%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP001^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:22:59 AM UTC 2026
% Result : Theorem 1.24s 0.46s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 73
% Syntax : Number of formulae : 614 ( 341 unt; 0 typ; 0 def)
% Number of atoms : 3899 (1217 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 8767 (1048 ~;1070 |; 12 &;6514 @)
% ( 33 <=>; 90 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 13 con; 0-4 aty)
% Number of variables : 1241 ( 251 ^; 984 !; 6 ?;1241 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_del,type,
del: $tType ).
thf(tp_tp__i,type,
tp__i: $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_2Ebool_2EARB,type,
c_2Ebool_2EARB: del > $i ).
thf(tp_c_2Ebool_2EBOUNDED,type,
c_2Ebool_2EBOUNDED: $i ).
thf(tp_c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND: del > $i ).
thf(tp_c_2Ebool_2EDATATYPE,type,
c_2Ebool_2EDATATYPE: del > $i ).
thf(tp_c_2Ebool_2EF,type,
c_2Ebool_2EF: $i ).
thf(tp_c_2Ebool_2EIN,type,
c_2Ebool_2EIN: del > $i ).
thf(tp_c_2Ebool_2ELET,type,
c_2Ebool_2ELET: del > del > $i ).
thf(tp_c_2Ebool_2EONE__ONE,type,
c_2Ebool_2EONE__ONE: del > del > $i ).
thf(tp_c_2Ebool_2EONTO,type,
c_2Ebool_2EONTO: del > del > $i ).
thf(tp_c_2Ebool_2ERES__ABSTRACT,type,
c_2Ebool_2ERES__ABSTRACT: del > del > $i ).
thf(tp_c_2Ebool_2ERES__EXISTS,type,
c_2Ebool_2ERES__EXISTS: del > $i ).
thf(tp_c_2Ebool_2ERES__EXISTS__UNIQUE,type,
c_2Ebool_2ERES__EXISTS__UNIQUE: del > $i ).
thf(tp_c_2Ebool_2ERES__FORALL,type,
c_2Ebool_2ERES__FORALL: del > $i ).
thf(tp_c_2Ebool_2ERES__SELECT,type,
c_2Ebool_2ERES__SELECT: del > $i ).
thf(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
thf(tp_c_2Ebool_2ETYPE__DEFINITION,type,
c_2Ebool_2ETYPE__DEFINITION: del > del > $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_3F,type,
c_2Ebool_2E_3F: del > $i ).
thf(tp_c_2Ebool_2E_3F_21,type,
c_2Ebool_2E_3F_21: del > $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_2Eitself__case,type,
c_2Ebool_2Eitself__case: del > del > $i ).
thf(tp_c_2Ebool_2Eliteral__case,type,
c_2Ebool_2Eliteral__case: del > del > $i ).
thf(tp_c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value: 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_2Emin_2E_40,type,
c_2Emin_2E_40: del > $i ).
thf(tp_ind,type,
ind: del ).
thf(tp_inj__i,type,
inj__i: tp__i > $i ).
thf(tp_inj__o,type,
inj__o: $o > $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_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY267,type,
sK3_SY267: del > ( $i > $i ) > del > $i ).
thf(tp_sK4_SY259,type,
sK4_SY259: $i > del > $i ).
thf(tp_sK5_SY269,type,
sK5_SY269: del > $i > $i > del > $i ).
thf(tp_sK6_SY252,type,
sK6_SY252: $i > del > $i ).
thf(tp_surj__i,type,
surj__i: $i > tp__i ).
thf(tp_ty_2Ebool_2Eitself,type,
ty_2Ebool_2Eitself: del > del ).
thf(1,axiom,
! [A_27a: del] :
( ( c_2Ebool_2EDATATYPE @ A_27a )
= ( lam @ A_27a
@ ^ [V0x: $i] : c_2Ebool_2ET ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EDATATYPE__TAG__DEF) ).
thf(2,axiom,
( c_2Ebool_2EBOUNDED
= ( lam @ bool
@ ^ [V0v: $i] : c_2Ebool_2ET ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EBOUNDED__DEF) ).
thf(3,axiom,
! [A_27a: del] :
( ( c_2Ebool_2ERES__SELECT @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ERES__SELECT__DEF) ).
thf(4,axiom,
! [A_27a: del] :
( ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V0p )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ V1m @ V2x ) ) ) )
@ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
@ ( lam @ A_27a
@ ^ [V3x: $i] :
( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
@ ( lam @ A_27a
@ ^ [V4y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1m @ V3x ) ) @ ( ap @ V1m @ V4y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) ).
thf(5,axiom,
! [A_27a: del] :
( ( c_2Ebool_2ERES__EXISTS @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ERES__EXISTS__DEF) ).
thf(6,axiom,
! [A_27a: del] :
( ( c_2Ebool_2ERES__FORALL @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ERES__FORALL__DEF) ).
thf(7,axiom,
! [A_27a: del] :
( ( c_2Ebool_2EIN @ A_27a )
= ( lam @ A_27a
@ ^ [V0x: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1f: $i] : ( ap @ V1f @ V0x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EIN__DEF) ).
thf(8,axiom,
! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2Eliteral__case__DEF) ).
thf(9,axiom,
? [V0f: $i] :
( ( mem @ V0f @ ( arr @ ind @ ind ) )
& ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ V0f ) )
& ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ V0f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EINFINITY__AX) ).
thf(10,axiom,
! [X: $i] :
( ( mem @ X @ ind )
=> ( X
= ( inj__i @ ( surj__i @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_iso_mem_i) ).
thf(11,axiom,
! [X: tp__i] : ( mem @ ( inj__i @ X ) @ ind ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_mem_i) ).
thf(12,axiom,
! [X: tp__i] :
( ( surj__i @ ( inj__i @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_i) ).
thf(13,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( p @ ( ap @ V0P @ V1x ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ESELECT__AX) ).
thf(14,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( arr @ A_27a @ A_27b ) )
=> ( ( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0t @ V1x ) )
= V0t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EETA__AX) ).
thf(15,axiom,
! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ( ( p @ V0t )
<=> $true )
| ( ( p @ V0t )
<=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EBOOL__CASES__AX) ).
thf(16,axiom,
! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( lam @ ( arr @ A_27b @ A_27a )
@ ^ [V1rep: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ A_27b )
@ ( lam @ A_27b
@ ^ [V2x_27: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27b )
@ ( lam @ A_27b
@ ^ [V3x_27_27: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V1rep @ V2x_27 ) ) @ ( ap @ V1rep @ V3x_27_27 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V2x_27 ) @ V3x_27_27 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V4x: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ V0P @ V4x ) )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27b )
@ ( lam @ A_27b
@ ^ [V5x_27: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V4x ) @ ( ap @ V1rep @ V5x_27 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ETYPE__DEFINITION) ).
thf(17,axiom,
! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2EONTO @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27b )
@ ( lam @ A_27b
@ ^ [V1y: $i] :
( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V1y ) @ ( ap @ V0f @ V2x ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EONTO__DEF) ).
thf(18,axiom,
! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V1x1: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x2: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V1x1 ) ) @ ( ap @ V0f @ V2x2 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x1 ) @ V2x2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EONE__ONE__DEF) ).
thf(19,axiom,
! [A_27a: del] :
( ( c_2Ebool_2ECOND @ A_27a )
= ( lam @ bool
@ ^ [V0t: $i] :
( lam @ A_27a
@ ^ [V1t1: $i] :
( lam @ A_27a
@ ^ [V2t2: $i] :
( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V1t1 ) ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V2t2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ECOND__DEF) ).
thf(20,axiom,
! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2ELET @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ELET__DEF) ).
thf(21,axiom,
! [A_27a: del] :
( ( c_2Ebool_2E_3F_21 @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Ebool_2E_3F @ A_27a ) @ V0P ) )
@ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V1x: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V1x ) ) @ ( ap @ V0P @ V2y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V2y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF) ).
thf(22,axiom,
( c_2Ebool_2E_7E
= ( lam @ bool
@ ^ [V0t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t ) @ c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ENOT__DEF) ).
thf(23,axiom,
( $false
<=> ! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( p @ V0t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EF__DEF) ).
thf(24,axiom,
( c_2Ebool_2E_5C_2F
= ( lam @ bool
@ ^ [V0t1: $i] :
( lam @ bool
@ ^ [V1t2: $i] :
( ap @ ( c_2Ebool_2E_21 @ bool )
@ ( lam @ bool
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ V2t ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) @ V2t ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EOR__DEF) ).
thf(25,axiom,
( c_2Ebool_2E_2F_5C
= ( lam @ bool
@ ^ [V0t1: $i] :
( lam @ bool
@ ^ [V1t2: $i] :
( ap @ ( c_2Ebool_2E_21 @ bool )
@ ( lam @ bool
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) ) @ V2t ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EAND__DEF) ).
thf(26,axiom,
! [A_27a: del] :
( ( c_2Ebool_2E_3F @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] : ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EEXISTS__DEF) ).
thf(27,axiom,
! [A_27a: del] :
( ( c_2Ebool_2E_21 @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ bool ) ) @ V0P )
@ ( lam @ A_27a
@ ^ [V1x: $i] : c_2Ebool_2ET ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2EFORALL__DEF) ).
thf(28,axiom,
( $true
<=> ( ( lam @ bool
@ ^ [V0x: $i] : V0x )
= ( lam @ bool
@ ^ [V1x: $i] : V1x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Ebool_2ET__DEF) ).
thf(29,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
<=> ~ ( p @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_neg_p) ).
thf(30,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
thf(31,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2Ethe__value) ).
thf(32,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2Eliteral__case) ).
thf(33,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eitself__case @ A_27a @ A_27b ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ( arr @ A_27b @ A_27b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2Eitself__case) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',ax_or_p) ).
thf(35,axiom,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_5C_2F) ).
thf(36,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ A_27a ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ETYPE__DEFINITION) ).
thf(37,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_true_p) ).
thf(38,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(39,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__SELECT @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ERES__SELECT) ).
thf(40,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ERES__FORALL) ).
thf(41,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ERES__EXISTS__UNIQUE) ).
thf(42,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ERES__EXISTS) ).
thf(43,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ERES__ABSTRACT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ERES__ABSTRACT) ).
thf(44,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONTO @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EONTO) ).
thf(45,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EONE__ONE) ).
thf(46,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ELET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ELET) ).
thf(47,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2EIN @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EIN) ).
thf(48,axiom,
~ ( p @ c_2Ebool_2EF ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_false_p) ).
thf(49,axiom,
mem @ c_2Ebool_2EF @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
thf(50,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2EDATATYPE @ A_27a ) @ ( arr @ A_27a @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EDATATYPE) ).
thf(51,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2ECOND @ A_27a ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ECOND) ).
thf(52,axiom,
mem @ c_2Ebool_2EBOUNDED @ ( arr @ bool @ bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EBOUNDED) ).
thf(53,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2EARB @ A_27a ) @ A_27a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EARB) ).
thf(54,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_3F_21) ).
thf(55,axiom,
! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ Q ) )
<=> ? [X: $i] :
( ( mem @ X @ A )
& ( p @ ( ap @ Q @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_ex_p) ).
thf(56,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_3F) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',ax_and_p) ).
thf(58,axiom,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',ax_all_p) ).
thf(60,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(61,axiom,
! [A_27a: del] : ( mem @ ( c_2Emin_2E_40 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Emin_2E_40) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',ax_imp_p) ).
thf(63,axiom,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',ax_eq_p) ).
thf(65,axiom,
! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(66,axiom,
! [A: del,F: $i > $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',funcext) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',lam_tp) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',ap_tp) ).
thf(70,axiom,
! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(71,axiom,
! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(72,axiom,
! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(73,conjecture,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(74,negated_conjecture,
$true = $false,
inference(negate_conjecture,[status(cth)],[73]) ).
thf(75,plain,
$true = $false,
inference(unfold_def,[status(thm)],[74]) ).
thf(76,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2EDATATYPE @ A_27a )
= ( lam @ A_27a
@ ^ [V0x: $i] : c_2Ebool_2ET ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(77,plain,
( ( c_2Ebool_2EBOUNDED
= ( lam @ bool
@ ^ [V0v: $i] : c_2Ebool_2ET ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(78,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ERES__SELECT @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(79,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V0p )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ V1m @ V2x ) ) ) )
@ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
@ ( lam @ A_27a
@ ^ [V3x: $i] :
( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
@ ( lam @ A_27a
@ ^ [V4y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1m @ V3x ) ) @ ( ap @ V1m @ V4y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(80,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ERES__EXISTS @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(81,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ERES__FORALL @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(82,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2EIN @ A_27a )
= ( lam @ A_27a
@ ^ [V0x: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1f: $i] : ( ap @ V1f @ V0x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(83,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(84,plain,
( ( ? [V0f: $i] :
( ( mem @ V0f @ ( arr @ ind @ ind ) )
& ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ V0f ) )
& ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ V0f ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(85,plain,
( ( ! [X: $i] :
( ( mem @ X @ ind )
=> ( X
= ( inj__i @ ( surj__i @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(86,plain,
( ( ! [X: tp__i] : ( mem @ ( inj__i @ X ) @ ind ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(87,plain,
( ( ! [X: tp__i] :
( ( surj__i @ ( inj__i @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(88,plain,
( ( ! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( p @ ( ap @ V0P @ V1x ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(89,plain,
( ( ! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( arr @ A_27a @ A_27b ) )
=> ( ( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0t @ V1x ) )
= V0t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(90,plain,
( ( ! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ( ( p @ V0t )
<=> $true )
| ( ( p @ V0t )
<=> $false ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(91,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( lam @ ( arr @ A_27b @ A_27a )
@ ^ [V1rep: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ A_27b )
@ ( lam @ A_27b
@ ^ [V2x_27: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27b )
@ ( lam @ A_27b
@ ^ [V3x_27_27: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V1rep @ V2x_27 ) ) @ ( ap @ V1rep @ V3x_27_27 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V2x_27 ) @ V3x_27_27 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V4x: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ V0P @ V4x ) )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27b )
@ ( lam @ A_27b
@ ^ [V5x_27: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V4x ) @ ( ap @ V1rep @ V5x_27 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(92,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2EONTO @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27b )
@ ( lam @ A_27b
@ ^ [V1y: $i] :
( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V1y ) @ ( ap @ V0f @ V2x ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(93,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V1x1: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x2: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V1x1 ) ) @ ( ap @ V0f @ V2x2 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x1 ) @ V2x2 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(94,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ECOND @ A_27a )
= ( lam @ bool
@ ^ [V0t: $i] :
( lam @ A_27a
@ ^ [V1t1: $i] :
( lam @ A_27a
@ ^ [V2t2: $i] :
( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V1t1 ) ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V2t2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(95,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2ELET @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(96,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2E_3F_21 @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Ebool_2E_3F @ A_27a ) @ V0P ) )
@ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V1x: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V1x ) ) @ ( ap @ V0P @ V2y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V2y ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(97,plain,
( ( c_2Ebool_2E_7E
= ( lam @ bool
@ ^ [V0t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t ) @ c_2Ebool_2EF ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(98,plain,
( ( $false
<=> ! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( p @ V0t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(99,plain,
( ( c_2Ebool_2E_5C_2F
= ( lam @ bool
@ ^ [V0t1: $i] :
( lam @ bool
@ ^ [V1t2: $i] :
( ap @ ( c_2Ebool_2E_21 @ bool )
@ ( lam @ bool
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ V2t ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) @ V2t ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(100,plain,
( ( c_2Ebool_2E_2F_5C
= ( lam @ bool
@ ^ [V0t1: $i] :
( lam @ bool
@ ^ [V1t2: $i] :
( ap @ ( c_2Ebool_2E_21 @ bool )
@ ( lam @ bool
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) ) @ V2t ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(101,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2E_3F @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] : ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(102,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2E_21 @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ bool ) ) @ V0P )
@ ( lam @ A_27a
@ ^ [V1x: $i] : c_2Ebool_2ET ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(103,plain,
( ( $true
<=> ( ( lam @ bool
@ ^ [V0x: $i] : V0x )
= ( lam @ bool
@ ^ [V1x: $i] : V1x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(104,plain,
( ( ! [Q: $i] :
( ( mem @ Q @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
<=> ~ ( p @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(105,plain,
( ( mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(106,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(107,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(108,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eitself__case @ A_27a @ A_27b ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ( arr @ A_27b @ A_27b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(109,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)],[34]) ).
thf(110,plain,
( ( mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(111,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ A_27a ) @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(112,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(113,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(114,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__SELECT @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(115,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(116,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(117,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(118,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ERES__ABSTRACT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(119,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONTO @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(120,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(121,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ELET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(122,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2EIN @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(123,plain,
( ( ~ ( p @ c_2Ebool_2EF ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(124,plain,
( ( mem @ c_2Ebool_2EF @ bool )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(125,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2EDATATYPE @ A_27a ) @ ( arr @ A_27a @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(126,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)],[51]) ).
thf(127,plain,
( ( mem @ c_2Ebool_2EBOUNDED @ ( arr @ bool @ bool ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(128,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2EARB @ A_27a ) @ A_27a ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(129,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(130,plain,
( ( ! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ Q ) )
<=> ? [X: $i] :
( ( mem @ X @ A )
& ( p @ ( ap @ Q @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(131,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(132,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)],[57]) ).
thf(133,plain,
( ( mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(134,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)],[59]) ).
thf(135,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(136,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_40 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(137,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)],[62]) ).
thf(138,plain,
( ( mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(139,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)],[64]) ).
thf(140,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(141,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(142,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)],[67]) ).
thf(143,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)],[68]) ).
thf(144,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)],[69]) ).
thf(145,plain,
( ( ! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(146,plain,
( ( ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(147,plain,
( ( ! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(148,plain,
( ( ~ $true ) = $true ),
inference(polarity_switch,[status(thm)],[75]) ).
thf(149,plain,
( ( ! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(150,plain,
( ( ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(151,plain,
( ( ! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(152,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)],[144]) ).
thf(153,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(copy,[status(thm)],[143]) ).
thf(154,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(copy,[status(thm)],[142]) ).
thf(155,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(156,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(157,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(copy,[status(thm)],[139]) ).
thf(158,plain,
( ( mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(159,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(copy,[status(thm)],[137]) ).
thf(160,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_40 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(161,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(162,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(copy,[status(thm)],[134]) ).
thf(163,plain,
( ( mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(164,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(copy,[status(thm)],[132]) ).
thf(165,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(166,plain,
( ( ! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ Q ) )
<=> ? [X: $i] :
( ( mem @ X @ A )
& ( p @ ( ap @ Q @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(167,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(168,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2EARB @ A_27a ) @ A_27a ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(169,plain,
( ( mem @ c_2Ebool_2EBOUNDED @ ( arr @ bool @ bool ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(170,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)],[126]) ).
thf(171,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2EDATATYPE @ A_27a ) @ ( arr @ A_27a @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(172,plain,
( ( mem @ c_2Ebool_2EF @ bool )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(173,plain,
( ( ~ ( p @ c_2Ebool_2EF ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(174,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2EIN @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(175,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ELET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(176,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(177,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONTO @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(178,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ERES__ABSTRACT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(179,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(180,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(181,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(182,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__SELECT @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(183,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(184,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(185,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ A_27a ) @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(186,plain,
( ( mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(187,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(copy,[status(thm)],[109]) ).
thf(188,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eitself__case @ A_27a @ A_27b ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ( arr @ A_27b @ A_27b ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(189,plain,
( ( ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(190,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(191,plain,
( ( mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(192,plain,
( ( ! [Q: $i] :
( ( mem @ Q @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
<=> ~ ( p @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(193,plain,
( ( $true
<=> ( ( lam @ bool
@ ^ [V0x: $i] : V0x )
= ( lam @ bool
@ ^ [V1x: $i] : V1x ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(194,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2E_21 @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ bool ) ) @ V0P )
@ ( lam @ A_27a
@ ^ [V1x: $i] : c_2Ebool_2ET ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(195,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2E_3F @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] : ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(196,plain,
( ( c_2Ebool_2E_2F_5C
= ( lam @ bool
@ ^ [V0t1: $i] :
( lam @ bool
@ ^ [V1t2: $i] :
( ap @ ( c_2Ebool_2E_21 @ bool )
@ ( lam @ bool
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) ) @ V2t ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(197,plain,
( ( c_2Ebool_2E_5C_2F
= ( lam @ bool
@ ^ [V0t1: $i] :
( lam @ bool
@ ^ [V1t2: $i] :
( ap @ ( c_2Ebool_2E_21 @ bool )
@ ( lam @ bool
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ V2t ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) @ V2t ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(198,plain,
( ( $false
<=> ! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( p @ V0t ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(199,plain,
( ( c_2Ebool_2E_7E
= ( lam @ bool
@ ^ [V0t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t ) @ c_2Ebool_2EF ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(200,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2E_3F_21 @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Ebool_2E_3F @ A_27a ) @ V0P ) )
@ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V1x: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V1x ) ) @ ( ap @ V0P @ V2y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V2y ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(201,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2ELET @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(202,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ECOND @ A_27a )
= ( lam @ bool
@ ^ [V0t: $i] :
( lam @ A_27a
@ ^ [V1t1: $i] :
( lam @ A_27a
@ ^ [V2t2: $i] :
( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V1t1 ) ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V2t2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(203,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V1x1: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x2: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V1x1 ) ) @ ( ap @ V0f @ V2x2 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x1 ) @ V2x2 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(204,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2EONTO @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27b )
@ ( lam @ A_27b
@ ^ [V1y: $i] :
( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V1y ) @ ( ap @ V0f @ V2x ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(205,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( lam @ ( arr @ A_27b @ A_27a )
@ ^ [V1rep: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ A_27b )
@ ( lam @ A_27b
@ ^ [V2x_27: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27b )
@ ( lam @ A_27b
@ ^ [V3x_27_27: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V1rep @ V2x_27 ) ) @ ( ap @ V1rep @ V3x_27_27 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V2x_27 ) @ V3x_27_27 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V4x: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ V0P @ V4x ) )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27b )
@ ( lam @ A_27b
@ ^ [V5x_27: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V4x ) @ ( ap @ V1rep @ V5x_27 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(206,plain,
( ( ! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ( ( p @ V0t )
<=> $true )
| ( ( p @ V0t )
<=> $false ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(207,plain,
( ( ! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( arr @ A_27a @ A_27b ) )
=> ( ( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0t @ V1x ) )
= V0t ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(208,plain,
( ( ! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( p @ ( ap @ V0P @ V1x ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(209,plain,
( ( ! [X: tp__i] :
( ( surj__i @ ( inj__i @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(210,plain,
( ( ! [X: tp__i] : ( mem @ ( inj__i @ X ) @ ind ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(211,plain,
( ( ! [X: $i] :
( ( mem @ X @ ind )
=> ( X
= ( inj__i @ ( surj__i @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(212,plain,
( ( ? [V0f: $i] :
( ( mem @ V0f @ ( arr @ ind @ ind ) )
& ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ V0f ) )
& ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ V0f ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(213,plain,
( ( ! [A_27a: del,A_27b: del] :
( ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b )
= ( lam @ ( arr @ A_27a @ A_27b )
@ ^ [V0f: $i] :
( lam @ A_27a
@ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(214,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2EIN @ A_27a )
= ( lam @ A_27a
@ ^ [V0x: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1f: $i] : ( ap @ V1f @ V0x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(215,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ERES__FORALL @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(216,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ERES__EXISTS @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(217,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V0p )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ V1m @ V2x ) ) ) )
@ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
@ ( lam @ A_27a
@ ^ [V3x: $i] :
( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
@ ( lam @ A_27a
@ ^ [V4y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1m @ V3x ) ) @ ( ap @ V1m @ V4y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(218,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2ERES__SELECT @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0p: $i] :
( lam @ ( arr @ A_27a @ bool )
@ ^ [V1m: $i] :
( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(219,plain,
( ( c_2Ebool_2EBOUNDED
= ( lam @ bool
@ ^ [V0v: $i] : c_2Ebool_2ET ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(220,plain,
( ( ! [A_27a: del] :
( ( c_2Ebool_2EDATATYPE @ A_27a )
= ( lam @ A_27a
@ ^ [V0x: $i] : c_2Ebool_2ET ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(221,plain,
( ( ~ $true ) = $true ),
inference(copy,[status(thm)],[148]) ).
thf(222,plain,
( ( ~ ( ~ ( ~ $false
| ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) ) )
| ~ ( ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) )
| $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(223,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( SX0
= ( inj__o @ ( p @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(224,plain,
( ( ! [SX0: del,SX1: del,SX2: $i] :
( ~ ( mem @ SX2 @ ( arr @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( mem @ SX3 @ ( arr @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( mem @ SX4 @ SX0 )
| ( ( ap @ SX2 @ SX4 )
= ( ap @ SX3 @ SX4 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(225,plain,
( ( ! [SX0: del,SX1: $i > $i,SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( ( ap @ ( lam @ SX0 @ SX1 ) @ SX2 )
= ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(226,plain,
( ( ~ ( ~ ( ~ $true
| ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) ) )
| ~ ( ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
!= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) )
| $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(227,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SX0 ) @ SX1 ) )
| ~ ( ~ ( p @ SX0 )
| ~ ( p @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( p @ SX0 )
| ~ ( p @ SX1 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SX0 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(228,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( ~ ( ~ ( p @ SX0 )
| $true )
| ~ ( ~ $true
| ( p @ SX0 ) ) )
| ~ ( ~ ( ~ ( p @ SX0 )
| $false )
| ~ ( ~ $false
| ( p @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(229,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_3F @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( mem @ SX2 @ SX0 )
| ~ ( p @ ( ap @ SX1 @ SX2 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( mem @ SX2 @ SX0 )
| ~ ( p @ ( ap @ SX1 @ SX2 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_3F @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(230,plain,
( ( ! [SX0: del,SX1: del,SX2: $i] :
( ~ ( mem @ SX2 @ ( arr @ SX0 @ SX1 ) )
| ( ( lam @ SX0
@ ^ [SX3: $i] : ( ap @ SX2 @ SX3 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(231,plain,
( ( ! [SX0: del,SX1: del,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( mem @ SX3 @ SX0 )
| ( mem @ ( SX2 @ SX3 ) @ SX1 ) )
| ( mem @ ( lam @ SX0 @ SX2 ) @ ( arr @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(232,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 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(233,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( mem @ SX0 @ ( arr @ ind @ ind ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ SX0 ) ) )
| ~ ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(234,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ( ( SX1 != SX2 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(235,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 ) )
| ~ ( ~ ( ( p @ SX0 )
| ( p @ SX1 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SX0 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(236,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ~ ( p @ ( ap @ SX1 @ SX2 ) )
| ( p @ ( ap @ SX1 @ ( ap @ ( c_2Emin_2E_40 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(237,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ ind )
| ( SX0
= ( inj__i @ ( surj__i @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(238,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) )
| ~ ( p @ SX0 ) )
| ~ ( ~ ~ ( p @ SX0 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(239,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SX0 ) @ SX1 ) )
| ~ ( p @ SX0 )
| ( p @ SX1 ) )
| ~ ( ~ ( ~ ( p @ SX0 )
| ( p @ SX1 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SX0 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(240,plain,
( ( ! [SX0: del,SX1: del,SX2: $i] :
( ~ ( mem @ SX2 @ ( arr @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( mem @ SX3 @ SX0 )
| ( mem @ ( ap @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(241,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[149]) ).
thf(242,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[149]) ).
thf(243,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[149]) ).
thf(244,plain,
! [SV2: $o] :
( ( mem @ ( inj__o @ SV2 ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[150]) ).
thf(245,plain,
( ( mem @ ( inj__o @ $true ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[150]) ).
thf(246,plain,
( ( mem @ ( inj__o @ $false ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[150]) ).
thf(247,plain,
! [SV3: del] :
( ( mem @ ( c_2Emin_2E_3D @ SV3 ) @ ( arr @ SV3 @ ( arr @ SV3 @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(248,plain,
! [SV4: del] :
( ( mem @ ( c_2Emin_2E_40 @ SV4 ) @ ( arr @ ( arr @ SV4 @ bool ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(249,plain,
! [SV5: del] :
( ( mem @ ( c_2Ebool_2E_21 @ SV5 ) @ ( arr @ ( arr @ SV5 @ bool ) @ bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(250,plain,
! [SV6: del] :
( ( mem @ ( c_2Ebool_2E_3F @ SV6 ) @ ( arr @ ( arr @ SV6 @ bool ) @ bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(251,plain,
! [SV7: del] :
( ( mem @ ( c_2Ebool_2E_3F_21 @ SV7 ) @ ( arr @ ( arr @ SV7 @ bool ) @ bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(252,plain,
! [SV8: del] :
( ( mem @ ( c_2Ebool_2EARB @ SV8 ) @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(253,plain,
! [SV9: del] :
( ( mem @ ( c_2Ebool_2ECOND @ SV9 ) @ ( arr @ bool @ ( arr @ SV9 @ ( arr @ SV9 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(254,plain,
! [SV10: del] :
( ( mem @ ( c_2Ebool_2EDATATYPE @ SV10 ) @ ( arr @ SV10 @ bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(255,plain,
( ( p @ c_2Ebool_2EF )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(256,plain,
! [SV11: del] :
( ( mem @ ( c_2Ebool_2EIN @ SV11 ) @ ( arr @ SV11 @ ( arr @ ( arr @ SV11 @ bool ) @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(257,plain,
! [SV12: del] :
( ( ! [SY149: del] : ( mem @ ( c_2Ebool_2ELET @ SV12 @ SY149 ) @ ( arr @ ( arr @ SV12 @ SY149 ) @ ( arr @ SV12 @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(258,plain,
! [SV13: del] :
( ( ! [SY150: del] : ( mem @ ( c_2Ebool_2EONE__ONE @ SV13 @ SY150 ) @ ( arr @ ( arr @ SV13 @ SY150 ) @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(259,plain,
! [SV14: del] :
( ( ! [SY151: del] : ( mem @ ( c_2Ebool_2EONTO @ SV14 @ SY151 ) @ ( arr @ ( arr @ SV14 @ SY151 ) @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(260,plain,
! [SV15: del] :
( ( ! [SY152: del] : ( mem @ ( c_2Ebool_2ERES__ABSTRACT @ SV15 @ SY152 ) @ ( arr @ ( arr @ SV15 @ bool ) @ ( arr @ ( arr @ SV15 @ SY152 ) @ ( arr @ SV15 @ SY152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(261,plain,
! [SV16: del] :
( ( mem @ ( c_2Ebool_2ERES__EXISTS @ SV16 ) @ ( arr @ ( arr @ SV16 @ bool ) @ ( arr @ ( arr @ SV16 @ bool ) @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(262,plain,
! [SV17: del] :
( ( mem @ ( c_2Ebool_2ERES__EXISTS__UNIQUE @ SV17 ) @ ( arr @ ( arr @ SV17 @ bool ) @ ( arr @ ( arr @ SV17 @ bool ) @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(263,plain,
! [SV18: del] :
( ( mem @ ( c_2Ebool_2ERES__FORALL @ SV18 ) @ ( arr @ ( arr @ SV18 @ bool ) @ ( arr @ ( arr @ SV18 @ bool ) @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(264,plain,
! [SV19: del] :
( ( mem @ ( c_2Ebool_2ERES__SELECT @ SV19 ) @ ( arr @ ( arr @ SV19 @ bool ) @ ( arr @ ( arr @ SV19 @ bool ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(265,plain,
! [SV20: del] :
( ( ! [SY153: del] : ( mem @ ( c_2Ebool_2ETYPE__DEFINITION @ SV20 @ SY153 ) @ ( arr @ ( arr @ SV20 @ bool ) @ ( arr @ ( arr @ SY153 @ SV20 ) @ bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(266,plain,
! [SV21: del] :
( ( ! [SY154: del] : ( mem @ ( c_2Ebool_2Eitself__case @ SV21 @ SY154 ) @ ( arr @ ( ty_2Ebool_2Eitself @ SV21 ) @ ( arr @ SY154 @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(267,plain,
! [SV22: del] :
( ( ! [SY155: del] : ( mem @ ( c_2Ebool_2Eliteral__case @ SV22 @ SY155 ) @ ( arr @ ( arr @ SV22 @ SY155 ) @ ( arr @ SV22 @ SY155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(268,plain,
! [SV23: del] :
( ( mem @ ( c_2Ebool_2Ethe__value @ SV23 ) @ ( ty_2Ebool_2Eitself @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(269,plain,
! [SV24: del] :
( ( ( c_2Ebool_2E_21 @ SV24 )
= ( lam @ ( arr @ SV24 @ bool )
@ ^ [SY156: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ SV24 @ bool ) ) @ SY156 )
@ ( lam @ SV24
@ ^ [V1x: $i] : c_2Ebool_2ET ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(270,plain,
! [SV25: del] :
( ( ( c_2Ebool_2E_3F @ SV25 )
= ( lam @ ( arr @ SV25 @ bool )
@ ^ [SY158: $i] : ( ap @ SY158 @ ( ap @ ( c_2Emin_2E_40 @ SV25 ) @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(271,plain,
! [SV26: del] :
( ( ( c_2Ebool_2E_3F_21 @ SV26 )
= ( lam @ ( arr @ SV26 @ bool )
@ ^ [SY159: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Ebool_2E_3F @ SV26 ) @ SY159 ) )
@ ( ap @ ( c_2Ebool_2E_21 @ SV26 )
@ ( lam @ SV26
@ ^ [SY160: $i] :
( ap @ ( c_2Ebool_2E_21 @ SV26 )
@ ( lam @ SV26
@ ^ [SY161: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ SY159 @ SY160 ) ) @ ( ap @ SY159 @ SY161 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV26 ) @ SY160 ) @ SY161 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(272,plain,
! [SV27: del] :
( ( ! [SY162: del] :
( ( c_2Ebool_2ELET @ SV27 @ SY162 )
= ( lam @ ( arr @ SV27 @ SY162 )
@ ^ [SY163: $i] :
( lam @ SV27
@ ^ [V1x: $i] : ( ap @ SY163 @ V1x ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(273,plain,
! [SV28: del] :
( ( ( c_2Ebool_2ECOND @ SV28 )
= ( lam @ bool
@ ^ [SY165: $i] :
( lam @ SV28
@ ^ [SY166: $i] :
( lam @ SV28
@ ^ [SY167: $i] :
( ap @ ( c_2Emin_2E_40 @ SV28 )
@ ( lam @ SV28
@ ^ [SY168: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ SY165 ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SY168 ) @ SY166 ) ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ SY165 ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV28 ) @ SY168 ) @ SY167 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(274,plain,
! [SV29: del] :
( ( ! [SY169: del] :
( ( c_2Ebool_2EONE__ONE @ SV29 @ SY169 )
= ( lam @ ( arr @ SV29 @ SY169 )
@ ^ [SY170: $i] :
( ap @ ( c_2Ebool_2E_21 @ SV29 )
@ ( lam @ SV29
@ ^ [SY171: $i] :
( ap @ ( c_2Ebool_2E_21 @ SV29 )
@ ( lam @ SV29
@ ^ [SY172: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SY169 ) @ ( ap @ SY170 @ SY171 ) ) @ ( ap @ SY170 @ SY172 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV29 ) @ SY171 ) @ SY172 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(275,plain,
! [SV30: del] :
( ( ! [SY173: del] :
( ( c_2Ebool_2EONTO @ SV30 @ SY173 )
= ( lam @ ( arr @ SV30 @ SY173 )
@ ^ [SY174: $i] :
( ap @ ( c_2Ebool_2E_21 @ SY173 )
@ ( lam @ SY173
@ ^ [SY175: $i] :
( ap @ ( c_2Ebool_2E_3F @ SV30 )
@ ( lam @ SV30
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ SY173 ) @ SY175 ) @ ( ap @ SY174 @ V2x ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(276,plain,
! [SV31: del] :
( ( ! [SY177: del] :
( ( c_2Ebool_2ETYPE__DEFINITION @ SV31 @ SY177 )
= ( lam @ ( arr @ SV31 @ bool )
@ ^ [SY178: $i] :
( lam @ ( arr @ SY177 @ SV31 )
@ ^ [SY179: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ SY177 )
@ ( lam @ SY177
@ ^ [SY180: $i] :
( ap @ ( c_2Ebool_2E_21 @ SY177 )
@ ( lam @ SY177
@ ^ [SY181: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV31 ) @ ( ap @ SY179 @ SY180 ) ) @ ( ap @ SY179 @ SY181 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SY177 ) @ SY180 ) @ SY181 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_21 @ SV31 )
@ ( lam @ SV31
@ ^ [SY182: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ SY178 @ SY182 ) )
@ ( ap @ ( c_2Ebool_2E_3F @ SY177 )
@ ( lam @ SY177
@ ^ [SY183: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV31 ) @ SY182 ) @ ( ap @ SY179 @ SY183 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(277,plain,
! [SV32: tp__i] :
( ( ( surj__i @ ( inj__i @ SV32 ) )
= SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(278,plain,
! [SV33: tp__i] :
( ( mem @ ( inj__i @ SV33 ) @ ind )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(279,plain,
! [SV34: del] :
( ( ! [SY184: del] :
( ( c_2Ebool_2Eliteral__case @ SV34 @ SY184 )
= ( lam @ ( arr @ SV34 @ SY184 )
@ ^ [SY185: $i] :
( lam @ SV34
@ ^ [V1x: $i] : ( ap @ SY185 @ V1x ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(280,plain,
! [SV35: del] :
( ( ( c_2Ebool_2EIN @ SV35 )
= ( lam @ SV35
@ ^ [SY187: $i] :
( lam @ ( arr @ SV35 @ bool )
@ ^ [V1f: $i] : ( ap @ V1f @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(281,plain,
! [SV36: del] :
( ( ( c_2Ebool_2ERES__FORALL @ SV36 )
= ( lam @ ( arr @ SV36 @ bool )
@ ^ [SY189: $i] :
( lam @ ( arr @ SV36 @ bool )
@ ^ [SY190: $i] :
( ap @ ( c_2Ebool_2E_21 @ SV36 )
@ ( lam @ SV36
@ ^ [SY191: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ SV36 ) @ SY191 ) @ SY189 ) ) @ ( ap @ SY190 @ SY191 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(282,plain,
! [SV37: del] :
( ( ( c_2Ebool_2ERES__EXISTS @ SV37 )
= ( lam @ ( arr @ SV37 @ bool )
@ ^ [SY192: $i] :
( lam @ ( arr @ SV37 @ bool )
@ ^ [SY193: $i] :
( ap @ ( c_2Ebool_2E_3F @ SV37 )
@ ( lam @ SV37
@ ^ [SY194: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ SV37 ) @ SY194 ) @ SY192 ) ) @ ( ap @ SY193 @ SY194 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(283,plain,
! [SV38: del] :
( ( ( c_2Ebool_2ERES__EXISTS__UNIQUE @ SV38 )
= ( lam @ ( arr @ SV38 @ bool )
@ ^ [SY195: $i] :
( lam @ ( arr @ SV38 @ bool )
@ ^ [SY196: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ SV38 ) @ SY195 )
@ ( lam @ SV38
@ ^ [V2x: $i] : ( ap @ SY196 @ V2x ) ) ) )
@ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ SV38 ) @ SY195 )
@ ( lam @ SV38
@ ^ [SY198: $i] :
( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ SV38 ) @ SY195 )
@ ( lam @ SV38
@ ^ [SY199: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ SY196 @ SY198 ) ) @ ( ap @ SY196 @ SY199 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV38 ) @ SY198 ) @ SY199 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(284,plain,
! [SV39: del] :
( ( ( c_2Ebool_2ERES__SELECT @ SV39 )
= ( lam @ ( arr @ SV39 @ bool )
@ ^ [SY200: $i] :
( lam @ ( arr @ SV39 @ bool )
@ ^ [SY201: $i] :
( ap @ ( c_2Emin_2E_40 @ SV39 )
@ ( lam @ SV39
@ ^ [SY202: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ SV39 ) @ SY202 ) @ SY200 ) ) @ ( ap @ SY201 @ SY202 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(285,plain,
! [SV40: del] :
( ( ( c_2Ebool_2EDATATYPE @ SV40 )
= ( lam @ SV40
@ ^ [V0x: $i] : c_2Ebool_2ET ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(286,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(287,plain,
( ( ~ ( ~ $false
| ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) ) )
| ~ ( ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) )
| $false ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(288,plain,
! [SV41: $i] :
( ( ~ ( mem @ SV41 @ bool )
| ( SV41
= ( inj__o @ ( p @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(289,plain,
! [SV42: del] :
( ( ! [SY204: del,SY205: $i] :
( ~ ( mem @ SY205 @ ( arr @ SV42 @ SY204 ) )
| ! [SY206: $i] :
( ~ ( mem @ SY206 @ ( arr @ SV42 @ SY204 ) )
| ~ ! [SY207: $i] :
( ~ ( mem @ SY207 @ SV42 )
| ( ( ap @ SY205 @ SY207 )
= ( ap @ SY206 @ SY207 ) ) )
| ( SY205 = SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(290,plain,
! [SV43: del] :
( ( ! [SY208: $i > $i,SY209: $i] :
( ~ ( mem @ SY209 @ SV43 )
| ( ( ap @ ( lam @ SV43 @ SY208 ) @ SY209 )
= ( SY208 @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(291,plain,
( ( ~ ( ~ $true
| ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) ) )
| ~ ( ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
!= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) )
| $true ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(292,plain,
! [SV44: $i] :
( ( ~ ( mem @ SV44 @ bool )
| ! [SY210: $i] :
( ~ ( mem @ SY210 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SY210 ) )
| ~ ( ~ ( p @ SV44 )
| ~ ( p @ SY210 ) ) )
| ~ ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SY210 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SY210 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(293,plain,
! [SV45: $i] :
( ( ~ ( mem @ SV45 @ bool )
| ~ ( ~ ( ~ ( p @ SV45 )
| $true )
| ~ ( ~ $true
| ( p @ SV45 ) ) )
| ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(294,plain,
! [SV46: del] :
( ( ! [SY211: $i] :
( ~ ( mem @ SY211 @ ( arr @ SV46 @ bool ) )
| ~ ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SY211 ) )
| ~ ! [SY212: $i] :
~ ~ ( ~ ( mem @ SY212 @ SV46 )
| ~ ( p @ ( ap @ SY211 @ SY212 ) ) ) )
| ~ ( ~ ~ ! [SY213: $i] :
~ ~ ( ~ ( mem @ SY213 @ SV46 )
| ~ ( p @ ( ap @ SY211 @ SY213 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SY211 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(295,plain,
! [SV47: del] :
( ( ! [SY214: del,SY215: $i] :
( ~ ( mem @ SY215 @ ( arr @ SV47 @ SY214 ) )
| ( ( lam @ SV47
@ ^ [SX3: $i] : ( ap @ SY215 @ SX3 ) )
= SY215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(296,plain,
! [SV48: del] :
( ( ! [SY217: del,SY218: $i > $i] :
( ~ ! [SY219: $i] :
( ~ ( mem @ SY219 @ SV48 )
| ( mem @ ( SY218 @ SY219 ) @ SY217 ) )
| ( mem @ ( lam @ SV48 @ SY218 ) @ ( arr @ SV48 @ SY217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(297,plain,
! [SV49: del] :
( ( ! [SY220: $i] :
( ~ ( mem @ SY220 @ ( arr @ SV49 @ bool ) )
| ~ ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SY220 ) )
| ! [SY221: $i] :
( ~ ( mem @ SY221 @ SV49 )
| ( p @ ( ap @ SY220 @ SY221 ) ) ) )
| ~ ( ~ ! [SY222: $i] :
( ~ ( mem @ SY222 @ SV49 )
| ( p @ ( ap @ SY220 @ SY222 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SY220 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(298,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( mem @ SX0 @ ( arr @ ind @ ind ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ SX0 ) ) )
| ~ ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(299,plain,
! [SV50: del] :
( ( ! [SY223: $i] :
( ~ ( mem @ SY223 @ SV50 )
| ! [SY224: $i] :
( ~ ( mem @ SY224 @ SV50 )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SY223 ) @ SY224 ) )
| ( SY223 = SY224 ) )
| ~ ( ( SY223 != SY224 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SY223 ) @ SY224 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(300,plain,
! [SV51: $i] :
( ( ~ ( mem @ SV51 @ bool )
| ! [SY225: $i] :
( ~ ( mem @ SY225 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SY225 ) )
| ( p @ SV51 )
| ( p @ SY225 ) )
| ~ ( ~ ( ( p @ SV51 )
| ( p @ SY225 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SY225 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(301,plain,
! [SV52: del] :
( ( ! [SY226: $i] :
( ~ ( mem @ SY226 @ ( arr @ SV52 @ bool ) )
| ! [SY227: $i] :
( ~ ( mem @ SY227 @ SV52 )
| ~ ( p @ ( ap @ SY226 @ SY227 ) )
| ( p @ ( ap @ SY226 @ ( ap @ ( c_2Emin_2E_40 @ SV52 ) @ SY226 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(302,plain,
! [SV53: $i] :
( ( ~ ( mem @ SV53 @ ind )
| ( SV53
= ( inj__i @ ( surj__i @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(303,plain,
! [SV54: $i] :
( ( ~ ( mem @ SV54 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
| ~ ( p @ SV54 ) )
| ~ ( ~ ~ ( p @ SV54 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(304,plain,
! [SV55: $i] :
( ( ~ ( mem @ SV55 @ bool )
| ! [SY228: $i] :
( ~ ( mem @ SY228 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SY228 ) )
| ~ ( p @ SV55 )
| ( p @ SY228 ) )
| ~ ( ~ ( ~ ( p @ SV55 )
| ( p @ SY228 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SY228 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(305,plain,
! [SV56: del] :
( ( ! [SY229: del,SY230: $i] :
( ~ ( mem @ SY230 @ ( arr @ SV56 @ SY229 ) )
| ! [SY231: $i] :
( ~ ( mem @ SY231 @ SV56 )
| ( mem @ ( ap @ SY230 @ SY231 ) @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(306,plain,
! [SV1: $o] :
( ( ~ ( ( p @ ( inj__o @ SV1 ) )
| SV1 )
| ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[241]) ).
thf(307,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[241]) ).
thf(308,plain,
( ( ~ ( ( p @ ( inj__o @ $true ) )
| $true )
| ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[242]) ).
thf(309,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[242]) ).
thf(310,plain,
( ( ~ ( ( p @ ( inj__o @ $false ) )
| $false )
| ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[243]) ).
thf(311,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[243]) ).
thf(312,plain,
! [SV57: del,SV12: del] :
( ( mem @ ( c_2Ebool_2ELET @ SV12 @ SV57 ) @ ( arr @ ( arr @ SV12 @ SV57 ) @ ( arr @ SV12 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(313,plain,
! [SV58: del,SV13: del] :
( ( mem @ ( c_2Ebool_2EONE__ONE @ SV13 @ SV58 ) @ ( arr @ ( arr @ SV13 @ SV58 ) @ bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(314,plain,
! [SV59: del,SV14: del] :
( ( mem @ ( c_2Ebool_2EONTO @ SV14 @ SV59 ) @ ( arr @ ( arr @ SV14 @ SV59 ) @ bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(315,plain,
! [SV60: del,SV15: del] :
( ( mem @ ( c_2Ebool_2ERES__ABSTRACT @ SV15 @ SV60 ) @ ( arr @ ( arr @ SV15 @ bool ) @ ( arr @ ( arr @ SV15 @ SV60 ) @ ( arr @ SV15 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(316,plain,
! [SV61: del,SV20: del] :
( ( mem @ ( c_2Ebool_2ETYPE__DEFINITION @ SV20 @ SV61 ) @ ( arr @ ( arr @ SV20 @ bool ) @ ( arr @ ( arr @ SV61 @ SV20 ) @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(317,plain,
! [SV62: del,SV21: del] :
( ( mem @ ( c_2Ebool_2Eitself__case @ SV21 @ SV62 ) @ ( arr @ ( ty_2Ebool_2Eitself @ SV21 ) @ ( arr @ SV62 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(318,plain,
! [SV63: del,SV22: del] :
( ( mem @ ( c_2Ebool_2Eliteral__case @ SV22 @ SV63 ) @ ( arr @ ( arr @ SV22 @ SV63 ) @ ( arr @ SV22 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(319,plain,
! [SV64: del,SV27: del] :
( ( ( c_2Ebool_2ELET @ SV27 @ SV64 )
= ( lam @ ( arr @ SV27 @ SV64 )
@ ^ [SY163: $i] :
( lam @ SV27
@ ^ [V1x: $i] : ( ap @ SY163 @ V1x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(320,plain,
! [SV65: del,SV29: del] :
( ( ( c_2Ebool_2EONE__ONE @ SV29 @ SV65 )
= ( lam @ ( arr @ SV29 @ SV65 )
@ ^ [SY234: $i] :
( ap @ ( c_2Ebool_2E_21 @ SV29 )
@ ( lam @ SV29
@ ^ [SY235: $i] :
( ap @ ( c_2Ebool_2E_21 @ SV29 )
@ ( lam @ SV29
@ ^ [SY236: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV65 ) @ ( ap @ SY234 @ SY235 ) ) @ ( ap @ SY234 @ SY236 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV29 ) @ SY235 ) @ SY236 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(321,plain,
! [SV66: del,SV30: del] :
( ( ( c_2Ebool_2EONTO @ SV30 @ SV66 )
= ( lam @ ( arr @ SV30 @ SV66 )
@ ^ [SY237: $i] :
( ap @ ( c_2Ebool_2E_21 @ SV66 )
@ ( lam @ SV66
@ ^ [SY238: $i] :
( ap @ ( c_2Ebool_2E_3F @ SV30 )
@ ( lam @ SV30
@ ^ [SY239: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV66 ) @ SY238 ) @ ( ap @ SY237 @ SY239 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(322,plain,
! [SV67: del,SV31: del] :
( ( ( c_2Ebool_2ETYPE__DEFINITION @ SV31 @ SV67 )
= ( lam @ ( arr @ SV31 @ bool )
@ ^ [SY240: $i] :
( lam @ ( arr @ SV67 @ SV31 )
@ ^ [SY241: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ SV67 )
@ ( lam @ SV67
@ ^ [SY242: $i] :
( ap @ ( c_2Ebool_2E_21 @ SV67 )
@ ( lam @ SV67
@ ^ [SY243: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV31 ) @ ( ap @ SY241 @ SY242 ) ) @ ( ap @ SY241 @ SY243 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV67 ) @ SY242 ) @ SY243 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_21 @ SV31 )
@ ( lam @ SV31
@ ^ [SY244: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ SY240 @ SY244 ) )
@ ( ap @ ( c_2Ebool_2E_3F @ SV67 )
@ ( lam @ SV67
@ ^ [SY183: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV31 ) @ SY244 ) @ ( ap @ SY241 @ SY183 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(323,plain,
! [SV68: del,SV34: del] :
( ( ( c_2Ebool_2Eliteral__case @ SV34 @ SV68 )
= ( lam @ ( arr @ SV34 @ SV68 )
@ ^ [SY185: $i] :
( lam @ SV34
@ ^ [V1x: $i] : ( ap @ SY185 @ V1x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(324,plain,
( ( ~ ( ~ $false
| ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(325,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(326,plain,
! [SV41: $i] :
( ( ( ~ ( mem @ SV41 @ bool ) )
= $true )
| ( ( SV41
= ( inj__o @ ( p @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(327,plain,
! [SV69: del,SV42: del] :
( ( ! [SY248: $i] :
( ~ ( mem @ SY248 @ ( arr @ SV42 @ SV69 ) )
| ! [SY249: $i] :
( ~ ( mem @ SY249 @ ( arr @ SV42 @ SV69 ) )
| ~ ! [SY207: $i] :
( ~ ( mem @ SY207 @ SV42 )
| ( ( ap @ SY248 @ SY207 )
= ( ap @ SY249 @ SY207 ) ) )
| ( SY248 = SY249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(328,plain,
! [SV70: $i > $i,SV43: del] :
( ( ! [SY251: $i] :
( ~ ( mem @ SY251 @ SV43 )
| ( ( ap @ ( lam @ SV43 @ SV70 ) @ SY251 )
= ( SV70 @ SY251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(329,plain,
( ( ~ ( ~ $true
| ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(330,plain,
( ( ~ ( ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
!= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) )
| $true ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(331,plain,
! [SV44: $i] :
( ( ( ~ ( mem @ SV44 @ bool ) )
= $true )
| ( ( ! [SY210: $i] :
( ~ ( mem @ SY210 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SY210 ) )
| ~ ( ~ ( p @ SV44 )
| ~ ( p @ SY210 ) ) )
| ~ ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SY210 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SY210 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(332,plain,
! [SV45: $i] :
( ( ( ~ ( mem @ SV45 @ bool ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $true )
| ~ ( ~ $true
| ( p @ SV45 ) ) )
| ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(333,plain,
! [SV46: del,SV71: $i] :
( ( ~ ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
| ~ ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
| ~ ! [SY252: $i] :
~ ~ ( ~ ( mem @ SY252 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY252 ) ) ) )
| ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( mem @ SY253 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY253 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(334,plain,
! [SV72: del,SV47: del] :
( ( ! [SY254: $i] :
( ~ ( mem @ SY254 @ ( arr @ SV47 @ SV72 ) )
| ( ( lam @ SV47
@ ^ [SX3: $i] : ( ap @ SY254 @ SX3 ) )
= SY254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(335,plain,
! [SV73: del,SV48: del] :
( ( ! [SY256: $i > $i] :
( ~ ! [SY257: $i] :
( ~ ( mem @ SY257 @ SV48 )
| ( mem @ ( SY256 @ SY257 ) @ SV73 ) )
| ( mem @ ( lam @ SV48 @ SY256 ) @ ( arr @ SV48 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(336,plain,
! [SV49: del,SV74: $i] :
( ( ~ ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
| ~ ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
| ! [SY258: $i] :
( ~ ( mem @ SY258 @ SV49 )
| ( p @ ( ap @ SV74 @ SY258 ) ) ) )
| ~ ( ~ ! [SY259: $i] :
( ~ ( mem @ SY259 @ SV49 )
| ( p @ ( ap @ SV74 @ SY259 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(337,plain,
( ( ~ ~ ( ~ ~ ( ~ ( mem @ sK1_SX0 @ ( arr @ ind @ ind ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ sK1_SX0 ) ) )
| ~ ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[298]) ).
thf(338,plain,
! [SV50: del,SV75: $i] :
( ( ~ ( mem @ SV75 @ SV50 )
| ! [SY260: $i] :
( ~ ( mem @ SY260 @ SV50 )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SY260 ) )
| ( SV75 = SY260 ) )
| ~ ( ( SV75 != SY260 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SY260 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(339,plain,
! [SV51: $i] :
( ( ( ~ ( mem @ SV51 @ bool ) )
= $true )
| ( ( ! [SY225: $i] :
( ~ ( mem @ SY225 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SY225 ) )
| ( p @ SV51 )
| ( p @ SY225 ) )
| ~ ( ~ ( ( p @ SV51 )
| ( p @ SY225 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SY225 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(340,plain,
! [SV52: del,SV76: $i] :
( ( ~ ( mem @ SV76 @ ( arr @ SV52 @ bool ) )
| ! [SY261: $i] :
( ~ ( mem @ SY261 @ SV52 )
| ~ ( p @ ( ap @ SV76 @ SY261 ) )
| ( p @ ( ap @ SV76 @ ( ap @ ( c_2Emin_2E_40 @ SV52 ) @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(341,plain,
! [SV53: $i] :
( ( ( ~ ( mem @ SV53 @ ind ) )
= $true )
| ( ( SV53
= ( inj__i @ ( surj__i @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(342,plain,
! [SV54: $i] :
( ( ( ~ ( mem @ SV54 @ bool ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
| ~ ( p @ SV54 ) )
| ~ ( ~ ~ ( p @ SV54 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(343,plain,
! [SV55: $i] :
( ( ( ~ ( mem @ SV55 @ bool ) )
= $true )
| ( ( ! [SY228: $i] :
( ~ ( mem @ SY228 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SY228 ) )
| ~ ( p @ SV55 )
| ( p @ SY228 ) )
| ~ ( ~ ( ~ ( p @ SV55 )
| ( p @ SY228 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SY228 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(344,plain,
! [SV77: del,SV56: del] :
( ( ! [SY262: $i] :
( ~ ( mem @ SY262 @ ( arr @ SV56 @ SV77 ) )
| ! [SY263: $i] :
( ~ ( mem @ SY263 @ SV56 )
| ( mem @ ( ap @ SY262 @ SY263 ) @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(345,plain,
! [SV1: $o] :
( ( ( ~ ( ( p @ ( inj__o @ SV1 ) )
| SV1 ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(346,plain,
( ( ( ~ ( ( p @ ( inj__o @ $true ) )
| $true ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(347,plain,
( ( ( ~ ( ( p @ ( inj__o @ $false ) )
| $false ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(348,plain,
( ( ~ $false
| ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(349,plain,
( ( ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) )
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(350,plain,
! [SV41: $i] :
( ( ( mem @ SV41 @ bool )
= $false )
| ( ( SV41
= ( inj__o @ ( p @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(351,plain,
! [SV69: del,SV42: del,SV78: $i] :
( ( ~ ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
| ! [SY264: $i] :
( ~ ( mem @ SY264 @ ( arr @ SV42 @ SV69 ) )
| ~ ! [SY265: $i] :
( ~ ( mem @ SY265 @ SV42 )
| ( ( ap @ SV78 @ SY265 )
= ( ap @ SY264 @ SY265 ) ) )
| ( SV78 = SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(352,plain,
! [SV70: $i > $i,SV43: del,SV79: $i] :
( ( ~ ( mem @ SV79 @ SV43 )
| ( ( ap @ ( lam @ SV43 @ SV70 ) @ SV79 )
= ( SV70 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(353,plain,
( ( ~ $true
| ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(354,plain,
( ( ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
!= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) )
| $true )
= $true ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(355,plain,
! [SV44: $i] :
( ( ( mem @ SV44 @ bool )
= $false )
| ( ( ! [SY210: $i] :
( ~ ( mem @ SY210 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SY210 ) )
| ~ ( ~ ( p @ SV44 )
| ~ ( p @ SY210 ) ) )
| ~ ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SY210 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SY210 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(356,plain,
! [SV45: $i] :
( ( ( mem @ SV45 @ bool )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $true )
| ~ ( ~ $true
| ( p @ SV45 ) ) )
| ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(357,plain,
! [SV46: del,SV71: $i] :
( ( ( ~ ( mem @ SV71 @ ( arr @ SV46 @ bool ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
| ~ ! [SY252: $i] :
~ ~ ( ~ ( mem @ SY252 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY252 ) ) ) )
| ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( mem @ SY253 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY253 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(358,plain,
! [SV72: del,SV47: del,SV80: $i] :
( ( ~ ( mem @ SV80 @ ( arr @ SV47 @ SV72 ) )
| ( ( lam @ SV47
@ ^ [SY266: $i] : ( ap @ SV80 @ SY266 ) )
= SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(359,plain,
! [SV73: del,SV81: $i > $i,SV48: del] :
( ( ~ ! [SY267: $i] :
( ~ ( mem @ SY267 @ SV48 )
| ( mem @ ( SV81 @ SY267 ) @ SV73 ) )
| ( mem @ ( lam @ SV48 @ SV81 ) @ ( arr @ SV48 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(360,plain,
! [SV49: del,SV74: $i] :
( ( ( ~ ( mem @ SV74 @ ( arr @ SV49 @ bool ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
| ! [SY258: $i] :
( ~ ( mem @ SY258 @ SV49 )
| ( p @ ( ap @ SV74 @ SY258 ) ) ) )
| ~ ( ~ ! [SY259: $i] :
( ~ ( mem @ SY259 @ SV49 )
| ( p @ ( ap @ SV74 @ SY259 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(361,plain,
( ( ~ ( ~ ~ ( ~ ( mem @ sK1_SX0 @ ( arr @ ind @ ind ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ sK1_SX0 ) ) )
| ~ ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ sK1_SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(362,plain,
! [SV50: del,SV75: $i] :
( ( ( ~ ( mem @ SV75 @ SV50 ) )
= $true )
| ( ( ! [SY260: $i] :
( ~ ( mem @ SY260 @ SV50 )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SY260 ) )
| ( SV75 = SY260 ) )
| ~ ( ( SV75 != SY260 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(363,plain,
! [SV51: $i] :
( ( ( mem @ SV51 @ bool )
= $false )
| ( ( ! [SY225: $i] :
( ~ ( mem @ SY225 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SY225 ) )
| ( p @ SV51 )
| ( p @ SY225 ) )
| ~ ( ~ ( ( p @ SV51 )
| ( p @ SY225 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SY225 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(364,plain,
! [SV52: del,SV76: $i] :
( ( ( ~ ( mem @ SV76 @ ( arr @ SV52 @ bool ) ) )
= $true )
| ( ( ! [SY261: $i] :
( ~ ( mem @ SY261 @ SV52 )
| ~ ( p @ ( ap @ SV76 @ SY261 ) )
| ( p @ ( ap @ SV76 @ ( ap @ ( c_2Emin_2E_40 @ SV52 ) @ SV76 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(365,plain,
! [SV53: $i] :
( ( ( mem @ SV53 @ ind )
= $false )
| ( ( SV53
= ( inj__i @ ( surj__i @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(366,plain,
! [SV54: $i] :
( ( ( mem @ SV54 @ bool )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
| ~ ( p @ SV54 ) )
| ~ ( ~ ~ ( p @ SV54 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(367,plain,
! [SV55: $i] :
( ( ( mem @ SV55 @ bool )
= $false )
| ( ( ! [SY228: $i] :
( ~ ( mem @ SY228 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SY228 ) )
| ~ ( p @ SV55 )
| ( p @ SY228 ) )
| ~ ( ~ ( ~ ( p @ SV55 )
| ( p @ SY228 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SY228 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(368,plain,
! [SV77: del,SV56: del,SV82: $i] :
( ( ~ ( mem @ SV82 @ ( arr @ SV56 @ SV77 ) )
| ! [SY268: $i] :
( ~ ( mem @ SY268 @ SV56 )
| ( mem @ ( ap @ SV82 @ SY268 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(369,plain,
! [SV1: $o] :
( ( ( ( p @ ( inj__o @ SV1 ) )
| SV1 )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(370,plain,
( ( ( ( p @ ( inj__o @ $true ) )
| $true )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(371,plain,
( ( ( ( p @ ( inj__o @ $false ) )
| $false )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(372,plain,
( ( ( ~ $false ) = $true )
| ( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(373,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(374,plain,
! [SV69: del,SV42: del,SV78: $i] :
( ( ( ~ ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) ) )
= $true )
| ( ( ! [SY264: $i] :
( ~ ( mem @ SY264 @ ( arr @ SV42 @ SV69 ) )
| ~ ! [SY265: $i] :
( ~ ( mem @ SY265 @ SV42 )
| ( ( ap @ SV78 @ SY265 )
= ( ap @ SY264 @ SY265 ) ) )
| ( SV78 = SY264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(375,plain,
! [SV70: $i > $i,SV43: del,SV79: $i] :
( ( ( ~ ( mem @ SV79 @ SV43 ) )
= $true )
| ( ( ( ap @ ( lam @ SV43 @ SV70 ) @ SV79 )
= ( SV70 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(376,plain,
( ( ( ~ $true ) = $true )
| ( ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(377,plain,
( ( ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
!= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(378,plain,
! [SV44: $i,SV83: $i] :
( ( ( ~ ( mem @ SV83 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
| ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) )
| ~ ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) ) ) ) )
= $true )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(379,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $true )
| ~ ( ~ $true
| ( p @ SV45 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(380,plain,
! [SV46: del,SV71: $i] :
( ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
| ~ ! [SY252: $i] :
~ ~ ( ~ ( mem @ SY252 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY252 ) ) ) )
| ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( mem @ SY253 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY253 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(381,plain,
! [SV72: del,SV47: del,SV80: $i] :
( ( ( ~ ( mem @ SV80 @ ( arr @ SV47 @ SV72 ) ) )
= $true )
| ( ( ( lam @ SV47
@ ^ [SY266: $i] : ( ap @ SV80 @ SY266 ) )
= SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(382,plain,
! [SV73: del,SV81: $i > $i,SV48: del] :
( ( ( ~ ! [SY267: $i] :
( ~ ( mem @ SY267 @ SV48 )
| ( mem @ ( SV81 @ SY267 ) @ SV73 ) ) )
= $true )
| ( ( mem @ ( lam @ SV48 @ SV81 ) @ ( arr @ SV48 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(383,plain,
! [SV49: del,SV74: $i] :
( ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
| ! [SY258: $i] :
( ~ ( mem @ SY258 @ SV49 )
| ( p @ ( ap @ SV74 @ SY258 ) ) ) )
| ~ ( ~ ! [SY259: $i] :
( ~ ( mem @ SY259 @ SV49 )
| ( p @ ( ap @ SV74 @ SY259 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(384,plain,
( ( ~ ~ ( ~ ( mem @ sK1_SX0 @ ( arr @ ind @ ind ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ sK1_SX0 ) ) )
| ~ ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(385,plain,
! [SV50: del,SV75: $i] :
( ( ( mem @ SV75 @ SV50 )
= $false )
| ( ( ! [SY260: $i] :
( ~ ( mem @ SY260 @ SV50 )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SY260 ) )
| ( SV75 = SY260 ) )
| ~ ( ( SV75 != SY260 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(386,plain,
! [SV51: $i,SV84: $i] :
( ( ( ~ ( mem @ SV84 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
| ( p @ SV51 )
| ( p @ SV84 ) )
| ~ ( ~ ( ( p @ SV51 )
| ( p @ SV84 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) ) ) ) )
= $true )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(387,plain,
! [SV52: del,SV76: $i] :
( ( ( mem @ SV76 @ ( arr @ SV52 @ bool ) )
= $false )
| ( ( ! [SY261: $i] :
( ~ ( mem @ SY261 @ SV52 )
| ~ ( p @ ( ap @ SV76 @ SY261 ) )
| ( p @ ( ap @ SV76 @ ( ap @ ( c_2Emin_2E_40 @ SV52 ) @ SV76 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(388,plain,
! [SV54: $i] :
( ( ( ~ ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
| ~ ( p @ SV54 ) )
| ~ ( ~ ~ ( p @ SV54 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) ) ) )
= $false )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(389,plain,
! [SV55: $i,SV85: $i] :
( ( ( ~ ( mem @ SV85 @ bool )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
| ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ~ ( ~ ( ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) ) ) ) )
= $true )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(390,plain,
! [SV77: del,SV56: del,SV82: $i] :
( ( ( ~ ( mem @ SV82 @ ( arr @ SV56 @ SV77 ) ) )
= $true )
| ( ( ! [SY268: $i] :
( ~ ( mem @ SY268 @ SV56 )
| ( mem @ ( ap @ SV82 @ SY268 ) @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(391,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(392,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(393,plain,
( ( ( p @ ( inj__o @ $true ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(394,plain,
( ( $true = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(395,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(396,plain,
( ( $false = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(397,plain,
( ( $false = $false )
| ( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(398,plain,
( ( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ( p @ SX0 ) ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(399,plain,
! [SV69: del,SV42: del,SV78: $i] :
( ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false )
| ( ( ! [SY264: $i] :
( ~ ( mem @ SY264 @ ( arr @ SV42 @ SV69 ) )
| ~ ! [SY265: $i] :
( ~ ( mem @ SY265 @ SV42 )
| ( ( ap @ SV78 @ SY265 )
= ( ap @ SY264 @ SY265 ) ) )
| ( SV78 = SY264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(400,plain,
! [SV70: $i > $i,SV43: del,SV79: $i] :
( ( ( mem @ SV79 @ SV43 )
= $false )
| ( ( ( ap @ ( lam @ SV43 @ SV70 ) @ SV79 )
= ( SV70 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(401,plain,
( ( $true = $false )
| ( ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(402,plain,
( ( ( ( lam @ bool
@ ^ [SX0: $i] : SX0 )
= ( lam @ bool
@ ^ [SX0: $i] : SX0 ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(403,plain,
! [SV44: $i,SV83: $i] :
( ( ( ~ ( mem @ SV83 @ bool ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
| ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) )
| ~ ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) ) ) ) )
= $true )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(404,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ( p @ SV45 )
| $true )
| ~ ( ~ $true
| ( p @ SV45 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(405,plain,
! [SV71: $i,SV46: del] :
( ( ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
| ~ ! [SY252: $i] :
~ ~ ( ~ ( mem @ SY252 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY252 ) ) ) )
| ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( mem @ SY253 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY253 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) ) ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(406,plain,
! [SV72: del,SV47: del,SV80: $i] :
( ( ( mem @ SV80 @ ( arr @ SV47 @ SV72 ) )
= $false )
| ( ( ( lam @ SV47
@ ^ [SY266: $i] : ( ap @ SV80 @ SY266 ) )
= SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(407,plain,
! [SV73: del,SV81: $i > $i,SV48: del] :
( ( ( ! [SY267: $i] :
( ~ ( mem @ SY267 @ SV48 )
| ( mem @ ( SV81 @ SY267 ) @ SV73 ) ) )
= $false )
| ( ( mem @ ( lam @ SV48 @ SV81 ) @ ( arr @ SV48 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(408,plain,
! [SV74: $i,SV49: del] :
( ( ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
| ! [SY258: $i] :
( ~ ( mem @ SY258 @ SV49 )
| ( p @ ( ap @ SV74 @ SY258 ) ) ) )
| ~ ( ~ ! [SY259: $i] :
( ~ ( mem @ SY259 @ SV49 )
| ( p @ ( ap @ SV74 @ SY259 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) ) ) )
= $false )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(409,plain,
( ( ~ ~ ( ~ ( mem @ sK1_SX0 @ ( arr @ ind @ ind ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(410,plain,
( ( ~ ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(411,plain,
! [SV75: $i,SV50: del,SV86: $i] :
( ( ( ~ ( mem @ SV86 @ SV50 )
| ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) )
| ( SV75 = SV86 ) )
| ~ ( ( SV75 != SV86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) ) ) ) )
= $true )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(412,plain,
! [SV51: $i,SV84: $i] :
( ( ( ~ ( mem @ SV84 @ bool ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
| ( p @ SV51 )
| ( p @ SV84 ) )
| ~ ( ~ ( ( p @ SV51 )
| ( p @ SV84 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) ) ) ) )
= $true )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(413,plain,
! [SV76: $i,SV52: del,SV87: $i] :
( ( ( ~ ( mem @ SV87 @ SV52 )
| ~ ( p @ ( ap @ SV76 @ SV87 ) )
| ( p @ ( ap @ SV76 @ ( ap @ ( c_2Emin_2E_40 @ SV52 ) @ SV76 ) ) ) )
= $true )
| ( ( mem @ SV76 @ ( arr @ SV52 @ bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(414,plain,
! [SV54: $i] :
( ( ( ~ ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
| ~ ( p @ SV54 ) ) )
= $false )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(415,plain,
! [SV54: $i] :
( ( ( ~ ( ~ ~ ( p @ SV54 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) ) ) )
= $false )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(416,plain,
! [SV55: $i,SV85: $i] :
( ( ( ~ ( mem @ SV85 @ bool ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
| ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ~ ( ~ ( ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) ) ) ) )
= $true )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(417,plain,
! [SV77: del,SV56: del,SV82: $i] :
( ( ( mem @ SV82 @ ( arr @ SV56 @ SV77 ) )
= $false )
| ( ( ! [SY268: $i] :
( ~ ( mem @ SY268 @ SV56 )
| ( mem @ ( ap @ SV82 @ SY268 ) @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(418,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 )
= $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(419,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(420,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true )
= $false )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(421,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true )
= $false )
| ( $true = $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(422,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false )
= $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(423,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(424,plain,
! [SV88: $i] :
( ( ( ~ ( mem @ SV88 @ bool )
| ( p @ SV88 ) )
= $true )
| ( $false = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(425,plain,
( ( ( ~ ( mem @ sK2_SX0 @ bool )
| ( p @ sK2_SX0 ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_forall_neg,[status(esa)],[398]) ).
thf(426,plain,
! [SV78: $i,SV69: del,SV42: del,SV89: $i] :
( ( ( ~ ( mem @ SV89 @ ( arr @ SV42 @ SV69 ) )
| ~ ! [SY269: $i] :
( ~ ( mem @ SY269 @ SV42 )
| ( ( ap @ SV78 @ SY269 )
= ( ap @ SV89 @ SY269 ) ) )
| ( SV78 = SV89 ) )
= $true )
| ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(427,plain,
! [SV44: $i,SV83: $i] :
( ( ( mem @ SV83 @ bool )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
| ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) )
| ~ ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) ) ) ) )
= $true )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(428,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ( p @ SV45 )
| $true ) )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(429,plain,
! [SV45: $i] :
( ( ( ~ ( ~ $true
| ( p @ SV45 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(430,plain,
! [SV71: $i,SV46: del] :
( ( ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
| ~ ! [SY252: $i] :
~ ~ ( ~ ( mem @ SY252 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY252 ) ) ) ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(431,plain,
! [SV71: $i,SV46: del] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( mem @ SY253 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY253 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) ) ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(432,plain,
! [SV48: del,SV81: $i > $i,SV73: del] :
( ( ( ~ ( mem @ ( sK3_SY267 @ SV73 @ SV81 @ SV48 ) @ SV48 )
| ( mem @ ( SV81 @ ( sK3_SY267 @ SV73 @ SV81 @ SV48 ) ) @ SV73 ) )
= $false )
| ( ( mem @ ( lam @ SV48 @ SV81 ) @ ( arr @ SV48 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[407]) ).
thf(433,plain,
! [SV74: $i,SV49: del] :
( ( ( ~ ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
| ! [SY258: $i] :
( ~ ( mem @ SY258 @ SV49 )
| ( p @ ( ap @ SV74 @ SY258 ) ) ) ) )
= $false )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(434,plain,
! [SV74: $i,SV49: del] :
( ( ( ~ ( ~ ! [SY259: $i] :
( ~ ( mem @ SY259 @ SV49 )
| ( p @ ( ap @ SV74 @ SY259 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) ) ) )
= $false )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(435,plain,
( ( ~ ( ~ ( mem @ sK1_SX0 @ ( arr @ ind @ ind ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ sK1_SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(436,plain,
( ( ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(437,plain,
! [SV75: $i,SV50: del,SV86: $i] :
( ( ( ~ ( mem @ SV86 @ SV50 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) )
| ( SV75 = SV86 ) )
| ~ ( ( SV75 != SV86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) ) ) ) )
= $true )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(438,plain,
! [SV51: $i,SV84: $i] :
( ( ( mem @ SV84 @ bool )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
| ( p @ SV51 )
| ( p @ SV84 ) )
| ~ ( ~ ( ( p @ SV51 )
| ( p @ SV84 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) ) ) ) )
= $true )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(439,plain,
! [SV76: $i,SV52: del,SV87: $i] :
( ( ( ~ ( mem @ SV87 @ SV52 ) )
= $true )
| ( ( ~ ( p @ ( ap @ SV76 @ SV87 ) )
| ( p @ ( ap @ SV76 @ ( ap @ ( c_2Emin_2E_40 @ SV52 ) @ SV76 ) ) ) )
= $true )
| ( ( mem @ SV76 @ ( arr @ SV52 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(440,plain,
! [SV54: $i] :
( ( ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
| ~ ( p @ SV54 ) )
= $true )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(441,plain,
! [SV54: $i] :
( ( ( ~ ~ ( p @ SV54 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) ) )
= $true )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(442,plain,
! [SV55: $i,SV85: $i] :
( ( ( mem @ SV85 @ bool )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
| ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ~ ( ~ ( ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) ) ) ) )
= $true )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(443,plain,
! [SV77: del,SV82: $i,SV56: del,SV90: $i] :
( ( ( ~ ( mem @ SV90 @ SV56 )
| ( mem @ ( ap @ SV82 @ SV90 ) @ SV77 ) )
= $true )
| ( ( mem @ SV82 @ ( arr @ SV56 @ SV77 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(444,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) ) )
= $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(445,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(446,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) ) )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(447,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $false )
| ( SV1 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(448,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) ) )
= $false )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(449,plain,
( ( ( ~ $true ) = $false )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(450,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) ) )
= $false )
| ( $true = $false ) ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(451,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false ) ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(452,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) ) )
= $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(453,plain,
( ( ( ~ $false ) = $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(454,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(455,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(456,plain,
! [SV88: $i] :
( ( ( ~ ( mem @ SV88 @ bool ) )
= $true )
| ( ( p @ SV88 )
= $true )
| ( $false = $false ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(457,plain,
( ( ( ~ ( mem @ sK2_SX0 @ bool ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(458,plain,
( ( ( p @ sK2_SX0 )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(459,plain,
! [SV78: $i,SV69: del,SV42: del,SV89: $i] :
( ( ( ~ ( mem @ SV89 @ ( arr @ SV42 @ SV69 ) ) )
= $true )
| ( ( ~ ! [SY269: $i] :
( ~ ( mem @ SY269 @ SV42 )
| ( ( ap @ SV78 @ SY269 )
= ( ap @ SV89 @ SY269 ) ) )
| ( SV78 = SV89 ) )
= $true )
| ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(460,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
| ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) )
| ~ ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) ) ) )
= $false )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(461,plain,
! [SV45: $i] :
( ( ( ~ ( p @ SV45 )
| $true )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(462,plain,
! [SV45: $i] :
( ( ( ~ $true
| ( p @ SV45 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(463,plain,
! [SV71: $i,SV46: del] :
( ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
| ~ ! [SY252: $i] :
~ ~ ( ~ ( mem @ SY252 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY252 ) ) ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(464,plain,
! [SV71: $i,SV46: del] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( mem @ SY253 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY253 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(465,plain,
! [SV48: del,SV81: $i > $i,SV73: del] :
( ( ( ~ ( mem @ ( sK3_SY267 @ SV73 @ SV81 @ SV48 ) @ SV48 ) )
= $false )
| ( ( mem @ ( lam @ SV48 @ SV81 ) @ ( arr @ SV48 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(466,plain,
! [SV48: del,SV73: del,SV81: $i > $i] :
( ( ( mem @ ( SV81 @ ( sK3_SY267 @ SV73 @ SV81 @ SV48 ) ) @ SV73 )
= $false )
| ( ( mem @ ( lam @ SV48 @ SV81 ) @ ( arr @ SV48 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(467,plain,
! [SV74: $i,SV49: del] :
( ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
| ! [SY258: $i] :
( ~ ( mem @ SY258 @ SV49 )
| ( p @ ( ap @ SV74 @ SY258 ) ) ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(468,plain,
! [SV74: $i,SV49: del] :
( ( ( ~ ! [SY259: $i] :
( ~ ( mem @ SY259 @ SV49 )
| ( p @ ( ap @ SV74 @ SY259 ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(469,plain,
( ( ~ ( mem @ sK1_SX0 @ ( arr @ ind @ ind ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(470,plain,
( ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ sK1_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(471,plain,
! [SV75: $i,SV50: del,SV86: $i] :
( ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( ~ ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) )
| ( SV75 = SV86 ) )
| ~ ( ( SV75 != SV86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) ) ) ) )
= $true )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(472,plain,
! [SV84: $i,SV51: $i] :
( ( ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
| ( p @ SV51 )
| ( p @ SV84 ) )
| ~ ( ~ ( ( p @ SV51 )
| ( p @ SV84 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) ) ) )
= $false )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(473,plain,
! [SV76: $i,SV52: del,SV87: $i] :
( ( ( mem @ SV87 @ SV52 )
= $false )
| ( ( ~ ( p @ ( ap @ SV76 @ SV87 ) )
| ( p @ ( ap @ SV76 @ ( ap @ ( c_2Emin_2E_40 @ SV52 ) @ SV76 ) ) ) )
= $true )
| ( ( mem @ SV76 @ ( arr @ SV52 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(474,plain,
! [SV54: $i] :
( ( ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) ) )
= $true )
| ( ( ~ ( p @ SV54 ) )
= $true )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(475,plain,
! [SV54: $i] :
( ( ( ~ ~ ( p @ SV54 ) )
= $true )
| ( ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
= $true )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(476,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
| ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ~ ( ~ ( ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) ) ) )
= $false )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(477,plain,
! [SV77: del,SV82: $i,SV56: del,SV90: $i] :
( ( ( ~ ( mem @ SV90 @ SV56 ) )
= $true )
| ( ( mem @ ( ap @ SV82 @ SV90 ) @ SV77 )
= $true )
| ( ( mem @ SV82 @ ( arr @ SV56 @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(478,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(479,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(480,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( SV1 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(481,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( SV1 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(482,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(483,plain,
( ( $true = $true )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(484,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( $true = $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(485,plain,
( ( $true = $true )
| ( $true = $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(486,plain,
( ( ( p @ ( inj__o @ $false ) )
= $true )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(487,plain,
( ( $false = $true )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(488,plain,
( ( ( p @ ( inj__o @ $false ) )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(489,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(490,plain,
! [SV88: $i] :
( ( ( mem @ SV88 @ bool )
= $false )
| ( ( p @ SV88 )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(491,plain,
( ( ( mem @ sK2_SX0 @ bool )
= $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(492,plain,
! [SV78: $i,SV69: del,SV42: del,SV89: $i] :
( ( ( mem @ SV89 @ ( arr @ SV42 @ SV69 ) )
= $false )
| ( ( ~ ! [SY269: $i] :
( ~ ( mem @ SY269 @ SV42 )
| ( ( ap @ SV78 @ SY269 )
= ( ap @ SV89 @ SY269 ) ) )
| ( SV78 = SV89 ) )
= $true )
| ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(493,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
| ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) ) )
= $false )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(494,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) ) ) )
= $false )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(495,plain,
! [SV45: $i] :
( ( ( ~ ( p @ SV45 ) )
= $true )
| ( $true = $true )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(496,plain,
! [SV45: $i] :
( ( ( ~ $true ) = $true )
| ( ( p @ SV45 )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(497,plain,
! [SV71: $i,SV46: del] :
( ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) ) )
= $true )
| ( ( ~ ! [SY252: $i] :
~ ~ ( ~ ( mem @ SY252 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY252 ) ) ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(498,plain,
! [SV71: $i,SV46: del] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( mem @ SY253 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY253 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(499,plain,
! [SV48: del,SV81: $i > $i,SV73: del] :
( ( ( mem @ ( sK3_SY267 @ SV73 @ SV81 @ SV48 ) @ SV48 )
= $true )
| ( ( mem @ ( lam @ SV48 @ SV81 ) @ ( arr @ SV48 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(500,plain,
! [SV74: $i,SV49: del] :
( ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) ) )
= $true )
| ( ( ! [SY258: $i] :
( ~ ( mem @ SY258 @ SV49 )
| ( p @ ( ap @ SV74 @ SY258 ) ) ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(501,plain,
! [SV74: $i,SV49: del] :
( ( ( ~ ! [SY259: $i] :
( ~ ( mem @ SY259 @ SV49 )
| ( p @ ( ap @ SV74 @ SY259 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(502,plain,
( ( ~ ( mem @ sK1_SX0 @ ( arr @ ind @ ind ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(503,plain,
( ( ~ ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(504,plain,
! [SV86: $i,SV75: $i,SV50: del] :
( ( ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) )
| ( SV75 = SV86 ) )
| ~ ( ( SV75 != SV86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) ) ) )
= $false )
| ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(505,plain,
! [SV84: $i,SV51: $i] :
( ( ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
| ( p @ SV51 )
| ( p @ SV84 ) ) )
= $false )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(506,plain,
! [SV84: $i,SV51: $i] :
( ( ( ~ ( ~ ( ( p @ SV51 )
| ( p @ SV84 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) ) ) )
= $false )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(507,plain,
! [SV52: del,SV87: $i,SV76: $i] :
( ( ( ~ ( p @ ( ap @ SV76 @ SV87 ) ) )
= $true )
| ( ( p @ ( ap @ SV76 @ ( ap @ ( c_2Emin_2E_40 @ SV52 ) @ SV76 ) ) )
= $true )
| ( ( mem @ SV87 @ SV52 )
= $false )
| ( ( mem @ SV76 @ ( arr @ SV52 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(508,plain,
! [SV54: $i] :
( ( ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
= $false )
| ( ( ~ ( p @ SV54 ) )
= $true )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(509,plain,
! [SV54: $i] :
( ( ( ~ ( p @ SV54 ) )
= $false )
| ( ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
= $true )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(510,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
| ~ ( p @ SV55 )
| ( p @ SV85 ) ) )
= $false )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(511,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( ~ ( ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) ) ) )
= $false )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(512,plain,
! [SV77: del,SV82: $i,SV56: del,SV90: $i] :
( ( ( mem @ SV90 @ SV56 )
= $false )
| ( ( mem @ ( ap @ SV82 @ SV90 ) @ SV77 )
= $true )
| ( ( mem @ SV82 @ ( arr @ SV56 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(513,plain,
! [SV69: del,SV89: $i,SV78: $i,SV42: del] :
( ( ( ~ ! [SY269: $i] :
( ~ ( mem @ SY269 @ SV42 )
| ( ( ap @ SV78 @ SY269 )
= ( ap @ SV89 @ SY269 ) ) ) )
= $true )
| ( ( SV78 = SV89 )
= $true )
| ( ( mem @ SV89 @ ( arr @ SV42 @ SV69 ) )
= $false )
| ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(514,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
| ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(515,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(516,plain,
! [SV45: $i] :
( ( ( p @ SV45 )
= $false )
| ( $true = $true )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(517,plain,
! [SV45: $i] :
( ( $true = $false )
| ( ( p @ SV45 )
= $true )
| ( ( ~ ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) ) )
= $true )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(518,plain,
! [SV71: $i,SV46: del] :
( ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $false )
| ( ( ~ ! [SY252: $i] :
~ ~ ( ~ ( mem @ SY252 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY252 ) ) ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(519,plain,
! [SV71: $i,SV46: del] :
( ( ( ~ ! [SY253: $i] :
~ ~ ( ~ ( mem @ SY253 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY253 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(520,plain,
! [SV74: $i,SV49: del] :
( ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $false )
| ( ( ! [SY258: $i] :
( ~ ( mem @ SY258 @ SV49 )
| ( p @ ( ap @ SV74 @ SY258 ) ) ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(521,plain,
! [SV74: $i,SV49: del] :
( ( ( ! [SY259: $i] :
( ~ ( mem @ SY259 @ SV49 )
| ( p @ ( ap @ SV74 @ SY259 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(522,plain,
( ( mem @ sK1_SX0 @ ( arr @ ind @ ind ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(523,plain,
( ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(524,plain,
! [SV86: $i,SV75: $i,SV50: del] :
( ( ( ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) )
| ( SV75 = SV86 ) ) )
= $false )
| ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(525,plain,
! [SV50: del,SV86: $i,SV75: $i] :
( ( ( ~ ( ( SV75 != SV86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) ) ) )
= $false )
| ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(526,plain,
! [SV84: $i,SV51: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
| ( p @ SV51 )
| ( p @ SV84 ) )
= $true )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(527,plain,
! [SV84: $i,SV51: $i] :
( ( ( ~ ( ( p @ SV51 )
| ( p @ SV84 ) )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) ) )
= $true )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(528,plain,
! [SV52: del,SV87: $i,SV76: $i] :
( ( ( p @ ( ap @ SV76 @ SV87 ) )
= $false )
| ( ( p @ ( ap @ SV76 @ ( ap @ ( c_2Emin_2E_40 @ SV52 ) @ SV76 ) ) )
= $true )
| ( ( mem @ SV87 @ SV52 )
= $false )
| ( ( mem @ SV76 @ ( arr @ SV52 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(529,plain,
! [SV54: $i] :
( ( ( p @ SV54 )
= $false )
| ( ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
= $false )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(530,plain,
! [SV54: $i] :
( ( ( p @ SV54 )
= $true )
| ( ( p @ ( ap @ c_2Ebool_2E_7E @ SV54 ) )
= $true )
| ( ( mem @ SV54 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(531,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
| ~ ( p @ SV55 )
| ( p @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(532,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( ~ ( p @ SV55 )
| ( p @ SV85 ) )
| ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(533,plain,
! [SV69: del,SV89: $i,SV78: $i,SV42: del] :
( ( ( ! [SY269: $i] :
( ~ ( mem @ SY269 @ SV42 )
| ( ( ap @ SV78 @ SY269 )
= ( ap @ SV89 @ SY269 ) ) ) )
= $false )
| ( ( SV78 = SV89 )
= $true )
| ( ( mem @ SV89 @ ( arr @ SV42 @ SV69 ) )
= $false )
| ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(534,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) ) )
= $true )
| ( ( ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(535,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(536,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) )
= $false )
| ( $true = $true )
| ( ( p @ SV45 )
= $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(537,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ( p @ SV45 )
| $false )
| ~ ( ~ $false
| ( p @ SV45 ) ) )
= $false )
| ( ( p @ SV45 )
= $true )
| ( $true = $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(538,plain,
! [SV71: $i,SV46: del] :
( ( ( ! [SY252: $i] :
~ ~ ( ~ ( mem @ SY252 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY252 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(539,plain,
! [SV71: $i,SV46: del] :
( ( ( ! [SY253: $i] :
~ ~ ( ~ ( mem @ SY253 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SY253 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(540,plain,
! [SV74: $i,SV49: del,SV91: $i] :
( ( ( ~ ( mem @ SV91 @ SV49 )
| ( p @ ( ap @ SV74 @ SV91 ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $false )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(541,plain,
! [SV49: del,SV74: $i] :
( ( ( ~ ( mem @ ( sK4_SY259 @ SV74 @ SV49 ) @ SV49 )
| ( p @ ( ap @ SV74 @ ( sK4_SY259 @ SV74 @ SV49 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[521]) ).
thf(542,plain,
! [SV86: $i,SV75: $i,SV50: del] :
( ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) )
| ( SV75 = SV86 ) )
= $true )
| ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(543,plain,
! [SV50: del,SV86: $i,SV75: $i] :
( ( ( ( SV75 != SV86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) ) )
= $true )
| ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(544,plain,
! [SV84: $i,SV51: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) ) )
= $true )
| ( ( ( p @ SV51 )
| ( p @ SV84 ) )
= $true )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(545,plain,
! [SV84: $i,SV51: $i] :
( ( ( ~ ( ( p @ SV51 )
| ( p @ SV84 ) ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
= $true )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(546,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) ) )
= $true )
| ( ( ~ ( p @ SV55 )
| ( p @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(547,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( ~ ( p @ SV55 )
| ( p @ SV85 ) ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(548,plain,
! [SV42: del,SV78: $i,SV89: $i,SV69: del] :
( ( ( ~ ( mem @ ( sK5_SY269 @ SV69 @ SV89 @ SV78 @ SV42 ) @ SV42 )
| ( ( ap @ SV78 @ ( sK5_SY269 @ SV69 @ SV89 @ SV78 @ SV42 ) )
= ( ap @ SV89 @ ( sK5_SY269 @ SV69 @ SV89 @ SV78 @ SV42 ) ) ) )
= $false )
| ( ( SV78 = SV89 )
= $true )
| ( ( mem @ SV89 @ ( arr @ SV42 @ SV69 ) )
= $false )
| ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[533]) ).
thf(549,plain,
! [SV83: $i,SV44: $i] :
( ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $false )
| ( ( ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(550,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(551,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ( p @ SV45 )
| $false ) )
= $false )
| ( $true = $true )
| ( ( p @ SV45 )
= $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(552,plain,
! [SV45: $i] :
( ( ( ~ ( ~ $false
| ( p @ SV45 ) ) )
= $false )
| ( $true = $true )
| ( ( p @ SV45 )
= $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(553,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ( p @ SV45 )
| $false ) )
= $false )
| ( ( p @ SV45 )
= $true )
| ( $true = $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(554,plain,
! [SV45: $i] :
( ( ( ~ ( ~ $false
| ( p @ SV45 ) ) )
= $false )
| ( ( p @ SV45 )
= $true )
| ( $true = $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(555,plain,
! [SV46: del,SV71: $i] :
( ( ( ~ ~ ( ~ ( mem @ ( sK6_SY252 @ SV71 @ SV46 ) @ SV46 )
| ~ ( p @ ( ap @ SV71 @ ( sK6_SY252 @ SV71 @ SV46 ) ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[538]) ).
thf(556,plain,
! [SV71: $i,SV46: del,SV92: $i] :
( ( ( ~ ~ ( ~ ( mem @ SV92 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SV92 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(557,plain,
! [SV74: $i,SV49: del,SV91: $i] :
( ( ( ~ ( mem @ SV91 @ SV49 ) )
= $true )
| ( ( p @ ( ap @ SV74 @ SV91 ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $false )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(558,plain,
! [SV49: del,SV74: $i] :
( ( ( ~ ( mem @ ( sK4_SY259 @ SV74 @ SV49 ) @ SV49 ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(559,plain,
! [SV49: del,SV74: $i] :
( ( ( p @ ( ap @ SV74 @ ( sK4_SY259 @ SV74 @ SV49 ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(560,plain,
! [SV86: $i,SV75: $i,SV50: del] :
( ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) ) )
= $true )
| ( ( SV75 = SV86 )
= $true )
| ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(561,plain,
! [SV50: del,SV86: $i,SV75: $i] :
( ( ( SV75 != SV86 )
= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) )
= $true )
| ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(562,plain,
! [SV84: $i,SV51: $i] :
( ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
= $false )
| ( ( ( p @ SV51 )
| ( p @ SV84 ) )
= $true )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(563,plain,
! [SV84: $i,SV51: $i] :
( ( ( ( p @ SV51 )
| ( p @ SV84 ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
= $true )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(564,plain,
! [SV85: $i,SV55: $i] :
( ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
= $false )
| ( ( ~ ( p @ SV55 )
| ( p @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(565,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( p @ SV55 )
| ( p @ SV85 ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(566,plain,
! [SV42: del,SV78: $i,SV89: $i,SV69: del] :
( ( ( ~ ( mem @ ( sK5_SY269 @ SV69 @ SV89 @ SV78 @ SV42 ) @ SV42 ) )
= $false )
| ( ( SV78 = SV89 )
= $true )
| ( ( mem @ SV89 @ ( arr @ SV42 @ SV69 ) )
= $false )
| ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(567,plain,
! [SV42: del,SV89: $i,SV69: del,SV78: $i] :
( ( ( ( ap @ SV78 @ ( sK5_SY269 @ SV69 @ SV89 @ SV78 @ SV42 ) )
= ( ap @ SV89 @ ( sK5_SY269 @ SV69 @ SV89 @ SV78 @ SV42 ) ) )
= $false )
| ( ( SV78 = SV89 )
= $true )
| ( ( mem @ SV89 @ ( arr @ SV42 @ SV69 ) )
= $false )
| ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(568,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $false )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(569,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( p @ SV44 )
| ~ ( p @ SV83 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(570,plain,
! [SV45: $i] :
( ( ( ~ ( p @ SV45 )
| $false )
= $true )
| ( $true = $true )
| ( ( p @ SV45 )
= $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(571,plain,
! [SV45: $i] :
( ( ( ~ $false
| ( p @ SV45 ) )
= $true )
| ( $true = $true )
| ( ( p @ SV45 )
= $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(572,plain,
! [SV45: $i] :
( ( ( ~ ( p @ SV45 )
| $false )
= $true )
| ( ( p @ SV45 )
= $true )
| ( $true = $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(573,plain,
! [SV45: $i] :
( ( ( ~ $false
| ( p @ SV45 ) )
= $true )
| ( ( p @ SV45 )
= $true )
| ( $true = $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(574,plain,
! [SV46: del,SV71: $i] :
( ( ( ~ ( ~ ( mem @ ( sK6_SY252 @ SV71 @ SV46 ) @ SV46 )
| ~ ( p @ ( ap @ SV71 @ ( sK6_SY252 @ SV71 @ SV46 ) ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(575,plain,
! [SV71: $i,SV46: del,SV92: $i] :
( ( ( ~ ( ~ ( mem @ SV92 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SV92 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(576,plain,
! [SV74: $i,SV49: del,SV91: $i] :
( ( ( mem @ SV91 @ SV49 )
= $false )
| ( ( p @ ( ap @ SV74 @ SV91 ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $false )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(577,plain,
! [SV49: del,SV74: $i] :
( ( ( mem @ ( sK4_SY259 @ SV74 @ SV49 ) @ SV49 )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV49 ) @ SV74 ) )
= $true )
| ( ( mem @ SV74 @ ( arr @ SV49 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(578,plain,
! [SV86: $i,SV75: $i,SV50: del] :
( ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) )
= $false )
| ( ( SV75 = SV86 )
= $true )
| ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(579,plain,
! [SV50: del,SV86: $i,SV75: $i] :
( ( ( SV75 = SV86 )
= $false )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV50 ) @ SV75 ) @ SV86 ) )
= $true )
| ( ( mem @ SV86 @ SV50 )
= $false )
| ( ( mem @ SV75 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(580,plain,
! [SV84: $i,SV51: $i] :
( ( ( p @ SV51 )
= $true )
| ( ( p @ SV84 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
= $false )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(581,plain,
! [SV84: $i,SV51: $i] :
( ( ( p @ SV51 )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
= $true )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(582,plain,
! [SV51: $i,SV84: $i] :
( ( ( p @ SV84 )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ SV51 ) @ SV84 ) )
= $true )
| ( ( mem @ SV84 @ bool )
= $false )
| ( ( mem @ SV51 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(583,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( p @ SV55 ) )
= $true )
| ( ( p @ SV85 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
= $false )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(584,plain,
! [SV85: $i,SV55: $i] :
( ( ( ~ ( p @ SV55 ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[565]) ).
thf(585,plain,
! [SV55: $i,SV85: $i] :
( ( ( p @ SV85 )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[565]) ).
thf(586,plain,
! [SV42: del,SV78: $i,SV89: $i,SV69: del] :
( ( ( mem @ ( sK5_SY269 @ SV69 @ SV89 @ SV78 @ SV42 ) @ SV42 )
= $true )
| ( ( SV78 = SV89 )
= $true )
| ( ( mem @ SV89 @ ( arr @ SV42 @ SV69 ) )
= $false )
| ( ( mem @ SV78 @ ( arr @ SV42 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(587,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( p @ SV44 ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $false )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(588,plain,
! [SV44: $i,SV83: $i] :
( ( ( ~ ( p @ SV83 ) )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $false )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(589,plain,
! [SV83: $i,SV44: $i] :
( ( ( ~ ( p @ SV44 ) )
= $true )
| ( ( ~ ( p @ SV83 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(590,plain,
! [SV45: $i] :
( ( ( ~ ( p @ SV45 ) )
= $true )
| ( $false = $true )
| ( $true = $true )
| ( ( p @ SV45 )
= $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(591,plain,
! [SV45: $i] :
( ( ( ~ $false ) = $true )
| ( ( p @ SV45 )
= $true )
| ( $true = $true )
| ( ( p @ SV45 )
= $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(592,plain,
! [SV45: $i] :
( ( ( ~ ( p @ SV45 ) )
= $true )
| ( $false = $true )
| ( ( p @ SV45 )
= $true )
| ( $true = $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(593,plain,
! [SV45: $i] :
( ( ( ~ $false ) = $true )
| ( ( p @ SV45 )
= $true )
| ( ( p @ SV45 )
= $true )
| ( $true = $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(594,plain,
! [SV46: del,SV71: $i] :
( ( ( ~ ( mem @ ( sK6_SY252 @ SV71 @ SV46 ) @ SV46 )
| ~ ( p @ ( ap @ SV71 @ ( sK6_SY252 @ SV71 @ SV46 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(595,plain,
! [SV71: $i,SV46: del,SV92: $i] :
( ( ( ~ ( mem @ SV92 @ SV46 )
| ~ ( p @ ( ap @ SV71 @ SV92 ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(596,plain,
! [SV85: $i,SV55: $i] :
( ( ( p @ SV55 )
= $false )
| ( ( p @ SV85 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
= $false )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(597,plain,
! [SV85: $i,SV55: $i] :
( ( ( p @ SV55 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ SV55 ) @ SV85 ) )
= $true )
| ( ( mem @ SV85 @ bool )
= $false )
| ( ( mem @ SV55 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(598,plain,
! [SV83: $i,SV44: $i] :
( ( ( p @ SV44 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $false )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(599,plain,
! [SV44: $i,SV83: $i] :
( ( ( p @ SV83 )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $false )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(600,plain,
! [SV83: $i,SV44: $i] :
( ( ( p @ SV44 )
= $false )
| ( ( ~ ( p @ SV83 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(601,plain,
! [SV45: $i] :
( ( ( p @ SV45 )
= $false )
| ( $false = $true )
| ( $true = $true )
| ( ( p @ SV45 )
= $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(602,plain,
! [SV45: $i] :
( ( $false = $false )
| ( ( p @ SV45 )
= $true )
| ( $true = $true )
| ( ( p @ SV45 )
= $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(603,plain,
! [SV45: $i] :
( ( ( p @ SV45 )
= $false )
| ( $false = $true )
| ( ( p @ SV45 )
= $true )
| ( $true = $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(604,plain,
! [SV45: $i] :
( ( $false = $false )
| ( ( p @ SV45 )
= $true )
| ( ( p @ SV45 )
= $true )
| ( $true = $false )
| ( ( mem @ SV45 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(605,plain,
! [SV46: del,SV71: $i] :
( ( ( ~ ( mem @ ( sK6_SY252 @ SV71 @ SV46 ) @ SV46 ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(606,plain,
! [SV46: del,SV71: $i] :
( ( ( ~ ( p @ ( ap @ SV71 @ ( sK6_SY252 @ SV71 @ SV46 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(607,plain,
! [SV71: $i,SV46: del,SV92: $i] :
( ( ( ~ ( mem @ SV92 @ SV46 ) )
= $true )
| ( ( ~ ( p @ ( ap @ SV71 @ SV92 ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(608,plain,
! [SV44: $i,SV83: $i] :
( ( ( p @ SV83 )
= $false )
| ( ( p @ SV44 )
= $false )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ SV44 ) @ SV83 ) )
= $true )
| ( ( mem @ SV83 @ bool )
= $false )
| ( ( mem @ SV44 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(609,plain,
! [SV46: del,SV71: $i] :
( ( ( mem @ ( sK6_SY252 @ SV71 @ SV46 ) @ SV46 )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(610,plain,
! [SV46: del,SV71: $i] :
( ( ( p @ ( ap @ SV71 @ ( sK6_SY252 @ SV71 @ SV46 ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $false )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(611,plain,
! [SV71: $i,SV46: del,SV92: $i] :
( ( ( mem @ SV92 @ SV46 )
= $false )
| ( ( ~ ( p @ ( ap @ SV71 @ SV92 ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(612,plain,
! [SV46: del,SV92: $i,SV71: $i] :
( ( ( p @ ( ap @ SV71 @ SV92 ) )
= $false )
| ( ( mem @ SV92 @ SV46 )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ SV46 ) @ SV71 ) )
= $true )
| ( ( mem @ SV71 @ ( arr @ SV46 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(613,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[158,612,610,609,608,604,603,602,601,599,598,597,596,586,585,582,581,580,579,578,577,576,567,559,530,529,528,523,522,512,499,491,490,489,488,487,486,485,484,483,482,481,480,479,478,470,466,458,406,402,401,400,365,350,323,322,321,320,319,318,317,316,315,314,313,312,311,309,307,286,285,284,283,282,281,280,278,277,273,271,270,269,268,264,263,262,261,256,255,254,253,252,251,250,249,248,247,246,245,244,219,199,197,196,191,186,184,183,172,169,163]) ).
thf(614,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[613]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP001^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 11:07:31 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.24/0.46
% 1.24/0.46 No.of.Axioms: 72
% 1.24/0.46
% 1.24/0.46 Length.of.Defs: 0
% 1.24/0.46
% 1.24/0.46 Contains.Choice.Funs: false
% 1.24/0.46 ..................
% 1.24/0.46
% 1.24/0.46 ********************************
% 1.24/0.46 * All subproblems solved! *
% 1.24/0.46 ********************************
% 1.24/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:72,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:613,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.24/0.46
% 1.24/0.46 %**** Beginning of derivation protocol ****
% 1.24/0.46 % SZS output start CNFRefutation
% See solution above
% 0.44/0.46
% 0.44/0.46 %**** End of derivation protocol ****
% 0.44/0.46 %**** no. of clauses in derivation: 614 ****
% 0.44/0.46 %**** clause counter: 613 ****
% 0.44/0.46
% 0.44/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:72,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:613,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------