TSTP Solution File: ITP015^2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ITP015^2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.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 : 600s
% DateTime : Sat Jul 16 23:43:37 EDT 2022
% Result : Theorem 38.79s 38.97s
% Output : CNFRefutation 39.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 107
% Syntax : Number of formulae : 791 ( 353 unt; 49 typ; 0 def)
% Number of atoms : 7505 (2624 equ; 0 cnn)
% Maximal formula atoms : 13 ( 10 avg)
% Number of connectives : 20550 (2707 ~;3236 |; 72 &;14431 @)
% ( 26 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 5 ( 3 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 21 con; 0-4 aty)
% Number of variables : 2204 ( 0 ^2204 !; 0 ?;2204 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_del,type,
del: $tType ).
thf(tp_tp__ty_2Einteger_2Eint,type,
tp__ty_2Einteger_2Eint: $tType ).
thf(tp_tp__ty_2Enum_2Enum,type,
tp__ty_2Enum_2Enum: $tType ).
thf(tp_ap,type,
ap: $i > $i > $i ).
thf(tp_arr,type,
arr: del > del > del ).
thf(tp_bool,type,
bool: del ).
thf(tp_c_2Earithmetic_2EMOD,type,
c_2Earithmetic_2EMOD: $i ).
thf(tp_c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND: del > $i ).
thf(tp_c_2Ebool_2EF,type,
c_2Ebool_2EF: $i ).
thf(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
thf(tp_c_2Ebool_2E_21,type,
c_2Ebool_2E_21: del > $i ).
thf(tp_c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $i ).
thf(tp_c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $i ).
thf(tp_c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
thf(tp_c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value: del > $i ).
thf(tp_c_2Einteger_2ENum,type,
c_2Einteger_2ENum: $i ).
thf(tp_c_2Einteger_2Eint__lt,type,
c_2Einteger_2Eint__lt: $i ).
thf(tp_c_2Einteger_2Eint__neg,type,
c_2Einteger_2Eint__neg: $i ).
thf(tp_c_2Einteger_2Eint__of__num,type,
c_2Einteger_2Eint__of__num: $i ).
thf(tp_c_2Einteger__word_2Ei2w,type,
c_2Einteger__word_2Ei2w: del > $i ).
thf(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
thf(tp_c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $i ).
thf(tp_c_2Enum_2E0,type,
c_2Enum_2E0: $i ).
thf(tp_c_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: $i ).
thf(tp_c_2Ewords_2Edimword,type,
c_2Ewords_2Edimword: del > $i ).
thf(tp_c_2Ewords_2En2w,type,
c_2Ewords_2En2w: del > $i ).
thf(tp_c_2Ewords_2Eword__2comp,type,
c_2Ewords_2Eword__2comp: del > $i ).
thf(tp_fo__c_2Earithmetic_2EMOD,type,
fo__c_2Earithmetic_2EMOD: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(tp_fo__c_2Einteger_2ENum,type,
fo__c_2Einteger_2ENum: tp__ty_2Einteger_2Eint > tp__ty_2Enum_2Enum ).
thf(tp_fo__c_2Einteger_2Eint__neg,type,
fo__c_2Einteger_2Eint__neg: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(tp_fo__c_2Einteger_2Eint__of__num,type,
fo__c_2Einteger_2Eint__of__num: tp__ty_2Enum_2Enum > tp__ty_2Einteger_2Eint ).
thf(tp_fo__c_2Enum_2E0,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
thf(tp_ind,type,
ind: del ).
thf(tp_inj__o,type,
inj__o: $o > $i ).
thf(tp_inj__ty_2Einteger_2Eint,type,
inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).
thf(tp_inj__ty_2Enum_2Enum,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
thf(tp_lam,type,
lam: del > ( $i > $i ) > $i ).
thf(tp_mem,type,
mem: $i > del > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_sK1_A_27a,type,
sK1_A_27a: del ).
thf(tp_sK2_X,type,
sK2_X: $i > del > $i ).
thf(tp_sK3_X,type,
sK3_X: $i > $i > del > del > $i ).
thf(tp_sK4_X,type,
sK4_X: ( $i > $i ) > del > del > $i ).
thf(tp_surj__ty_2Einteger_2Eint,type,
surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).
thf(tp_surj__ty_2Enum_2Enum,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
thf(tp_ty_2Ebool_2Eitself,type,
ty_2Ebool_2Eitself: del > del ).
thf(tp_ty_2Efcp_2Ecart,type,
ty_2Efcp_2Ecart: del > del > del ).
thf(tp_ty_2Einteger_2Eint,type,
ty_2Einteger_2Eint: del ).
thf(tp_ty_2Enum_2Enum,type,
ty_2Enum_2Enum: del ).
thf(1,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ewords_2EWORD__NEG__0) ).
thf(2,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ewords_2En2w__11) ).
thf(3,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eprim__rec_2ENOT__LESS__0) ).
thf(4,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Einteger__word_2Ei2w__def) ).
thf(5,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= V0n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger_2ENUM__OF__INT) ).
thf(6,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
<=> ( ( V0n != fo__c_2Enum_2E0 )
| ( V1m != fo__c_2Enum_2E0 ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__LT__CALCULATE) ).
thf(7,axiom,
( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__NEG__0) ).
thf(8,axiom,
! [A_27a: del] :
( ! [V0t1: $i] :
( ( mem @ V0t1 @ A_27a )
=> ! [V1t2: $i] :
( ( mem @ V1t2 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
= V0t1 ) ) )
& ! [V2t1: $i] :
( ( mem @ V2t1 @ A_27a )
=> ! [V3t2: $i] :
( ( mem @ V3t2 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ V3t2 )
= V3t2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2Ebool__case__thm) ).
thf(9,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ bool )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ bool )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3x_27: $i] :
( ( mem @ V3x_27 @ A_27a )
=> ! [V4y: $i] :
( ( mem @ V4y @ A_27a )
=> ! [V5y_27: $i] :
( ( mem @ V5y_27 @ A_27a )
=> ( ( ( ( p @ V0P )
<=> ( p @ V1Q ) )
& ( ( p @ V1Q )
=> ( V2x = V3x_27 ) )
& ( ~ ( p @ V1Q )
=> ( V4y = V5y_27 ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CONG) ).
thf(11,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ A_27a )
=> ( ( V0x = V1y )
<=> ( V1y = V0x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EEQ__SYM__EQ) ).
thf(16,axiom,
! [A: del,X: $i] :
( ( mem @ X @ A )
=> ! [Y: $i] :
( ( mem @ Y @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
<=> ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).
thf(17,axiom,
! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(18,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ewords_2Eword__2comp) ).
thf(19,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2En2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ewords_2En2w) ).
thf(20,axiom,
( ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Enum_2E0) ).
thf(21,axiom,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Enum_2E0) ).
thf(22,axiom,
! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
<=> ! [X: $i] :
( ( mem @ X @ A )
=> ( p @ ( ap @ Q @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p) ).
thf(23,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(24,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EMOD @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Earithmetic_2EMOD) ).
thf(25,axiom,
mem @ c_2Earithmetic_2EMOD @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Earithmetic_2EMOD) ).
thf(26,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Edimword @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Enum_2Enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ewords_2Edimword) ).
thf(27,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2Ethe__value) ).
thf(28,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
<=> ~ ( p @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p) ).
thf(29,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
thf(30,axiom,
mem @ c_2Eprim__rec_2E_3C @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eprim__rec_2E_3C) ).
thf(31,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( arr @ ty_2Einteger_2Eint @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Einteger__word_2Ei2w) ).
thf(32,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2ECOND @ A_27a ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ECOND) ).
thf(33,axiom,
mem @ c_2Einteger_2Eint__lt @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__lt) ).
thf(34,axiom,
! [X0: tp__ty_2Enum_2Enum] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__of__num @ X0 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__of__num) ).
thf(35,axiom,
mem @ c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__of__num) ).
thf(36,axiom,
! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Einteger_2ENum @ X0 ) )
= ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2ENum) ).
thf(37,axiom,
mem @ c_2Einteger_2ENum @ ( arr @ ty_2Einteger_2Eint @ ty_2Enum_2Enum ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Einteger_2ENum) ).
thf(38,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Enum_2Enum )
=> ( X
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Enum_2Enum) ).
thf(39,axiom,
! [X: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X ) @ ty_2Enum_2Enum ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Enum_2Enum) ).
thf(40,axiom,
! [X: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Enum_2Enum) ).
thf(41,axiom,
! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X0 ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__neg) ).
thf(42,axiom,
mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__neg) ).
thf(43,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Einteger_2Eint )
=> ( X
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Einteger_2Eint) ).
thf(44,axiom,
! [X: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X ) @ ty_2Einteger_2Eint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Einteger_2Eint) ).
thf(45,axiom,
! [X: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Einteger_2Eint) ).
thf(46,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
<=> ( ( p @ Q )
& ( p @ R ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p) ).
thf(47,axiom,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
thf(48,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
<=> ( ( p @ Q )
| ( p @ R ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_or_p) ).
thf(49,axiom,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_5C_2F) ).
thf(50,axiom,
~ ( p @ c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
thf(51,axiom,
mem @ c_2Ebool_2EF @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
thf(52,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
thf(53,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(54,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
<=> ( ( p @ Q )
=> ( p @ R ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_imp_p) ).
thf(55,axiom,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E) ).
thf(56,axiom,
! [A: del,F: $i > $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta) ).
thf(57,axiom,
! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [G: $i] :
( ( mem @ G @ ( arr @ A @ B ) )
=> ( ! [X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ F @ X )
= ( ap @ G @ X ) ) )
=> ( F = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(58,axiom,
! [A: del,B: del,F: $i > $i] :
( ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( F @ X ) @ B ) )
=> ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam_tp) ).
thf(59,axiom,
! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
thf(60,axiom,
! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(61,axiom,
! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(62,axiom,
! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(63,conjecture,
! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger__word_2Ei2w__0) ).
thf(64,negated_conjecture,
( ( ! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[63]) ).
thf(65,plain,
( ( ! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[64]) ).
thf(66,plain,
( ( ! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(67,plain,
( ( ! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(68,plain,
( ( ! [V0n: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(69,plain,
( ( ! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(70,plain,
( ( ! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= V0n ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(71,plain,
( ( ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
<=> ( ( V0n != fo__c_2Enum_2E0 )
| ( V1m != fo__c_2Enum_2E0 ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
<=> $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(72,plain,
( ( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(73,plain,
( ( ! [A_27a: del] :
( ! [V0t1: $i] :
( ( mem @ V0t1 @ A_27a )
=> ! [V1t2: $i] :
( ( mem @ V1t2 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
= V0t1 ) ) )
& ! [V2t1: $i] :
( ( mem @ V2t1 @ A_27a )
=> ! [V3t2: $i] :
( ( mem @ V3t2 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ V3t2 )
= V3t2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(74,plain,
( ( ! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ bool )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ bool )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3x_27: $i] :
( ( mem @ V3x_27 @ A_27a )
=> ! [V4y: $i] :
( ( mem @ V4y @ A_27a )
=> ! [V5y_27: $i] :
( ( mem @ V5y_27 @ A_27a )
=> ( ( ( ( p @ V0P )
<=> ( p @ V1Q ) )
& ( ( p @ V1Q )
=> ( V2x = V3x_27 ) )
& ( ~ ( p @ V1Q )
=> ( V4y = V5y_27 ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(76,plain,
( ( ! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ A_27a )
=> ( ( V0x = V1y )
<=> ( V1y = V0x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(81,plain,
( ( ! [A: del,X: $i] :
( ( mem @ X @ A )
=> ! [Y: $i] :
( ( mem @ Y @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
<=> ( X = Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(82,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(83,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(84,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ewords_2En2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(85,plain,
( ( ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 )
= c_2Enum_2E0 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(86,plain,
( ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(87,plain,
( ( ! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
<=> ! [X: $i] :
( ( mem @ X @ A )
=> ( p @ ( ap @ Q @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(88,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(89,plain,
( ( ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EMOD @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(90,plain,
( ( mem @ c_2Earithmetic_2EMOD @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(91,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ewords_2Edimword @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Enum_2Enum ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(92,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(93,plain,
( ( ! [Q: $i] :
( ( mem @ Q @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
<=> ~ ( p @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(94,plain,
( ( mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(95,plain,
( ( mem @ c_2Eprim__rec_2E_3C @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(96,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( arr @ ty_2Einteger_2Eint @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(97,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ECOND @ A_27a ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(98,plain,
( ( mem @ c_2Einteger_2Eint__lt @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(99,plain,
( ( ! [X0: tp__ty_2Enum_2Enum] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__of__num @ X0 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(100,plain,
( ( mem @ c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(101,plain,
( ( ! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Einteger_2ENum @ X0 ) )
= ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(102,plain,
( ( mem @ c_2Einteger_2ENum @ ( arr @ ty_2Einteger_2Eint @ ty_2Enum_2Enum ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(103,plain,
( ( ! [X: $i] :
( ( mem @ X @ ty_2Enum_2Enum )
=> ( X
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(104,plain,
( ( ! [X: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X ) @ ty_2Enum_2Enum ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(105,plain,
( ( ! [X: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(106,plain,
( ( ! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X0 ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(107,plain,
( ( mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(108,plain,
( ( ! [X: $i] :
( ( mem @ X @ ty_2Einteger_2Eint )
=> ( X
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(109,plain,
( ( ! [X: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X ) @ ty_2Einteger_2Eint ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(110,plain,
( ( ! [X: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(111,plain,
( ( ! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
<=> ( ( p @ Q )
& ( p @ R ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(112,plain,
( ( mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(113,plain,
( ( ! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
<=> ( ( p @ Q )
| ( p @ R ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(114,plain,
( ( mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(115,plain,
( ( ~ ( p @ c_2Ebool_2EF ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(116,plain,
( ( mem @ c_2Ebool_2EF @ bool )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(117,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(118,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(119,plain,
( ( ! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
<=> ( ( p @ Q )
=> ( p @ R ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(120,plain,
( ( mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(121,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(122,plain,
( ( ! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [G: $i] :
( ( mem @ G @ ( arr @ A @ B ) )
=> ( ! [X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ F @ X )
= ( ap @ G @ X ) ) )
=> ( F = G ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(123,plain,
( ( ! [A: del,B: del,F: $i > $i] :
( ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( F @ X ) @ B ) )
=> ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(124,plain,
( ( ! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(125,plain,
( ( ! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(126,plain,
( ( ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(127,plain,
( ( ! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(128,plain,
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ sK1_A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ sK1_A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(129,plain,
( ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ sK1_A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
!= ( ap @ ( c_2Ewords_2En2w @ sK1_A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[128]) ).
thf(130,plain,
( ( ! [A_27a: del] :
( ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) )
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) )
& ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
| ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(131,plain,
( ( ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
| ( V0n != fo__c_2Enum_2E0 )
| ( V1m != fo__c_2Enum_2E0 ) )
& ! [V0n: tp__ty_2Enum_2Enum] :
( ( V0n = fo__c_2Enum_2E0 )
| ! [V1m: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( V1m = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(132,plain,
( ( ! [A_27a: del,V0t1: $i] :
( ~ ( mem @ V0t1 @ A_27a )
| ! [V1t2: $i] :
( ~ ( mem @ V1t2 @ A_27a )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
= V0t1 ) ) )
& ! [A_27a: del,V2t1: $i] :
( ~ ( mem @ V2t1 @ A_27a )
| ! [V3t2: $i] :
( ~ ( mem @ V3t2 @ A_27a )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ V3t2 )
= V3t2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(133,plain,
( ( ! [A_27a: del,V0P: $i] :
( ~ ( mem @ V0P @ bool )
| ! [V1Q: $i] :
( ~ ( mem @ V1Q @ bool )
| ! [V2x: $i] :
( ~ ( mem @ V2x @ A_27a )
| ! [V3x_27: $i] :
( ~ ( mem @ V3x_27 @ A_27a )
| ! [V4y: $i] :
( ~ ( mem @ V4y @ A_27a )
| ( ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ~ ( p @ V0P )
| ~ ( p @ V1Q )
| ( p @ V1Q )
| ~ ( p @ V1Q )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ~ ( p @ V0P )
| ~ ( p @ V1Q )
| ( V2x != V3x_27 )
| ~ ( p @ V1Q )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ( p @ V0P )
| ( p @ V1Q )
| ( p @ V1Q )
| ~ ( p @ V1Q )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ( p @ V0P )
| ( p @ V1Q )
| ( V2x != V3x_27 )
| ~ ( p @ V1Q )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ~ ( p @ V0P )
| ~ ( p @ V1Q )
| ( p @ V1Q )
| ( V4y != V5y_27 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ~ ( p @ V0P )
| ~ ( p @ V1Q )
| ( V2x != V3x_27 )
| ( V4y != V5y_27 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ( p @ V0P )
| ( p @ V1Q )
| ( p @ V1Q )
| ( V4y != V5y_27 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ( p @ V0P )
| ( p @ V1Q )
| ( V2x != V3x_27 )
| ( V4y != V5y_27 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(135,plain,
( ( ! [A_27a: del,V0x: $i] :
( ~ ( mem @ V0x @ A_27a )
| ( ! [V1y: $i] :
( ~ ( mem @ V1y @ A_27a )
| ( V0x != V1y )
| ( V1y = V0x ) )
& ! [V1y: $i] :
( ~ ( mem @ V1y @ A_27a )
| ( V1y != V0x )
| ( V0x = V1y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(139,plain,
( ( ! [A: del,X: $i] :
( ~ ( mem @ X @ A )
| ( ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ( X != Y )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) ) )
& ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
| ( X = Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(140,plain,
( ( ! [A: del,Q: $i] :
( ~ ( mem @ Q @ ( arr @ A @ bool ) )
| ( ( mem @ ( sK2_X @ Q @ A ) @ A )
& ~ ( p @ ( ap @ Q @ ( sK2_X @ Q @ A ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) ) )
& ! [A: del,Q: $i] :
( ~ ( mem @ Q @ ( arr @ A @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( p @ ( ap @ Q @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(141,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
| ~ ( p @ Q ) )
& ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( p @ Q )
| ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(142,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ ty_2Enum_2Enum )
| ( X
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(143,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ ty_2Einteger_2Eint )
| ( X
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(144,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ Q )
| ~ ( p @ R )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
| ( p @ Q ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
| ( p @ R ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(145,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
| ( p @ Q )
| ( p @ R ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ Q )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ R )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(146,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ( p @ Q )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ R )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
| ~ ( p @ Q )
| ( p @ R ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(147,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(148,plain,
( ( ! [A: del,B: del,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [G: $i] :
( ~ ( mem @ G @ ( arr @ A @ B ) )
| ( ( mem @ ( sK3_X @ G @ F @ B @ A ) @ A )
& ( ( ap @ F @ ( sK3_X @ G @ F @ B @ A ) )
!= ( ap @ G @ ( sK3_X @ G @ F @ B @ A ) ) ) )
| ( F = G ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(149,plain,
( ( ! [A: del,B: del,F: $i > $i] :
( ( ( mem @ ( sK4_X @ F @ B @ A ) @ A )
& ~ ( mem @ ( F @ ( sK4_X @ F @ B @ A ) ) @ B ) )
| ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(150,plain,
( ( ! [A: del,B: del,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(151,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ bool )
| ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(152,plain,
( ( ! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(153,plain,
( ( ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(154,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ bool )
| ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(155,plain,
( ( ! [A: del,B: del,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(156,plain,
( ( ! [A: del,B: del,F: $i > $i] :
( ( ( mem @ ( sK4_X @ F @ B @ A ) @ A )
& ~ ( mem @ ( F @ ( sK4_X @ F @ B @ A ) ) @ B ) )
| ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(157,plain,
( ( ! [A: del,B: del,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [G: $i] :
( ~ ( mem @ G @ ( arr @ A @ B ) )
| ( ( mem @ ( sK3_X @ G @ F @ B @ A ) @ A )
& ( ( ap @ F @ ( sK3_X @ G @ F @ B @ A ) )
!= ( ap @ G @ ( sK3_X @ G @ F @ B @ A ) ) ) )
| ( F = G ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(158,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(159,plain,
( ( mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(160,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ( p @ Q )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ R )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
| ~ ( p @ Q )
| ( p @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(161,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(162,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(163,plain,
( ( mem @ c_2Ebool_2EF @ bool )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(164,plain,
( ( ~ ( p @ c_2Ebool_2EF ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(165,plain,
( ( mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(166,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
| ( p @ Q )
| ( p @ R ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ Q )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ R )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(167,plain,
( ( mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(168,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ Q )
| ~ ( p @ R )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
| ( p @ Q ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
| ( p @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(169,plain,
( ( ! [X: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(170,plain,
( ( ! [X: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X ) @ ty_2Einteger_2Eint ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(171,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ ty_2Einteger_2Eint )
| ( X
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(172,plain,
( ( mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(173,plain,
( ( ! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X0 ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(174,plain,
( ( ! [X: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(175,plain,
( ( ! [X: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X ) @ ty_2Enum_2Enum ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(176,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ ty_2Enum_2Enum )
| ( X
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(177,plain,
( ( mem @ c_2Einteger_2ENum @ ( arr @ ty_2Einteger_2Eint @ ty_2Enum_2Enum ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(178,plain,
( ( ! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Einteger_2ENum @ X0 ) )
= ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(179,plain,
( ( mem @ c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(180,plain,
( ( ! [X0: tp__ty_2Enum_2Enum] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__of__num @ X0 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(181,plain,
( ( mem @ c_2Einteger_2Eint__lt @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(182,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ECOND @ A_27a ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(183,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( arr @ ty_2Einteger_2Eint @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(184,plain,
( ( mem @ c_2Eprim__rec_2E_3C @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(185,plain,
( ( mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(186,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
| ~ ( p @ Q ) )
& ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( p @ Q )
| ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(187,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(188,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ewords_2Edimword @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Enum_2Enum ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(189,plain,
( ( mem @ c_2Earithmetic_2EMOD @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(190,plain,
( ( ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EMOD @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(191,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(192,plain,
( ( ! [A: del,Q: $i] :
( ~ ( mem @ Q @ ( arr @ A @ bool ) )
| ( ( mem @ ( sK2_X @ Q @ A ) @ A )
& ~ ( p @ ( ap @ Q @ ( sK2_X @ Q @ A ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) ) )
& ! [A: del,Q: $i] :
( ~ ( mem @ Q @ ( arr @ A @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( p @ ( ap @ Q @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(193,plain,
( ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(194,plain,
( ( ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 )
= c_2Enum_2E0 )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(195,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ewords_2En2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(196,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(197,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(198,plain,
( ( ! [A: del,X: $i] :
( ~ ( mem @ X @ A )
| ( ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ( X != Y )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) ) )
& ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
| ( X = Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(203,plain,
( ( ! [A_27a: del,V0x: $i] :
( ~ ( mem @ V0x @ A_27a )
| ( ! [V1y: $i] :
( ~ ( mem @ V1y @ A_27a )
| ( V0x != V1y )
| ( V1y = V0x ) )
& ! [V1y: $i] :
( ~ ( mem @ V1y @ A_27a )
| ( V1y != V0x )
| ( V0x = V1y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(205,plain,
( ( ! [A_27a: del,V0P: $i] :
( ~ ( mem @ V0P @ bool )
| ! [V1Q: $i] :
( ~ ( mem @ V1Q @ bool )
| ! [V2x: $i] :
( ~ ( mem @ V2x @ A_27a )
| ! [V3x_27: $i] :
( ~ ( mem @ V3x_27 @ A_27a )
| ! [V4y: $i] :
( ~ ( mem @ V4y @ A_27a )
| ( ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ~ ( p @ V0P )
| ~ ( p @ V1Q )
| ( p @ V1Q )
| ~ ( p @ V1Q )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ~ ( p @ V0P )
| ~ ( p @ V1Q )
| ( V2x != V3x_27 )
| ~ ( p @ V1Q )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ( p @ V0P )
| ( p @ V1Q )
| ( p @ V1Q )
| ~ ( p @ V1Q )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ( p @ V0P )
| ( p @ V1Q )
| ( V2x != V3x_27 )
| ~ ( p @ V1Q )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ~ ( p @ V0P )
| ~ ( p @ V1Q )
| ( p @ V1Q )
| ( V4y != V5y_27 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ~ ( p @ V0P )
| ~ ( p @ V1Q )
| ( V2x != V3x_27 )
| ( V4y != V5y_27 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ( p @ V0P )
| ( p @ V1Q )
| ( p @ V1Q )
| ( V4y != V5y_27 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) )
& ! [V5y_27: $i] :
( ~ ( mem @ V5y_27 @ A_27a )
| ( p @ V0P )
| ( p @ V1Q )
| ( V2x != V3x_27 )
| ( V4y != V5y_27 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(206,plain,
( ( ! [A_27a: del,V0t1: $i] :
( ~ ( mem @ V0t1 @ A_27a )
| ! [V1t2: $i] :
( ~ ( mem @ V1t2 @ A_27a )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
= V0t1 ) ) )
& ! [A_27a: del,V2t1: $i] :
( ~ ( mem @ V2t1 @ A_27a )
| ! [V3t2: $i] :
( ~ ( mem @ V3t2 @ A_27a )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ V3t2 )
= V3t2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(207,plain,
( ( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(208,plain,
( ( ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
| ( V0n != fo__c_2Enum_2E0 )
| ( V1m != fo__c_2Enum_2E0 ) )
& ! [V0n: tp__ty_2Enum_2Enum] :
( ( V0n = fo__c_2Enum_2E0 )
| ! [V1m: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( V1m = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
& ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(209,plain,
( ( ! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= V0n ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(210,plain,
( ( ! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(211,plain,
( ( ! [V0n: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(212,plain,
( ( ! [A_27a: del] :
( ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) )
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) )
& ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
| ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(213,plain,
( ( ! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(214,plain,
( ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ sK1_A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
!= ( ap @ ( c_2Ewords_2En2w @ sK1_A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(215,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( SX1 != SX2 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(216,plain,
( ( ! [SX0: del,SX1: del,SX2: $i > $i] :
( ~ ( ~ ( mem @ ( sK4_X @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( mem @ ( SX2 @ ( sK4_X @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( mem @ ( lam @ SX0 @ SX2 ) @ ( arr @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(217,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( SX1 != SX2 )
| ( SX2 = SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( SX2 != SX1 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(218,plain,
( ( ~ ( ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ c_2Ebool_2ET ) @ SX1 ) @ SX2 )
= SX1 ) ) )
| ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ c_2Ebool_2EF ) @ SX1 ) @ SX2 )
= SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(220,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SX0 ) @ SX1 ) )
| ( p @ SX0 )
| ( p @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ SX0 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SX0 ) @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ SX1 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SX0 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(221,plain,
( ( ! [SX0: del] :
~ ( ~ ! [SX1: tp__ty_2Enum_2Enum,SX2: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ SX0 ) @ ( inj__ty_2Enum_2Enum @ SX1 ) )
!= ( ap @ ( c_2Ewords_2En2w @ SX0 ) @ ( inj__ty_2Enum_2Enum @ SX2 ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SX0 ) @ ( c_2Ebool_2Ethe__value @ SX0 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SX2 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SX0 ) @ ( c_2Ebool_2Ethe__value @ SX0 ) ) ) ) ) )
| ~ ! [SX1: tp__ty_2Enum_2Enum,SX2: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SX0 ) @ ( c_2Ebool_2Ethe__value @ SX0 ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SX2 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SX0 ) @ ( c_2Ebool_2Ethe__value @ SX0 ) ) ) ) )
| ( ( ap @ ( c_2Ewords_2En2w @ SX0 ) @ ( inj__ty_2Enum_2Enum @ SX1 ) )
= ( ap @ ( c_2Ewords_2En2w @ SX0 ) @ ( inj__ty_2Enum_2Enum @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(222,plain,
( ( ! [SX0: del,SX1: del,SX2: $i] :
( ~ ( mem @ SX2 @ ( arr @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( mem @ SX3 @ ( arr @ SX0 @ SX1 ) )
| ~ ( ~ ( mem @ ( sK3_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( ap @ SX2 @ ( sK3_X @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( ap @ SX3 @ ( sK3_X @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(223,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(224,plain,
( ( ~ ( ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( ~ ( mem @ ( sK2_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( p @ ( ap @ SX1 @ ( sK2_X @ SX1 @ SX0 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(225,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) )
| ~ ( p @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(227,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ( p @ SX0 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SX0 ) @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ SX1 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SX0 ) @ SX1 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SX0 ) @ SX1 ) )
| ~ ( p @ SX0 )
| ( p @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(228,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ bool )
| ! [SX3: $i] :
( ~ ( mem @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( mem @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( mem @ SX5 @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SX6: $i] :
( ~ ( mem @ SX6 @ SX0 )
| ~ ( p @ SX1 )
| ~ ( p @ SX2 )
| ( p @ SX2 )
| ~ ( p @ SX2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX1 ) @ SX3 ) @ SX5 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX2 ) @ SX4 ) @ SX6 ) ) )
| ~ ! [SX6: $i] :
( ~ ( mem @ SX6 @ SX0 )
| ~ ( p @ SX1 )
| ~ ( p @ SX2 )
| ( SX3 != SX4 )
| ~ ( p @ SX2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX1 ) @ SX3 ) @ SX5 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX2 ) @ SX4 ) @ SX6 ) ) ) )
| ~ ~ ( ~ ! [SX6: $i] :
( ~ ( mem @ SX6 @ SX0 )
| ( p @ SX1 )
| ( p @ SX2 )
| ( p @ SX2 )
| ~ ( p @ SX2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX1 ) @ SX3 ) @ SX5 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX2 ) @ SX4 ) @ SX6 ) ) )
| ~ ! [SX6: $i] :
( ~ ( mem @ SX6 @ SX0 )
| ( p @ SX1 )
| ( p @ SX2 )
| ( SX3 != SX4 )
| ~ ( p @ SX2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX1 ) @ SX3 ) @ SX5 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX2 ) @ SX4 ) @ SX6 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX6: $i] :
( ~ ( mem @ SX6 @ SX0 )
| ~ ( p @ SX1 )
| ~ ( p @ SX2 )
| ( p @ SX2 )
| ( SX5 != SX6 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX1 ) @ SX3 ) @ SX5 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX2 ) @ SX4 ) @ SX6 ) ) )
| ~ ! [SX6: $i] :
( ~ ( mem @ SX6 @ SX0 )
| ~ ( p @ SX1 )
| ~ ( p @ SX2 )
| ( SX3 != SX4 )
| ( SX5 != SX6 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX1 ) @ SX3 ) @ SX5 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX2 ) @ SX4 ) @ SX6 ) ) ) )
| ~ ~ ( ~ ! [SX6: $i] :
( ~ ( mem @ SX6 @ SX0 )
| ( p @ SX1 )
| ( p @ SX2 )
| ( p @ SX2 )
| ( SX5 != SX6 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX1 ) @ SX3 ) @ SX5 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX2 ) @ SX4 ) @ SX6 ) ) )
| ~ ! [SX6: $i] :
( ~ ( mem @ SX6 @ SX0 )
| ( p @ SX1 )
| ( p @ SX2 )
| ( SX3 != SX4 )
| ( SX5 != SX6 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX1 ) @ SX3 ) @ SX5 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ SX2 ) @ SX4 ) @ SX6 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(229,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ SX0 )
| ~ ( p @ SX1 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SX0 ) @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SX0 ) @ SX1 ) )
| ( p @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SX0 ) @ SX1 ) )
| ( p @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(230,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[152]) ).
thf(231,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[152]) ).
thf(232,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[152]) ).
thf(233,plain,
! [SV2: $o] :
( ( mem @ ( inj__o @ SV2 ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[153]) ).
thf(234,plain,
( ( mem @ ( inj__o @ $true ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[153]) ).
thf(235,plain,
( ( mem @ ( inj__o @ $false ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[153]) ).
thf(236,plain,
! [SV3: $i] :
( ( ~ ( mem @ SV3 @ bool )
| ( SV3
= ( inj__o @ ( p @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(237,plain,
! [SV4: del] :
( ( ! [SY85: del,SY86: $i] :
( ~ ( mem @ SY86 @ ( arr @ SV4 @ SY85 ) )
| ! [SY87: $i] :
( ~ ( mem @ SY87 @ SV4 )
| ( mem @ ( ap @ SY86 @ SY87 ) @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(238,plain,
! [SV5: del] :
( ( ! [SY88: $i > $i,SY89: $i] :
( ~ ( mem @ SY89 @ SV5 )
| ( ( ap @ ( lam @ SV5 @ SY88 ) @ SY89 )
= ( SY88 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(239,plain,
( ( p @ c_2Ebool_2EF )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(240,plain,
! [SV6: tp__ty_2Einteger_2Eint] :
( ( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ SV6 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(241,plain,
! [SV7: tp__ty_2Einteger_2Eint] :
( ( mem @ ( inj__ty_2Einteger_2Eint @ SV7 ) @ ty_2Einteger_2Eint )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(242,plain,
! [SV8: $i] :
( ( ~ ( mem @ SV8 @ ty_2Einteger_2Eint )
| ( SV8
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(243,plain,
! [SV9: tp__ty_2Einteger_2Eint] :
( ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ SV9 ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(244,plain,
! [SV10: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ SV10 ) )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(245,plain,
! [SV11: tp__ty_2Enum_2Enum] :
( ( mem @ ( inj__ty_2Enum_2Enum @ SV11 ) @ ty_2Enum_2Enum )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(246,plain,
! [SV12: $i] :
( ( ~ ( mem @ SV12 @ ty_2Enum_2Enum )
| ( SV12
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(247,plain,
! [SV13: tp__ty_2Einteger_2Eint] :
( ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Einteger_2ENum @ SV13 ) )
= ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(248,plain,
! [SV14: tp__ty_2Enum_2Enum] :
( ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__of__num @ SV14 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(249,plain,
! [SV15: del] :
( ( mem @ ( c_2Ebool_2ECOND @ SV15 ) @ ( arr @ bool @ ( arr @ SV15 @ ( arr @ SV15 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(250,plain,
! [SV16: del] :
( ( mem @ ( c_2Einteger__word_2Ei2w @ SV16 ) @ ( arr @ ty_2Einteger_2Eint @ ( ty_2Efcp_2Ecart @ bool @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(251,plain,
! [SV17: del] :
( ( mem @ ( c_2Ebool_2Ethe__value @ SV17 ) @ ( ty_2Ebool_2Eitself @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(252,plain,
! [SV18: del] :
( ( mem @ ( c_2Ewords_2Edimword @ SV18 ) @ ( arr @ ( ty_2Ebool_2Eitself @ SV18 ) @ ty_2Enum_2Enum ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(253,plain,
! [SV19: tp__ty_2Enum_2Enum] :
( ( ! [SY90: tp__ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EMOD @ SV19 @ SY90 ) )
= ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV19 ) ) @ ( inj__ty_2Enum_2Enum @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(254,plain,
! [SV20: del] :
( ( mem @ ( c_2Ebool_2E_21 @ SV20 ) @ ( arr @ ( arr @ SV20 @ bool ) @ bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(255,plain,
! [SV21: del] :
( ( mem @ ( c_2Ewords_2En2w @ SV21 ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(256,plain,
! [SV22: del] :
( ( mem @ ( c_2Ewords_2Eword__2comp @ SV22 ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ SV22 ) @ ( ty_2Efcp_2Ecart @ bool @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(257,plain,
! [SV23: del] :
( ( mem @ ( c_2Emin_2E_3D @ SV23 ) @ ( arr @ SV23 @ ( arr @ SV23 @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(260,plain,
! [SV24: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV24 ) ) ) )
= SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(261,plain,
! [SV25: del] :
( ( ! [SY91: tp__ty_2Einteger_2Eint] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ SV25 ) @ ( inj__ty_2Einteger_2Eint @ SY91 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ SV25 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ SY91 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ SV25 ) @ ( ap @ ( c_2Ewords_2En2w @ SV25 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ SY91 ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ SV25 ) @ ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ SY91 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(262,plain,
! [SV26: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV26 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(263,plain,
! [SV27: del] :
( ( ( ap @ ( c_2Ewords_2Eword__2comp @ SV27 ) @ ( ap @ ( c_2Ewords_2En2w @ SV27 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ SV27 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(264,plain,
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ sK1_A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ sK1_A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(265,plain,
! [SV28: del] :
( ( ! [SY92: $i] :
( ~ ( mem @ SY92 @ SV28 )
| ~ ( ~ ! [SY93: $i] :
( ~ ( mem @ SY93 @ SV28 )
| ( SY92 != SY93 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SY92 ) @ SY93 ) ) )
| ~ ! [SY94: $i] :
( ~ ( mem @ SY94 @ SV28 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SY92 ) @ SY94 ) )
| ( SY92 = SY94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(266,plain,
! [SV29: del] :
( ( ! [SY95: del,SY96: $i > $i] :
( ~ ( ~ ( mem @ ( sK4_X @ SY96 @ SY95 @ SV29 ) @ SV29 )
| ~ ~ ( mem @ ( SY96 @ ( sK4_X @ SY96 @ SY95 @ SV29 ) ) @ SY95 ) )
| ( mem @ ( lam @ SV29 @ SY96 ) @ ( arr @ SV29 @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(267,plain,
! [SV30: del] :
( ( ! [SY97: $i] :
( ~ ( mem @ SY97 @ SV30 )
| ~ ( ~ ! [SY98: $i] :
( ~ ( mem @ SY98 @ SV30 )
| ( SY97 != SY98 )
| ( SY98 = SY97 ) )
| ~ ! [SY99: $i] :
( ~ ( mem @ SY99 @ SV30 )
| ( SY99 != SY97 )
| ( SY97 = SY99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(268,plain,
( ( ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ c_2Ebool_2ET ) @ SX1 ) @ SX2 )
= SX1 ) ) )
| ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ c_2Ebool_2EF ) @ SX1 ) @ SX2 )
= SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(270,plain,
! [SV32: $i] :
( ( ~ ( mem @ SV32 @ bool )
| ~ ( ~ ! [SY108: $i] :
( ~ ( mem @ SY108 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY108 ) )
| ( p @ SV32 )
| ( p @ SY108 ) )
| ~ ~ ( ~ ! [SY109: $i] :
( ~ ( mem @ SY109 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( mem @ SY110 @ bool )
| ~ ( p @ SY110 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(271,plain,
! [SV33: del] :
( ( ~ ( ~ ! [SY111: tp__ty_2Enum_2Enum,SY112: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY111 ) )
!= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY112 ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY111 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY112 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) ) )
| ~ ! [SY113: tp__ty_2Enum_2Enum,SY114: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY113 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY114 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
| ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY113 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY114 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(272,plain,
! [SV34: del] :
( ( ! [SY115: del,SY116: $i] :
( ~ ( mem @ SY116 @ ( arr @ SV34 @ SY115 ) )
| ! [SY117: $i] :
( ~ ( mem @ SY117 @ ( arr @ SV34 @ SY115 ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY117 @ SY116 @ SY115 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SY116 @ ( sK3_X @ SY117 @ SY116 @ SY115 @ SV34 ) )
!= ( ap @ SY117 @ ( sK3_X @ SY117 @ SY116 @ SY115 @ SV34 ) ) ) ) )
| ( SY116 = SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(273,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(274,plain,
( ( ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( ~ ( mem @ ( sK2_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( p @ ( ap @ SX1 @ ( sK2_X @ SX1 @ SX0 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(275,plain,
( ( ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) )
| ~ ( p @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(277,plain,
! [SV36: $i] :
( ( ~ ( mem @ SV36 @ bool )
| ~ ( ~ ~ ( ~ ! [SY125: $i] :
( ~ ( mem @ SY125 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY125 ) ) )
| ~ ! [SY126: $i] :
( ~ ( mem @ SY126 @ bool )
| ~ ( p @ SY126 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY126 ) ) ) )
| ~ ! [SY127: $i] :
( ~ ( mem @ SY127 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY127 ) )
| ~ ( p @ SV36 )
| ( p @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(278,plain,
! [SV37: del] :
( ( ! [SY128: $i] :
( ~ ( mem @ SY128 @ bool )
| ! [SY129: $i] :
( ~ ( mem @ SY129 @ bool )
| ! [SY130: $i] :
( ~ ( mem @ SY130 @ SV37 )
| ! [SY131: $i] :
( ~ ( mem @ SY131 @ SV37 )
| ! [SY132: $i] :
( ~ ( mem @ SY132 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY133: $i] :
( ~ ( mem @ SY133 @ SV37 )
| ~ ( p @ SY128 )
| ~ ( p @ SY129 )
| ( p @ SY129 )
| ~ ( p @ SY129 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY128 ) @ SY130 ) @ SY132 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY129 ) @ SY131 ) @ SY133 ) ) )
| ~ ! [SY134: $i] :
( ~ ( mem @ SY134 @ SV37 )
| ~ ( p @ SY128 )
| ~ ( p @ SY129 )
| ( SY130 != SY131 )
| ~ ( p @ SY129 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY128 ) @ SY130 ) @ SY132 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY129 ) @ SY131 ) @ SY134 ) ) ) )
| ~ ~ ( ~ ! [SY135: $i] :
( ~ ( mem @ SY135 @ SV37 )
| ( p @ SY128 )
| ( p @ SY129 )
| ( p @ SY129 )
| ~ ( p @ SY129 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY128 ) @ SY130 ) @ SY132 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY129 ) @ SY131 ) @ SY135 ) ) )
| ~ ! [SY136: $i] :
( ~ ( mem @ SY136 @ SV37 )
| ( p @ SY128 )
| ( p @ SY129 )
| ( SY130 != SY131 )
| ~ ( p @ SY129 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY128 ) @ SY130 ) @ SY132 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY129 ) @ SY131 ) @ SY136 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY137: $i] :
( ~ ( mem @ SY137 @ SV37 )
| ~ ( p @ SY128 )
| ~ ( p @ SY129 )
| ( p @ SY129 )
| ( SY132 != SY137 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY128 ) @ SY130 ) @ SY132 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY129 ) @ SY131 ) @ SY137 ) ) )
| ~ ! [SY138: $i] :
( ~ ( mem @ SY138 @ SV37 )
| ~ ( p @ SY128 )
| ~ ( p @ SY129 )
| ( SY130 != SY131 )
| ( SY132 != SY138 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY128 ) @ SY130 ) @ SY132 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY129 ) @ SY131 ) @ SY138 ) ) ) )
| ~ ~ ( ~ ! [SY139: $i] :
( ~ ( mem @ SY139 @ SV37 )
| ( p @ SY128 )
| ( p @ SY129 )
| ( p @ SY129 )
| ( SY132 != SY139 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY128 ) @ SY130 ) @ SY132 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY129 ) @ SY131 ) @ SY139 ) ) )
| ~ ! [SY140: $i] :
( ~ ( mem @ SY140 @ SV37 )
| ( p @ SY128 )
| ( p @ SY129 )
| ( SY130 != SY131 )
| ( SY132 != SY140 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY128 ) @ SY130 ) @ SY132 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY129 ) @ SY131 ) @ SY140 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(279,plain,
! [SV38: $i] :
( ( ~ ( mem @ SV38 @ bool )
| ~ ( ~ ! [SY141: $i] :
( ~ ( mem @ SY141 @ bool )
| ~ ( p @ SV38 )
| ~ ( p @ SY141 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY141 ) ) )
| ~ ~ ( ~ ! [SY142: $i] :
( ~ ( mem @ SY142 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY142 ) )
| ( p @ SV38 ) )
| ~ ! [SY143: $i] :
( ~ ( mem @ SY143 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY143 ) )
| ( p @ SY143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(280,plain,
! [SV1: $o] :
( ( ~ ( ( p @ ( inj__o @ SV1 ) )
| SV1 )
| ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[230]) ).
thf(281,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[230]) ).
thf(282,plain,
( ( ~ ( ( p @ ( inj__o @ $true ) )
| $true )
| ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[231]) ).
thf(283,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[231]) ).
thf(284,plain,
( ( ~ ( ( p @ ( inj__o @ $false ) )
| $false )
| ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[232]) ).
thf(285,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[232]) ).
thf(286,plain,
! [SV3: $i] :
( ( ( ~ ( mem @ SV3 @ bool ) )
= $true )
| ( ( SV3
= ( inj__o @ ( p @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(287,plain,
! [SV39: del,SV4: del] :
( ( ! [SY144: $i] :
( ~ ( mem @ SY144 @ ( arr @ SV4 @ SV39 ) )
| ! [SY145: $i] :
( ~ ( mem @ SY145 @ SV4 )
| ( mem @ ( ap @ SY144 @ SY145 ) @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(288,plain,
! [SV40: $i > $i,SV5: del] :
( ( ! [SY146: $i] :
( ~ ( mem @ SY146 @ SV5 )
| ( ( ap @ ( lam @ SV5 @ SV40 ) @ SY146 )
= ( SV40 @ SY146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(289,plain,
! [SV8: $i] :
( ( ( ~ ( mem @ SV8 @ ty_2Einteger_2Eint ) )
= $true )
| ( ( SV8
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(290,plain,
! [SV12: $i] :
( ( ( ~ ( mem @ SV12 @ ty_2Enum_2Enum ) )
= $true )
| ( ( SV12
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(291,plain,
! [SV41: tp__ty_2Enum_2Enum,SV19: tp__ty_2Enum_2Enum] :
( ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EMOD @ SV19 @ SV41 ) )
= ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV19 ) ) @ ( inj__ty_2Enum_2Enum @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(294,plain,
! [SV44: tp__ty_2Einteger_2Eint,SV25: del] :
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ SV25 ) @ ( inj__ty_2Einteger_2Eint @ SV44 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ SV25 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ SV44 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ SV25 ) @ ( ap @ ( c_2Ewords_2En2w @ SV25 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ SV44 ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ SV25 ) @ ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(295,plain,
! [SV26: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV26 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(296,plain,
! [SV28: del,SV45: $i] :
( ( ~ ( mem @ SV45 @ SV28 )
| ~ ( ~ ! [SY148: $i] :
( ~ ( mem @ SY148 @ SV28 )
| ( SV45 != SY148 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY148 ) ) )
| ~ ! [SY149: $i] :
( ~ ( mem @ SY149 @ SV28 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY149 ) )
| ( SV45 = SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(297,plain,
! [SV29: del,SV46: del] :
( ( ! [SY150: $i > $i] :
( ~ ( ~ ( mem @ ( sK4_X @ SY150 @ SV46 @ SV29 ) @ SV29 )
| ~ ~ ( mem @ ( SY150 @ ( sK4_X @ SY150 @ SV46 @ SV29 ) ) @ SV46 ) )
| ( mem @ ( lam @ SV29 @ SY150 ) @ ( arr @ SV29 @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(298,plain,
! [SV30: del,SV47: $i] :
( ( ~ ( mem @ SV47 @ SV30 )
| ~ ( ~ ! [SY151: $i] :
( ~ ( mem @ SY151 @ SV30 )
| ( SV47 != SY151 )
| ( SY151 = SV47 ) )
| ~ ! [SY152: $i] :
( ~ ( mem @ SY152 @ SV30 )
| ( SY152 != SV47 )
| ( SV47 = SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(299,plain,
( ( ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ c_2Ebool_2ET ) @ SX1 ) @ SX2 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(300,plain,
( ( ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ c_2Ebool_2EF ) @ SX1 ) @ SX2 )
= SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(302,plain,
! [SV32: $i] :
( ( ( ~ ( mem @ SV32 @ bool ) )
= $true )
| ( ( ~ ( ~ ! [SY108: $i] :
( ~ ( mem @ SY108 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY108 ) )
| ( p @ SV32 )
| ( p @ SY108 ) )
| ~ ~ ( ~ ! [SY109: $i] :
( ~ ( mem @ SY109 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( mem @ SY110 @ bool )
| ~ ( p @ SY110 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY110 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(303,plain,
! [SV33: del] :
( ( ~ ! [SY111: tp__ty_2Enum_2Enum,SY112: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY111 ) )
!= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY112 ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY111 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY112 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) ) )
| ~ ! [SY113: tp__ty_2Enum_2Enum,SY114: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY113 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY114 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
| ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY113 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY114 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(304,plain,
! [SV48: del,SV34: del] :
( ( ! [SY153: $i] :
( ~ ( mem @ SY153 @ ( arr @ SV34 @ SV48 ) )
| ! [SY154: $i] :
( ~ ( mem @ SY154 @ ( arr @ SV34 @ SV48 ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY154 @ SY153 @ SV48 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SY153 @ ( sK3_X @ SY154 @ SY153 @ SV48 @ SV34 ) )
!= ( ap @ SY154 @ ( sK3_X @ SY154 @ SY153 @ SV48 @ SV34 ) ) ) ) )
| ( SY153 = SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(305,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(306,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(307,plain,
( ( ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( ~ ( mem @ ( sK2_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( p @ ( ap @ SX1 @ ( sK2_X @ SX1 @ SX0 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(308,plain,
( ( ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(309,plain,
( ( ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) )
| ~ ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(310,plain,
( ( ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(312,plain,
! [SV36: $i] :
( ( ( ~ ( mem @ SV36 @ bool ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY125: $i] :
( ~ ( mem @ SY125 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY125 ) ) )
| ~ ! [SY126: $i] :
( ~ ( mem @ SY126 @ bool )
| ~ ( p @ SY126 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY126 ) ) ) )
| ~ ! [SY127: $i] :
( ~ ( mem @ SY127 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY127 ) )
| ~ ( p @ SV36 )
| ( p @ SY127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(313,plain,
! [SV37: del,SV49: $i] :
( ( ~ ( mem @ SV49 @ bool )
| ! [SY155: $i] :
( ~ ( mem @ SY155 @ bool )
| ! [SY156: $i] :
( ~ ( mem @ SY156 @ SV37 )
| ! [SY157: $i] :
( ~ ( mem @ SY157 @ SV37 )
| ! [SY158: $i] :
( ~ ( mem @ SY158 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY159: $i] :
( ~ ( mem @ SY159 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( p @ SY155 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY159 ) ) )
| ~ ! [SY160: $i] :
( ~ ( mem @ SY160 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( SY156 != SY157 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY160 ) ) ) )
| ~ ~ ( ~ ! [SY161: $i] :
( ~ ( mem @ SY161 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( p @ SY155 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY161 ) ) )
| ~ ! [SY162: $i] :
( ~ ( mem @ SY162 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( SY156 != SY157 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY162 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY163: $i] :
( ~ ( mem @ SY163 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( p @ SY155 )
| ( SY158 != SY163 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY163 ) ) )
| ~ ! [SY164: $i] :
( ~ ( mem @ SY164 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( SY156 != SY157 )
| ( SY158 != SY164 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY164 ) ) ) )
| ~ ~ ( ~ ! [SY165: $i] :
( ~ ( mem @ SY165 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( p @ SY155 )
| ( SY158 != SY165 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY165 ) ) )
| ~ ! [SY166: $i] :
( ~ ( mem @ SY166 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( SY156 != SY157 )
| ( SY158 != SY166 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY166 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(314,plain,
! [SV38: $i] :
( ( ( ~ ( mem @ SV38 @ bool ) )
= $true )
| ( ( ~ ( ~ ! [SY141: $i] :
( ~ ( mem @ SY141 @ bool )
| ~ ( p @ SV38 )
| ~ ( p @ SY141 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY141 ) ) )
| ~ ~ ( ~ ! [SY142: $i] :
( ~ ( mem @ SY142 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY142 ) )
| ( p @ SV38 ) )
| ~ ! [SY143: $i] :
( ~ ( mem @ SY143 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY143 ) )
| ( p @ SY143 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(315,plain,
! [SV1: $o] :
( ( ( ~ ( ( p @ ( inj__o @ SV1 ) )
| SV1 ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(316,plain,
( ( ( ~ ( ( p @ ( inj__o @ $true ) )
| $true ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(317,plain,
( ( ( ~ ( ( p @ ( inj__o @ $false ) )
| $false ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(318,plain,
! [SV3: $i] :
( ( ( mem @ SV3 @ bool )
= $false )
| ( ( SV3
= ( inj__o @ ( p @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(319,plain,
! [SV39: del,SV4: del,SV50: $i] :
( ( ~ ( mem @ SV50 @ ( arr @ SV4 @ SV39 ) )
| ! [SY167: $i] :
( ~ ( mem @ SY167 @ SV4 )
| ( mem @ ( ap @ SV50 @ SY167 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(320,plain,
! [SV40: $i > $i,SV5: del,SV51: $i] :
( ( ~ ( mem @ SV51 @ SV5 )
| ( ( ap @ ( lam @ SV5 @ SV40 ) @ SV51 )
= ( SV40 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(321,plain,
! [SV8: $i] :
( ( ( mem @ SV8 @ ty_2Einteger_2Eint )
= $false )
| ( ( SV8
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(322,plain,
! [SV12: $i] :
( ( ( mem @ SV12 @ ty_2Enum_2Enum )
= $false )
| ( ( SV12
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(325,plain,
! [SV28: del,SV45: $i] :
( ( ( ~ ( mem @ SV45 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY148: $i] :
( ~ ( mem @ SY148 @ SV28 )
| ( SV45 != SY148 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY148 ) ) )
| ~ ! [SY149: $i] :
( ~ ( mem @ SY149 @ SV28 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY149 ) )
| ( SV45 = SY149 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(326,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ~ ( ~ ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
| ~ ~ ( mem @ ( SV53 @ ( sK4_X @ SV53 @ SV46 @ SV29 ) ) @ SV46 ) )
| ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(327,plain,
! [SV30: del,SV47: $i] :
( ( ( ~ ( mem @ SV47 @ SV30 ) )
= $true )
| ( ( ~ ( ~ ! [SY151: $i] :
( ~ ( mem @ SY151 @ SV30 )
| ( SV47 != SY151 )
| ( SY151 = SV47 ) )
| ~ ! [SY152: $i] :
( ~ ( mem @ SY152 @ SV30 )
| ( SY152 != SV47 )
| ( SV47 = SY152 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(328,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ c_2Ebool_2ET ) @ SX1 ) @ SX2 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(329,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SX0 ) @ c_2Ebool_2EF ) @ SX1 ) @ SX2 )
= SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(331,plain,
! [SV32: $i] :
( ( ( mem @ SV32 @ bool )
= $false )
| ( ( ~ ( ~ ! [SY108: $i] :
( ~ ( mem @ SY108 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY108 ) )
| ( p @ SV32 )
| ( p @ SY108 ) )
| ~ ~ ( ~ ! [SY109: $i] :
( ~ ( mem @ SY109 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( mem @ SY110 @ bool )
| ~ ( p @ SY110 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY110 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(332,plain,
! [SV33: del] :
( ( ~ ! [SY111: tp__ty_2Enum_2Enum,SY112: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY111 ) )
!= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY112 ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY111 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY112 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(333,plain,
! [SV33: del] :
( ( ~ ! [SY113: tp__ty_2Enum_2Enum,SY114: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY113 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY114 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
| ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY113 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY114 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(334,plain,
! [SV48: del,SV34: del,SV54: $i] :
( ( ~ ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
| ! [SY168: $i] :
( ~ ( mem @ SY168 @ ( arr @ SV34 @ SV48 ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY168 @ SV54 @ SV48 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SV54 @ ( sK3_X @ SY168 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SY168 @ ( sK3_X @ SY168 @ SV54 @ SV48 @ SV34 ) ) ) ) )
| ( SV54 = SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(335,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(336,plain,
( ( ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(337,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( ~ ( mem @ ( sK2_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( p @ ( ap @ SX1 @ ( sK2_X @ SX1 @ SX0 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(338,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(339,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) )
| ~ ( p @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(340,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(342,plain,
! [SV36: $i] :
( ( ( mem @ SV36 @ bool )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY125: $i] :
( ~ ( mem @ SY125 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY125 ) ) )
| ~ ! [SY126: $i] :
( ~ ( mem @ SY126 @ bool )
| ~ ( p @ SY126 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY126 ) ) ) )
| ~ ! [SY127: $i] :
( ~ ( mem @ SY127 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY127 ) )
| ~ ( p @ SV36 )
| ( p @ SY127 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(343,plain,
! [SV37: del,SV49: $i] :
( ( ( ~ ( mem @ SV49 @ bool ) )
= $true )
| ( ( ! [SY155: $i] :
( ~ ( mem @ SY155 @ bool )
| ! [SY156: $i] :
( ~ ( mem @ SY156 @ SV37 )
| ! [SY157: $i] :
( ~ ( mem @ SY157 @ SV37 )
| ! [SY158: $i] :
( ~ ( mem @ SY158 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY159: $i] :
( ~ ( mem @ SY159 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( p @ SY155 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY159 ) ) )
| ~ ! [SY160: $i] :
( ~ ( mem @ SY160 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( SY156 != SY157 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY160 ) ) ) )
| ~ ~ ( ~ ! [SY161: $i] :
( ~ ( mem @ SY161 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( p @ SY155 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY161 ) ) )
| ~ ! [SY162: $i] :
( ~ ( mem @ SY162 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( SY156 != SY157 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY162 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY163: $i] :
( ~ ( mem @ SY163 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( p @ SY155 )
| ( SY158 != SY163 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY163 ) ) )
| ~ ! [SY164: $i] :
( ~ ( mem @ SY164 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( SY156 != SY157 )
| ( SY158 != SY164 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY164 ) ) ) )
| ~ ~ ( ~ ! [SY165: $i] :
( ~ ( mem @ SY165 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( p @ SY155 )
| ( SY158 != SY165 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY165 ) ) )
| ~ ! [SY166: $i] :
( ~ ( mem @ SY166 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( SY156 != SY157 )
| ( SY158 != SY166 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY166 ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(344,plain,
! [SV38: $i] :
( ( ( mem @ SV38 @ bool )
= $false )
| ( ( ~ ( ~ ! [SY141: $i] :
( ~ ( mem @ SY141 @ bool )
| ~ ( p @ SV38 )
| ~ ( p @ SY141 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY141 ) ) )
| ~ ~ ( ~ ! [SY142: $i] :
( ~ ( mem @ SY142 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY142 ) )
| ( p @ SV38 ) )
| ~ ! [SY143: $i] :
( ~ ( mem @ SY143 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY143 ) )
| ( p @ SY143 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(345,plain,
! [SV1: $o] :
( ( ( ( p @ ( inj__o @ SV1 ) )
| SV1 )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(346,plain,
( ( ( ( p @ ( inj__o @ $true ) )
| $true )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(347,plain,
( ( ( ( p @ ( inj__o @ $false ) )
| $false )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(348,plain,
! [SV39: del,SV4: del,SV50: $i] :
( ( ( ~ ( mem @ SV50 @ ( arr @ SV4 @ SV39 ) ) )
= $true )
| ( ( ! [SY167: $i] :
( ~ ( mem @ SY167 @ SV4 )
| ( mem @ ( ap @ SV50 @ SY167 ) @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(349,plain,
! [SV40: $i > $i,SV5: del,SV51: $i] :
( ( ( ~ ( mem @ SV51 @ SV5 ) )
= $true )
| ( ( ( ap @ ( lam @ SV5 @ SV40 ) @ SV51 )
= ( SV40 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(351,plain,
! [SV28: del,SV45: $i] :
( ( ( mem @ SV45 @ SV28 )
= $false )
| ( ( ~ ( ~ ! [SY148: $i] :
( ~ ( mem @ SY148 @ SV28 )
| ( SV45 != SY148 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY148 ) ) )
| ~ ! [SY149: $i] :
( ~ ( mem @ SY149 @ SV28 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY149 ) )
| ( SV45 = SY149 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(352,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( ~ ( ~ ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
| ~ ~ ( mem @ ( SV53 @ ( sK4_X @ SV53 @ SV46 @ SV29 ) ) @ SV46 ) ) )
= $true )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(353,plain,
! [SV30: del,SV47: $i] :
( ( ( mem @ SV47 @ SV30 )
= $false )
| ( ( ~ ( ~ ! [SY151: $i] :
( ~ ( mem @ SY151 @ SV30 )
| ( SV47 != SY151 )
| ( SY151 = SV47 ) )
| ~ ! [SY152: $i] :
( ~ ( mem @ SY152 @ SV30 )
| ( SY152 != SV47 )
| ( SV47 = SY152 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(354,plain,
! [SV55: del] :
( ( ! [SY169: $i] :
( ~ ( mem @ SY169 @ SV55 )
| ! [SY170: $i] :
( ~ ( mem @ SY170 @ SV55 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV55 ) @ c_2Ebool_2ET ) @ SY169 ) @ SY170 )
= SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(355,plain,
! [SV56: del] :
( ( ! [SY171: $i] :
( ~ ( mem @ SY171 @ SV56 )
| ! [SY172: $i] :
( ~ ( mem @ SY172 @ SV56 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV56 ) @ c_2Ebool_2EF ) @ SY171 ) @ SY172 )
= SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(357,plain,
! [SV32: $i] :
( ( ( ~ ! [SY108: $i] :
( ~ ( mem @ SY108 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY108 ) )
| ( p @ SV32 )
| ( p @ SY108 ) )
| ~ ~ ( ~ ! [SY109: $i] :
( ~ ( mem @ SY109 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( mem @ SY110 @ bool )
| ~ ( p @ SY110 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY110 ) ) ) ) )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(358,plain,
! [SV33: del] :
( ( ! [SY111: tp__ty_2Enum_2Enum,SY112: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY111 ) )
!= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY112 ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY111 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY112 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(359,plain,
! [SV33: del] :
( ( ! [SY113: tp__ty_2Enum_2Enum,SY114: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY113 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY114 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
| ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY113 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY114 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(360,plain,
! [SV48: del,SV34: del,SV54: $i] :
( ( ( ~ ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) ) )
= $true )
| ( ( ! [SY168: $i] :
( ~ ( mem @ SY168 @ ( arr @ SV34 @ SV48 ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY168 @ SV54 @ SV48 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SV54 @ ( sK3_X @ SY168 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SY168 @ ( sK3_X @ SY168 @ SV54 @ SV48 @ SV34 ) ) ) ) )
| ( SV54 = SY168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(361,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(362,plain,
! [SV57: tp__ty_2Enum_2Enum] :
( ( ! [SY173: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV57 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SY173 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(363,plain,
! [SV58: del] :
( ( ! [SY174: $i] :
( ~ ( mem @ SY174 @ ( arr @ SV58 @ bool ) )
| ~ ( ~ ( mem @ ( sK2_X @ SY174 @ SV58 ) @ SV58 )
| ~ ~ ( p @ ( ap @ SY174 @ ( sK2_X @ SY174 @ SV58 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(364,plain,
! [SV59: del] :
( ( ! [SY175: $i] :
( ~ ( mem @ SY175 @ ( arr @ SV59 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV59 ) @ SY175 ) )
| ! [SY176: $i] :
( ~ ( mem @ SY176 @ SV59 )
| ( p @ ( ap @ SY175 @ SY176 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(365,plain,
! [SV60: $i] :
( ( ~ ( mem @ SV60 @ bool )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV60 ) )
| ~ ( p @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(366,plain,
! [SV61: $i] :
( ( ~ ( mem @ SV61 @ bool )
| ( p @ SV61 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(368,plain,
! [SV36: $i] :
( ( ( ~ ~ ( ~ ! [SY125: $i] :
( ~ ( mem @ SY125 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY125 ) ) )
| ~ ! [SY126: $i] :
( ~ ( mem @ SY126 @ bool )
| ~ ( p @ SY126 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY126 ) ) ) )
| ~ ! [SY127: $i] :
( ~ ( mem @ SY127 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY127 ) )
| ~ ( p @ SV36 )
| ( p @ SY127 ) ) )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(369,plain,
! [SV37: del,SV49: $i] :
( ( ( mem @ SV49 @ bool )
= $false )
| ( ( ! [SY155: $i] :
( ~ ( mem @ SY155 @ bool )
| ! [SY156: $i] :
( ~ ( mem @ SY156 @ SV37 )
| ! [SY157: $i] :
( ~ ( mem @ SY157 @ SV37 )
| ! [SY158: $i] :
( ~ ( mem @ SY158 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY159: $i] :
( ~ ( mem @ SY159 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( p @ SY155 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY159 ) ) )
| ~ ! [SY160: $i] :
( ~ ( mem @ SY160 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( SY156 != SY157 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY160 ) ) ) )
| ~ ~ ( ~ ! [SY161: $i] :
( ~ ( mem @ SY161 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( p @ SY155 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY161 ) ) )
| ~ ! [SY162: $i] :
( ~ ( mem @ SY162 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( SY156 != SY157 )
| ~ ( p @ SY155 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY162 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY163: $i] :
( ~ ( mem @ SY163 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( p @ SY155 )
| ( SY158 != SY163 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY163 ) ) )
| ~ ! [SY164: $i] :
( ~ ( mem @ SY164 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SY155 )
| ( SY156 != SY157 )
| ( SY158 != SY164 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY164 ) ) ) )
| ~ ~ ( ~ ! [SY165: $i] :
( ~ ( mem @ SY165 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( p @ SY155 )
| ( SY158 != SY165 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY165 ) ) )
| ~ ! [SY166: $i] :
( ~ ( mem @ SY166 @ SV37 )
| ( p @ SV49 )
| ( p @ SY155 )
| ( SY156 != SY157 )
| ( SY158 != SY166 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY156 ) @ SY158 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SY155 ) @ SY157 ) @ SY166 ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(370,plain,
! [SV38: $i] :
( ( ( ~ ! [SY141: $i] :
( ~ ( mem @ SY141 @ bool )
| ~ ( p @ SV38 )
| ~ ( p @ SY141 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY141 ) ) )
| ~ ~ ( ~ ! [SY142: $i] :
( ~ ( mem @ SY142 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY142 ) )
| ( p @ SV38 ) )
| ~ ! [SY143: $i] :
( ~ ( mem @ SY143 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY143 ) )
| ( p @ SY143 ) ) ) )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(371,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(372,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(374,plain,
( ( $true = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(375,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(377,plain,
! [SV39: del,SV4: del,SV50: $i] :
( ( ( mem @ SV50 @ ( arr @ SV4 @ SV39 ) )
= $false )
| ( ( ! [SY167: $i] :
( ~ ( mem @ SY167 @ SV4 )
| ( mem @ ( ap @ SV50 @ SY167 ) @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(378,plain,
! [SV40: $i > $i,SV5: del,SV51: $i] :
( ( ( mem @ SV51 @ SV5 )
= $false )
| ( ( ( ap @ ( lam @ SV5 @ SV40 ) @ SV51 )
= ( SV40 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(379,plain,
! [SV45: $i,SV28: del] :
( ( ( ~ ! [SY148: $i] :
( ~ ( mem @ SY148 @ SV28 )
| ( SV45 != SY148 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY148 ) ) )
| ~ ! [SY149: $i] :
( ~ ( mem @ SY149 @ SV28 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY149 ) )
| ( SV45 = SY149 ) ) )
= $false )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(380,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( ~ ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
| ~ ~ ( mem @ ( SV53 @ ( sK4_X @ SV53 @ SV46 @ SV29 ) ) @ SV46 ) )
= $false )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(381,plain,
! [SV47: $i,SV30: del] :
( ( ( ~ ! [SY151: $i] :
( ~ ( mem @ SY151 @ SV30 )
| ( SV47 != SY151 )
| ( SY151 = SV47 ) )
| ~ ! [SY152: $i] :
( ~ ( mem @ SY152 @ SV30 )
| ( SY152 != SV47 )
| ( SV47 = SY152 ) ) )
= $false )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(382,plain,
! [SV55: del,SV63: $i] :
( ( ~ ( mem @ SV63 @ SV55 )
| ! [SY183: $i] :
( ~ ( mem @ SY183 @ SV55 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV55 ) @ c_2Ebool_2ET ) @ SV63 ) @ SY183 )
= SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(383,plain,
! [SV56: del,SV64: $i] :
( ( ~ ( mem @ SV64 @ SV56 )
| ! [SY184: $i] :
( ~ ( mem @ SY184 @ SV56 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV56 ) @ c_2Ebool_2EF ) @ SV64 ) @ SY184 )
= SY184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(386,plain,
! [SV32: $i] :
( ( ( ~ ! [SY108: $i] :
( ~ ( mem @ SY108 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY108 ) )
| ( p @ SV32 )
| ( p @ SY108 ) ) )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(387,plain,
! [SV32: $i] :
( ( ( ~ ~ ( ~ ! [SY109: $i] :
( ~ ( mem @ SY109 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( mem @ SY110 @ bool )
| ~ ( p @ SY110 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY110 ) ) ) ) )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(388,plain,
! [SV65: tp__ty_2Enum_2Enum,SV33: del] :
( ( ! [SY185: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV65 ) )
!= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY185 ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV65 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY185 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(389,plain,
! [SV33: del,SV66: tp__ty_2Enum_2Enum] :
( ( ! [SY186: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV66 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SY186 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
| ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV66 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SY186 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(390,plain,
! [SV48: del,SV34: del,SV54: $i] :
( ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false )
| ( ( ! [SY168: $i] :
( ~ ( mem @ SY168 @ ( arr @ SV34 @ SV48 ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY168 @ SV54 @ SV48 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SV54 @ ( sK3_X @ SY168 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SY168 @ ( sK3_X @ SY168 @ SV54 @ SV48 @ SV34 ) ) ) ) )
| ( SV54 = SY168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(391,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(392,plain,
( ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(393,plain,
! [SV67: tp__ty_2Enum_2Enum,SV57: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV57 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV67 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(394,plain,
! [SV58: del,SV68: $i] :
( ( ~ ( mem @ SV68 @ ( arr @ SV58 @ bool ) )
| ~ ( ~ ( mem @ ( sK2_X @ SV68 @ SV58 ) @ SV58 )
| ~ ~ ( p @ ( ap @ SV68 @ ( sK2_X @ SV68 @ SV58 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(395,plain,
! [SV59: del,SV69: $i] :
( ( ~ ( mem @ SV69 @ ( arr @ SV59 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV59 ) @ SV69 ) )
| ! [SY187: $i] :
( ~ ( mem @ SY187 @ SV59 )
| ( p @ ( ap @ SV69 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(396,plain,
! [SV60: $i] :
( ( ( ~ ( mem @ SV60 @ bool ) )
= $true )
| ( ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV60 ) )
| ~ ( p @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(397,plain,
! [SV61: $i] :
( ( ( ~ ( mem @ SV61 @ bool ) )
= $true )
| ( ( ( p @ SV61 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(399,plain,
! [SV36: $i] :
( ( ( ~ ~ ( ~ ! [SY125: $i] :
( ~ ( mem @ SY125 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY125 ) ) )
| ~ ! [SY126: $i] :
( ~ ( mem @ SY126 @ bool )
| ~ ( p @ SY126 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY126 ) ) ) ) )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(400,plain,
! [SV36: $i] :
( ( ( ~ ! [SY127: $i] :
( ~ ( mem @ SY127 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY127 ) )
| ~ ( p @ SV36 )
| ( p @ SY127 ) ) )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(401,plain,
! [SV49: $i,SV37: del,SV70: $i] :
( ( ( ~ ( mem @ SV70 @ bool )
| ! [SY188: $i] :
( ~ ( mem @ SY188 @ SV37 )
| ! [SY189: $i] :
( ~ ( mem @ SY189 @ SV37 )
| ! [SY190: $i] :
( ~ ( mem @ SY190 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY191: $i] :
( ~ ( mem @ SY191 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY191 ) ) )
| ~ ! [SY192: $i] :
( ~ ( mem @ SY192 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SY188 != SY189 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY192 ) ) ) )
| ~ ~ ( ~ ! [SY193: $i] :
( ~ ( mem @ SY193 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY193 ) ) )
| ~ ! [SY194: $i] :
( ~ ( mem @ SY194 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SY188 != SY189 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY194 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY195: $i] :
( ~ ( mem @ SY195 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SY190 != SY195 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY195 ) ) )
| ~ ! [SY196: $i] :
( ~ ( mem @ SY196 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SY188 != SY189 )
| ( SY190 != SY196 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY196 ) ) ) )
| ~ ~ ( ~ ! [SY197: $i] :
( ~ ( mem @ SY197 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SY190 != SY197 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY197 ) ) )
| ~ ! [SY198: $i] :
( ~ ( mem @ SY198 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SY188 != SY189 )
| ( SY190 != SY198 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY198 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(402,plain,
! [SV38: $i] :
( ( ( ~ ! [SY141: $i] :
( ~ ( mem @ SY141 @ bool )
| ~ ( p @ SV38 )
| ~ ( p @ SY141 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY141 ) ) ) )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(403,plain,
! [SV38: $i] :
( ( ( ~ ~ ( ~ ! [SY142: $i] :
( ~ ( mem @ SY142 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY142 ) )
| ( p @ SV38 ) )
| ~ ! [SY143: $i] :
( ~ ( mem @ SY143 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY143 ) )
| ( p @ SY143 ) ) ) )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(404,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 )
= $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(405,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(407,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true )
= $false )
| ( $true = $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(408,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false )
= $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(410,plain,
! [SV39: del,SV50: $i,SV4: del,SV71: $i] :
( ( ( ~ ( mem @ SV71 @ SV4 )
| ( mem @ ( ap @ SV50 @ SV71 ) @ SV39 ) )
= $true )
| ( ( mem @ SV50 @ ( arr @ SV4 @ SV39 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(411,plain,
! [SV45: $i,SV28: del] :
( ( ( ~ ! [SY148: $i] :
( ~ ( mem @ SY148 @ SV28 )
| ( SV45 != SY148 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY148 ) ) ) )
= $false )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(412,plain,
! [SV45: $i,SV28: del] :
( ( ( ~ ! [SY149: $i] :
( ~ ( mem @ SY149 @ SV28 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY149 ) )
| ( SV45 = SY149 ) ) )
= $false )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(413,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( ~ ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 ) )
= $false )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(414,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( ~ ~ ( mem @ ( SV53 @ ( sK4_X @ SV53 @ SV46 @ SV29 ) ) @ SV46 ) )
= $false )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(415,plain,
! [SV47: $i,SV30: del] :
( ( ( ~ ! [SY151: $i] :
( ~ ( mem @ SY151 @ SV30 )
| ( SV47 != SY151 )
| ( SY151 = SV47 ) ) )
= $false )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(416,plain,
! [SV47: $i,SV30: del] :
( ( ( ~ ! [SY152: $i] :
( ~ ( mem @ SY152 @ SV30 )
| ( SY152 != SV47 )
| ( SV47 = SY152 ) ) )
= $false )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(417,plain,
! [SV55: del,SV63: $i] :
( ( ( ~ ( mem @ SV63 @ SV55 ) )
= $true )
| ( ( ! [SY183: $i] :
( ~ ( mem @ SY183 @ SV55 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV55 ) @ c_2Ebool_2ET ) @ SV63 ) @ SY183 )
= SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(418,plain,
! [SV56: del,SV64: $i] :
( ( ( ~ ( mem @ SV64 @ SV56 ) )
= $true )
| ( ( ! [SY184: $i] :
( ~ ( mem @ SY184 @ SV56 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV56 ) @ c_2Ebool_2EF ) @ SV64 ) @ SY184 )
= SY184 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(421,plain,
! [SV32: $i] :
( ( ( ! [SY108: $i] :
( ~ ( mem @ SY108 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY108 ) )
| ( p @ SV32 )
| ( p @ SY108 ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(422,plain,
! [SV32: $i] :
( ( ( ~ ( ~ ! [SY109: $i] :
( ~ ( mem @ SY109 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( mem @ SY110 @ bool )
| ~ ( p @ SY110 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY110 ) ) ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(423,plain,
! [SV72: tp__ty_2Enum_2Enum,SV65: tp__ty_2Enum_2Enum,SV33: del] :
( ( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV65 ) )
!= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV72 ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV65 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV72 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(424,plain,
! [SV73: tp__ty_2Enum_2Enum,SV33: del,SV66: tp__ty_2Enum_2Enum] :
( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV66 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV73 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
| ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV66 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(425,plain,
! [SV54: $i,SV48: del,SV34: del,SV74: $i] :
( ( ( ~ ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) )
| ~ ( ~ ( mem @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SV54 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SV74 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) ) ) ) )
| ( SV54 = SV74 ) )
= $true )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(426,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(427,plain,
( ( ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(428,plain,
! [SV67: tp__ty_2Enum_2Enum,SV57: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV57 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV67 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(429,plain,
! [SV58: del,SV68: $i] :
( ( ( ~ ( mem @ SV68 @ ( arr @ SV58 @ bool ) ) )
= $true )
| ( ( ~ ( ~ ( mem @ ( sK2_X @ SV68 @ SV58 ) @ SV58 )
| ~ ~ ( p @ ( ap @ SV68 @ ( sK2_X @ SV68 @ SV58 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(430,plain,
! [SV59: del,SV69: $i] :
( ( ( ~ ( mem @ SV69 @ ( arr @ SV59 @ bool ) ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV59 ) @ SV69 ) )
| ! [SY187: $i] :
( ~ ( mem @ SY187 @ SV59 )
| ( p @ ( ap @ SV69 @ SY187 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(431,plain,
! [SV60: $i] :
( ( ( mem @ SV60 @ bool )
= $false )
| ( ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV60 ) )
| ~ ( p @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(432,plain,
! [SV61: $i] :
( ( ( mem @ SV61 @ bool )
= $false )
| ( ( ( p @ SV61 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(434,plain,
! [SV36: $i] :
( ( ( ~ ( ~ ! [SY125: $i] :
( ~ ( mem @ SY125 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY125 ) ) )
| ~ ! [SY126: $i] :
( ~ ( mem @ SY126 @ bool )
| ~ ( p @ SY126 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY126 ) ) ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(435,plain,
! [SV36: $i] :
( ( ( ! [SY127: $i] :
( ~ ( mem @ SY127 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY127 ) )
| ~ ( p @ SV36 )
| ( p @ SY127 ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(436,plain,
! [SV49: $i,SV37: del,SV70: $i] :
( ( ( ~ ( mem @ SV70 @ bool ) )
= $true )
| ( ( ! [SY188: $i] :
( ~ ( mem @ SY188 @ SV37 )
| ! [SY189: $i] :
( ~ ( mem @ SY189 @ SV37 )
| ! [SY190: $i] :
( ~ ( mem @ SY190 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY191: $i] :
( ~ ( mem @ SY191 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY191 ) ) )
| ~ ! [SY192: $i] :
( ~ ( mem @ SY192 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SY188 != SY189 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY192 ) ) ) )
| ~ ~ ( ~ ! [SY193: $i] :
( ~ ( mem @ SY193 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY193 ) ) )
| ~ ! [SY194: $i] :
( ~ ( mem @ SY194 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SY188 != SY189 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY194 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY195: $i] :
( ~ ( mem @ SY195 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SY190 != SY195 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY195 ) ) )
| ~ ! [SY196: $i] :
( ~ ( mem @ SY196 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SY188 != SY189 )
| ( SY190 != SY196 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY196 ) ) ) )
| ~ ~ ( ~ ! [SY197: $i] :
( ~ ( mem @ SY197 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SY190 != SY197 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY197 ) ) )
| ~ ! [SY198: $i] :
( ~ ( mem @ SY198 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SY188 != SY189 )
| ( SY190 != SY198 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY198 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(437,plain,
! [SV38: $i] :
( ( ( ! [SY141: $i] :
( ~ ( mem @ SY141 @ bool )
| ~ ( p @ SV38 )
| ~ ( p @ SY141 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY141 ) ) ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(438,plain,
! [SV38: $i] :
( ( ( ~ ( ~ ! [SY142: $i] :
( ~ ( mem @ SY142 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY142 ) )
| ( p @ SV38 ) )
| ~ ! [SY143: $i] :
( ~ ( mem @ SY143 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY143 ) )
| ( p @ SY143 ) ) ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(440,plain,
! [SV1: $o] :
( ( ( ~ SV1 )
= $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(441,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) ) )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(445,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) ) )
= $false )
| ( $true = $false ) ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(448,plain,
( ( ( ~ $false )
= $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(451,plain,
! [SV39: del,SV50: $i,SV4: del,SV71: $i] :
( ( ( ~ ( mem @ SV71 @ SV4 ) )
= $true )
| ( ( mem @ ( ap @ SV50 @ SV71 ) @ SV39 )
= $true )
| ( ( mem @ SV50 @ ( arr @ SV4 @ SV39 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(452,plain,
! [SV45: $i,SV28: del] :
( ( ( ! [SY148: $i] :
( ~ ( mem @ SY148 @ SV28 )
| ( SV45 != SY148 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY148 ) ) ) )
= $true )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(453,plain,
! [SV45: $i,SV28: del] :
( ( ( ! [SY149: $i] :
( ~ ( mem @ SY149 @ SV28 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SY149 ) )
| ( SV45 = SY149 ) ) )
= $true )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(454,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
= $true )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(455,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( ~ ( mem @ ( SV53 @ ( sK4_X @ SV53 @ SV46 @ SV29 ) ) @ SV46 ) )
= $true )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(456,plain,
! [SV47: $i,SV30: del] :
( ( ( ! [SY151: $i] :
( ~ ( mem @ SY151 @ SV30 )
| ( SV47 != SY151 )
| ( SY151 = SV47 ) ) )
= $true )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(457,plain,
! [SV47: $i,SV30: del] :
( ( ( ! [SY152: $i] :
( ~ ( mem @ SY152 @ SV30 )
| ( SY152 != SV47 )
| ( SV47 = SY152 ) ) )
= $true )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(458,plain,
! [SV55: del,SV63: $i] :
( ( ( mem @ SV63 @ SV55 )
= $false )
| ( ( ! [SY183: $i] :
( ~ ( mem @ SY183 @ SV55 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV55 ) @ c_2Ebool_2ET ) @ SV63 ) @ SY183 )
= SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(459,plain,
! [SV56: del,SV64: $i] :
( ( ( mem @ SV64 @ SV56 )
= $false )
| ( ( ! [SY184: $i] :
( ~ ( mem @ SY184 @ SV56 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV56 ) @ c_2Ebool_2EF ) @ SV64 ) @ SY184 )
= SY184 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(462,plain,
! [SV32: $i,SV75: $i] :
( ( ( ~ ( mem @ SV75 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV75 ) )
| ( p @ SV32 )
| ( p @ SV75 ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(463,plain,
! [SV32: $i] :
( ( ( ~ ! [SY109: $i] :
( ~ ( mem @ SY109 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( mem @ SY110 @ bool )
| ~ ( p @ SY110 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY110 ) ) ) )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(464,plain,
! [SV72: tp__ty_2Enum_2Enum,SV65: tp__ty_2Enum_2Enum,SV33: del] :
( ( ( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV65 ) )
!= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV72 ) ) ) )
= $true )
| ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV65 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV72 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(465,plain,
! [SV73: tp__ty_2Enum_2Enum,SV33: del,SV66: tp__ty_2Enum_2Enum] :
( ( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV66 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV73 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) ) )
= $true )
| ( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV66 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(466,plain,
! [SV54: $i,SV48: del,SV34: del,SV74: $i] :
( ( ( ~ ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) ) )
= $true )
| ( ( ~ ( ~ ( mem @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SV54 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SV74 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) ) ) ) )
| ( SV54 = SV74 ) )
= $true )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(467,plain,
( ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(468,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) )
| ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(469,plain,
! [SV58: del,SV68: $i] :
( ( ( mem @ SV68 @ ( arr @ SV58 @ bool ) )
= $false )
| ( ( ~ ( ~ ( mem @ ( sK2_X @ SV68 @ SV58 ) @ SV58 )
| ~ ~ ( p @ ( ap @ SV68 @ ( sK2_X @ SV68 @ SV58 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(470,plain,
! [SV59: del,SV69: $i] :
( ( ( mem @ SV69 @ ( arr @ SV59 @ bool ) )
= $false )
| ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV59 ) @ SV69 ) )
| ! [SY187: $i] :
( ~ ( mem @ SY187 @ SV59 )
| ( p @ ( ap @ SV69 @ SY187 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(471,plain,
! [SV60: $i] :
( ( ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV60 ) ) )
= $true )
| ( ( ~ ( p @ SV60 ) )
= $true )
| ( ( mem @ SV60 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(472,plain,
! [SV61: $i] :
( ( ( p @ SV61 )
= $true )
| ( ( p @ ( ap @ c_2Ebool_2E_7E @ SV61 ) )
= $true )
| ( ( mem @ SV61 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(474,plain,
! [SV36: $i] :
( ( ( ~ ! [SY125: $i] :
( ~ ( mem @ SY125 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY125 ) ) )
| ~ ! [SY126: $i] :
( ~ ( mem @ SY126 @ bool )
| ~ ( p @ SY126 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY126 ) ) ) )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(475,plain,
! [SV36: $i,SV76: $i] :
( ( ( ~ ( mem @ SV76 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV76 ) )
| ~ ( p @ SV36 )
| ( p @ SV76 ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(476,plain,
! [SV49: $i,SV37: del,SV70: $i] :
( ( ( mem @ SV70 @ bool )
= $false )
| ( ( ! [SY188: $i] :
( ~ ( mem @ SY188 @ SV37 )
| ! [SY189: $i] :
( ~ ( mem @ SY189 @ SV37 )
| ! [SY190: $i] :
( ~ ( mem @ SY190 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY191: $i] :
( ~ ( mem @ SY191 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY191 ) ) )
| ~ ! [SY192: $i] :
( ~ ( mem @ SY192 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SY188 != SY189 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY192 ) ) ) )
| ~ ~ ( ~ ! [SY193: $i] :
( ~ ( mem @ SY193 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY193 ) ) )
| ~ ! [SY194: $i] :
( ~ ( mem @ SY194 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SY188 != SY189 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY194 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY195: $i] :
( ~ ( mem @ SY195 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SY190 != SY195 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY195 ) ) )
| ~ ! [SY196: $i] :
( ~ ( mem @ SY196 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SY188 != SY189 )
| ( SY190 != SY196 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY196 ) ) ) )
| ~ ~ ( ~ ! [SY197: $i] :
( ~ ( mem @ SY197 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SY190 != SY197 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY197 ) ) )
| ~ ! [SY198: $i] :
( ~ ( mem @ SY198 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SY188 != SY189 )
| ( SY190 != SY198 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SY188 ) @ SY190 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY189 ) @ SY198 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(477,plain,
! [SV38: $i,SV77: $i] :
( ( ( ~ ( mem @ SV77 @ bool )
| ~ ( p @ SV38 )
| ~ ( p @ SV77 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV77 ) ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(478,plain,
! [SV38: $i] :
( ( ( ~ ! [SY142: $i] :
( ~ ( mem @ SY142 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY142 ) )
| ( p @ SV38 ) )
| ~ ! [SY143: $i] :
( ~ ( mem @ SY143 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY143 ) )
| ( p @ SY143 ) ) )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(480,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(481,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( SV1 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(485,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( $true = $false ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(488,plain,
( ( $false = $true )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(491,plain,
! [SV39: del,SV50: $i,SV4: del,SV71: $i] :
( ( ( mem @ SV71 @ SV4 )
= $false )
| ( ( mem @ ( ap @ SV50 @ SV71 ) @ SV39 )
= $true )
| ( ( mem @ SV50 @ ( arr @ SV4 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(492,plain,
! [SV45: $i,SV28: del,SV78: $i] :
( ( ( ~ ( mem @ SV78 @ SV28 )
| ( SV45 != SV78 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV78 ) ) )
= $true )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(493,plain,
! [SV45: $i,SV28: del,SV79: $i] :
( ( ( ~ ( mem @ SV79 @ SV28 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV79 ) )
| ( SV45 = SV79 ) )
= $true )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(494,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( mem @ ( SV53 @ ( sK4_X @ SV53 @ SV46 @ SV29 ) ) @ SV46 )
= $false )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(495,plain,
! [SV47: $i,SV30: del,SV80: $i] :
( ( ( ~ ( mem @ SV80 @ SV30 )
| ( SV47 != SV80 )
| ( SV80 = SV47 ) )
= $true )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(496,plain,
! [SV47: $i,SV30: del,SV81: $i] :
( ( ( ~ ( mem @ SV81 @ SV30 )
| ( SV81 != SV47 )
| ( SV47 = SV81 ) )
= $true )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(497,plain,
! [SV63: $i,SV55: del,SV82: $i] :
( ( ( ~ ( mem @ SV82 @ SV55 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV55 ) @ c_2Ebool_2ET ) @ SV63 ) @ SV82 )
= SV63 ) )
= $true )
| ( ( mem @ SV63 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(498,plain,
! [SV64: $i,SV56: del,SV83: $i] :
( ( ( ~ ( mem @ SV83 @ SV56 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV56 ) @ c_2Ebool_2EF ) @ SV64 ) @ SV83 )
= SV83 ) )
= $true )
| ( ( mem @ SV64 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(503,plain,
! [SV32: $i,SV75: $i] :
( ( ( ~ ( mem @ SV75 @ bool ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV75 ) )
| ( p @ SV32 )
| ( p @ SV75 ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(504,plain,
! [SV32: $i] :
( ( ( ~ ! [SY109: $i] :
( ~ ( mem @ SY109 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY109 ) ) ) )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(505,plain,
! [SV32: $i] :
( ( ( ~ ! [SY110: $i] :
( ~ ( mem @ SY110 @ bool )
| ~ ( p @ SY110 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY110 ) ) ) )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(506,plain,
! [SV72: tp__ty_2Enum_2Enum,SV65: tp__ty_2Enum_2Enum,SV33: del] :
( ( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV65 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV72 ) ) )
= $false )
| ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV65 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV72 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(507,plain,
! [SV73: tp__ty_2Enum_2Enum,SV33: del,SV66: tp__ty_2Enum_2Enum] :
( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV66 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV73 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
= $false )
| ( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV66 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(508,plain,
! [SV54: $i,SV48: del,SV34: del,SV74: $i] :
( ( ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) )
= $false )
| ( ( ~ ( ~ ( mem @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SV54 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SV74 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) ) ) ) )
| ( SV54 = SV74 ) )
= $true )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(509,plain,
( ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(510,plain,
( ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(511,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(512,plain,
( ( ~ ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(513,plain,
! [SV58: del,SV68: $i] :
( ( ( ~ ( ~ ( mem @ ( sK2_X @ SV68 @ SV58 ) @ SV58 )
| ~ ~ ( p @ ( ap @ SV68 @ ( sK2_X @ SV68 @ SV58 ) ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) )
= $true )
| ( ( mem @ SV68 @ ( arr @ SV58 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(514,plain,
! [SV69: $i,SV59: del] :
( ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV59 ) @ SV69 ) ) )
= $true )
| ( ( ! [SY187: $i] :
( ~ ( mem @ SY187 @ SV59 )
| ( p @ ( ap @ SV69 @ SY187 ) ) ) )
= $true )
| ( ( mem @ SV69 @ ( arr @ SV59 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(515,plain,
! [SV60: $i] :
( ( ( p @ ( ap @ c_2Ebool_2E_7E @ SV60 ) )
= $false )
| ( ( ~ ( p @ SV60 ) )
= $true )
| ( ( mem @ SV60 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(518,plain,
! [SV36: $i] :
( ( ( ~ ! [SY125: $i] :
( ~ ( mem @ SY125 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY125 ) ) ) )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(519,plain,
! [SV36: $i] :
( ( ( ~ ! [SY126: $i] :
( ~ ( mem @ SY126 @ bool )
| ~ ( p @ SY126 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY126 ) ) ) )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(520,plain,
! [SV36: $i,SV76: $i] :
( ( ( ~ ( mem @ SV76 @ bool ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV76 ) )
| ~ ( p @ SV36 )
| ( p @ SV76 ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(521,plain,
! [SV70: $i,SV49: $i,SV37: del,SV84: $i] :
( ( ( ~ ( mem @ SV84 @ SV37 )
| ! [SY199: $i] :
( ~ ( mem @ SY199 @ SV37 )
| ! [SY200: $i] :
( ~ ( mem @ SY200 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY201: $i] :
( ~ ( mem @ SY201 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY201 ) ) )
| ~ ! [SY202: $i] :
( ~ ( mem @ SY202 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SY199 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY202 ) ) ) )
| ~ ~ ( ~ ! [SY203: $i] :
( ~ ( mem @ SY203 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY203 ) ) )
| ~ ! [SY204: $i] :
( ~ ( mem @ SY204 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SY199 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY204 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY205: $i] :
( ~ ( mem @ SY205 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SY200 != SY205 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY205 ) ) )
| ~ ! [SY206: $i] :
( ~ ( mem @ SY206 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SY199 )
| ( SY200 != SY206 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY206 ) ) ) )
| ~ ~ ( ~ ! [SY207: $i] :
( ~ ( mem @ SY207 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SY200 != SY207 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY207 ) ) )
| ~ ! [SY208: $i] :
( ~ ( mem @ SY208 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SY199 )
| ( SY200 != SY208 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY208 ) ) ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(522,plain,
! [SV38: $i,SV77: $i] :
( ( ( ~ ( mem @ SV77 @ bool ) )
= $true )
| ( ( ~ ( p @ SV38 )
| ~ ( p @ SV77 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV77 ) ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(523,plain,
! [SV38: $i] :
( ( ( ~ ! [SY142: $i] :
( ~ ( mem @ SY142 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY142 ) )
| ( p @ SV38 ) ) )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(524,plain,
! [SV38: $i] :
( ( ( ~ ! [SY143: $i] :
( ~ ( mem @ SY143 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY143 ) )
| ( p @ SY143 ) ) )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(525,plain,
! [SV45: $i,SV28: del,SV78: $i] :
( ( ( ~ ( mem @ SV78 @ SV28 ) )
= $true )
| ( ( ( SV45 != SV78 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV78 ) ) )
= $true )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(526,plain,
! [SV45: $i,SV28: del,SV79: $i] :
( ( ( ~ ( mem @ SV79 @ SV28 ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV79 ) )
| ( SV45 = SV79 ) )
= $true )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(527,plain,
! [SV47: $i,SV30: del,SV80: $i] :
( ( ( ~ ( mem @ SV80 @ SV30 ) )
= $true )
| ( ( ( SV47 != SV80 )
| ( SV80 = SV47 ) )
= $true )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(528,plain,
! [SV47: $i,SV30: del,SV81: $i] :
( ( ( ~ ( mem @ SV81 @ SV30 ) )
= $true )
| ( ( ( SV81 != SV47 )
| ( SV47 = SV81 ) )
= $true )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(529,plain,
! [SV63: $i,SV55: del,SV82: $i] :
( ( ( ~ ( mem @ SV82 @ SV55 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV55 ) @ c_2Ebool_2ET ) @ SV63 ) @ SV82 )
= SV63 )
= $true )
| ( ( mem @ SV63 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(530,plain,
! [SV64: $i,SV56: del,SV83: $i] :
( ( ( ~ ( mem @ SV83 @ SV56 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV56 ) @ c_2Ebool_2EF ) @ SV64 ) @ SV83 )
= SV83 )
= $true )
| ( ( mem @ SV64 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(535,plain,
! [SV32: $i,SV75: $i] :
( ( ( mem @ SV75 @ bool )
= $false )
| ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV75 ) )
| ( p @ SV32 )
| ( p @ SV75 ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(536,plain,
! [SV32: $i] :
( ( ( ! [SY109: $i] :
( ~ ( mem @ SY109 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY109 ) ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(537,plain,
! [SV32: $i] :
( ( ( ! [SY110: $i] :
( ~ ( mem @ SY110 @ bool )
| ~ ( p @ SY110 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SY110 ) ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(538,plain,
! [SV34: del,SV48: del,SV54: $i,SV74: $i] :
( ( ( ~ ( ~ ( mem @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SV54 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SV74 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) ) ) ) ) )
= $true )
| ( ( SV54 = SV74 )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) )
= $false )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(539,plain,
( ( ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(540,plain,
( ( ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(541,plain,
( ( ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( SX0 != fo__c_2Enum_2E0 )
| ( SX1 != fo__c_2Enum_2E0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(542,plain,
( ( ~ ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(543,plain,
! [SV58: del,SV68: $i] :
( ( ( ~ ( mem @ ( sK2_X @ SV68 @ SV58 ) @ SV58 )
| ~ ~ ( p @ ( ap @ SV68 @ ( sK2_X @ SV68 @ SV58 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) )
= $true )
| ( ( mem @ SV68 @ ( arr @ SV58 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(544,plain,
! [SV69: $i,SV59: del] :
( ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV59 ) @ SV69 ) )
= $false )
| ( ( ! [SY187: $i] :
( ~ ( mem @ SY187 @ SV59 )
| ( p @ ( ap @ SV69 @ SY187 ) ) ) )
= $true )
| ( ( mem @ SV69 @ ( arr @ SV59 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(545,plain,
! [SV60: $i] :
( ( ( p @ SV60 )
= $false )
| ( ( p @ ( ap @ c_2Ebool_2E_7E @ SV60 ) )
= $false )
| ( ( mem @ SV60 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(548,plain,
! [SV36: $i] :
( ( ( ! [SY125: $i] :
( ~ ( mem @ SY125 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY125 ) ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(549,plain,
! [SV36: $i] :
( ( ( ! [SY126: $i] :
( ~ ( mem @ SY126 @ bool )
| ~ ( p @ SY126 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SY126 ) ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(550,plain,
! [SV36: $i,SV76: $i] :
( ( ( mem @ SV76 @ bool )
= $false )
| ( ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV76 ) )
| ~ ( p @ SV36 )
| ( p @ SV76 ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(551,plain,
! [SV70: $i,SV49: $i,SV37: del,SV84: $i] :
( ( ( ~ ( mem @ SV84 @ SV37 ) )
= $true )
| ( ( ! [SY199: $i] :
( ~ ( mem @ SY199 @ SV37 )
| ! [SY200: $i] :
( ~ ( mem @ SY200 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY201: $i] :
( ~ ( mem @ SY201 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY201 ) ) )
| ~ ! [SY202: $i] :
( ~ ( mem @ SY202 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SY199 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY202 ) ) ) )
| ~ ~ ( ~ ! [SY203: $i] :
( ~ ( mem @ SY203 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY203 ) ) )
| ~ ! [SY204: $i] :
( ~ ( mem @ SY204 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SY199 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY204 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY205: $i] :
( ~ ( mem @ SY205 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SY200 != SY205 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY205 ) ) )
| ~ ! [SY206: $i] :
( ~ ( mem @ SY206 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SY199 )
| ( SY200 != SY206 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY206 ) ) ) )
| ~ ~ ( ~ ! [SY207: $i] :
( ~ ( mem @ SY207 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SY200 != SY207 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY207 ) ) )
| ~ ! [SY208: $i] :
( ~ ( mem @ SY208 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SY199 )
| ( SY200 != SY208 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY208 ) ) ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(552,plain,
! [SV38: $i,SV77: $i] :
( ( ( mem @ SV77 @ bool )
= $false )
| ( ( ~ ( p @ SV38 )
| ~ ( p @ SV77 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV77 ) ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(553,plain,
! [SV38: $i] :
( ( ( ! [SY142: $i] :
( ~ ( mem @ SY142 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY142 ) )
| ( p @ SV38 ) ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(554,plain,
! [SV38: $i] :
( ( ( ! [SY143: $i] :
( ~ ( mem @ SY143 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SY143 ) )
| ( p @ SY143 ) ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(555,plain,
! [SV45: $i,SV28: del,SV78: $i] :
( ( ( mem @ SV78 @ SV28 )
= $false )
| ( ( ( SV45 != SV78 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV78 ) ) )
= $true )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(556,plain,
! [SV45: $i,SV28: del,SV79: $i] :
( ( ( mem @ SV79 @ SV28 )
= $false )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV79 ) )
| ( SV45 = SV79 ) )
= $true )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(557,plain,
! [SV47: $i,SV30: del,SV80: $i] :
( ( ( mem @ SV80 @ SV30 )
= $false )
| ( ( ( SV47 != SV80 )
| ( SV80 = SV47 ) )
= $true )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(558,plain,
! [SV47: $i,SV30: del,SV81: $i] :
( ( ( mem @ SV81 @ SV30 )
= $false )
| ( ( ( SV81 != SV47 )
| ( SV47 = SV81 ) )
= $true )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(559,plain,
! [SV63: $i,SV55: del,SV82: $i] :
( ( ( mem @ SV82 @ SV55 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV55 ) @ c_2Ebool_2ET ) @ SV63 ) @ SV82 )
= SV63 )
= $true )
| ( ( mem @ SV63 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(560,plain,
! [SV64: $i,SV56: del,SV83: $i] :
( ( ( mem @ SV83 @ SV56 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV56 ) @ c_2Ebool_2EF ) @ SV64 ) @ SV83 )
= SV83 )
= $true )
| ( ( mem @ SV64 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(565,plain,
! [SV75: $i,SV32: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV75 ) ) )
= $true )
| ( ( ( p @ SV32 )
| ( p @ SV75 ) )
= $true )
| ( ( mem @ SV75 @ bool )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(566,plain,
! [SV32: $i,SV85: $i] :
( ( ( ~ ( mem @ SV85 @ bool )
| ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV85 ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(567,plain,
! [SV32: $i,SV86: $i] :
( ( ( ~ ( mem @ SV86 @ bool )
| ~ ( p @ SV86 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV86 ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(568,plain,
! [SV34: del,SV48: del,SV54: $i,SV74: $i] :
( ( ( ~ ( mem @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) @ SV34 )
| ~ ( ( ( ap @ SV54 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SV74 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) ) ) ) )
= $false )
| ( ( SV54 = SV74 )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) )
= $false )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(569,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(570,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(571,plain,
! [SV87: tp__ty_2Enum_2Enum] :
( ( ! [SY209: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV87 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SY209 ) ) ) )
| ( SV87 != fo__c_2Enum_2E0 )
| ( SY209 != fo__c_2Enum_2E0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(572,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(573,plain,
! [SV58: del,SV68: $i] :
( ( ( ~ ( mem @ ( sK2_X @ SV68 @ SV58 ) @ SV58 ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) )
= $true )
| ( ( mem @ SV68 @ ( arr @ SV58 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(574,plain,
! [SV58: del,SV68: $i] :
( ( ( ~ ~ ( p @ ( ap @ SV68 @ ( sK2_X @ SV68 @ SV58 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) )
= $true )
| ( ( mem @ SV68 @ ( arr @ SV58 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(575,plain,
! [SV69: $i,SV59: del,SV88: $i] :
( ( ( ~ ( mem @ SV88 @ SV59 )
| ( p @ ( ap @ SV69 @ SV88 ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV59 ) @ SV69 ) )
= $false )
| ( ( mem @ SV69 @ ( arr @ SV59 @ bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(578,plain,
! [SV36: $i,SV89: $i] :
( ( ( ~ ( mem @ SV89 @ bool )
| ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV89 ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(579,plain,
! [SV36: $i,SV90: $i] :
( ( ( ~ ( mem @ SV90 @ bool )
| ~ ( p @ SV90 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV90 ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(580,plain,
! [SV76: $i,SV36: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV76 ) ) )
= $true )
| ( ( ~ ( p @ SV36 )
| ( p @ SV76 ) )
= $true )
| ( ( mem @ SV76 @ bool )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(581,plain,
! [SV70: $i,SV49: $i,SV37: del,SV84: $i] :
( ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( ! [SY199: $i] :
( ~ ( mem @ SY199 @ SV37 )
| ! [SY200: $i] :
( ~ ( mem @ SY200 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY201: $i] :
( ~ ( mem @ SY201 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY201 ) ) )
| ~ ! [SY202: $i] :
( ~ ( mem @ SY202 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SY199 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY202 ) ) ) )
| ~ ~ ( ~ ! [SY203: $i] :
( ~ ( mem @ SY203 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY203 ) ) )
| ~ ! [SY204: $i] :
( ~ ( mem @ SY204 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SY199 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY204 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY205: $i] :
( ~ ( mem @ SY205 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SY200 != SY205 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY205 ) ) )
| ~ ! [SY206: $i] :
( ~ ( mem @ SY206 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SY199 )
| ( SY200 != SY206 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY206 ) ) ) )
| ~ ~ ( ~ ! [SY207: $i] :
( ~ ( mem @ SY207 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SY200 != SY207 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY207 ) ) )
| ~ ! [SY208: $i] :
( ~ ( mem @ SY208 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SY199 )
| ( SY200 != SY208 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY200 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SY199 ) @ SY208 ) ) ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(582,plain,
! [SV77: $i,SV38: $i] :
( ( ( ~ ( p @ SV38 )
| ~ ( p @ SV77 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV77 ) )
= $true )
| ( ( mem @ SV77 @ bool )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(583,plain,
! [SV38: $i,SV91: $i] :
( ( ( ~ ( mem @ SV91 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV91 ) )
| ( p @ SV38 ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(584,plain,
! [SV38: $i,SV92: $i] :
( ( ( ~ ( mem @ SV92 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV92 ) )
| ( p @ SV92 ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(585,plain,
! [SV28: del,SV78: $i,SV45: $i] :
( ( ( ( SV45 != SV78 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV78 ) )
= $true )
| ( ( mem @ SV78 @ SV28 )
= $false )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(586,plain,
! [SV79: $i,SV45: $i,SV28: del] :
( ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV79 ) ) )
= $true )
| ( ( SV45 = SV79 )
= $true )
| ( ( mem @ SV79 @ SV28 )
= $false )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(587,plain,
! [SV30: del,SV80: $i,SV47: $i] :
( ( ( ( SV47 != SV80 ) )
= $true )
| ( ( SV80 = SV47 )
= $true )
| ( ( mem @ SV80 @ SV30 )
= $false )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(588,plain,
! [SV30: del,SV47: $i,SV81: $i] :
( ( ( ( SV81 != SV47 ) )
= $true )
| ( ( SV47 = SV81 )
= $true )
| ( ( mem @ SV81 @ SV30 )
= $false )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(597,plain,
! [SV75: $i,SV32: $i] :
( ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV75 ) )
= $false )
| ( ( ( p @ SV32 )
| ( p @ SV75 ) )
= $true )
| ( ( mem @ SV75 @ bool )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(598,plain,
! [SV32: $i,SV85: $i] :
( ( ( ~ ( mem @ SV85 @ bool ) )
= $true )
| ( ( ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV85 ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(599,plain,
! [SV32: $i,SV86: $i] :
( ( ( ~ ( mem @ SV86 @ bool ) )
= $true )
| ( ( ~ ( p @ SV86 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV86 ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(600,plain,
! [SV34: del,SV48: del,SV54: $i,SV74: $i] :
( ( ( ~ ( mem @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) @ SV34 ) )
= $false )
| ( ( SV54 = SV74 )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) )
= $false )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(601,plain,
! [SV34: del,SV48: del,SV74: $i,SV54: $i] :
( ( ( ~ ( ( ( ap @ SV54 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SV74 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) ) ) ) )
= $false )
| ( ( SV54 = SV74 )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) )
= $false )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(602,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(603,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(604,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(605,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(606,plain,
! [SV93: tp__ty_2Enum_2Enum,SV87: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV87 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV93 ) ) ) )
| ( SV87 != fo__c_2Enum_2E0 )
| ( SV93 != fo__c_2Enum_2E0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(607,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(608,plain,
( ( ~ ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(609,plain,
! [SV58: del,SV68: $i] :
( ( ( mem @ ( sK2_X @ SV68 @ SV58 ) @ SV58 )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) )
= $true )
| ( ( mem @ SV68 @ ( arr @ SV58 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(610,plain,
! [SV58: del,SV68: $i] :
( ( ( ~ ( p @ ( ap @ SV68 @ ( sK2_X @ SV68 @ SV58 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) )
= $true )
| ( ( mem @ SV68 @ ( arr @ SV58 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(611,plain,
! [SV69: $i,SV59: del,SV88: $i] :
( ( ( ~ ( mem @ SV88 @ SV59 ) )
= $true )
| ( ( p @ ( ap @ SV69 @ SV88 ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV59 ) @ SV69 ) )
= $false )
| ( ( mem @ SV69 @ ( arr @ SV59 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(616,plain,
! [SV36: $i,SV89: $i] :
( ( ( ~ ( mem @ SV89 @ bool ) )
= $true )
| ( ( ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV89 ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(617,plain,
! [SV36: $i,SV90: $i] :
( ( ( ~ ( mem @ SV90 @ bool ) )
= $true )
| ( ( ~ ( p @ SV90 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV90 ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(618,plain,
! [SV76: $i,SV36: $i] :
( ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV76 ) )
= $false )
| ( ( ~ ( p @ SV36 )
| ( p @ SV76 ) )
= $true )
| ( ( mem @ SV76 @ bool )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(619,plain,
! [SV84: $i,SV70: $i,SV49: $i,SV37: del,SV94: $i] :
( ( ( ~ ( mem @ SV94 @ SV37 )
| ! [SY210: $i] :
( ~ ( mem @ SY210 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY211: $i] :
( ~ ( mem @ SY211 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY211 ) ) )
| ~ ! [SY212: $i] :
( ~ ( mem @ SY212 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY212 ) ) ) )
| ~ ~ ( ~ ! [SY213: $i] :
( ~ ( mem @ SY213 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY213 ) ) )
| ~ ! [SY214: $i] :
( ~ ( mem @ SY214 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY214 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY215: $i] :
( ~ ( mem @ SY215 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SY210 != SY215 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY215 ) ) )
| ~ ! [SY216: $i] :
( ~ ( mem @ SY216 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SY210 != SY216 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY216 ) ) ) )
| ~ ~ ( ~ ! [SY217: $i] :
( ~ ( mem @ SY217 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SY210 != SY217 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY217 ) ) )
| ~ ! [SY218: $i] :
( ~ ( mem @ SY218 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SY210 != SY218 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY218 ) ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(620,plain,
! [SV77: $i,SV38: $i] :
( ( ( ~ ( p @ SV38 ) )
= $true )
| ( ( ~ ( p @ SV77 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV77 ) )
= $true )
| ( ( mem @ SV77 @ bool )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(621,plain,
! [SV38: $i,SV91: $i] :
( ( ( ~ ( mem @ SV91 @ bool ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV91 ) )
| ( p @ SV38 ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(622,plain,
! [SV38: $i,SV92: $i] :
( ( ( ~ ( mem @ SV92 @ bool ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV92 ) )
| ( p @ SV92 ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(623,plain,
! [SV28: del,SV78: $i,SV45: $i] :
( ( ( SV45 = SV78 )
= $false )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV78 ) )
= $true )
| ( ( mem @ SV78 @ SV28 )
= $false )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(624,plain,
! [SV79: $i,SV45: $i,SV28: del] :
( ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV45 ) @ SV79 ) )
= $false )
| ( ( SV45 = SV79 )
= $true )
| ( ( mem @ SV79 @ SV28 )
= $false )
| ( ( mem @ SV45 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(625,plain,
! [SV30: del,SV80: $i,SV47: $i] :
( ( ( SV47 = SV80 )
= $false )
| ( ( SV80 = SV47 )
= $true )
| ( ( mem @ SV80 @ SV30 )
= $false )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(626,plain,
! [SV30: del,SV47: $i,SV81: $i] :
( ( ( SV81 = SV47 )
= $false )
| ( ( SV47 = SV81 )
= $true )
| ( ( mem @ SV81 @ SV30 )
= $false )
| ( ( mem @ SV47 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(635,plain,
! [SV75: $i,SV32: $i] :
( ( ( p @ SV32 )
= $true )
| ( ( p @ SV75 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV75 ) )
= $false )
| ( ( mem @ SV75 @ bool )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(636,plain,
! [SV32: $i,SV85: $i] :
( ( ( mem @ SV85 @ bool )
= $false )
| ( ( ~ ( p @ SV32 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV85 ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(637,plain,
! [SV32: $i,SV86: $i] :
( ( ( mem @ SV86 @ bool )
= $false )
| ( ( ~ ( p @ SV86 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV86 ) ) )
= $true )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(638,plain,
! [SV34: del,SV48: del,SV54: $i,SV74: $i] :
( ( ( mem @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) @ SV34 )
= $true )
| ( ( SV54 = SV74 )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) )
= $false )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(639,plain,
! [SV34: del,SV48: del,SV74: $i,SV54: $i] :
( ( ( ( ( ap @ SV54 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) )
!= ( ap @ SV74 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) ) ) )
= $true )
| ( ( SV54 = SV74 )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) )
= $false )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(640,plain,
( ( ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(641,plain,
( ( ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX0 ) ) @ ( inj__ty_2Enum_2Enum @ SX1 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(642,plain,
( ( ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(643,plain,
( ( ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SX1 ) ) @ ( inj__ty_2Enum_2Enum @ SX0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(644,plain,
! [SV93: tp__ty_2Enum_2Enum,SV87: tp__ty_2Enum_2Enum] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV87 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV93 ) ) ) ) )
= $true )
| ( ( ( SV87 != fo__c_2Enum_2E0 )
| ( SV93 != fo__c_2Enum_2E0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(645,plain,
( ( ! [SX0: tp__ty_2Enum_2Enum] :
( ( SX0 = fo__c_2Enum_2E0 )
| ! [SX1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(646,plain,
( ( ! [SX0: tp__ty_2Enum_2Enum,SX1: tp__ty_2Enum_2Enum] :
( ( SX1 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(647,plain,
! [SV58: del,SV68: $i] :
( ( ( p @ ( ap @ SV68 @ ( sK2_X @ SV68 @ SV58 ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV58 ) @ SV68 ) )
= $true )
| ( ( mem @ SV68 @ ( arr @ SV58 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(648,plain,
! [SV69: $i,SV59: del,SV88: $i] :
( ( ( mem @ SV88 @ SV59 )
= $false )
| ( ( p @ ( ap @ SV69 @ SV88 ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV59 ) @ SV69 ) )
= $false )
| ( ( mem @ SV69 @ ( arr @ SV59 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(653,plain,
! [SV36: $i,SV89: $i] :
( ( ( mem @ SV89 @ bool )
= $false )
| ( ( ( p @ SV36 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV89 ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(654,plain,
! [SV36: $i,SV90: $i] :
( ( ( mem @ SV90 @ bool )
= $false )
| ( ( ~ ( p @ SV90 )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV90 ) ) )
= $true )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(655,plain,
! [SV76: $i,SV36: $i] :
( ( ( ~ ( p @ SV36 ) )
= $true )
| ( ( p @ SV76 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV76 ) )
= $false )
| ( ( mem @ SV76 @ bool )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(656,plain,
! [SV84: $i,SV70: $i,SV49: $i,SV37: del,SV94: $i] :
( ( ( ~ ( mem @ SV94 @ SV37 ) )
= $true )
| ( ( ! [SY210: $i] :
( ~ ( mem @ SY210 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY211: $i] :
( ~ ( mem @ SY211 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY211 ) ) )
| ~ ! [SY212: $i] :
( ~ ( mem @ SY212 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY212 ) ) ) )
| ~ ~ ( ~ ! [SY213: $i] :
( ~ ( mem @ SY213 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY213 ) ) )
| ~ ! [SY214: $i] :
( ~ ( mem @ SY214 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY214 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY215: $i] :
( ~ ( mem @ SY215 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SY210 != SY215 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY215 ) ) )
| ~ ! [SY216: $i] :
( ~ ( mem @ SY216 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SY210 != SY216 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY216 ) ) ) )
| ~ ~ ( ~ ! [SY217: $i] :
( ~ ( mem @ SY217 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SY210 != SY217 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY217 ) ) )
| ~ ! [SY218: $i] :
( ~ ( mem @ SY218 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SY210 != SY218 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY218 ) ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(657,plain,
! [SV77: $i,SV38: $i] :
( ( ( p @ SV38 )
= $false )
| ( ( ~ ( p @ SV77 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV77 ) )
= $true )
| ( ( mem @ SV77 @ bool )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(658,plain,
! [SV38: $i,SV91: $i] :
( ( ( mem @ SV91 @ bool )
= $false )
| ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV91 ) )
| ( p @ SV38 ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(659,plain,
! [SV38: $i,SV92: $i] :
( ( ( mem @ SV92 @ bool )
= $false )
| ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV92 ) )
| ( p @ SV92 ) )
= $true )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(668,plain,
! [SV85: $i,SV32: $i] :
( ( ( ~ ( p @ SV32 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(669,plain,
! [SV32: $i,SV86: $i] :
( ( ( ~ ( p @ SV86 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV86 ) )
= $true )
| ( ( mem @ SV86 @ bool )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(670,plain,
! [SV34: del,SV48: del,SV74: $i,SV54: $i] :
( ( ( ( ap @ SV54 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) )
= ( ap @ SV74 @ ( sK3_X @ SV74 @ SV54 @ SV48 @ SV34 ) ) )
= $false )
| ( ( SV54 = SV74 )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV34 @ SV48 ) )
= $false )
| ( ( mem @ SV54 @ ( arr @ SV34 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(671,plain,
! [SV103: tp__ty_2Enum_2Enum] :
( ( ! [SY219: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV103 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SY219 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV103 ) ) @ ( inj__ty_2Enum_2Enum @ SY219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(672,plain,
! [SV104: tp__ty_2Enum_2Enum] :
( ( ! [SY220: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV104 ) ) @ ( inj__ty_2Enum_2Enum @ SY220 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV104 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SY220 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(673,plain,
! [SV105: tp__ty_2Enum_2Enum] :
( ( ! [SY221: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV105 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SY221 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SY221 ) ) @ ( inj__ty_2Enum_2Enum @ SV105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(674,plain,
! [SV106: tp__ty_2Enum_2Enum] :
( ( ! [SY222: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SY222 ) ) @ ( inj__ty_2Enum_2Enum @ SV106 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV106 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SY222 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(675,plain,
! [SV93: tp__ty_2Enum_2Enum,SV87: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV87 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV93 ) ) ) )
= $false )
| ( ( ( SV87 != fo__c_2Enum_2E0 )
| ( SV93 != fo__c_2Enum_2E0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(676,plain,
! [SV107: tp__ty_2Enum_2Enum] :
( ( ( SV107 = fo__c_2Enum_2E0 )
| ! [SY223: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SY223 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(677,plain,
! [SV108: tp__ty_2Enum_2Enum] :
( ( ! [SY224: tp__ty_2Enum_2Enum] :
( ( SY224 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SY224 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(682,plain,
! [SV89: $i,SV36: $i] :
( ( ( p @ SV36 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV89 ) )
= $true )
| ( ( mem @ SV89 @ bool )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(683,plain,
! [SV36: $i,SV90: $i] :
( ( ( ~ ( p @ SV90 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV90 ) )
= $true )
| ( ( mem @ SV90 @ bool )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(684,plain,
! [SV76: $i,SV36: $i] :
( ( ( p @ SV36 )
= $false )
| ( ( p @ SV76 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV76 ) )
= $false )
| ( ( mem @ SV76 @ bool )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(685,plain,
! [SV84: $i,SV70: $i,SV49: $i,SV37: del,SV94: $i] :
( ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( ! [SY210: $i] :
( ~ ( mem @ SY210 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY211: $i] :
( ~ ( mem @ SY211 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY211 ) ) )
| ~ ! [SY212: $i] :
( ~ ( mem @ SY212 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY212 ) ) ) )
| ~ ~ ( ~ ! [SY213: $i] :
( ~ ( mem @ SY213 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY213 ) ) )
| ~ ! [SY214: $i] :
( ~ ( mem @ SY214 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY214 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY215: $i] :
( ~ ( mem @ SY215 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SY210 != SY215 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY215 ) ) )
| ~ ! [SY216: $i] :
( ~ ( mem @ SY216 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SY210 != SY216 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY216 ) ) ) )
| ~ ~ ( ~ ! [SY217: $i] :
( ~ ( mem @ SY217 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SY210 != SY217 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY217 ) ) )
| ~ ! [SY218: $i] :
( ~ ( mem @ SY218 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SY210 != SY218 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SY210 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY218 ) ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(686,plain,
! [SV38: $i,SV77: $i] :
( ( ( p @ SV77 )
= $false )
| ( ( p @ SV38 )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV77 ) )
= $true )
| ( ( mem @ SV77 @ bool )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(687,plain,
! [SV91: $i,SV38: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV91 ) ) )
= $true )
| ( ( p @ SV38 )
= $true )
| ( ( mem @ SV91 @ bool )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(688,plain,
! [SV92: $i,SV38: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV92 ) ) )
= $true )
| ( ( p @ SV92 )
= $true )
| ( ( mem @ SV92 @ bool )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(697,plain,
! [SV85: $i,SV32: $i] :
( ( ( p @ SV32 )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(698,plain,
! [SV32: $i,SV86: $i] :
( ( ( p @ SV86 )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV32 ) @ SV86 ) )
= $true )
| ( ( mem @ SV86 @ bool )
= $false )
| ( ( mem @ SV32 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(699,plain,
! [SV111: tp__ty_2Enum_2Enum,SV103: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV103 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV111 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV103 ) ) @ ( inj__ty_2Enum_2Enum @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(700,plain,
! [SV112: tp__ty_2Enum_2Enum,SV104: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV104 ) ) @ ( inj__ty_2Enum_2Enum @ SV112 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV104 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(701,plain,
! [SV113: tp__ty_2Enum_2Enum,SV105: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV105 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV113 ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV113 ) ) @ ( inj__ty_2Enum_2Enum @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(702,plain,
! [SV106: tp__ty_2Enum_2Enum,SV114: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV114 ) ) @ ( inj__ty_2Enum_2Enum @ SV106 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV106 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV114 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(703,plain,
! [SV93: tp__ty_2Enum_2Enum,SV87: tp__ty_2Enum_2Enum] :
( ( ( ( SV87 != fo__c_2Enum_2E0 ) )
= $true )
| ( ( ( SV93 != fo__c_2Enum_2E0 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV87 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV93 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(704,plain,
! [SV107: tp__ty_2Enum_2Enum] :
( ( ( SV107 = fo__c_2Enum_2E0 )
= $true )
| ( ( ! [SY223: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(705,plain,
! [SV108: tp__ty_2Enum_2Enum,SV115: tp__ty_2Enum_2Enum] :
( ( ( SV115 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(712,plain,
! [SV36: $i,SV90: $i] :
( ( ( p @ SV90 )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV36 ) @ SV90 ) )
= $true )
| ( ( mem @ SV90 @ bool )
= $false )
| ( ( mem @ SV36 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(713,plain,
! [SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV116: $i] :
( ( ( ~ ( mem @ SV116 @ SV37 )
| ~ ( ~ ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
| ~ ~ ( ~ ! [SY227: $i] :
( ~ ( mem @ SY227 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY227 ) ) )
| ~ ! [SY228: $i] :
( ~ ( mem @ SY228 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY228 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
| ~ ~ ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(714,plain,
! [SV91: $i,SV38: $i] :
( ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV91 ) )
= $false )
| ( ( p @ SV38 )
= $true )
| ( ( mem @ SV91 @ bool )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(715,plain,
! [SV92: $i,SV38: $i] :
( ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV38 ) @ SV92 ) )
= $false )
| ( ( p @ SV92 )
= $true )
| ( ( mem @ SV92 @ bool )
= $false )
| ( ( mem @ SV38 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(724,plain,
! [SV111: tp__ty_2Enum_2Enum,SV103: tp__ty_2Enum_2Enum] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV103 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV111 ) ) ) ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV103 ) ) @ ( inj__ty_2Enum_2Enum @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(725,plain,
! [SV112: tp__ty_2Enum_2Enum,SV104: tp__ty_2Enum_2Enum] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV104 ) ) @ ( inj__ty_2Enum_2Enum @ SV112 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV104 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(726,plain,
! [SV113: tp__ty_2Enum_2Enum,SV105: tp__ty_2Enum_2Enum] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV105 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV113 ) ) ) ) ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV113 ) ) @ ( inj__ty_2Enum_2Enum @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(727,plain,
! [SV106: tp__ty_2Enum_2Enum,SV114: tp__ty_2Enum_2Enum] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV114 ) ) @ ( inj__ty_2Enum_2Enum @ SV106 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV106 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV114 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(728,plain,
! [SV93: tp__ty_2Enum_2Enum,SV87: tp__ty_2Enum_2Enum] :
( ( ( SV87 = fo__c_2Enum_2E0 )
= $false )
| ( ( ( SV93 != fo__c_2Enum_2E0 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV87 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV93 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(729,plain,
! [SV117: tp__ty_2Enum_2Enum,SV107: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV117 ) ) ) )
= $true )
| ( ( SV107 = fo__c_2Enum_2E0 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(730,plain,
! [SV108: tp__ty_2Enum_2Enum,SV115: tp__ty_2Enum_2Enum] :
( ( ( SV115 = fo__c_2Enum_2E0 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(737,plain,
! [SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV116: $i] :
( ( ( ~ ( mem @ SV116 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
| ~ ~ ( ~ ! [SY227: $i] :
( ~ ( mem @ SY227 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY227 ) ) )
| ~ ! [SY228: $i] :
( ~ ( mem @ SY228 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY228 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
| ~ ~ ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(746,plain,
! [SV111: tp__ty_2Enum_2Enum,SV103: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV103 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV111 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV103 ) ) @ ( inj__ty_2Enum_2Enum @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(747,plain,
! [SV112: tp__ty_2Enum_2Enum,SV104: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV104 ) ) @ ( inj__ty_2Enum_2Enum @ SV112 ) ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV104 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(748,plain,
! [SV113: tp__ty_2Enum_2Enum,SV105: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV105 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV113 ) ) ) ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV113 ) ) @ ( inj__ty_2Enum_2Enum @ SV105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(749,plain,
! [SV106: tp__ty_2Enum_2Enum,SV114: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ SV114 ) ) @ ( inj__ty_2Enum_2Enum @ SV106 ) ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV106 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV114 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(750,plain,
! [SV87: tp__ty_2Enum_2Enum,SV93: tp__ty_2Enum_2Enum] :
( ( ( SV93 = fo__c_2Enum_2E0 )
= $false )
| ( ( SV87 = fo__c_2Enum_2E0 )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV87 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV93 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(757,plain,
! [SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV116: $i] :
( ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
| ~ ~ ( ~ ! [SY227: $i] :
( ~ ( mem @ SY227 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY227 ) ) )
| ~ ! [SY228: $i] :
( ~ ( mem @ SY228 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY228 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
| ~ ~ ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) ) ) ) )
= $true )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(772,plain,
! [SV94: $i,SV116: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
| ~ ~ ( ~ ! [SY227: $i] :
( ~ ( mem @ SY227 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY227 ) ) )
| ~ ! [SY228: $i] :
( ~ ( mem @ SY228 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY228 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
| ~ ~ ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(787,plain,
! [SV94: $i,SV116: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
| ~ ~ ( ~ ! [SY227: $i] :
( ~ ( mem @ SY227 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY227 ) ) )
| ~ ! [SY228: $i] :
( ~ ( mem @ SY228 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY228 ) ) ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(788,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
| ~ ~ ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(803,plain,
! [SV94: $i,SV116: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
| ~ ~ ( ~ ! [SY227: $i] :
( ~ ( mem @ SY227 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY227 ) ) )
| ~ ! [SY228: $i] :
( ~ ( mem @ SY228 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY228 ) ) ) ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(804,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ( ~ ~ ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
| ~ ~ ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[788]) ).
thf(817,plain,
! [SV94: $i,SV116: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
| ~ ~ ( ~ ! [SY227: $i] :
( ~ ( mem @ SY227 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY227 ) ) )
| ~ ! [SY228: $i] :
( ~ ( mem @ SY228 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY228 ) ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(818,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ~ ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
| ~ ~ ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(826,plain,
! [SV94: $i,SV116: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(828,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ~ ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(829,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ~ ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(834,plain,
! [SV94: $i,SV116: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(836,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(837,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(842,plain,
! [SV94: $i,SV116: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ! [SY225: $i] :
( ~ ( mem @ SY225 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY225 ) ) )
| ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(844,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ! [SY229: $i] :
( ~ ( mem @ SY229 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY229 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY229 ) ) )
| ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(845,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) )
| ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(848,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[842]) ).
thf(852,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[844]) ).
thf(853,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(854,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ~ ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(856,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ! [SY226: $i] :
( ~ ( mem @ SY226 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY226 ) ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(860,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ! [SY230: $i] :
( ~ ( mem @ SY230 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY230 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY230 ) ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(861,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SY231 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY231 ) ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(862,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del] :
( ( ( ! [SY232: $i] :
( ~ ( mem @ SY232 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SY232 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SY232 ) ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(864,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV123: $i] :
( ( ( ~ ( mem @ SV123 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(868,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV127: $i] :
( ( ( ~ ( mem @ SV127 @ SV37 )
| ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SV127 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(869,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del,SV128: $i] :
( ( ( ~ ( mem @ SV128 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SV128 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(870,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV129: $i] :
( ( ( ~ ( mem @ SV129 @ SV37 )
| ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SV129 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(872,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV123: $i] :
( ( ( ~ ( mem @ SV123 @ SV37 ) )
= $true )
| ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(876,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV127: $i] :
( ( ( ~ ( mem @ SV127 @ SV37 ) )
= $true )
| ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SV127 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(877,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del,SV128: $i] :
( ( ( ~ ( mem @ SV128 @ SV37 ) )
= $true )
| ( ( ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SV128 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(878,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV129: $i] :
( ( ( ~ ( mem @ SV129 @ SV37 ) )
= $true )
| ( ( ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SV129 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(880,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV123: $i] :
( ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(884,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV127: $i] :
( ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SV127 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(885,plain,
! [SV94: $i,SV84: $i,SV116: $i,SV70: $i,SV49: $i,SV37: del,SV128: $i] :
( ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SV128 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(886,plain,
! [SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV37: del,SV129: $i] :
( ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SV129 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) ) )
= $true )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(888,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ~ ( p @ SV70 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(892,plain,
! [SV37: del,SV127: $i,SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SV127 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(893,plain,
! [SV94: $i,SV84: $i,SV37: del,SV128: $i,SV116: $i,SV70: $i,SV49: $i] :
( ( ( ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 )
| ( SV116 != SV128 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) )
= $true )
| ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(894,plain,
! [SV37: del,SV129: $i,SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 )
| ( SV116 != SV129 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) )
= $true )
| ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(896,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 ) )
= $true )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(900,plain,
! [SV37: del,SV127: $i,SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 )
| ( SV84 != SV94 ) )
= $true )
| ( ( ( SV116 != SV127 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(901,plain,
! [SV94: $i,SV84: $i,SV37: del,SV128: $i,SV116: $i,SV70: $i,SV49: $i] :
( ( ( ( p @ SV49 )
| ( p @ SV70 )
| ( p @ SV70 ) )
= $true )
| ( ( ( SV116 != SV128 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) )
= $true )
| ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(902,plain,
! [SV37: del,SV129: $i,SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ( p @ SV49 )
| ( p @ SV70 )
| ( SV84 != SV94 ) )
= $true )
| ( ( ( SV116 != SV129 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) )
= $true )
| ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(904,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 ) )
= $true )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(908,plain,
! [SV37: del,SV127: $i,SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ~ ( p @ SV49 )
| ~ ( p @ SV70 ) )
= $true )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ( SV116 != SV127 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(909,plain,
! [SV94: $i,SV84: $i,SV37: del,SV128: $i,SV116: $i,SV70: $i,SV49: $i] :
( ( ( ( p @ SV49 )
| ( p @ SV70 ) )
= $true )
| ( ( p @ SV70 )
= $true )
| ( ( ( SV116 != SV128 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) )
= $true )
| ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(910,plain,
! [SV37: del,SV129: $i,SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ( p @ SV49 )
| ( p @ SV70 ) )
= $true )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ( SV116 != SV129 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) )
= $true )
| ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(912,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ~ ( p @ SV49 ) )
= $true )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(916,plain,
! [SV37: del,SV127: $i,SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( ~ ( p @ SV49 ) )
= $true )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ( SV116 != SV127 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(917,plain,
! [SV94: $i,SV84: $i,SV37: del,SV128: $i,SV116: $i,SV70: $i,SV49: $i] :
( ( ( p @ SV49 )
= $true )
| ( ( p @ SV70 )
= $true )
| ( ( p @ SV70 )
= $true )
| ( ( ( SV116 != SV128 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) )
= $true )
| ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(918,plain,
! [SV37: del,SV129: $i,SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( p @ SV49 )
= $true )
| ( ( p @ SV70 )
= $true )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ( SV116 != SV129 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) )
= $true )
| ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(920,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( p @ SV49 )
= $false )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(924,plain,
! [SV37: del,SV127: $i,SV116: $i,SV94: $i,SV84: $i,SV70: $i,SV49: $i] :
( ( ( p @ SV49 )
= $false )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ( SV116 != SV127 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(925,plain,
! [SV94: $i,SV84: $i,SV37: del,SV49: $i,SV70: $i,SV128: $i,SV116: $i] :
( ( ( SV116 = SV128 )
= $false )
| ( ( p @ SV70 )
= $true )
| ( ( p @ SV70 )
= $true )
| ( ( p @ SV49 )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) )
= $true )
| ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(926,plain,
! [SV37: del,SV129: $i,SV116: $i,SV49: $i,SV70: $i,SV94: $i,SV84: $i] :
( ( ( SV84 = SV94 )
= $false )
| ( ( p @ SV70 )
= $true )
| ( ( p @ SV49 )
= $true )
| ( ( ( SV116 != SV129 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) )
= $true )
| ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(928,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV84: $i,SV49: $i,SV70: $i] :
( ( ( p @ SV70 )
= $false )
| ( ( p @ SV49 )
= $false )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(931,plain,
! [SV37: del,SV127: $i,SV116: $i,SV94: $i,SV84: $i,SV49: $i,SV70: $i] :
( ( ( p @ SV70 )
= $false )
| ( ( p @ SV49 )
= $false )
| ( ( ( SV84 != SV94 ) )
= $true )
| ( ( ( SV116 != SV127 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(932,plain,
! [SV37: del,SV94: $i,SV84: $i,SV70: $i,SV49: $i,SV129: $i,SV116: $i] :
( ( ( SV116 = SV129 )
= $false )
| ( ( p @ SV49 )
= $true )
| ( ( p @ SV70 )
= $true )
| ( ( SV84 = SV94 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) )
= $true )
| ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(934,plain,
! [SV123: $i,SV116: $i,SV37: del,SV70: $i,SV49: $i,SV94: $i,SV84: $i] :
( ( ( SV84 = SV94 )
= $false )
| ( ( p @ SV49 )
= $false )
| ( ( p @ SV70 )
= $false )
| ( ( ~ ( p @ SV70 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(936,plain,
! [SV37: del,SV127: $i,SV116: $i,SV70: $i,SV49: $i,SV94: $i,SV84: $i] :
( ( ( SV84 = SV94 )
= $false )
| ( ( p @ SV49 )
= $false )
| ( ( p @ SV70 )
= $false )
| ( ( ( SV116 != SV127 ) )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(937,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV84: $i,SV49: $i,SV70: $i] :
( ( ( p @ SV70 )
= $false )
| ( ( p @ SV70 )
= $false )
| ( ( p @ SV49 )
= $false )
| ( ( SV84 = SV94 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(938,plain,
! [SV37: del,SV94: $i,SV84: $i,SV49: $i,SV70: $i,SV127: $i,SV116: $i] :
( ( ( SV116 = SV127 )
= $false )
| ( ( p @ SV70 )
= $false )
| ( ( p @ SV49 )
= $false )
| ( ( SV84 = SV94 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(939,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
= $true ),
inference(prim_subst,[status(thm)],[281:[bind(SV1,$thf( $true ))]]) ).
thf(940,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
= $true ),
inference(prim_subst,[status(thm)],[281:[bind(SV1,$thf( $false ))]]) ).
thf(941,plain,
! [SV130: $o] :
( ( ( p @ ( inj__o @ ~ SV130 ) )
= ( ~ SV130 ) )
= $true ),
inference(prim_subst,[status(thm)],[281:[bind(SV1,$thf( ~ ( SV130 ) ))]]) ).
thf(946,plain,
( ( $false = $true )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(prim_subst,[status(thm)],[480:[bind(SV1,$thf( $false ))]]) ).
thf(947,plain,
! [SV130: $o] :
( ( ( ~ SV130 )
= $true )
| ( ( p @ ( inj__o @ ~ SV130 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[480:[bind(SV1,$thf( ~ ( SV130 ) ))]]) ).
thf(948,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[481:[bind(SV1,$thf( $true ))]]) ).
thf(950,plain,
! [SV130: $o] :
( ( ( p @ ( inj__o @ ~ SV130 ) )
= $true )
| ( ( ~ SV130 )
= $false ) ),
inference(prim_subst,[status(thm)],[481:[bind(SV1,$thf( ~ ( SV130 ) ))]]) ).
thf(954,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true )
| ( ( ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
= ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[454]) ).
thf(955,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( ( SV1
= ( ~ ( p @ ( inj__o @ SV1 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[480]) ).
thf(956,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( ( SV1
= ( ~ ( p @ ( inj__o @ SV1 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[481]) ).
thf(958,plain,
! [SV117: tp__ty_2Enum_2Enum,SV107: tp__ty_2Enum_2Enum] :
( ( ( SV107 = fo__c_2Enum_2E0 )
= $true )
| ( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV117 ) ) ) )
= ( SV107 = fo__c_2Enum_2E0 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[729]) ).
thf(959,plain,
! [SV108: tp__ty_2Enum_2Enum,SV115: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) )
= $true )
| ( ( ( SV115 = fo__c_2Enum_2E0 )
= ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[730]) ).
thf(960,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( SV1 = $false ) ),
inference(extcnf_equal_pos,[status(thm)],[281]) ).
thf(961,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $false )
| ( SV1 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[281]) ).
thf(962,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( $true = $false ) ),
inference(extcnf_equal_pos,[status(thm)],[283]) ).
thf(965,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[285]) ).
thf(966,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( ~ ( ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
| ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) ) )
| ~ ( ~ ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
| ~ ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) ) ) )
= $false )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[954]) ).
thf(968,plain,
! [SV1: $o] :
( ( ( ~ ( SV1
| ~ ( p @ ( inj__o @ SV1 ) ) )
| ~ ( ~ SV1
| ~ ~ ( p @ ( inj__o @ SV1 ) ) ) )
= $false )
| ( SV1 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[955]) ).
thf(970,plain,
! [SV1: $o] :
( ( ( ~ ( SV1
| ~ ( p @ ( inj__o @ SV1 ) ) )
| ~ ( ~ SV1
| ~ ~ ( p @ ( inj__o @ SV1 ) ) ) )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[956]) ).
thf(974,plain,
! [SV117: tp__ty_2Enum_2Enum,SV107: tp__ty_2Enum_2Enum] :
( ( ( ~ ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV117 ) ) ) )
| ( SV107 = fo__c_2Enum_2E0 ) )
| ~ ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV117 ) ) ) )
| ( SV107 != fo__c_2Enum_2E0 ) ) )
= $false )
| ( ( SV107 = fo__c_2Enum_2E0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[958]) ).
thf(976,plain,
! [SV108: tp__ty_2Enum_2Enum,SV115: tp__ty_2Enum_2Enum] :
( ( ( ~ ( ( SV115 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) ) )
| ~ ( ( SV115 != fo__c_2Enum_2E0 )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) ) ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[959]) ).
thf(978,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( ~ ( ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
| ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) ) ) )
= $false )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(980,plain,
! [SV1: $o] :
( ( ( ~ ( SV1
| ~ ( p @ ( inj__o @ SV1 ) ) ) )
= $false )
| ( SV1 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(983,plain,
! [SV1: $o] :
( ( ( ~ ( ~ SV1
| ~ ~ ( p @ ( inj__o @ SV1 ) ) ) )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(986,plain,
! [SV117: tp__ty_2Enum_2Enum,SV107: tp__ty_2Enum_2Enum] :
( ( ( ~ ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV117 ) ) ) )
| ( SV107 = fo__c_2Enum_2E0 ) ) )
= $false )
| ( ( SV107 = fo__c_2Enum_2E0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(988,plain,
! [SV108: tp__ty_2Enum_2Enum,SV115: tp__ty_2Enum_2Enum] :
( ( ( ~ ( ( SV115 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) ) ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(990,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
| ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) ) )
= $true )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(992,plain,
! [SV1: $o] :
( ( ( SV1
| ~ ( p @ ( inj__o @ SV1 ) ) )
= $true )
| ( SV1 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(995,plain,
! [SV1: $o] :
( ( ( ~ SV1
| ~ ~ ( p @ ( inj__o @ SV1 ) ) )
= $true )
| ( SV1 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(998,plain,
! [SV117: tp__ty_2Enum_2Enum,SV107: tp__ty_2Enum_2Enum] :
( ( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV117 ) ) ) )
| ( SV107 = fo__c_2Enum_2E0 ) )
= $true )
| ( ( SV107 = fo__c_2Enum_2E0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1000,plain,
! [SV108: tp__ty_2Enum_2Enum,SV115: tp__ty_2Enum_2Enum] :
( ( ( ( SV115 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1002,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
= $true )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1004,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( ( ~ ( p @ ( inj__o @ SV1 ) ) )
= $true )
| ( SV1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1007,plain,
! [SV1: $o] :
( ( ( ~ SV1 )
= $true )
| ( ( ~ ~ ( p @ ( inj__o @ SV1 ) ) )
= $true )
| ( SV1 = $false ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1010,plain,
! [SV117: tp__ty_2Enum_2Enum,SV107: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV117 ) ) ) )
= $true )
| ( ( SV107 = fo__c_2Enum_2E0 )
= $true )
| ( ( SV107 = fo__c_2Enum_2E0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1012,plain,
! [SV108: tp__ty_2Enum_2Enum,SV115: tp__ty_2Enum_2Enum] :
( ( ( SV115 = fo__c_2Enum_2E0 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1015,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $false )
| ( SV1 = $true )
| ( SV1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1018,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( ( ~ ~ ( p @ ( inj__o @ SV1 ) ) )
= $true )
| ( SV1 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1025,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) ) )
= $false )
| ( SV1 = $false )
| ( SV1 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1030,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( SV1 = $false )
| ( SV1 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1034,plain,
( ( ( ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
= ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
= $false )
| ( ( ( c_2Einteger__word_2Ei2w @ sK1_A_27a )
= ( c_2Ewords_2En2w @ sK1_A_27a ) )
= $false ) ),
inference(extuni,[status(esa)],[264]) ).
thf(1036,plain,
! [SV72: tp__ty_2Enum_2Enum,SV33: del,SV65: tp__ty_2Enum_2Enum] :
( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV65 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV72 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) ) )
= $true )
| ( ( ( inj__ty_2Enum_2Enum @ SV65 )
= ( inj__ty_2Enum_2Enum @ SV72 ) )
= $false ) ),
inference(extuni,[status(esa)],[506]) ).
thf(1038,plain,
! [SV73: tp__ty_2Enum_2Enum,SV66: tp__ty_2Enum_2Enum,SV33: del] :
( ( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV66 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV73 ) ) )
= $true )
| ( ( ( inj__ty_2Enum_2Enum @ SV66 )
= ( inj__ty_2Enum_2Enum @ SV73 ) )
= $false ) ),
inference(extuni,[status(esa)],[507]) ).
thf(1039,plain,
! [SV73: tp__ty_2Enum_2Enum,SV66: tp__ty_2Enum_2Enum,SV33: del] :
( ( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV66 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV73 ) ) )
= $true )
| ( ( ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV66 ) )
= ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV73 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[507]) ).
thf(1040,plain,
! [SV73: tp__ty_2Enum_2Enum,SV66: tp__ty_2Enum_2Enum,SV33: del] :
( ( ( ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV66 ) )
= ( ap @ ( c_2Ewords_2En2w @ SV33 ) @ ( inj__ty_2Enum_2Enum @ SV73 ) ) )
= $true )
| ( ( ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV66 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) )
= ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ SV73 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ SV33 ) @ ( c_2Ebool_2Ethe__value @ SV33 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[507]) ).
thf(1041,plain,
! [SV28: del,SV78: $i] :
( ( ( mem @ SV78 @ SV28 )
= $false )
| ( ( mem @ SV78 @ SV28 )
= $false )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV78 ) @ SV78 ) )
= $true ) ),
inference(extuni,[status(esa)],[623:[bind(SV45,$thf( SV78 ))]]) ).
thf(1045,plain,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= $false ),
inference(extuni,[status(esa)],[750:[bind(SV87,$thf( fo__c_2Enum_2E0 )),bind(SV93,$thf( fo__c_2Enum_2E0 ))]]) ).
thf(1046,plain,
! [SV128: $i,SV94: $i,SV37: del,SV84: $i,SV70: $i,SV49: $i] :
( ( ( mem @ SV49 @ bool )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV128 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) )
= $true )
| ( ( p @ SV49 )
= $true )
| ( ( p @ SV70 )
= $true )
| ( ( p @ SV70 )
= $true ) ),
inference(extuni,[status(esa)],[925:[bind(SV116,$thf( SV128 ))]]) ).
thf(1048,plain,
! [SV129: $i,SV37: del,SV94: $i,SV70: $i,SV49: $i] :
( ( ( mem @ SV49 @ bool )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV94 ) @ SV129 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) )
= $true )
| ( ( p @ SV70 )
= $true )
| ( ( p @ SV49 )
= $true ) ),
inference(extuni,[status(esa)],[932:[bind(SV84,$thf( SV94 )),bind(SV116,$thf( SV129 ))]]) ).
thf(1050,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV70: $i,SV49: $i] :
( ( ( mem @ SV49 @ bool )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV94 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( p @ SV49 )
= $false )
| ( ( p @ SV70 )
= $false )
| ( ( p @ SV70 )
= $false ) ),
inference(extuni,[status(esa)],[937:[bind(SV84,$thf( SV94 ))]]) ).
thf(1051,plain,
! [SV127: $i,SV37: del,SV94: $i,SV70: $i,SV49: $i] :
( ( ( mem @ SV49 @ bool )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV94 ) @ SV127 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( p @ SV49 )
= $false )
| ( ( p @ SV70 )
= $false ) ),
inference(extuni,[status(esa)],[938:[bind(SV84,$thf( SV94 )),bind(SV116,$thf( SV127 ))]]) ).
thf(1052,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( $true = $false ) ),
inference(extcnf_equal_pos,[status(thm)],[939]) ).
thf(1055,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[940]) ).
thf(1056,plain,
! [SV130: $o] :
( ( ( p @ ( inj__o @ ~ SV130 ) )
= $true )
| ( ( ~ SV130 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[941]) ).
thf(1057,plain,
! [SV130: $o] :
( ( ( p @ ( inj__o @ ~ SV130 ) )
= $false )
| ( ( ~ SV130 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[941]) ).
thf(1058,plain,
! [SV130: $o] :
( ( SV130 = $false )
| ( ( p @ ( inj__o @ ~ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1059,plain,
! [SV130: $o] :
( ( SV130 = $true )
| ( ( p @ ( inj__o @ ~ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1060,plain,
! [SV130: $o] :
( ( SV130 = $false )
| ( ( p @ ( inj__o @ ~ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1061,plain,
! [SV130: $o] :
( ( SV130 = $true )
| ( ( p @ ( inj__o @ ~ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1064,plain,
( ( p @ ( inj__o @ $true ) )
= $true ),
inference(sim,[status(thm)],[485]) ).
thf(1065,plain,
( ( p @ ( inj__o @ $false ) )
= $false ),
inference(sim,[status(thm)],[488]) ).
thf(1066,plain,
! [SV94: $i,SV84: $i,SV37: del,SV49: $i,SV70: $i,SV128: $i,SV116: $i] :
( ( ( SV116 = SV128 )
= $false )
| ( ( p @ SV70 )
= $true )
| ( ( p @ SV49 )
= $true )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) )
= $true )
| ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(sim,[status(thm)],[925]) ).
thf(1067,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV84: $i,SV49: $i,SV70: $i] :
( ( ( p @ SV70 )
= $false )
| ( ( p @ SV49 )
= $false )
| ( ( SV84 = SV94 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV49 @ bool )
= $false ) ),
inference(sim,[status(thm)],[937]) ).
thf(1068,plain,
! [SV29: del,SV46: del,SV53: $i > $i] :
( ( ( mem @ ( sK4_X @ SV53 @ SV46 @ SV29 ) @ SV29 )
= $true )
| ( ( mem @ ( lam @ SV29 @ SV53 ) @ ( arr @ SV29 @ SV46 ) )
= $true ) ),
inference(sim,[status(thm)],[1002]) ).
thf(1069,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $false )
| ( SV1 = $true ) ),
inference(sim,[status(thm)],[1015]) ).
thf(1070,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( SV1 = $false ) ),
inference(sim,[status(thm)],[1030]) ).
thf(1071,plain,
! [SV117: tp__ty_2Enum_2Enum,SV107: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV107 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV117 ) ) ) )
= $true )
| ( ( SV107 = fo__c_2Enum_2E0 )
= $true ) ),
inference(sim,[status(thm)],[1010]) ).
thf(1072,plain,
! [SV108: tp__ty_2Enum_2Enum,SV115: tp__ty_2Enum_2Enum] :
( ( ( SV115 = fo__c_2Enum_2E0 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV108 ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ SV115 ) ) ) )
= $true ) ),
inference(sim,[status(thm)],[1012]) ).
thf(1073,plain,
( ( p @ ( inj__o @ $true ) )
= $true ),
inference(sim,[status(thm)],[962]) ).
thf(1074,plain,
( ( p @ ( inj__o @ $false ) )
= $false ),
inference(sim,[status(thm)],[965]) ).
thf(1075,plain,
( ( p @ ( inj__o @ $true ) )
= $true ),
inference(sim,[status(thm)],[485]) ).
thf(1076,plain,
( ( p @ ( inj__o @ $false ) )
= $false ),
inference(sim,[status(thm)],[488]) ).
thf(1077,plain,
! [SV28: del,SV78: $i] :
( ( ( mem @ SV78 @ SV28 )
= $false )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SV78 ) @ SV78 ) )
= $true ) ),
inference(sim,[status(thm)],[1041]) ).
thf(1078,plain,
! [SV128: $i,SV94: $i,SV37: del,SV84: $i,SV70: $i,SV49: $i] :
( ( ( mem @ SV49 @ bool )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV84 @ SV37 )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV128 @ SV37 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV84 ) @ SV128 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV128 ) )
= $true )
| ( ( p @ SV49 )
= $true )
| ( ( p @ SV70 )
= $true ) ),
inference(sim,[status(thm)],[1046]) ).
thf(1079,plain,
! [SV129: $i,SV37: del,SV94: $i,SV70: $i,SV49: $i] :
( ( ( mem @ SV49 @ bool )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV129 @ SV37 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV94 ) @ SV129 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV129 ) )
= $true )
| ( ( p @ SV70 )
= $true )
| ( ( p @ SV49 )
= $true ) ),
inference(sim,[status(thm)],[1048]) ).
thf(1080,plain,
! [SV123: $i,SV116: $i,SV37: del,SV94: $i,SV70: $i,SV49: $i] :
( ( ( mem @ SV49 @ bool )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV116 @ SV37 )
= $false )
| ( ( mem @ SV123 @ SV37 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV94 ) @ SV116 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV123 ) )
= $true )
| ( ( p @ SV49 )
= $false )
| ( ( p @ SV70 )
= $false ) ),
inference(sim,[status(thm)],[1050]) ).
thf(1081,plain,
! [SV127: $i,SV37: del,SV94: $i,SV70: $i,SV49: $i] :
( ( ( mem @ SV49 @ bool )
= $false )
| ( ( mem @ SV70 @ bool )
= $false )
| ( ( mem @ SV94 @ SV37 )
= $false )
| ( ( mem @ SV127 @ SV37 )
= $false )
| ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV49 ) @ SV94 ) @ SV127 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ SV37 ) @ SV70 ) @ SV94 ) @ SV127 ) )
= $true )
| ( ( p @ SV49 )
= $false )
| ( ( p @ SV70 )
= $false ) ),
inference(sim,[status(thm)],[1051]) ).
thf(1082,plain,
( ( p @ ( inj__o @ $true ) )
= $true ),
inference(sim,[status(thm)],[1052]) ).
thf(1083,plain,
( ( p @ ( inj__o @ $false ) )
= $false ),
inference(sim,[status(thm)],[1055]) ).
thf(1084,plain,
( ( p @ ( inj__o @ $false ) )
= $false ),
inference(sim,[status(thm)],[946]) ).
thf(1085,plain,
( ( p @ ( inj__o @ $true ) )
= $true ),
inference(sim,[status(thm)],[948]) ).
thf(1086,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[159,1085,1084,1083,1082,1081,1080,1079,1078,1077,1076,1075,1074,1073,1072,1071,1070,1069,1068,1067,1066,1065,1064,1061,1060,1059,1058,1045,1040,1039,1038,1036,1034,961,960,938,932,750,749,748,747,746,730,729,715,714,712,698,697,686,684,682,670,648,647,638,635,626,625,624,623,609,560,559,545,507,506,494,491,481,480,472,454,428,378,322,321,318,295,294,291,285,283,281,264,263,260,257,256,255,254,252,251,250,249,248,247,245,244,243,241,240,239,235,234,233,207,194,193,189,185,184,181,179,177,172,167,165,163,162,161]) ).
thf(1087,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1086]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP015^2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 3 07:44:36 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.37 .
% 0.20/0.40
% 0.20/0.40 No.of.Axioms: 62
% 0.20/0.40
% 0.20/0.40 Length.of.Defs: 0
% 0.20/0.40
% 0.20/0.40 Contains.Choice.Funs: false
% 0.20/0.42 ..
% 0.20/0.45 (rf:0,axioms:62,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:0,translation:fof_full)..................................................................................eprover: CPU time limit exceeded, terminating
% 26.19/26.36 .........
% 38.79/38.97
% 38.79/38.97 ********************************
% 38.79/38.97 * All subproblems solved! *
% 38.79/38.97 ********************************
% 38.79/38.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:62,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1086,loop_count:0,foatp_calls:2,translation:fof_full)
% 39.12/39.34
% 39.12/39.34 %**** Beginning of derivation protocol ****
% 39.12/39.34 % SZS output start CNFRefutation
% See solution above
% 39.12/39.34
% 39.12/39.34 %**** End of derivation protocol ****
% 39.12/39.34 %**** no. of clauses in derivation: 742 ****
% 39.12/39.34 %**** clause counter: 1086 ****
% 39.12/39.34
% 39.12/39.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:62,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1086,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------