2) (@ (@ tptp.minus_1788767276_nat_a A2) B2)))))
% 0.26/0.71 (assert (forall ((X (-> tptp.nat tptp.b)) (B2 tptp.set_nat_b) (A2 tptp.set_nat_b)) (=> (@ (@ tptp.member_nat_b X) B2) (= (@ (@ tptp.minus_780847917_nat_b (@ (@ tptp.insert_nat_b X) A2)) B2) (@ (@ tptp.minus_780847917_nat_b A2) B2)))))
% 0.26/0.71 (assert (forall ((X tptp.a) (B2 tptp.set_a) (A2 tptp.set_a)) (=> (@ (@ tptp.member_a X) B2) (= (@ (@ tptp.minus_minus_set_a (@ (@ tptp.insert_a X) A2)) B2) (@ (@ tptp.minus_minus_set_a A2) B2)))))
% 0.26/0.71 (assert (forall ((A (-> tptp.nat tptp.a)) (B2 tptp.set_nat_a) (B (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.member_nat_a A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_nat_a B) B2))))))
% 0.26/0.71 (assert (forall ((A (-> tptp.nat tptp.b)) (B2 tptp.set_nat_b) (B (-> tptp.nat tptp.b))) (let ((_let_1 (@ tptp.member_nat_b A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_nat_b B) B2))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B2 tptp.set_a) (B tptp.a)) (let ((_let_1 (@ tptp.member_a A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_a B) B2))))))
% 0.26/0.71 (assert (forall ((A (-> tptp.nat tptp.a)) (B (-> tptp.nat tptp.a)) (A2 tptp.set_nat_a)) (let ((_let_1 (@ tptp.member_nat_a A))) (= (@ _let_1 (@ (@ tptp.insert_nat_a B) A2)) (or (= A B) (@ _let_1 A2))))))
% 0.26/0.71 (assert (forall ((A (-> tptp.nat tptp.b)) (B (-> tptp.nat tptp.b)) (A2 tptp.set_nat_b)) (let ((_let_1 (@ tptp.member_nat_b A))) (= (@ _let_1 (@ (@ tptp.insert_nat_b B) A2)) (or (= A B) (@ _let_1 A2))))))
% 0.26/0.71 (assert (forall ((A tptp.a) (B tptp.a) (A2 tptp.set_a)) (let ((_let_1 (@ tptp.member_a A))) (= (@ _let_1 (@ (@ tptp.insert_a B) A2)) (or (= A B) (@ _let_1 A2))))))
% 0.26/0.71 (assert (forall ((X tptp.a) (A2 tptp.set_a)) (let ((_let_1 (@ tptp.insert_a X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) H) (@ (@ tptp.member_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) H))))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) H) (= (@ tptp.carrie1074654371t_unit (@ (@ tptp.mdl_a_b_c tptp.m) H)) H))))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) H) (@ (@ tptp.module1821517916unit_d (@ (@ tptp.mdl_a_b_c tptp.m) H)) tptp.r))))
% 0.26/0.71 (assert (forall ((H tptp.set_a) (N3 tptp.set_a)) (let ((_let_1 (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m))) (=> (@ _let_1 H) (=> (@ _let_1 N3) (=> (@ (@ tptp.ord_less_eq_set_a H) N3) (@ (@ (@ tptp.submod903911234t_unit tptp.r) (@ (@ tptp.mdl_a_b_c tptp.m) N3)) H)))))))
% 0.26/0.71 (assert (forall ((H tptp.set_a) (H2 tptp.a)) (let ((_let_1 (@ tptp.member_a H2))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ _let_1 H) (@ _let_1 (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H)))))))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a H))) (=> (@ _let_1 (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ _let_1 (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H))))))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (let ((_let_1 (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)))) (let ((_let_2 (@ _let_1 H))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (= (@ _let_1 _let_2) _let_2))))))
% 0.26/0.71 (assert (forall ((K tptp.set_a) (H tptp.set_a) (A2 tptp.set_b)) (let ((_let_1 (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2))) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 K)) (@ _let_1 H))))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a)) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c tptp.m))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) _let_1) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H)) _let_1))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (N3 tptp.set_a) (H tptp.set_a)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) N3) (=> (@ (@ tptp.ord_less_eq_set_a H) N3) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H)) N3))))))
% 0.26/0.71 (assert (forall ((H tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ (@ (@ tptp.genera1692266857t_unit tptp.r) (@ (@ tptp.mdl_a_b_c tptp.m) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) H))) H))))
% 0.26/0.71 (assert (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) (@ (@ tptp.insert_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) tptp.bot_bot_set_a)))
% 0.26/0.71 (assert (= (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) tptp.bot_bot_set_a) (@ (@ tptp.insert_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) tptp.bot_bot_set_a)))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.26/0.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 0.26/0.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 0.26/0.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (= (= (@ (@ tptp.minus_minus_set_a A2) B2) tptp.bot_bot_set_a) (@ (@ tptp.ord_less_eq_set_a A2) B2))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a A2) tptp.bot_bot_set_a) (= A2 tptp.bot_bot_set_a))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a tptp.bot_bot_set_a) A2)))
% 0.26/0.71 (assert (forall ((X (-> tptp.nat tptp.a)) (A2 tptp.set_nat_a) (B2 tptp.set_nat_a)) (= (@ (@ tptp.ord_le157368549_nat_a (@ (@ tptp.insert_nat_a X) A2)) B2) (and (@ (@ tptp.member_nat_a X) B2) (@ (@ tptp.ord_le157368549_nat_a A2) B2)))))
% 0.26/0.71 (assert (forall ((X (-> tptp.nat tptp.b)) (A2 tptp.set_nat_b) (B2 tptp.set_nat_b)) (= (@ (@ tptp.ord_le1296932838_nat_b (@ (@ tptp.insert_nat_b X) A2)) B2) (and (@ (@ tptp.member_nat_b X) B2) (@ (@ tptp.ord_le1296932838_nat_b A2) B2)))))
% 0.26/0.71 (assert (forall ((X tptp.a) (A2 tptp.set_a) (B2 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.insert_a X) A2)) B2) (and (@ (@ tptp.member_a X) B2) (@ (@ tptp.ord_less_eq_set_a A2) B2)))))
% 0.26/0.71 (assert (forall ((A tptp.a) (A2 tptp.set_a)) (let ((_let_1 (@ tptp.insert_a A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_a A2) (@ _let_1 tptp.bot_bot_set_a))) (@ _let_1 A2)))))
% 0.26/0.71 (assert (forall ((A (-> tptp.nat tptp.a))) (@ (@ tptp.member_nat_a A) (@ (@ tptp.insert_nat_a A) tptp.bot_bot_set_nat_a))))
% 0.26/0.71 (assert (forall ((A (-> tptp.nat tptp.b))) (@ (@ tptp.member_nat_b A) (@ (@ tptp.insert_nat_b A) tptp.bot_bot_set_nat_b))))
% 0.26/0.71 (assert (forall ((A tptp.a)) (@ (@ tptp.member_a A) (@ (@ tptp.insert_a A) tptp.bot_bot_set_a))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a)) (let ((_let_1 (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m))) (let ((_let_2 (@ _let_1 A2))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (= (@ _let_2 (@ (@ _let_1 (@ tptp.carrie2079586589xt_b_d tptp.r)) H)) (@ _let_2 H))))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a)) (let ((_let_1 (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ (@ tptp.ord_less_eq_set_a (@ (@ _let_1 A2) H)) (@ (@ _let_1 (@ tptp.carrie2079586589xt_b_d tptp.r)) H)))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ (@ tptp.member_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))))
% 0.26/0.71 (assert (forall ((H tptp.set_a) (H1 tptp.set_a)) (let ((_let_1 (@ (@ tptp.generator_b_d_a_c tptp.r) tptp.m))) (=> (@ _let_1 H) (=> (@ (@ tptp.ord_less_eq_set_a H1) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H1)) (@ _let_1 H1)))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b)) (let ((_let_1 (@ (@ tptp.insert_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) tptp.bot_bot_set_a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (= (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) _let_1) _let_1)))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a)) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c tptp.m))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ (@ tptp.generator_b_d_a_c tptp.r) tptp.m) H) (=> (= (@ (@ (@ tptp.smodul818989740_d_a_c tptp.r) tptp.m) A2) _let_1) (= (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H) _let_1)))))))
% 0.26/0.71 (assert (forall ((A tptp.a)) (= (@ tptp.collect_a (lambda ((X3 tptp.a)) (= X3 A))) (@ (@ tptp.insert_a A) tptp.bot_bot_set_a))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H)))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))))))
% 0.26/0.71 (assert (forall ((A2 tptp.set_b) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a M) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ tptp.insert_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) tptp.bot_bot_set_a)))) (= (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) M) (@ tptp.zero_a1261444626_a_b_c tptp.m)))))))
% 1.45/1.76 (assert (@ (@ tptp.member_nat_a tptp.g) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat K4) tptp.m2)))) (lambda ((Uu tptp.nat)) (@ (@ tptp.insert_a tptp.h2) tptp.h1)))))
% 1.45/1.76 (assert (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) tptp.m2) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) tptp.m2) (=> (= (@ tptp.g X4) (@ tptp.g Y3)) (= X4 Y3)))))))
% 1.45/1.76 (assert (@ (@ tptp.member_nat_b tptp.t) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat K4) tptp.m2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d tptp.r)))))
% 1.45/1.76 (assert (= (@ tptp.g tptp.m2) tptp.h2))
% 1.45/1.76 (assert (@ (@ tptp.module_e_b_f_d tptp.n) tptp.r))
% 1.45/1.76 (assert (@ (@ (@ tptp.free_g1087686480_d_a_c tptp.r) tptp.m) tptp.h))
% 1.45/1.76 (assert (@ (@ tptp.ord_less_eq_set_a tptp.h1) tptp.h))
% 1.45/1.76 (assert true)
% 1.45/1.76 (assert (@ (@ tptp.ideal_b_d tptp.r) (@ tptp.carrie2079586589xt_b_d tptp.r)))
% 1.45/1.76 (assert (@ (@ tptp.ord_less_eq_set_a tptp.h) (@ tptp.carrie2021454486_a_b_c tptp.m)))
% 1.45/1.76 (assert (@ (@ tptp.ord_less_eq_set_a tptp.h1) (@ tptp.carrie2021454486_a_b_c tptp.m)))
% 1.45/1.76 (assert (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) tptp.h1)) (@ tptp.carrie2021454486_a_b_c tptp.m)))
% 1.45/1.76 (assert (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) tptp.m2) tptp.t) tptp.g)) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) (@ (@ tptp.insert_a tptp.h2) tptp.h1))))
% 1.45/1.76 (assert (= tptp.x (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) tptp.m2) tptp.t) tptp.g)))
% 1.45/1.76 (assert (@ (@ tptp.member_a tptp.h2) tptp.h))
% 1.45/1.76 (assert (not (@ (@ tptp.member_a tptp.h2) tptp.h1)))
% 1.45/1.76 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.m2))
% 1.45/1.76 (assert (@ (@ tptp.member_a tptp.h2) (@ tptp.carrie2021454486_a_b_c tptp.m)))
% 1.45/1.76 (assert (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) (@ (@ tptp.insert_a tptp.h2) tptp.bot_bot_set_a))))
% 1.45/1.76 (assert (@ (@ tptp.ord_less_eq_nat tptp.xa) (@ (@ tptp.minus_minus_nat tptp.m2) (@ tptp.suc tptp.zero_zero_nat))))
% 1.45/1.76 (assert (let ((_let_1 (@ tptp.g tptp.xa))) (or (= _let_1 tptp.h2) (@ (@ tptp.member_a _let_1) tptp.h1))))
% 1.45/1.76 (assert (not (@ (@ tptp.member_a (@ tptp.g tptp.xa)) tptp.h1)))
% 1.45/1.76 (set-info :filename cvc5---1.0.5_20326)
% 1.45/1.76 (check-sat-assuming ( true ))
% 1.45/1.76 ------- get file name : TPTP file name is ITP026^1
% 1.45/1.76 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20326.smt2...
% 1.45/1.76 --- Run --ho-elim --full-saturate-quant at 10...
% 1.45/1.76 % SZS status Theorem for ITP026^1
% 1.45/1.76 % SZS output start Proof for ITP026^1
% 1.45/1.76 (
% 1.45/1.76 (let ((_let_1 (@ tptp.g tptp.xa))) (let ((_let_2 (@ (@ tptp.member_a _let_1) tptp.h1))) (let ((_let_3 (not _let_2))) (let ((_let_4 (or (= _let_1 tptp.h2) _let_2))) (let ((_let_5 (@ (@ tptp.minus_minus_nat tptp.m2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_6 (@ (@ tptp.ord_less_eq_nat tptp.xa) _let_5))) (let ((_let_7 (@ tptp.insert_a tptp.h2))) (let ((_let_8 (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m))) (let ((_let_9 (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m))) (let ((_let_10 (@ tptp.carrie2021454486_a_b_c tptp.m))) (let ((_let_11 (@ tptp.member_a tptp.h2))) (let ((_let_12 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.m2))) (let ((_let_13 (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) tptp.m2) tptp.t) tptp.g))) (let ((_let_14 (= tptp.x _let_13))) (let ((_let_15 (@ tptp.ord_less_eq_set_a tptp.h1))) (let ((_let_16 (@ tptp.ideal_b_d tptp.r))) (let ((_let_17 (@ tptp.g tptp.m2))) (let ((_let_18 (= _let_17 tptp.h2))) (let ((_let_19 (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) tptp.m2) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) tptp.m2) (=> (= (@ tptp.g X4) (@ tptp.g Y3)) (= X4 Y3)))))))) (let ((_let_20 (@ tptp.zero_a1261444626_a_b_c tptp.m))) (let ((_let_21 (@ (@ tptp.insert_a _let_20) tptp.bot_bot_set_a))) (let ((_let_22 (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N4) (= M6 N4)))))) (let ((_let_23 (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))) (let ((_let_24 (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))) (let ((_let_25 (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))) (let ((_let_26 (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))) (let ((_let_27 (ho_487 k_486 tptp.m2))) (let ((_let_28 (ho_227 _let_27 (ho_227 k_226 tptp.zero_zero_nat)))) (let ((_let_29 (ho_168 k_167 tptp.xa))) (let ((_let_30 (ho_166 _let_29 _let_28))) (let ((_let_31 (= tptp.xa _let_28))) (let ((_let_32 (not _let_31))) (let ((_let_33 (not _let_30))) (let ((_let_34 (and _let_33 _let_32))) (let ((_let_35 (ho_227 k_226 _let_28))) (let ((_let_36 (= tptp.xa _let_35))) (let ((_let_37 (ho_166 (ho_168 k_167 _let_35) tptp.xa))) (let ((_let_38 (or _let_37 _let_36))) (let ((_let_39 (= _let_34 _let_38))) (let ((_let_40 (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (ho_227 k_226 N))) (= (and (not (ho_166 (ho_168 k_167 M) N)) (not (= M N))) (or (ho_166 (ho_168 k_167 _let_1) M) (= M _let_1))))))) (let ((_let_41 (ASSUME :args (_let_22)))) (let ((_let_42 (AND_INTRO (ASSUME :args (_let_14)) (SYMM (ASSUME :args (_let_18))) _let_41))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_23)) (TRANS (MACRO_SR_EQ_INTRO _let_42 :args (_let_23 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (or (@ (@ tptp.ord_less_nat _let_1) M) (= M _let_1)) (and (not (@ (@ tptp.ord_less_nat M) N)) (not (= M N)))))) _let_40))))))) (let ((_let_44 (= tptp.m2 (ho_227 _let_27 (ho_227 _let_27 tptp.m2))))) (let ((_let_45 (= tptp.m2 _let_35))) (let ((_let_46 (= tptp.m2 tptp.xa))) (let ((_let_47 (ho_177 k_176 tptp.xa))) (let ((_let_48 (= (ho_177 k_176 tptp.m2) _let_47))) (let ((_let_49 (not _let_48))) (let ((_let_50 (not _let_46))) (let ((_let_51 (ho_166 _let_29 tptp.m2))) (let ((_let_52 (not _let_51))) (let ((_let_53 (and _let_52 _let_50))) (let ((_let_54 (or _let_53 _let_49 _let_46))) (let ((_let_55 (ho_166 (ho_168 k_167 tptp.m2) tptp.xa))) (let ((_let_56 (or _let_51 _let_46 _let_55))) (let ((_let_57 (forall ((BOUND_VARIABLE_13668 tptp.nat)) (let ((_let_1 (ho_487 k_486 BOUND_VARIABLE_13668))) (= BOUND_VARIABLE_13668 (ho_227 _let_1 (ho_227 _let_1 BOUND_VARIABLE_13668))))))) (let ((_let_58 (_let_57))) (let ((_let_59 (ho_168 k_167 tptp.zero_zero_nat))) (let ((_let_60 (ho_166 _let_59 tptp.m2))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_45))) (let ((_let_63 (forall ((N tptp.nat)) (or (not (ho_166 (ho_168 k_167 tptp.zero_zero_nat) N)) (= N (ho_227 k_226 (ho_227 (ho_487 k_486 N) (ho_227 k_226 tptp.zero_zero_nat)))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_26)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N tptp.nat)) (or (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) _let_63))))))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_61 _let_45 (not _let_62)))) (EQ_RESOLVE (ASSUME :args (_let_12)) (PREPROCESS :args ((= _let_12 _let_60)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (tptp.m2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_166 _let_59 N) false))))) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_45 false _let_60 false _let_62)))) (let ((_let_66 (not _let_44))) (let ((_let_67 (not _let_45))) (let ((_let_68 (or))) (let ((_let_69 (not _let_36))) (let ((_let_70 (REFL :args (_let_67)))) (let ((_let_71 (ASSUME :args (_let_44)))) (let ((_let_72 (SYMM (SYMM _let_71)))) (let ((_let_73 (ASSUME :args (_let_45)))) (let ((_let_74 (SYMM _let_73))) (let ((_let_75 (ASSUME :args (_let_46)))) (let ((_let_76 (ASSUME :args (_let_69)))) (let ((_let_77 (ho_260 (ho_259 k_258 _let_47) tptp.h1))) (let ((_let_78 (forall ((X4 tptp.nat) (BOUND_VARIABLE_9890 tptp.nat)) (or (and (not (ho_166 (ho_168 k_167 X4) tptp.m2)) (not (= tptp.m2 X4))) (and (not (ho_166 (ho_168 k_167 BOUND_VARIABLE_9890) tptp.m2)) (not (= tptp.m2 BOUND_VARIABLE_9890))) (not (= (ho_177 k_176 BOUND_VARIABLE_9890) (ho_177 k_176 X4))) (= X4 BOUND_VARIABLE_9890))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_19)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_41 :args ((forall ((X4 tptp.nat) (BOUND_VARIABLE_9890 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat X4) tptp.m2)) (not (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_9890) tptp.m2)) (not (= (@ tptp.g X4) (@ tptp.g BOUND_VARIABLE_9890))) (= X4 BOUND_VARIABLE_9890))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X4 tptp.nat) (BOUND_VARIABLE_9890 tptp.nat)) (or (and (not (@ (@ tptp.ord_less_nat X4) tptp.m2)) (not (= tptp.m2 X4))) (and (not (@ (@ tptp.ord_less_nat BOUND_VARIABLE_9890) tptp.m2)) (not (= tptp.m2 BOUND_VARIABLE_9890))) (not (= (@ tptp.g X4) (@ tptp.g BOUND_VARIABLE_9890))) (= X4 BOUND_VARIABLE_9890))) _let_78))))))) (let ((_let_80 (forall ((M tptp.nat) (N tptp.nat)) (or (ho_166 (ho_168 k_167 M) N) (= M N) (ho_166 (ho_168 k_167 N) M))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_24)) (TRANS (MACRO_SR_EQ_INTRO _let_42 :args (_let_24 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M) N) (= M N) (@ (@ tptp.ord_less_nat N) M))) _let_80))))))) (let ((_let_82 (not _let_55))) (let ((_let_83 (not _let_37))) (let ((_let_84 (and _let_45 _let_83))) (let ((_let_85 (ASSUME :args (_let_83)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_39)) :args ((or _let_34 (not _let_38) (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_84)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_85 _let_73) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG (REFL :args (k_167)) (SYMM _let_74) :args (APPLY_UF ho_168)) (REFL :args (tptp.xa)) :args (APPLY_UF ho_166)) (FALSE_INTRO _let_85))) :args (_let_83 _let_45))) :args (_let_45 _let_83))) :args (true _let_84)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_37))) (REFL :args (_let_82)) :args _let_68)) :args ((or _let_37 _let_67 _let_82))) _let_65 (REORDERING (CNF_OR_POS :args (_let_56)) 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tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e) (J tptp.set_e) (K tptp.set_e)) (let ((_let_1 (@ (@ tptp.algebr168361254_d_e_f R) M3))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.free_g103796815_d_e_f R) M3) H) (=> (@ (@ tptp.ord_less_eq_set_e J) K) (=> (@ (@ tptp.ord_less_eq_set_e K) H) (@ (@ tptp.ord_less_eq_set_e (@ _let_1 J)) (@ _let_1 K)))))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (J tptp.set_a) (K tptp.set_a)) (let ((_let_1 (@ (@ tptp.algebr1039611956t_unit R) M3))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.free_g637607517t_unit R) M3) H) (=> (@ (@ tptp.ord_less_eq_set_a J) K) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 J)) (@ _let_1 K)))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (J tptp.set_a) (K tptp.set_a)) (let ((_let_1 (@ (@ tptp.algebr1152250919_d_a_c R) M3))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c R) M3) H) (=> (@ (@ tptp.ord_less_eq_set_a J) K) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 J)) (@ _let_1 K)))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_e A) (@ tptp.carrie730238621_e_b_f M3)) (@ (@ (@ tptp.submodule_b_d_e_f R) M3) (@ (@ (@ tptp.algebr168361254_d_e_f R) M3) A))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) (@ tptp.carrie1074654371t_unit M3)) (@ (@ (@ tptp.submod903911234t_unit R) M3) (@ (@ (@ tptp.algebr1039611956t_unit R) M3) A))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) (@ tptp.carrie2021454486_a_b_c M3)) (@ (@ (@ tptp.submodule_b_d_a_c R) M3) (@ (@ (@ tptp.algebr1152250919_d_a_c R) M3) A))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (K tptp.set_e) (X tptp.e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (not (= K tptp.bot_bot_set_e)) (=> (@ (@ tptp.ord_less_eq_set_e K) (@ tptp.carrie730238621_e_b_f M3)) (=> (@ (@ tptp.member_e X) (@ (@ (@ tptp.algebr168361254_d_e_f R) M3) K)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.e))) (and (@ (@ tptp.member_nat_e X2) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) K))) (exists ((Xa (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b Xa) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N2) Xa) X2))))))))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (K tptp.set_a) (X tptp.a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (not (= K tptp.bot_bot_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a K) (@ tptp.carrie1074654371t_unit M3)) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.algebr1039611956t_unit R) M3) K)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a X2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) K))) (exists ((Xa (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b Xa) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (= X (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N2) Xa) X2))))))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (K tptp.set_a) (X tptp.a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (not (= K tptp.bot_bot_set_a)) (=> (@ (@ tptp.ord_less_eq_set_a K) (@ tptp.carrie2021454486_a_b_c M3)) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.algebr1152250919_d_a_c R) M3) K)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a X2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) K))) (exists ((Xa (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b Xa) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N2) Xa) X2))))))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A tptp.set_e)) (let ((_let_1 (@ tptp.carrie730238621_e_b_f M3))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_e A) _let_1) (@ (@ tptp.ord_less_eq_set_e (@ (@ (@ tptp.algebr168361254_d_e_f R) M3) A)) _let_1))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a)) (let ((_let_1 (@ tptp.carrie1074654371t_unit M3))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) _let_1) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ tptp.algebr1039611956t_unit R) M3) A)) _let_1))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A tptp.set_a)) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c M3))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a A) _let_1) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ tptp.algebr1152250919_d_a_c R) M3) A)) _let_1))))) (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) tptp.m) tptp.m) (forall ((N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (@ (@ tptp.module1648870817unit_d (@ (@ (@ tptp.hOM_b_d_a_c_e_f tptp.r) tptp.m) N3)) tptp.r))) (forall ((N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_d_a_c_a_c tptp.r) tptp.m) N3)) tptp.r))) (forall ((N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_717364638t_unit tptp.r) tptp.m) N3)) tptp.r))) _let_26 (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.generator_b_d_a_c tptp.r) tptp.m) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)))) (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c tptp.r) tptp.m) H) (@ (@ (@ tptp.generator_b_d_a_c tptp.r) tptp.m) H))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_e) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.e))) (let ((_let_1 (@ tptp.carrie730238621_e_b_f M3))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_e H) _let_1) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_e M) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_e (@ (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N) S) M)) _let_1)))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c M3))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) _let_1) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a M) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N) S) M)) _let_1)))))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.carrie1074654371t_unit M3))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) _let_1) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a M) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N) S) M)) _let_1)))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_e) (N tptp.nat)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3)) (forall ((S2 (-> tptp.nat tptp.b)) (M2 (-> tptp.nat tptp.e))) (=> (and (@ (@ tptp.member_nat_b S2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_e M2) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H)))) (@ (@ tptp.member_e (@ (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N) S2) M2)) (@ tptp.carrie730238621_e_b_f M3)))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_a) (N tptp.nat)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3)) (forall ((S2 (-> tptp.nat tptp.b)) (M2 (-> tptp.nat tptp.a))) (=> (and (@ (@ tptp.member_nat_b S2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_a M2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H)))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N) S2) M2)) (@ tptp.carrie2021454486_a_b_c M3)))))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (H tptp.set_a) (N tptp.nat)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3)) (forall ((S2 (-> tptp.nat tptp.b)) (M2 (-> tptp.nat tptp.a))) (=> (and (@ (@ tptp.member_nat_b S2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_a M2) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H)))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N) S2) M2)) (@ tptp.carrie1074654371t_unit M3)))))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.e)) (G (-> tptp.nat tptp.e))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N) S))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (=> (@ (@ tptp.member_nat_e F) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (@ (@ tptp.member_nat_e G) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2)))) (= (@ _let_1 F) (@ _let_1 G)))))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N) S))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2)))) (= (@ _let_1 F) (@ _let_1 G)))))))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N) S))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2)))) (= (@ _let_1 F) (@ _let_1 G)))))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.e)) (G (-> tptp.nat tptp.e))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N) S))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3)) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (@ (@ tptp.member_nat_e F) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_nat_e G) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2))))) (= (@ _let_1 F) (@ _let_1 G))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N) S))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3)) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2))))) (= (@ _let_1 F) (@ _let_1 G))))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (let ((_let_1 (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N) S))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3)) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d R)))) (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_nat_a G) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (= (@ F X2) (@ G X2))))) (= (@ _let_1 F) (@ _let_1 G))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))) (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))) (forall ((N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo298454132_c_e_f tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo1752826100_f_a_c tptp.r) N3) tptp.m)))) (forall ((N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1857159554t_unit tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo1935876354it_a_c tptp.r) N3) tptp.m)))) (forall ((N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ tptp.misomo1282343797_c_a_c tptp.r))) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (=> (@ (@ _let_1 tptp.m) N3) (@ (@ _let_1 N3) tptp.m))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))) (forall ((A (-> tptp.nat tptp.a)) (P (-> (-> tptp.nat tptp.a) Bool))) (= (@ (@ tptp.member_nat_a A) (@ tptp.collect_nat_a P)) (@ P A))) (forall ((A (-> tptp.nat tptp.b)) (P (-> (-> tptp.nat tptp.b) Bool))) (= (@ (@ tptp.member_nat_b A) (@ tptp.collect_nat_b P)) (@ P A))) (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))) (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))) (forall ((A2 tptp.set_nat_a)) (= (@ tptp.collect_nat_a (lambda ((X3 (-> tptp.nat tptp.a))) (@ (@ tptp.member_nat_a X3) A2))) A2)) (forall ((A2 tptp.set_nat_b)) (= (@ tptp.collect_nat_b (lambda ((X3 (-> tptp.nat tptp.b))) (@ (@ tptp.member_nat_b X3) A2))) A2)) (forall ((A2 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X3 tptp.a)) (@ (@ tptp.member_a X3) A2))) A2)) (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A2))) A2)) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X2 tptp.nat)) (= (@ P X2) (@ Q X2))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))) (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))) _let_25 (forall ((M tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K2))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_e_b_f_d L) tptp.r) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c tptp.r) L) tptp.m) (=> (@ (@ (@ tptp.misomo298454132_c_e_f tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo768936435_f_e_f tptp.r) L) N3)))))) (forall ((L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d L) tptp.r) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c tptp.r) L) tptp.m) (=> (@ (@ (@ tptp.misomo1857159554t_unit tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo368157697t_unit tptp.r) L) N3)))))) (forall ((L tptp.carrie1963041556t_unit) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module1821517916unit_d L) tptp.r) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1935876354it_a_c tptp.r) L) tptp.m) (=> (@ (@ (@ tptp.misomo298454132_c_e_f tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo951986689it_e_f tptp.r) L) N3)))))) (forall ((L tptp.carrie1963041556t_unit) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module1821517916unit_d L) tptp.r) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1935876354it_a_c tptp.r) L) tptp.m) (=> (@ (@ (@ tptp.misomo1857159554t_unit tptp.r) tptp.m) N3) (@ (@ (@ tptp.misomo493403663t_unit tptp.r) L) N3)))))) (forall ((L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ (@ tptp.misomo1752826100_f_a_c tptp.r) L))) (=> (@ (@ tptp.module_e_b_f_d L) tptp.r) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (=> (@ _let_1 tptp.m) (=> (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) tptp.m) N3) (@ _let_1 N3))))))) (forall ((L tptp.carrie1963041556t_unit) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ (@ tptp.misomo1935876354it_a_c tptp.r) L))) (=> (@ (@ tptp.module1821517916unit_d L) tptp.r) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (=> (@ _let_1 tptp.m) (=> (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) tptp.m) N3) (@ _let_1 N3))))))) (forall ((L tptp.carrie722926983_a_b_c) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ tptp.misomo298454132_c_e_f tptp.r))) (=> (@ (@ tptp.module_a_b_c_d L) tptp.r) (=> (@ (@ tptp.module_e_b_f_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) L) tptp.m) (=> (@ (@ _let_1 tptp.m) N3) (@ (@ _let_1 L) N3))))))) (forall ((L tptp.carrie722926983_a_b_c) (N3 tptp.carrie1963041556t_unit)) (let ((_let_1 (@ tptp.misomo1857159554t_unit tptp.r))) (=> (@ (@ tptp.module_a_b_c_d L) tptp.r) (=> (@ (@ tptp.module1821517916unit_d N3) tptp.r) (=> (@ (@ (@ tptp.misomo1282343797_c_a_c tptp.r) L) tptp.m) (=> (@ (@ _let_1 tptp.m) N3) (@ (@ _let_1 L) N3))))))) (forall ((L tptp.carrie722926983_a_b_c) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ tptp.misomo1282343797_c_a_c tptp.r))) (let ((_let_2 (@ _let_1 L))) (=> (@ (@ tptp.module_a_b_c_d L) tptp.r) (=> (@ (@ tptp.module_a_b_c_d N3) tptp.r) (=> (@ _let_2 tptp.m) (=> (@ (@ _let_1 tptp.m) N3) (@ _let_2 N3)))))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (@ (@ tptp.module241733029unit_d (@ (@ (@ tptp.hOM_b_d_e_f_e_f R) M3) N3)) R)))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (@ (@ tptp.module1330273449unit_d (@ (@ (@ tptp.hOM_b_d_e_f_a_c R) M3) N3)) R)))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (@ (@ tptp.module1330273449unit_d (@ (@ (@ tptp.hOM_b_1375846429t_unit R) M3) N3)) R)))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (@ (@ tptp.module1648870817unit_d (@ (@ (@ tptp.hOM_b_d_a_c_e_f R) M3) N3)) R)))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_d_a_c_a_c R) M3) N3)) R)))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_717364638t_unit R) M3) N3)) R)))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (@ (@ tptp.module1648870817unit_d (@ (@ (@ tptp.hOM_b_1959675421it_e_f R) M3) N3)) R)))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_796081438it_a_c R) M3) N3)) R)))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (@ (@ tptp.module589927589unit_d (@ (@ (@ tptp.hOM_b_1103679019t_unit R) M3) N3)) R)))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ tptp.misomo768936435_f_e_f R))) (let ((_let_2 (@ _let_1 L))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ _let_2 M3) (=> (@ (@ _let_1 M3) N3) (@ _let_2 N3))))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ tptp.misomo1752826100_f_a_c R))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ (@ tptp.misomo768936435_f_e_f R) L) M3) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 L) N3)))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1963041556t_unit)) (let ((_let_1 (@ tptp.misomo368157697t_unit R))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo768936435_f_e_f R) L) M3) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 L) N3)))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie722926983_a_b_c) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ (@ tptp.misomo298454132_c_e_f R) L))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_a_b_c_d L) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ _let_1 M3) (=> (@ (@ (@ tptp.misomo768936435_f_e_f R) M3) N3) (@ _let_1 N3)))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie722926983_a_b_c) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_a_b_c_d L) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo298454132_c_e_f R) L) M3) (=> (@ (@ (@ tptp.misomo368157697t_unit R) M3) N3) (@ (@ (@ tptp.misomo1857159554t_unit R) L) N3))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1963041556t_unit) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ (@ tptp.misomo951986689it_e_f R) L))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d L) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ _let_1 M3) (=> (@ (@ (@ tptp.misomo768936435_f_e_f R) M3) N3) (@ _let_1 N3)))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1963041556t_unit) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d L) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ (@ tptp.misomo951986689it_e_f R) L) M3) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c R) M3) N3) (@ (@ (@ tptp.misomo1935876354it_a_c R) L) N3))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1963041556t_unit) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d L) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo951986689it_e_f R) L) M3) (=> (@ (@ (@ tptp.misomo368157697t_unit R) M3) N3) (@ (@ (@ tptp.misomo493403663t_unit R) L) N3))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c R) L) M3) (=> (@ (@ (@ tptp.misomo298454132_c_e_f R) M3) N3) (@ (@ (@ tptp.misomo768936435_f_e_f R) L) N3))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (L tptp.carrie1821755406_e_b_f) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_e_b_f_d L) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c R) L) M3) (=> (@ (@ (@ tptp.misomo1857159554t_unit R) M3) N3) (@ (@ (@ tptp.misomo368157697t_unit R) L) N3))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (@ (@ (@ tptp.misomo768936435_f_e_f R) M3) M3))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (@ (@ (@ tptp.misomo493403663t_unit R) M3) M3))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (@ (@ (@ tptp.misomo1282343797_c_a_c R) M3) M3))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (let ((_let_1 (@ tptp.misomo768936435_f_e_f R))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 N3) M3)))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ (@ tptp.misomo1752826100_f_a_c R) M3) N3) (@ (@ (@ tptp.misomo298454132_c_e_f R) N3) M3))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo368157697t_unit R) M3) N3) (@ (@ (@ tptp.misomo951986689it_e_f R) N3) M3))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ (@ (@ tptp.misomo298454132_c_e_f R) M3) N3) (@ (@ (@ tptp.misomo1752826100_f_a_c R) N3) M3))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ (@ tptp.misomo1857159554t_unit R) M3) N3) (@ (@ (@ tptp.misomo1935876354it_a_c R) N3) M3))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1821755406_e_b_f)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module_e_b_f_d N3) R) (=> (@ (@ (@ tptp.misomo951986689it_e_f R) M3) N3) (@ (@ (@ tptp.misomo368157697t_unit R) N3) M3))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ (@ tptp.misomo1935876354it_a_c R) M3) N3) (@ (@ (@ tptp.misomo1857159554t_unit R) N3) M3))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie1963041556t_unit)) (let ((_let_1 (@ tptp.misomo493403663t_unit R))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.module1821517916unit_d N3) R) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 N3) M3)))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (N3 tptp.carrie722926983_a_b_c)) (let ((_let_1 (@ tptp.misomo1282343797_c_a_c R))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.module_a_b_c_d N3) R) (=> (@ (@ _let_1 M3) N3) (@ (@ _let_1 N3) M3)))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.free_g103796815_d_e_f R) M3) H) (@ (@ (@ tptp.generator_b_d_e_f R) M3) H)))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.free_g637607517t_unit R) M3) H) (@ (@ (@ tptp.genera1692266857t_unit R) M3) H)))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c R) M3) H) (@ (@ (@ tptp.generator_b_d_a_c R) M3) H)))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.generator_b_d_e_f R) M3) H) (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.generator_b_d_a_c R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.genera1692266857t_unit R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (@ (@ tptp.ideal_b_d R) (@ (@ tptp.annihilator_b_d_e_f R) M3)))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (@ (@ tptp.ideal_b_d R) (@ (@ tptp.annihi259882159t_unit R) M3)))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (@ (@ tptp.ideal_b_d R) (@ (@ tptp.annihilator_b_d_a_c R) M3)))) (forall ((P (-> tptp.nat Bool)) (K2 tptp.nat) (B tptp.nat)) (=> (@ P K2) (=> (forall ((Y tptp.nat)) (=> (@ P Y) (@ (@ tptp.ord_less_eq_nat Y) B))) (exists ((X2 tptp.nat)) (and (@ P X2) (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) X2)))))))) _let_24 (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((I tptp.nat) (J3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J3) (=> (@ (@ tptp.ord_less_eq_nat J3) K2) (@ _let_1 K2))))) (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y4)) (= X Y4))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_nat Y4) X)))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2)))))) (@ P N))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P M2))) (@ P N2))) (@ P 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 ((I tptp.nat) (J3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J3)) K2) (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) J3)))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (@ (@ (@ tptp.submodule_b_d_e_f R) M3) (@ (@ (@ tptp.smodul1982583723_d_e_f R) M3) A2))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (@ (@ (@ tptp.submod903911234t_unit R) M3) (@ (@ (@ tptp.smodul132175289t_unit R) M3) A2))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (@ (@ (@ tptp.submodule_b_d_a_c R) M3) (@ (@ (@ tptp.smodul818989740_d_a_c R) M3) A2))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (P tptp.set_e) (Q tptp.set_e)) (let ((_let_1 (@ (@ tptp.submodule_b_d_e_f R) M3))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ _let_1 P) (=> (@ _let_1 Q) (@ (@ tptp.ideal_b_d R) (@ (@ (@ (@ tptp.quotie169863047_d_e_f R) M3) P) Q))))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (P tptp.set_a) (Q tptp.set_a)) (let ((_let_1 (@ (@ tptp.submod903911234t_unit R) M3))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ _let_1 P) (=> (@ _let_1 Q) (@ (@ tptp.ideal_b_d R) (@ (@ (@ (@ tptp.quotie1196826005t_unit R) M3) P) Q))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (P tptp.set_a) (Q tptp.set_a)) (let ((_let_1 (@ (@ tptp.submodule_b_d_a_c R) M3))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ _let_1 P) (=> (@ _let_1 Q) (@ (@ tptp.ideal_b_d R) (@ (@ (@ (@ tptp.quotie1153752712_d_a_c R) M3) P) Q))))))) (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X2 tptp.nat)) (@ (@ R X2) X2)) (=> (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ R X2))) (=> (@ _let_1 Y) (=> (@ (@ R Y) Z) (@ _let_1 Z))))) (=> (forall ((N2 tptp.nat)) (@ (@ R N2) (@ tptp.suc N2))) (@ (@ R M) N)))))) (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ P M2))) (@ P N2))) (@ P N))) _let_23 (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))) (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))) (forall ((P (-> tptp.nat Bool)) (Nat tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((Nat3 tptp.nat)) (=> (@ P Nat3) (@ P (@ tptp.suc Nat3)))) (@ P Nat)))) (forall ((Y4 tptp.nat)) (=> (not (= Y4 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y4 (@ tptp.suc Nat3))))))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((P (-> tptp.nat Bool)) (K2 tptp.nat)) (=> (@ P K2) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P tptp.zero_zero_nat)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X2 tptp.nat)) (@ (@ P X2) tptp.zero_zero_nat)) (=> (forall ((Y tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y))) (=> (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ P X2) Y) (@ (@ P (@ tptp.suc X2)) (@ tptp.suc Y)))) (@ (@ P M) N))))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc N2)))) (@ P N)))) (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))) (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))) (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))) (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))) (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J3 tptp.nat)) (=> (forall ((I2 tptp.nat) (J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J4) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J4)))) (=> (@ (@ tptp.ord_less_eq_nat I) J3) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J3))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))) _let_22 (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N4) (not (= M6 N4))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))) (forall ((I tptp.nat) (J3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J3) (=> (forall ((I2 tptp.nat)) (=> (= J3 (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J3) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I))))) (forall ((I tptp.nat) (J3 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J3) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J4 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J4) (=> (@ (@ tptp.ord_less_nat J4) K3) (=> (@ _let_1 J4) (=> (@ (@ P J4) K3) (@ _let_1 K3))))))) (@ (@ P I) J3))))) (forall ((I tptp.nat) (J3 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (=> (@ (@ tptp.ord_less_nat J3) K2) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K2)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M7 tptp.nat)) (and (= M (@ tptp.suc M7)) (@ (@ tptp.ord_less_nat N) M7))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P N) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))) (forall ((I tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K2) (not (forall ((J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J4) (not (= K2 (@ tptp.suc J4)))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((I tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (=> (not (= K2 (@ tptp.suc I))) (not (forall ((J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J4) (not (= K2 (@ tptp.suc J4))))))))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2))))))) (@ P N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)) (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N) L2)))) (forall ((K2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ _let_1 N))))))) (forall ((K2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((K2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K2) (@ (@ tptp.minus_minus_nat N) K2)) (= M N)))))) (forall ((P (-> tptp.nat Bool)) (K2 tptp.nat) (I tptp.nat)) (=> (@ P K2) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P (@ (@ tptp.minus_minus_nat K2) I))))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))) (forall ((J3 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) K2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J3) N)) K2))) (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (@ tptp.ring_b_d R))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (@ tptp.ring_b_d R))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (@ tptp.ring_b_d R))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (X tptp.e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.member_e X) (@ (@ (@ tptp.smodul1982583723_d_e_f R) M3) A2)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b X2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) A2))) (exists ((Xa (-> tptp.nat tptp.e))) (and (@ (@ tptp.member_nat_e Xa) (@ (@ tptp.pi_nat_e (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie730238621_e_b_f M3)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_e_f R) M3) N2) X2) Xa)))))))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (X tptp.a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.smodul132175289t_unit R) M3) A2)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b X2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) A2))) (exists ((Xa (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a Xa) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie1074654371t_unit M3)))) (= X (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit R) M3) N2) X2) Xa)))))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (A2 tptp.set_b) (X tptp.a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ tptp.ideal_b_d R) A2) (=> (@ (@ tptp.member_a X) (@ (@ (@ tptp.smodul818989740_d_a_c R) M3) A2)) (exists ((N2 tptp.nat) (X2 (-> tptp.nat tptp.b))) (and (@ (@ tptp.member_nat_b X2) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) A2))) (exists ((Xa (-> tptp.nat tptp.a))) (and (@ (@ tptp.member_nat_a Xa) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2021454486_a_b_c M3)))) (= X (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c R) M3) N2) X2) Xa)))))))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N))))) (forall ((F (-> tptp.nat tptp.set_a)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_a (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_a (@ F N5)) (@ F N))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.set_a)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_a (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_a (@ F N)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N5))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))) (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N4)) __flatten_var_0))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((I tptp.nat) (J3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J3) (=> (@ P J3) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J3) (=> (@ P (@ tptp.suc N2)) (@ P N2))))) (@ P I))))) (forall ((I tptp.nat) (J3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J3) (=> (@ P I) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J3) (=> (@ P N2) (@ P (@ tptp.suc N2)))))) (@ P J3))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (not (@ P I4)))) (@ P K3)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J2 tptp.nat)) (and (= M (@ tptp.suc J2)) (@ (@ tptp.ord_less_nat J2) N)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))) (forall ((K2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.ord_less_nat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e) (H2 tptp.e)) (let ((_let_1 (@ tptp.member_e H2))) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.submodule_b_d_e_f R) M3) H) (=> (@ _let_1 H) (@ _let_1 (@ tptp.carrie730238621_e_b_f M3))))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (H2 tptp.a)) (let ((_let_1 (@ tptp.member_a H2))) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.submodule_b_d_a_c R) M3) H) (=> (@ _let_1 H) (@ _let_1 (@ tptp.carrie2021454486_a_b_c M3))))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a) (H2 tptp.a)) (let ((_let_1 (@ tptp.member_a H2))) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.submod903911234t_unit R) M3) H) (=> (@ _let_1 H) (@ _let_1 (@ tptp.carrie1074654371t_unit M3))))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (@ (@ (@ tptp.submodule_b_d_e_f R) M3) (@ tptp.carrie730238621_e_b_f M3)))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (@ (@ (@ tptp.submodule_b_d_a_c R) M3) (@ tptp.carrie2021454486_a_b_c M3)))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (@ (@ (@ tptp.submod903911234t_unit R) M3) (@ tptp.carrie1074654371t_unit M3)))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K3) (not (@ P I4)))) (@ P (@ tptp.suc K3))))))) (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.submodule_b_d_e_f R) M3) H) (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.submodule_b_d_a_c R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.submod903911234t_unit R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3))))) (forall ((M3 tptp.carrie1821755406_e_b_f) (R tptp.carrie1950868226xt_b_d) (H tptp.set_e)) (=> (@ (@ tptp.module_e_b_f_d M3) R) (=> (@ (@ (@ tptp.free_g103796815_d_e_f R) M3) H) (@ (@ tptp.ord_less_eq_set_e H) (@ tptp.carrie730238621_e_b_f M3))))) (forall ((M3 tptp.carrie722926983_a_b_c) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module_a_b_c_d M3) R) (=> (@ (@ (@ tptp.free_g1087686480_d_a_c R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c M3))))) (forall ((M3 tptp.carrie1963041556t_unit) (R tptp.carrie1950868226xt_b_d) (H tptp.set_a)) (=> (@ (@ tptp.module1821517916unit_d M3) R) (=> (@ (@ (@ tptp.free_g637607517t_unit R) M3) H) (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie1074654371t_unit M3))))) (forall ((H tptp.set_a) (K tptp.set_a) (F (-> tptp.nat tptp.a)) (N tptp.nat) (S (-> tptp.nat tptp.b))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (=> (and (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) K))) (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d tptp.r))))) (= (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit tptp.r) (@ (@ tptp.mdl_a_b_c tptp.m) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) K))) N) S) F) (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)))))) (forall ((H tptp.set_a) (K tptp.set_a) (F (-> tptp.nat tptp.a)) (N tptp.nat) (S (-> tptp.nat tptp.b))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) K))) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d tptp.r)))) (= (@ (@ (@ (@ (@ tptp.l_comb1138968323t_unit tptp.r) (@ (@ tptp.mdl_a_b_c tptp.m) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) K))) N) S) F) (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F))))))) (forall ((A tptp.a) (A2 tptp.set_a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.insert_a B) tptp.bot_bot_set_a))) (= (= (@ (@ tptp.insert_a A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_a A2) _let_1))))) (forall ((B tptp.a) (A tptp.a) (A2 tptp.set_a)) (let ((_let_1 (@ (@ tptp.insert_a B) tptp.bot_bot_set_a))) (= (= _let_1 (@ (@ tptp.insert_a A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_a A2) _let_1))))) (forall ((A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H))))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H)))))) (forall ((A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H)))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))))) (forall ((A2 tptp.set_b) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (and (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (@ (@ tptp.member_nat_a M) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ tptp.insert_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) tptp.bot_bot_set_a))))) (= (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) M) (@ tptp.zero_a1261444626_a_b_c tptp.m))))) (@ (@ tptp.member_a _let_20) _let_10) (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_a A2) B2)))) (forall ((A2 tptp.set_nat_a) (B2 tptp.set_nat_a)) (=> (forall ((X2 (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.member_nat_a X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le157368549_nat_a A2) B2))) (forall ((A2 tptp.set_nat_b) (B2 tptp.set_nat_b)) (=> (forall ((X2 (-> tptp.nat tptp.b))) (let ((_let_1 (@ tptp.member_nat_b X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1296932838_nat_b A2) B2))) (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (=> (forall ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_a A2) B2))) (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B2) (=> (@ (@ tptp.ord_less_eq_set_a B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_a)) (= (@ (@ tptp.minus_minus_set_a A2) tptp.bot_bot_set_a) A2)) (forall ((A2 tptp.set_a)) (= (@ (@ tptp.minus_minus_set_a tptp.bot_bot_set_a) A2) tptp.bot_bot_set_a)) (forall ((A2 tptp.set_a)) (= (@ (@ tptp.minus_minus_set_a A2) A2) tptp.bot_bot_set_a)) (forall ((C (-> tptp.nat tptp.a))) (not (@ (@ tptp.member_nat_a C) tptp.bot_bot_set_nat_a))) (forall ((C (-> tptp.nat tptp.b))) (not (@ (@ tptp.member_nat_b C) tptp.bot_bot_set_nat_b))) (forall ((C tptp.a)) (not (@ (@ tptp.member_a C) tptp.bot_bot_set_a))) (forall ((A2 tptp.set_nat_a)) (= (forall ((X3 (-> tptp.nat tptp.a))) (not (@ (@ tptp.member_nat_a X3) A2))) (= A2 tptp.bot_bot_set_nat_a))) (forall ((A2 tptp.set_nat_b)) (= (forall ((X3 (-> tptp.nat tptp.b))) (not (@ (@ tptp.member_nat_b X3) A2))) (= A2 tptp.bot_bot_set_nat_b))) (forall ((A2 tptp.set_a)) (= (forall ((X3 tptp.a)) (not (@ (@ tptp.member_a X3) A2))) (= A2 tptp.bot_bot_set_a))) (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X3 tptp.nat)) (not (@ P X3))))) (forall ((P (-> tptp.a Bool))) (= (= (@ tptp.collect_a P) tptp.bot_bot_set_a) (forall ((X3 tptp.a)) (not (@ P X3))))) (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X3 tptp.nat)) (not (@ P X3))))) (forall ((P (-> tptp.a Bool))) (= (= tptp.bot_bot_set_a (@ tptp.collect_a P)) (forall ((X3 tptp.a)) (not (@ P X3))))) (forall ((X (-> tptp.nat tptp.a)) (A2 tptp.set_nat_a) (B2 tptp.set_nat_a)) (let ((_let_1 (@ tptp.minus_1788767276_nat_a A2))) (=> (not (@ (@ tptp.member_nat_a X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat_a X) B2)) (@ _let_1 B2))))) (forall ((X (-> tptp.nat tptp.b)) (A2 tptp.set_nat_b) (B2 tptp.set_nat_b)) (let ((_let_1 (@ tptp.minus_780847917_nat_b A2))) (=> (not (@ (@ tptp.member_nat_b X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat_b X) B2)) (@ _let_1 B2))))) (forall ((X tptp.a) (A2 tptp.set_a) (B2 tptp.set_a)) (let ((_let_1 (@ tptp.minus_minus_set_a A2))) (=> (not (@ (@ tptp.member_a X) A2)) (= (@ _let_1 (@ (@ tptp.insert_a X) B2)) (@ _let_1 B2))))) (forall ((X (-> tptp.nat tptp.a)) (B2 tptp.set_nat_a) (A2 tptp.set_nat_a)) (=> (@ (@ tptp.member_nat_a X) B2) (= (@ (@ tptp.minus_1788767276_nat_a (@ (@ tptp.insert_nat_a X) A2)) B2) (@ (@ tptp.minus_1788767276_nat_a A2) B2)))) (forall ((X (-> tptp.nat tptp.b)) (B2 tptp.set_nat_b) (A2 tptp.set_nat_b)) (=> (@ (@ tptp.member_nat_b X) B2) (= (@ (@ tptp.minus_780847917_nat_b (@ (@ tptp.insert_nat_b X) A2)) B2) (@ (@ tptp.minus_780847917_nat_b A2) B2)))) (forall ((X tptp.a) (B2 tptp.set_a) (A2 tptp.set_a)) (=> (@ (@ tptp.member_a X) B2) (= (@ (@ tptp.minus_minus_set_a (@ (@ tptp.insert_a X) A2)) B2) (@ (@ tptp.minus_minus_set_a A2) B2)))) (forall ((A (-> tptp.nat tptp.a)) (B2 tptp.set_nat_a) (B (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.member_nat_a A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_nat_a B) B2))))) (forall ((A (-> tptp.nat tptp.b)) (B2 tptp.set_nat_b) (B (-> tptp.nat tptp.b))) (let ((_let_1 (@ tptp.member_nat_b A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_nat_b B) B2))))) (forall ((A tptp.a) (B2 tptp.set_a) (B tptp.a)) (let ((_let_1 (@ tptp.member_a A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_a B) B2))))) (forall ((A (-> tptp.nat tptp.a)) (B (-> tptp.nat tptp.a)) (A2 tptp.set_nat_a)) (let ((_let_1 (@ tptp.member_nat_a A))) (= (@ _let_1 (@ (@ tptp.insert_nat_a B) A2)) (or (= A B) (@ _let_1 A2))))) (forall ((A (-> tptp.nat tptp.b)) (B (-> tptp.nat tptp.b)) (A2 tptp.set_nat_b)) (let ((_let_1 (@ tptp.member_nat_b A))) (= (@ _let_1 (@ (@ tptp.insert_nat_b B) A2)) (or (= A B) (@ _let_1 A2))))) (forall ((A tptp.a) (B tptp.a) (A2 tptp.set_a)) (let ((_let_1 (@ tptp.member_a A))) (= (@ _let_1 (@ (@ tptp.insert_a B) A2)) (or (= A B) (@ _let_1 A2))))) (forall ((X tptp.a) (A2 tptp.set_a)) (let ((_let_1 (@ tptp.insert_a X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) H) (@ (@ tptp.member_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) H))) (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) H) (= (@ tptp.carrie1074654371t_unit (@ (@ tptp.mdl_a_b_c tptp.m) H)) H))) (forall ((H tptp.set_a)) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) H) (@ (@ tptp.module1821517916unit_d (@ (@ tptp.mdl_a_b_c tptp.m) H)) tptp.r))) (forall ((H tptp.set_a) (N3 tptp.set_a)) (let ((_let_1 (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m))) (=> (@ _let_1 H) (=> (@ _let_1 N3) (=> (@ (@ tptp.ord_less_eq_set_a H) N3) (@ (@ (@ tptp.submod903911234t_unit tptp.r) (@ (@ tptp.mdl_a_b_c tptp.m) N3)) H)))))) (forall ((H tptp.set_a) (H2 tptp.a)) (let ((_let_1 (@ tptp.member_a H2))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ _let_1 H) (@ _let_1 (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H)))))) (forall ((H tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a H))) (=> (@ _let_1 (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ _let_1 (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H))))) (forall ((H tptp.set_a)) (let ((_let_1 (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)))) (let ((_let_2 (@ _let_1 H))) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (= (@ _let_1 _let_2) _let_2))))) (forall ((K tptp.set_a) (H tptp.set_a) (A2 tptp.set_b)) (let ((_let_1 (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2))) (=> (@ (@ tptp.ord_less_eq_set_a K) H) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 K)) (@ _let_1 H))))))) (forall ((A2 tptp.set_b) (H tptp.set_a)) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c tptp.m))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) _let_1) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H)) _let_1))))) (forall ((A2 tptp.set_b) (N3 tptp.set_a) (H tptp.set_a)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) N3) (=> (@ (@ tptp.ord_less_eq_set_a H) N3) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H)) N3))))) (forall ((H tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ (@ (@ tptp.genera1692266857t_unit tptp.r) (@ (@ tptp.mdl_a_b_c tptp.m) (@ (@ (@ tptp.algebr1152250919_d_a_c tptp.r) tptp.m) H))) H))) (@ _let_9 _let_21) (= (@ _let_8 tptp.bot_bot_set_a) _let_21) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)) (forall ((A2 tptp.set_a) (B2 tptp.set_a)) (= (= (@ (@ tptp.minus_minus_set_a A2) B2) tptp.bot_bot_set_a) (@ (@ tptp.ord_less_eq_set_a A2) B2))) (forall ((A2 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a A2) tptp.bot_bot_set_a) (= A2 tptp.bot_bot_set_a))) (forall ((A2 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a tptp.bot_bot_set_a) A2)) (forall ((X (-> tptp.nat tptp.a)) (A2 tptp.set_nat_a) (B2 tptp.set_nat_a)) (= (@ (@ tptp.ord_le157368549_nat_a (@ (@ tptp.insert_nat_a X) A2)) B2) (and (@ (@ tptp.member_nat_a X) B2) (@ (@ tptp.ord_le157368549_nat_a A2) B2)))) (forall ((X (-> tptp.nat tptp.b)) (A2 tptp.set_nat_b) (B2 tptp.set_nat_b)) (= (@ (@ tptp.ord_le1296932838_nat_b (@ (@ tptp.insert_nat_b X) A2)) B2) (and (@ (@ tptp.member_nat_b X) B2) (@ (@ tptp.ord_le1296932838_nat_b A2) B2)))) (forall ((X tptp.a) (A2 tptp.set_a) (B2 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.insert_a X) A2)) B2) (and (@ (@ tptp.member_a X) B2) (@ (@ tptp.ord_less_eq_set_a A2) B2)))) (forall ((A tptp.a) (A2 tptp.set_a)) (let ((_let_1 (@ tptp.insert_a A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_a A2) (@ _let_1 tptp.bot_bot_set_a))) (@ _let_1 A2)))) (forall ((A (-> tptp.nat tptp.a))) (@ (@ tptp.member_nat_a A) (@ (@ tptp.insert_nat_a A) tptp.bot_bot_set_nat_a))) (forall ((A (-> tptp.nat tptp.b))) (@ (@ tptp.member_nat_b A) (@ (@ tptp.insert_nat_b A) tptp.bot_bot_set_nat_b))) (forall ((A tptp.a)) (@ (@ tptp.member_a A) (@ (@ tptp.insert_a A) tptp.bot_bot_set_a))) (forall ((A2 tptp.set_b) (H tptp.set_a)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ (@ (@ tptp.submodule_b_d_a_c tptp.r) tptp.m) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))) (forall ((A2 tptp.set_b) (H tptp.set_a)) (let ((_let_1 (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m))) (let ((_let_2 (@ _let_1 A2))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (= (@ _let_2 (@ (@ _let_1 (@ tptp.carrie2079586589xt_b_d tptp.r)) H)) (@ _let_2 H))))))) (forall ((A2 tptp.set_b) (H tptp.set_a)) (let ((_let_1 (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ (@ tptp.ord_less_eq_set_a (@ (@ _let_1 A2) H)) (@ (@ _let_1 (@ tptp.carrie2079586589xt_b_d tptp.r)) H)))))) (forall ((A2 tptp.set_b) (H tptp.set_a)) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (@ (@ tptp.member_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))) (forall ((H tptp.set_a) (H1 tptp.set_a)) (let ((_let_1 (@ (@ tptp.generator_b_d_a_c tptp.r) tptp.m))) (=> (@ _let_1 H) (=> (@ (@ tptp.ord_less_eq_set_a H1) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) (@ tptp.carrie2079586589xt_b_d tptp.r)) H1)) (@ _let_1 H1)))))) (forall ((A2 tptp.set_b)) (let ((_let_1 (@ (@ tptp.insert_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) tptp.bot_bot_set_a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (= (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) _let_1) _let_1)))) (forall ((A2 tptp.set_b) (H tptp.set_a)) (let ((_let_1 (@ tptp.carrie2021454486_a_b_c tptp.m))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ (@ tptp.generator_b_d_a_c tptp.r) tptp.m) H) (=> (= (@ (@ (@ tptp.smodul818989740_d_a_c tptp.r) tptp.m) A2) _let_1) (= (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H) _let_1)))))) (forall ((A tptp.a)) (= (@ tptp.collect_a (lambda ((X3 tptp.a)) (= X3 A))) (@ (@ tptp.insert_a A) tptp.bot_bot_set_a))) (forall ((A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) H))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))))) (forall ((A2 tptp.set_b) (H tptp.set_a) (S (-> tptp.nat tptp.b)) (N tptp.nat) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.ord_less_eq_set_a H) (@ tptp.carrie2021454486_a_b_c tptp.m)) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a F) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H)))) (@ (@ tptp.member_a (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) F)) (@ (@ (@ (@ tptp.linear_span_b_d_a_c tptp.r) tptp.m) A2) H))))))) (forall ((A2 tptp.set_b) (S (-> tptp.nat tptp.b)) (N tptp.nat) (M (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ideal_b_d tptp.r) A2) (=> (@ (@ tptp.member_nat_b S) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) A2))) (=> (@ (@ tptp.member_nat_a M) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat J2) N)))) (lambda ((Uu tptp.nat)) (@ (@ tptp.insert_a (@ tptp.zero_a1261444626_a_b_c tptp.m)) tptp.bot_bot_set_a)))) (= (@ (@ (@ (@ (@ tptp.l_comb_b_d_a_c tptp.r) tptp.m) N) S) M) (@ tptp.zero_a1261444626_a_b_c tptp.m)))))) (@ (@ tptp.member_nat_a tptp.g) (@ (@ tptp.pi_nat_a (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat K4) tptp.m2)))) (lambda ((Uu tptp.nat)) (@ (@ tptp.insert_a tptp.h2) tptp.h1)))) _let_19 (@ (@ tptp.member_nat_b tptp.t) (@ (@ tptp.pi_nat_b (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat K4) tptp.m2)))) (lambda ((Uu tptp.nat)) (@ tptp.carrie2079586589xt_b_d tptp.r)))) _let_18 (@ (@ tptp.module_e_b_f_d tptp.n) tptp.r) (@ (@ (@ tptp.free_g1087686480_d_a_c tptp.r) tptp.m) tptp.h) (@ _let_15 tptp.h) true (@ _let_16 (@ tptp.carrie2079586589xt_b_d tptp.r)) (@ (@ tptp.ord_less_eq_set_a tptp.h) _let_10) (@ _let_15 _let_10) (@ (@ tptp.ord_less_eq_set_a (@ _let_8 tptp.h1)) _let_10) (@ (@ tptp.member_a _let_13) (@ _let_8 (@ _let_7 tptp.h1))) _let_14 (@ _let_11 tptp.h) (not (@ _let_11 tptp.h1)) _let_12 (@ _let_11 _let_10) (@ _let_9 (@ _let_8 (@ _let_7 tptp.bot_bot_set_a))) _let_6 _let_4 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.45/1.76 )
% 1.45/1.76 % SZS output end Proof for ITP026^1
% 1.45/1.76 % cvc5---1.0.5 exiting
% 1.45/1.76 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------