TSTP Solution File: ITP018+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ITP018+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 23:43:47 EDT 2022
% Result : Theorem 0.39s 0.62s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 55
% Syntax : Number of formulae : 328 ( 134 unt; 26 typ; 0 def)
% Number of atoms : 2172 ( 702 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 4744 ( 537 ~; 674 |; 12 &;3419 @)
% ( 8 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 9 con; 0-4 aty)
% Number of variables : 662 ( 0 ^ 662 !; 0 ?; 662 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ap,type,
ap: $i > $i > $i ).
thf(tp_arr,type,
arr: $i > $i > $i ).
thf(tp_bool,type,
bool: $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__negate,type,
c_2Ebinary__ieee_2Efloat__negate: $i > $i > $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__min,type,
c_2Ebinary__ieee_2Efloat__plus__min: $i > $i > $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__to__real,type,
c_2Ebinary__ieee_2Efloat__to__real: $i > $i > $i ).
thf(tp_c_2Ebinary__ieee_2Eulp,type,
c_2Ebinary__ieee_2Eulp: $i > $i > $i ).
thf(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
thf(tp_c_2Ebool_2E_21,type,
c_2Ebool_2E_21: $i > $i ).
thf(tp_c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value: $i > $i ).
thf(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: $i > $i ).
thf(tp_c_2Erealax_2Ereal__neg,type,
c_2Erealax_2Ereal__neg: $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_ind,type,
ind: $i ).
thf(tp_k,type,
k: $i > $i > $i ).
thf(tp_mem,type,
mem: $i > $i > $o ).
thf(tp_ne,type,
ne: $i > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_sK1_A_27t,type,
sK1_A_27t: $i ).
thf(tp_sK2_SY49,type,
sK2_SY49: $i ).
thf(tp_sK3_X,type,
sK3_X: $i > $i > $i ).
thf(tp_sK4_X,type,
sK4_X: $i > $i > $i > $i > $i ).
thf(tp_ty_2Ebinary__ieee_2Efloat,type,
ty_2Ebinary__ieee_2Efloat: $i > $i > $i ).
thf(tp_ty_2Ebool_2Eitself,type,
ty_2Ebool_2Eitself: $i > $i ).
thf(tp_ty_2Epair_2Eprod,type,
ty_2Epair_2Eprod: $i > $i > $i ).
thf(tp_ty_2Erealax_2Ereal,type,
ty_2Erealax_2Ereal: $i ).
thf(1,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( V0x = V0x )
<=> $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EREFL__CLAUSE) ).
thf(2,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(3,axiom,
! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eulp) ).
thf(4,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ! [A_27b: $i] :
( ( ne @ A_27b )
=> ! [V0x: $i] :
( ( mem @ V0x @ ( ty_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) )
=> ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b ) @ V0x ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ V0x ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(5,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [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(6,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ( 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(7,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [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(8,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ( 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(9,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_true_p) ).
thf(10,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(11,axiom,
! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( mem @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ty_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Eulp) ).
thf(12,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ( 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(13,axiom,
! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ty_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__to__real) ).
thf(14,axiom,
! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__plus__min) ).
thf(15,axiom,
! [A0: $i] :
( ( ne @ A0 )
=> ( ne @ ( ty_2Ebool_2Eitself @ A0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ne_ty_2Ebool_2Eitself) ).
thf(16,axiom,
! [A0: $i] :
( ( ne @ A0 )
=> ! [A1: $i] :
( ( ne @ A1 )
=> ( ne @ ( ty_2Epair_2Eprod @ A0 @ A1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ne_ty_2Epair_2Eprod) ).
thf(17,axiom,
! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__negate) ).
thf(18,axiom,
! [A0: $i] :
( ( ne @ A0 )
=> ! [A1: $i] :
( ( ne @ A1 )
=> ( ne @ ( ty_2Ebinary__ieee_2Efloat @ A0 @ A1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ne_ty_2Ebinary__ieee_2Efloat) ).
thf(19,axiom,
mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Erealax_2Ereal__neg) ).
thf(20,axiom,
ne @ ty_2Erealax_2Ereal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ne_ty_2Erealax_2Ereal) ).
thf(21,axiom,
! [A: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( i @ A ) @ X )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ibeta) ).
thf(22,axiom,
! [A: $i,Y: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kbeta) ).
thf(23,axiom,
! [A: $i,B: $i,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(24,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( ( p @ Q )
<=> ( p @ R ) )
=> ( Q = R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolext) ).
thf(25,axiom,
! [A: $i,B: $i,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(26,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( ne @ B )
=> ( ne @ ( arr @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arr_ne) ).
thf(27,axiom,
ne @ ind,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ind_ne) ).
thf(28,axiom,
ne @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bool_ne) ).
thf(29,conjecture,
! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eneg__ulp) ).
thf(30,negated_conjecture,
( ( ! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [A_27a: $i] :
( ( ne @ A_27a )
=> ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( V0x = V0x )
<=> $true ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,plain,
$true = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(34,plain,
( ( ! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [A_27a: $i] :
( ( ne @ A_27a )
=> ! [A_27b: $i] :
( ( ne @ A_27b )
=> ! [V0x: $i] :
( ( mem @ V0x @ ( ty_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) )
=> ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b ) @ V0x ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ V0x ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( ne @ A )
=> ! [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)],[5]) ).
thf(37,plain,
( ( ! [A_27a: $i] :
( ( ne @ A_27a )
=> ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( ne @ A )
=> ! [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)],[7]) ).
thf(39,plain,
( ( ! [A_27a: $i] :
( ( ne @ A_27a )
=> ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(40,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(41,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(42,plain,
( ( ! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( mem @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ty_2Erealax_2Ereal ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(43,plain,
( ( ! [A_27a: $i] :
( ( ne @ A_27a )
=> ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(44,plain,
( ( ! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ty_2Erealax_2Ereal ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(45,plain,
( ( ! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(46,plain,
( ( ! [A0: $i] :
( ( ne @ A0 )
=> ( ne @ ( ty_2Ebool_2Eitself @ A0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(47,plain,
( ( ! [A0: $i] :
( ( ne @ A0 )
=> ! [A1: $i] :
( ( ne @ A1 )
=> ( ne @ ( ty_2Epair_2Eprod @ A0 @ A1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(48,plain,
( ( ! [A_27t: $i] :
( ( ne @ A_27t )
=> ! [A_27w: $i] :
( ( ne @ A_27w )
=> ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(49,plain,
( ( ! [A0: $i] :
( ( ne @ A0 )
=> ! [A1: $i] :
( ( ne @ A1 )
=> ( ne @ ( ty_2Ebinary__ieee_2Efloat @ A0 @ A1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(50,plain,
( ( mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(51,plain,
( ( ne @ ty_2Erealax_2Ereal )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(52,plain,
( ( ! [A: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( i @ A ) @ X )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [A: $i,Y: $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,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)],[23]) ).
thf(55,plain,
( ( ! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( ( p @ Q )
<=> ( p @ R ) )
=> ( Q = R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(56,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( ne @ B )
=> ( ne @ ( arr @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(58,plain,
( ( ne @ ind )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(59,plain,
( ( ne @ bool )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(60,plain,
( ( ( ne @ sK1_A_27t )
=> ! [SY49: $i] :
( ( ne @ SY49 )
=> ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ SY49 ) ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ SY49 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(61,plain,
( ( ne @ sK1_A_27t )
= $true ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [SY49: $i] :
( ( ne @ SY49 )
=> ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ SY49 ) ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ SY49 ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(63,plain,
( ( ~ ! [SY49: $i] :
( ( ne @ SY49 )
=> ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ SY49 ) ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ SY49 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[62]) ).
thf(64,plain,
( ( ( ne @ sK2_SY49 )
& ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) )
!= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(65,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ! [V0x: $i] :
~ ( mem @ V0x @ A_27a )
| $true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(66,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(67,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ! [A_27b: $i] :
( ~ ( ne @ A_27b )
| ! [V0x: $i] :
( ~ ( mem @ V0x @ ( ty_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) )
| ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b ) @ V0x ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ V0x ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(68,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ( ! [Q: $i] :
( ~ ( mem @ Q @ ( arr @ A @ bool ) )
| ( ( mem @ ( sK3_X @ Q @ A ) @ A )
& ~ ( p @ ( ap @ Q @ ( sK3_X @ Q @ A ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) ) )
& ! [Q: $i] :
( ~ ( mem @ Q @ ( arr @ A @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( p @ ( ap @ Q @ X ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(69,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(70,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ( X != Y )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) ) )
& ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
| ( X = Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(71,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(72,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( mem @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ty_2Erealax_2Ereal ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(73,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(74,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ty_2Erealax_2Ereal ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(75,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(76,plain,
( ( ! [A0: $i] :
( ~ ( ne @ A0 )
| ( ne @ ( ty_2Ebool_2Eitself @ A0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(77,plain,
( ( ! [A0: $i] :
( ~ ( ne @ A0 )
| ! [A1: $i] :
( ~ ( ne @ A1 )
| ( ne @ ( ty_2Epair_2Eprod @ A0 @ A1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(78,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(79,plain,
( ( ! [A0: $i] :
( ~ ( ne @ A0 )
| ! [A1: $i] :
( ~ ( ne @ A1 )
| ( ne @ ( ty_2Ebinary__ieee_2Efloat @ A0 @ A1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(80,plain,
( ( ! [A: $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( i @ A ) @ X )
= X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(81,plain,
( ( ! [A: $i,Y: $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(82,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [G: $i] :
( ~ ( mem @ G @ ( arr @ A @ B ) )
| ( ( mem @ ( sK4_X @ G @ F @ B @ A ) @ A )
& ( ( ap @ F @ ( sK4_X @ G @ F @ B @ A ) )
!= ( ap @ G @ ( sK4_X @ G @ F @ B @ A ) ) ) )
| ( F = G ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(83,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ Q )
| ~ ( p @ R )
| ( Q = R ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ( p @ Q )
| ( p @ R )
| ( Q = R ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(84,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(85,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ! [B: $i] :
( ~ ( ne @ B )
| ( ne @ ( arr @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(86,plain,
( ( ne @ bool )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(87,plain,
( ( ne @ ind )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(88,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ! [B: $i] :
( ~ ( ne @ B )
| ( ne @ ( arr @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(89,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(90,plain,
( ( ! [Q: $i] :
( ~ ( mem @ Q @ bool )
| ( ! [R: $i] :
( ~ ( mem @ R @ bool )
| ~ ( p @ Q )
| ~ ( p @ R )
| ( Q = R ) )
& ! [R: $i] :
( ~ ( mem @ R @ bool )
| ( p @ Q )
| ( p @ R )
| ( Q = R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(91,plain,
( ( ! [A: $i,B: $i,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [G: $i] :
( ~ ( mem @ G @ ( arr @ A @ B ) )
| ( ( mem @ ( sK4_X @ G @ F @ B @ A ) @ A )
& ( ( ap @ F @ ( sK4_X @ G @ F @ B @ A ) )
!= ( ap @ G @ ( sK4_X @ G @ F @ B @ A ) ) ) )
| ( F = G ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(92,plain,
( ( ! [A: $i,Y: $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( k @ A @ Y ) @ X )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(93,plain,
( ( ! [A: $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( i @ A ) @ X )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(94,plain,
( ( ne @ ty_2Erealax_2Ereal )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(95,plain,
( ( mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(96,plain,
( ( ! [A0: $i] :
( ~ ( ne @ A0 )
| ! [A1: $i] :
( ~ ( ne @ A1 )
| ( ne @ ( ty_2Ebinary__ieee_2Efloat @ A0 @ A1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(97,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(98,plain,
( ( ! [A0: $i] :
( ~ ( ne @ A0 )
| ! [A1: $i] :
( ~ ( ne @ A1 )
| ( ne @ ( ty_2Epair_2Eprod @ A0 @ A1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(99,plain,
( ( ! [A0: $i] :
( ~ ( ne @ A0 )
| ( ne @ ( ty_2Ebool_2Eitself @ A0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(100,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(101,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ty_2Erealax_2Ereal ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(102,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(103,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( mem @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ty_2Erealax_2Ereal ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(104,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(105,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(106,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(107,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ( X != Y )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) ) )
& ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
| ( X = Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(108,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(109,plain,
( ( ! [A: $i] :
( ~ ( ne @ A )
| ( ! [Q: $i] :
( ~ ( mem @ Q @ ( arr @ A @ bool ) )
| ( ( mem @ ( sK3_X @ Q @ A ) @ A )
& ~ ( p @ ( ap @ Q @ ( sK3_X @ Q @ A ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) ) )
& ! [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)],[68]) ).
thf(110,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ! [A_27b: $i] :
( ~ ( ne @ A_27b )
| ! [V0x: $i] :
( ~ ( mem @ V0x @ ( ty_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) )
| ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b ) @ V0x ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ V0x ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(111,plain,
( ( ! [A_27t: $i] :
( ~ ( ne @ A_27t )
| ! [A_27w: $i] :
( ~ ( ne @ A_27w )
| ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27t @ A_27w ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(112,plain,
$true = $true,
inference(copy,[status(thm)],[33]) ).
thf(113,plain,
( ( ! [A_27a: $i] :
( ~ ( ne @ A_27a )
| ! [V0x: $i] :
~ ( mem @ V0x @ A_27a )
| $true ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(114,plain,
( ( ne @ sK1_A_27t )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(115,plain,
( ( ( ne @ sK2_SY49 )
& ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) )
!= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(116,plain,
( ( ~ ( ~ ( ne @ sK2_SY49 )
| ~ ( ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) )
!= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( mem @ SX2 @ ( arr @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( mem @ SX3 @ ( arr @ SX0 @ SX1 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( ap @ SX2 @ ( sK4_X @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( ap @ SX3 @ ( sK4_X @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(118,plain,
( ( ! [SX0: $i] :
( ~ ( mem @ SX0 @ bool )
| ~ ( ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ~ ( p @ SX0 )
| ~ ( p @ SX1 )
| ( SX0 = SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ bool )
| ( p @ SX0 )
| ( p @ SX1 )
| ( SX0 = SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(119,plain,
( ( ! [SX0: $i] :
( ~ ( ne @ SX0 )
| ! [SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( SX1 != SX2 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(120,plain,
( ( ! [SX0: $i] :
( ~ ( ne @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( p @ ( ap @ SX1 @ ( sK3_X @ SX1 @ SX0 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(121,plain,
! [SV1: $i] :
( ( ~ ( ne @ SV1 )
| ! [SY50: $i] :
( ~ ( ne @ SY50 )
| ( ne @ ( arr @ SV1 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(122,plain,
! [SV2: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ( mem @ SY52 @ ( arr @ SV2 @ SY51 ) )
| ! [SY53: $i] :
( ~ ( mem @ SY53 @ SV2 )
| ( mem @ ( ap @ SY52 @ SY53 ) @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(123,plain,
! [SV3: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( mem @ SY55 @ SV3 )
| ( ( ap @ ( k @ SV3 @ SY54 ) @ SY55 )
= SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(124,plain,
! [SV4: $i] :
( ( ! [SY56: $i] :
( ~ ( mem @ SY56 @ SV4 )
| ( ( ap @ ( i @ SV4 ) @ SY56 )
= SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(125,plain,
! [SV5: $i] :
( ( ~ ( ne @ SV5 )
| ! [SY57: $i] :
( ~ ( ne @ SY57 )
| ( ne @ ( ty_2Ebinary__ieee_2Efloat @ SV5 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(126,plain,
! [SV6: $i] :
( ( ~ ( ne @ SV6 )
| ! [SY58: $i] :
( ~ ( ne @ SY58 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ SV6 @ SY58 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SY58 ) @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SY58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(127,plain,
! [SV7: $i] :
( ( ~ ( ne @ SV7 )
| ! [SY59: $i] :
( ~ ( ne @ SY59 )
| ( ne @ ( ty_2Epair_2Eprod @ SV7 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(128,plain,
! [SV8: $i] :
( ( ~ ( ne @ SV8 )
| ( ne @ ( ty_2Ebool_2Eitself @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(129,plain,
! [SV9: $i] :
( ( ~ ( ne @ SV9 )
| ! [SY60: $i] :
( ~ ( ne @ SY60 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV9 @ SY60 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV9 @ SY60 ) ) @ ( ty_2Ebinary__ieee_2Efloat @ SV9 @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(130,plain,
! [SV10: $i] :
( ( ~ ( ne @ SV10 )
| ! [SY61: $i] :
( ~ ( ne @ SY61 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV10 @ SY61 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SY61 ) @ ty_2Erealax_2Ereal ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(131,plain,
! [SV11: $i] :
( ( ~ ( ne @ SV11 )
| ( mem @ ( c_2Ebool_2Ethe__value @ SV11 ) @ ( ty_2Ebool_2Eitself @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(132,plain,
! [SV12: $i] :
( ( ~ ( ne @ SV12 )
| ! [SY62: $i] :
( ~ ( ne @ SY62 )
| ( mem @ ( c_2Ebinary__ieee_2Eulp @ SV12 @ SY62 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV12 @ SY62 ) ) @ ty_2Erealax_2Ereal ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(133,plain,
! [SV13: $i] :
( ( ~ ( ne @ SV13 )
| ( mem @ ( c_2Emin_2E_3D @ SV13 ) @ ( arr @ SV13 @ ( arr @ SV13 @ bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(134,plain,
! [SV14: $i] :
( ( ~ ( ne @ SV14 )
| ( mem @ ( c_2Ebool_2E_21 @ SV14 ) @ ( arr @ ( arr @ SV14 @ bool ) @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(135,plain,
! [SV15: $i] :
( ( ~ ( ne @ SV15 )
| ! [SY63: $i] :
( ~ ( ne @ SY63 )
| ! [SY64: $i] :
( ~ ( mem @ SY64 @ ( ty_2Ebinary__ieee_2Efloat @ SV15 @ SY63 ) )
| ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SY63 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV15 @ SY63 ) @ SY64 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SY63 ) @ SY64 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(136,plain,
! [SV16: $i] :
( ( ~ ( ne @ SV16 )
| ! [SY65: $i] :
( ~ ( ne @ SY65 )
| ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ SV16 @ SY65 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SY65 ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV16 @ SY65 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV16 @ SY65 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SY65 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(137,plain,
! [SV17: $i] :
( ( ~ ( ne @ SV17 )
| ! [SY66: $i] :
~ ( mem @ SY66 @ SV17 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(138,plain,
( ( ~ ( ne @ sK2_SY49 )
| ~ ( ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) )
!= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(139,plain,
! [SV18: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ( mem @ SY68 @ ( arr @ SV18 @ SY67 ) )
| ! [SY69: $i] :
( ~ ( mem @ SY69 @ ( arr @ SV18 @ SY67 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY69 @ SY68 @ SY67 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SY68 @ ( sK4_X @ SY69 @ SY68 @ SY67 @ SV18 ) )
!= ( ap @ SY69 @ ( sK4_X @ SY69 @ SY68 @ SY67 @ SV18 ) ) ) ) )
| ( SY68 = SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(140,plain,
! [SV19: $i] :
( ( ~ ( mem @ SV19 @ bool )
| ~ ( ~ ! [SY70: $i] :
( ~ ( mem @ SY70 @ bool )
| ~ ( p @ SV19 )
| ~ ( p @ SY70 )
| ( SV19 = SY70 ) )
| ~ ! [SY71: $i] :
( ~ ( mem @ SY71 @ bool )
| ( p @ SV19 )
| ( p @ SY71 )
| ( SV19 = SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(141,plain,
! [SV20: $i] :
( ( ~ ( ne @ SV20 )
| ! [SY72: $i] :
( ~ ( mem @ SY72 @ SV20 )
| ~ ( ~ ! [SY73: $i] :
( ~ ( mem @ SY73 @ SV20 )
| ( SY72 != SY73 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SY72 ) @ SY73 ) ) )
| ~ ! [SY74: $i] :
( ~ ( mem @ SY74 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SY72 ) @ SY74 ) )
| ( SY72 = SY74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(142,plain,
! [SV21: $i] :
( ( ~ ( ne @ SV21 )
| ~ ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ ( arr @ SV21 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY75 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SY75 @ ( sK3_X @ SY75 @ SV21 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY75 ) ) )
| ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ ( arr @ SV21 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY76 ) )
| ! [SY77: $i] :
( ~ ( mem @ SY77 @ SV21 )
| ( p @ ( ap @ SY76 @ SY77 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(143,plain,
! [SV1: $i] :
( ( ( ~ ( ne @ SV1 ) )
= $true )
| ( ( ! [SY50: $i] :
( ~ ( ne @ SY50 )
| ( ne @ ( arr @ SV1 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(144,plain,
! [SV22: $i,SV2: $i] :
( ( ! [SY78: $i] :
( ~ ( mem @ SY78 @ ( arr @ SV2 @ SV22 ) )
| ! [SY79: $i] :
( ~ ( mem @ SY79 @ SV2 )
| ( mem @ ( ap @ SY78 @ SY79 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(145,plain,
! [SV23: $i,SV3: $i] :
( ( ! [SY80: $i] :
( ~ ( mem @ SY80 @ SV3 )
| ( ( ap @ ( k @ SV3 @ SV23 ) @ SY80 )
= SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(146,plain,
! [SV4: $i,SV24: $i] :
( ( ~ ( mem @ SV24 @ SV4 )
| ( ( ap @ ( i @ SV4 ) @ SV24 )
= SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(147,plain,
! [SV5: $i] :
( ( ( ~ ( ne @ SV5 ) )
= $true )
| ( ( ! [SY57: $i] :
( ~ ( ne @ SY57 )
| ( ne @ ( ty_2Ebinary__ieee_2Efloat @ SV5 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(148,plain,
! [SV6: $i] :
( ( ( ~ ( ne @ SV6 ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( ne @ SY58 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ SV6 @ SY58 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SY58 ) @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SY58 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(149,plain,
! [SV7: $i] :
( ( ( ~ ( ne @ SV7 ) )
= $true )
| ( ( ! [SY59: $i] :
( ~ ( ne @ SY59 )
| ( ne @ ( ty_2Epair_2Eprod @ SV7 @ SY59 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(150,plain,
! [SV8: $i] :
( ( ( ~ ( ne @ SV8 ) )
= $true )
| ( ( ne @ ( ty_2Ebool_2Eitself @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(151,plain,
! [SV9: $i] :
( ( ( ~ ( ne @ SV9 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( ne @ SY60 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV9 @ SY60 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV9 @ SY60 ) ) @ ( ty_2Ebinary__ieee_2Efloat @ SV9 @ SY60 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(152,plain,
! [SV10: $i] :
( ( ( ~ ( ne @ SV10 ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( ne @ SY61 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV10 @ SY61 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SY61 ) @ ty_2Erealax_2Ereal ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(153,plain,
! [SV11: $i] :
( ( ( ~ ( ne @ SV11 ) )
= $true )
| ( ( mem @ ( c_2Ebool_2Ethe__value @ SV11 ) @ ( ty_2Ebool_2Eitself @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(154,plain,
! [SV12: $i] :
( ( ( ~ ( ne @ SV12 ) )
= $true )
| ( ( ! [SY62: $i] :
( ~ ( ne @ SY62 )
| ( mem @ ( c_2Ebinary__ieee_2Eulp @ SV12 @ SY62 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV12 @ SY62 ) ) @ ty_2Erealax_2Ereal ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(155,plain,
! [SV13: $i] :
( ( ( ~ ( ne @ SV13 ) )
= $true )
| ( ( mem @ ( c_2Emin_2E_3D @ SV13 ) @ ( arr @ SV13 @ ( arr @ SV13 @ bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(156,plain,
! [SV14: $i] :
( ( ( ~ ( ne @ SV14 ) )
= $true )
| ( ( mem @ ( c_2Ebool_2E_21 @ SV14 ) @ ( arr @ ( arr @ SV14 @ bool ) @ bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(157,plain,
! [SV15: $i] :
( ( ( ~ ( ne @ SV15 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( ne @ SY63 )
| ! [SY64: $i] :
( ~ ( mem @ SY64 @ ( ty_2Ebinary__ieee_2Efloat @ SV15 @ SY63 ) )
| ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SY63 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV15 @ SY63 ) @ SY64 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SY63 ) @ SY64 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(158,plain,
! [SV16: $i] :
( ( ( ~ ( ne @ SV16 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( ne @ SY65 )
| ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ SV16 @ SY65 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SY65 ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV16 @ SY65 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV16 @ SY65 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SY65 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(159,plain,
! [SV17: $i] :
( ( ( ~ ( ne @ SV17 ) )
= $true )
| ( ( ! [SY66: $i] :
~ ( mem @ SY66 @ SV17 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(160,plain,
( ( ~ ( ne @ sK2_SY49 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(161,plain,
( ( ~ ( ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) )
!= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(162,plain,
! [SV25: $i,SV18: $i] :
( ( ! [SY81: $i] :
( ~ ( mem @ SY81 @ ( arr @ SV18 @ SV25 ) )
| ! [SY82: $i] :
( ~ ( mem @ SY82 @ ( arr @ SV18 @ SV25 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY82 @ SY81 @ SV25 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SY81 @ ( sK4_X @ SY82 @ SY81 @ SV25 @ SV18 ) )
!= ( ap @ SY82 @ ( sK4_X @ SY82 @ SY81 @ SV25 @ SV18 ) ) ) ) )
| ( SY81 = SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(163,plain,
! [SV19: $i] :
( ( ( ~ ( mem @ SV19 @ bool ) )
= $true )
| ( ( ~ ( ~ ! [SY70: $i] :
( ~ ( mem @ SY70 @ bool )
| ~ ( p @ SV19 )
| ~ ( p @ SY70 )
| ( SV19 = SY70 ) )
| ~ ! [SY71: $i] :
( ~ ( mem @ SY71 @ bool )
| ( p @ SV19 )
| ( p @ SY71 )
| ( SV19 = SY71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(164,plain,
! [SV20: $i] :
( ( ( ~ ( ne @ SV20 ) )
= $true )
| ( ( ! [SY72: $i] :
( ~ ( mem @ SY72 @ SV20 )
| ~ ( ~ ! [SY73: $i] :
( ~ ( mem @ SY73 @ SV20 )
| ( SY72 != SY73 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SY72 ) @ SY73 ) ) )
| ~ ! [SY74: $i] :
( ~ ( mem @ SY74 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SY72 ) @ SY74 ) )
| ( SY72 = SY74 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(165,plain,
! [SV21: $i] :
( ( ( ~ ( ne @ SV21 ) )
= $true )
| ( ( ~ ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ ( arr @ SV21 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY75 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SY75 @ ( sK3_X @ SY75 @ SV21 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY75 ) ) )
| ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ ( arr @ SV21 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY76 ) )
| ! [SY77: $i] :
( ~ ( mem @ SY77 @ SV21 )
| ( p @ ( ap @ SY76 @ SY77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(166,plain,
! [SV1: $i] :
( ( ( ne @ SV1 )
= $false )
| ( ( ! [SY50: $i] :
( ~ ( ne @ SY50 )
| ( ne @ ( arr @ SV1 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(167,plain,
! [SV22: $i,SV2: $i,SV26: $i] :
( ( ~ ( mem @ SV26 @ ( arr @ SV2 @ SV22 ) )
| ! [SY83: $i] :
( ~ ( mem @ SY83 @ SV2 )
| ( mem @ ( ap @ SV26 @ SY83 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(168,plain,
! [SV23: $i,SV3: $i,SV27: $i] :
( ( ~ ( mem @ SV27 @ SV3 )
| ( ( ap @ ( k @ SV3 @ SV23 ) @ SV27 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(169,plain,
! [SV4: $i,SV24: $i] :
( ( ( ~ ( mem @ SV24 @ SV4 ) )
= $true )
| ( ( ( ap @ ( i @ SV4 ) @ SV24 )
= SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(170,plain,
! [SV5: $i] :
( ( ( ne @ SV5 )
= $false )
| ( ( ! [SY57: $i] :
( ~ ( ne @ SY57 )
| ( ne @ ( ty_2Ebinary__ieee_2Efloat @ SV5 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(171,plain,
! [SV6: $i] :
( ( ( ne @ SV6 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( ne @ SY58 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ SV6 @ SY58 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SY58 ) @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SY58 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(172,plain,
! [SV7: $i] :
( ( ( ne @ SV7 )
= $false )
| ( ( ! [SY59: $i] :
( ~ ( ne @ SY59 )
| ( ne @ ( ty_2Epair_2Eprod @ SV7 @ SY59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(173,plain,
! [SV8: $i] :
( ( ( ne @ SV8 )
= $false )
| ( ( ne @ ( ty_2Ebool_2Eitself @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(174,plain,
! [SV9: $i] :
( ( ( ne @ SV9 )
= $false )
| ( ( ! [SY60: $i] :
( ~ ( ne @ SY60 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV9 @ SY60 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV9 @ SY60 ) ) @ ( ty_2Ebinary__ieee_2Efloat @ SV9 @ SY60 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(175,plain,
! [SV10: $i] :
( ( ( ne @ SV10 )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( ne @ SY61 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV10 @ SY61 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SY61 ) @ ty_2Erealax_2Ereal ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(176,plain,
! [SV11: $i] :
( ( ( ne @ SV11 )
= $false )
| ( ( mem @ ( c_2Ebool_2Ethe__value @ SV11 ) @ ( ty_2Ebool_2Eitself @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(177,plain,
! [SV12: $i] :
( ( ( ne @ SV12 )
= $false )
| ( ( ! [SY62: $i] :
( ~ ( ne @ SY62 )
| ( mem @ ( c_2Ebinary__ieee_2Eulp @ SV12 @ SY62 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV12 @ SY62 ) ) @ ty_2Erealax_2Ereal ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(178,plain,
! [SV13: $i] :
( ( ( ne @ SV13 )
= $false )
| ( ( mem @ ( c_2Emin_2E_3D @ SV13 ) @ ( arr @ SV13 @ ( arr @ SV13 @ bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(179,plain,
! [SV14: $i] :
( ( ( ne @ SV14 )
= $false )
| ( ( mem @ ( c_2Ebool_2E_21 @ SV14 ) @ ( arr @ ( arr @ SV14 @ bool ) @ bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(180,plain,
! [SV15: $i] :
( ( ( ne @ SV15 )
= $false )
| ( ( ! [SY63: $i] :
( ~ ( ne @ SY63 )
| ! [SY64: $i] :
( ~ ( mem @ SY64 @ ( ty_2Ebinary__ieee_2Efloat @ SV15 @ SY63 ) )
| ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SY63 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV15 @ SY63 ) @ SY64 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SY63 ) @ SY64 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(181,plain,
! [SV16: $i] :
( ( ( ne @ SV16 )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( ne @ SY65 )
| ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ SV16 @ SY65 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SY65 ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV16 @ SY65 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV16 @ SY65 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SY65 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(182,plain,
! [SV17: $i] :
( ( ( ne @ SV17 )
= $false )
| ( ( ! [SY66: $i] :
~ ( mem @ SY66 @ SV17 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(183,plain,
( ( ne @ sK2_SY49 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(184,plain,
( ( ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) )
!= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(185,plain,
! [SV25: $i,SV18: $i,SV28: $i] :
( ( ~ ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
| ! [SY84: $i] :
( ~ ( mem @ SY84 @ ( arr @ SV18 @ SV25 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY84 @ SV28 @ SV25 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SV28 @ ( sK4_X @ SY84 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SY84 @ ( sK4_X @ SY84 @ SV28 @ SV25 @ SV18 ) ) ) ) )
| ( SV28 = SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(186,plain,
! [SV19: $i] :
( ( ( mem @ SV19 @ bool )
= $false )
| ( ( ~ ( ~ ! [SY70: $i] :
( ~ ( mem @ SY70 @ bool )
| ~ ( p @ SV19 )
| ~ ( p @ SY70 )
| ( SV19 = SY70 ) )
| ~ ! [SY71: $i] :
( ~ ( mem @ SY71 @ bool )
| ( p @ SV19 )
| ( p @ SY71 )
| ( SV19 = SY71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(187,plain,
! [SV20: $i] :
( ( ( ne @ SV20 )
= $false )
| ( ( ! [SY72: $i] :
( ~ ( mem @ SY72 @ SV20 )
| ~ ( ~ ! [SY73: $i] :
( ~ ( mem @ SY73 @ SV20 )
| ( SY72 != SY73 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SY72 ) @ SY73 ) ) )
| ~ ! [SY74: $i] :
( ~ ( mem @ SY74 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SY72 ) @ SY74 ) )
| ( SY72 = SY74 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(188,plain,
! [SV21: $i] :
( ( ( ne @ SV21 )
= $false )
| ( ( ~ ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ ( arr @ SV21 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY75 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SY75 @ ( sK3_X @ SY75 @ SV21 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY75 ) ) )
| ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ ( arr @ SV21 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY76 ) )
| ! [SY77: $i] :
( ~ ( mem @ SY77 @ SV21 )
| ( p @ ( ap @ SY76 @ SY77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(189,plain,
! [SV1: $i,SV29: $i] :
( ( ( ~ ( ne @ SV29 )
| ( ne @ ( arr @ SV1 @ SV29 ) ) )
= $true )
| ( ( ne @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(190,plain,
! [SV22: $i,SV2: $i,SV26: $i] :
( ( ( ~ ( mem @ SV26 @ ( arr @ SV2 @ SV22 ) ) )
= $true )
| ( ( ! [SY83: $i] :
( ~ ( mem @ SY83 @ SV2 )
| ( mem @ ( ap @ SV26 @ SY83 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(191,plain,
! [SV23: $i,SV3: $i,SV27: $i] :
( ( ( ~ ( mem @ SV27 @ SV3 ) )
= $true )
| ( ( ( ap @ ( k @ SV3 @ SV23 ) @ SV27 )
= SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(192,plain,
! [SV4: $i,SV24: $i] :
( ( ( mem @ SV24 @ SV4 )
= $false )
| ( ( ( ap @ ( i @ SV4 ) @ SV24 )
= SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(193,plain,
! [SV5: $i,SV30: $i] :
( ( ( ~ ( ne @ SV30 )
| ( ne @ ( ty_2Ebinary__ieee_2Efloat @ SV5 @ SV30 ) ) )
= $true )
| ( ( ne @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(194,plain,
! [SV6: $i,SV31: $i] :
( ( ( ~ ( ne @ SV31 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ SV6 @ SV31 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SV31 ) @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SV31 ) ) ) )
= $true )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV7: $i,SV32: $i] :
( ( ( ~ ( ne @ SV32 )
| ( ne @ ( ty_2Epair_2Eprod @ SV7 @ SV32 ) ) )
= $true )
| ( ( ne @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(196,plain,
! [SV9: $i,SV33: $i] :
( ( ( ~ ( ne @ SV33 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV9 @ SV33 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV9 @ SV33 ) ) @ ( ty_2Ebinary__ieee_2Efloat @ SV9 @ SV33 ) ) ) )
= $true )
| ( ( ne @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(197,plain,
! [SV10: $i,SV34: $i] :
( ( ( ~ ( ne @ SV34 )
| ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV10 @ SV34 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SV34 ) @ ty_2Erealax_2Ereal ) ) )
= $true )
| ( ( ne @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(198,plain,
! [SV12: $i,SV35: $i] :
( ( ( ~ ( ne @ SV35 )
| ( mem @ ( c_2Ebinary__ieee_2Eulp @ SV12 @ SV35 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV12 @ SV35 ) ) @ ty_2Erealax_2Ereal ) ) )
= $true )
| ( ( ne @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(199,plain,
! [SV15: $i,SV36: $i] :
( ( ( ~ ( ne @ SV36 )
| ! [SY85: $i] :
( ~ ( mem @ SY85 @ ( ty_2Ebinary__ieee_2Efloat @ SV15 @ SV36 ) )
| ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV15 @ SV36 ) @ SY85 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ SY85 ) ) ) ) )
= $true )
| ( ( ne @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(200,plain,
! [SV16: $i,SV37: $i] :
( ( ( ~ ( ne @ SV37 )
| ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ SV16 @ SV37 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SV37 ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV16 @ SV37 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV16 @ SV37 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SV37 ) ) ) ) ) )
= $true )
| ( ( ne @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(201,plain,
! [SV17: $i] :
( ( ( ! [SY66: $i] :
~ ( mem @ SY66 @ SV17 ) )
= $true )
| ( $true = $true )
| ( ( ne @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(202,plain,
( ( ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ sK1_A_27t @ sK2_SY49 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ sK1_A_27t @ sK2_SY49 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ sK1_A_27t @ sK2_SY49 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(203,plain,
! [SV25: $i,SV18: $i,SV28: $i] :
( ( ( ~ ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) ) )
= $true )
| ( ( ! [SY84: $i] :
( ~ ( mem @ SY84 @ ( arr @ SV18 @ SV25 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY84 @ SV28 @ SV25 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SV28 @ ( sK4_X @ SY84 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SY84 @ ( sK4_X @ SY84 @ SV28 @ SV25 @ SV18 ) ) ) ) )
| ( SV28 = SY84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(204,plain,
! [SV19: $i] :
( ( ( ~ ! [SY70: $i] :
( ~ ( mem @ SY70 @ bool )
| ~ ( p @ SV19 )
| ~ ( p @ SY70 )
| ( SV19 = SY70 ) )
| ~ ! [SY71: $i] :
( ~ ( mem @ SY71 @ bool )
| ( p @ SV19 )
| ( p @ SY71 )
| ( SV19 = SY71 ) ) )
= $false )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(205,plain,
! [SV20: $i,SV38: $i] :
( ( ( ~ ( mem @ SV38 @ SV20 )
| ~ ( ~ ! [SY86: $i] :
( ~ ( mem @ SY86 @ SV20 )
| ( SV38 != SY86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY86 ) ) )
| ~ ! [SY87: $i] :
( ~ ( mem @ SY87 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY87 ) )
| ( SV38 = SY87 ) ) ) )
= $true )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(206,plain,
! [SV21: $i] :
( ( ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ ( arr @ SV21 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY75 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SY75 @ ( sK3_X @ SY75 @ SV21 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY75 ) ) )
| ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ ( arr @ SV21 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY76 ) )
| ! [SY77: $i] :
( ~ ( mem @ SY77 @ SV21 )
| ( p @ ( ap @ SY76 @ SY77 ) ) ) ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(207,plain,
! [SV1: $i,SV29: $i] :
( ( ( ~ ( ne @ SV29 ) )
= $true )
| ( ( ne @ ( arr @ SV1 @ SV29 ) )
= $true )
| ( ( ne @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(208,plain,
! [SV22: $i,SV2: $i,SV26: $i] :
( ( ( mem @ SV26 @ ( arr @ SV2 @ SV22 ) )
= $false )
| ( ( ! [SY83: $i] :
( ~ ( mem @ SY83 @ SV2 )
| ( mem @ ( ap @ SV26 @ SY83 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(209,plain,
! [SV23: $i,SV3: $i,SV27: $i] :
( ( ( mem @ SV27 @ SV3 )
= $false )
| ( ( ( ap @ ( k @ SV3 @ SV23 ) @ SV27 )
= SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(210,plain,
! [SV5: $i,SV30: $i] :
( ( ( ~ ( ne @ SV30 ) )
= $true )
| ( ( ne @ ( ty_2Ebinary__ieee_2Efloat @ SV5 @ SV30 ) )
= $true )
| ( ( ne @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(211,plain,
! [SV6: $i,SV31: $i] :
( ( ( ~ ( ne @ SV31 ) )
= $true )
| ( ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ SV6 @ SV31 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SV31 ) @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SV31 ) ) )
= $true )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(212,plain,
! [SV7: $i,SV32: $i] :
( ( ( ~ ( ne @ SV32 ) )
= $true )
| ( ( ne @ ( ty_2Epair_2Eprod @ SV7 @ SV32 ) )
= $true )
| ( ( ne @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(213,plain,
! [SV9: $i,SV33: $i] :
( ( ( ~ ( ne @ SV33 ) )
= $true )
| ( ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV9 @ SV33 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV9 @ SV33 ) ) @ ( ty_2Ebinary__ieee_2Efloat @ SV9 @ SV33 ) ) )
= $true )
| ( ( ne @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(214,plain,
! [SV10: $i,SV34: $i] :
( ( ( ~ ( ne @ SV34 ) )
= $true )
| ( ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV10 @ SV34 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SV34 ) @ ty_2Erealax_2Ereal ) )
= $true )
| ( ( ne @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(215,plain,
! [SV12: $i,SV35: $i] :
( ( ( ~ ( ne @ SV35 ) )
= $true )
| ( ( mem @ ( c_2Ebinary__ieee_2Eulp @ SV12 @ SV35 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV12 @ SV35 ) ) @ ty_2Erealax_2Ereal ) )
= $true )
| ( ( ne @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(216,plain,
! [SV15: $i,SV36: $i] :
( ( ( ~ ( ne @ SV36 ) )
= $true )
| ( ( ! [SY85: $i] :
( ~ ( mem @ SY85 @ ( ty_2Ebinary__ieee_2Efloat @ SV15 @ SV36 ) )
| ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV15 @ SV36 ) @ SY85 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ SY85 ) ) ) ) )
= $true )
| ( ( ne @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(217,plain,
! [SV16: $i,SV37: $i] :
( ( ( ~ ( ne @ SV37 ) )
= $true )
| ( ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ SV16 @ SV37 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SV37 ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV16 @ SV37 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV16 @ SV37 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SV37 ) ) ) ) )
= $true )
| ( ( ne @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(218,plain,
! [SV17: $i,SV39: $i] :
( ( ( ~ ( mem @ SV39 @ SV17 ) )
= $true )
| ( $true = $true )
| ( ( ne @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(219,plain,
! [SV25: $i,SV18: $i,SV28: $i] :
( ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false )
| ( ( ! [SY84: $i] :
( ~ ( mem @ SY84 @ ( arr @ SV18 @ SV25 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY84 @ SV28 @ SV25 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SV28 @ ( sK4_X @ SY84 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SY84 @ ( sK4_X @ SY84 @ SV28 @ SV25 @ SV18 ) ) ) ) )
| ( SV28 = SY84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(220,plain,
! [SV19: $i] :
( ( ( ~ ! [SY70: $i] :
( ~ ( mem @ SY70 @ bool )
| ~ ( p @ SV19 )
| ~ ( p @ SY70 )
| ( SV19 = SY70 ) ) )
= $false )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(221,plain,
! [SV19: $i] :
( ( ( ~ ! [SY71: $i] :
( ~ ( mem @ SY71 @ bool )
| ( p @ SV19 )
| ( p @ SY71 )
| ( SV19 = SY71 ) ) )
= $false )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(222,plain,
! [SV20: $i,SV38: $i] :
( ( ( ~ ( mem @ SV38 @ SV20 ) )
= $true )
| ( ( ~ ( ~ ! [SY86: $i] :
( ~ ( mem @ SY86 @ SV20 )
| ( SV38 != SY86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY86 ) ) )
| ~ ! [SY87: $i] :
( ~ ( mem @ SY87 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY87 ) )
| ( SV38 = SY87 ) ) ) )
= $true )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(223,plain,
! [SV21: $i] :
( ( ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ ( arr @ SV21 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY75 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SY75 @ ( sK3_X @ SY75 @ SV21 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY75 ) ) ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(224,plain,
! [SV21: $i] :
( ( ( ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ ( arr @ SV21 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY76 ) )
| ! [SY77: $i] :
( ~ ( mem @ SY77 @ SV21 )
| ( p @ ( ap @ SY76 @ SY77 ) ) ) ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(225,plain,
! [SV1: $i,SV29: $i] :
( ( ( ne @ SV29 )
= $false )
| ( ( ne @ ( arr @ SV1 @ SV29 ) )
= $true )
| ( ( ne @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(226,plain,
! [SV22: $i,SV26: $i,SV2: $i,SV40: $i] :
( ( ( ~ ( mem @ SV40 @ SV2 )
| ( mem @ ( ap @ SV26 @ SV40 ) @ SV22 ) )
= $true )
| ( ( mem @ SV26 @ ( arr @ SV2 @ SV22 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(227,plain,
! [SV5: $i,SV30: $i] :
( ( ( ne @ SV30 )
= $false )
| ( ( ne @ ( ty_2Ebinary__ieee_2Efloat @ SV5 @ SV30 ) )
= $true )
| ( ( ne @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(228,plain,
! [SV6: $i,SV31: $i] :
( ( ( ne @ SV31 )
= $false )
| ( ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ SV6 @ SV31 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SV31 ) @ ( ty_2Ebinary__ieee_2Efloat @ SV6 @ SV31 ) ) )
= $true )
| ( ( ne @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(229,plain,
! [SV7: $i,SV32: $i] :
( ( ( ne @ SV32 )
= $false )
| ( ( ne @ ( ty_2Epair_2Eprod @ SV7 @ SV32 ) )
= $true )
| ( ( ne @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(230,plain,
! [SV9: $i,SV33: $i] :
( ( ( ne @ SV33 )
= $false )
| ( ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV9 @ SV33 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV9 @ SV33 ) ) @ ( ty_2Ebinary__ieee_2Efloat @ SV9 @ SV33 ) ) )
= $true )
| ( ( ne @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(231,plain,
! [SV10: $i,SV34: $i] :
( ( ( ne @ SV34 )
= $false )
| ( ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV10 @ SV34 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SV34 ) @ ty_2Erealax_2Ereal ) )
= $true )
| ( ( ne @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(232,plain,
! [SV12: $i,SV35: $i] :
( ( ( ne @ SV35 )
= $false )
| ( ( mem @ ( c_2Ebinary__ieee_2Eulp @ SV12 @ SV35 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV12 @ SV35 ) ) @ ty_2Erealax_2Ereal ) )
= $true )
| ( ( ne @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV15: $i,SV36: $i] :
( ( ( ne @ SV36 )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( mem @ SY85 @ ( ty_2Ebinary__ieee_2Efloat @ SV15 @ SV36 ) )
| ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV15 @ SV36 ) @ SY85 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ SY85 ) ) ) ) )
= $true )
| ( ( ne @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(234,plain,
! [SV16: $i,SV37: $i] :
( ( ( ne @ SV37 )
= $false )
| ( ( ( ap @ ( c_2Ebinary__ieee_2Eulp @ SV16 @ SV37 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SV37 ) ) )
= ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV16 @ SV37 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV16 @ SV37 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV16 @ SV37 ) ) ) ) )
= $true )
| ( ( ne @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(235,plain,
! [SV17: $i,SV39: $i] :
( ( ( mem @ SV39 @ SV17 )
= $false )
| ( $true = $true )
| ( ( ne @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(236,plain,
! [SV28: $i,SV25: $i,SV18: $i,SV41: $i] :
( ( ( ~ ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SV28 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SV41 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) ) ) ) )
| ( SV28 = SV41 ) )
= $true )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(237,plain,
! [SV19: $i] :
( ( ( ! [SY70: $i] :
( ~ ( mem @ SY70 @ bool )
| ~ ( p @ SV19 )
| ~ ( p @ SY70 )
| ( SV19 = SY70 ) ) )
= $true )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(238,plain,
! [SV19: $i] :
( ( ( ! [SY71: $i] :
( ~ ( mem @ SY71 @ bool )
| ( p @ SV19 )
| ( p @ SY71 )
| ( SV19 = SY71 ) ) )
= $true )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(239,plain,
! [SV20: $i,SV38: $i] :
( ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ~ ( ~ ! [SY86: $i] :
( ~ ( mem @ SY86 @ SV20 )
| ( SV38 != SY86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY86 ) ) )
| ~ ! [SY87: $i] :
( ~ ( mem @ SY87 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY87 ) )
| ( SV38 = SY87 ) ) ) )
= $true )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(240,plain,
! [SV21: $i] :
( ( ( ! [SY75: $i] :
( ~ ( mem @ SY75 @ ( arr @ SV21 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY75 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SY75 @ ( sK3_X @ SY75 @ SV21 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY75 ) ) ) )
= $true )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(241,plain,
! [SV21: $i] :
( ( ( ! [SY76: $i] :
( ~ ( mem @ SY76 @ ( arr @ SV21 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SY76 ) )
| ! [SY77: $i] :
( ~ ( mem @ SY77 @ SV21 )
| ( p @ ( ap @ SY76 @ SY77 ) ) ) ) )
= $true )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(242,plain,
! [SV22: $i,SV26: $i,SV2: $i,SV40: $i] :
( ( ( ~ ( mem @ SV40 @ SV2 ) )
= $true )
| ( ( mem @ ( ap @ SV26 @ SV40 ) @ SV22 )
= $true )
| ( ( mem @ SV26 @ ( arr @ SV2 @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(243,plain,
! [SV36: $i,SV15: $i,SV42: $i] :
( ( ( ~ ( mem @ SV42 @ ( ty_2Ebinary__ieee_2Efloat @ SV15 @ SV36 ) )
| ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV15 @ SV36 ) @ SV42 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ SV42 ) ) ) )
= $true )
| ( ( ne @ SV36 )
= $false )
| ( ( ne @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV28: $i,SV25: $i,SV18: $i,SV41: $i] :
( ( ( ~ ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) ) )
= $true )
| ( ( ~ ( ~ ( mem @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SV28 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SV41 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) ) ) ) )
| ( SV28 = SV41 ) )
= $true )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(245,plain,
! [SV19: $i,SV43: $i] :
( ( ( ~ ( mem @ SV43 @ bool )
| ~ ( p @ SV19 )
| ~ ( p @ SV43 )
| ( SV19 = SV43 ) )
= $true )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(246,plain,
! [SV19: $i,SV44: $i] :
( ( ( ~ ( mem @ SV44 @ bool )
| ( p @ SV19 )
| ( p @ SV44 )
| ( SV19 = SV44 ) )
= $true )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(247,plain,
! [SV38: $i,SV20: $i] :
( ( ( ~ ! [SY86: $i] :
( ~ ( mem @ SY86 @ SV20 )
| ( SV38 != SY86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY86 ) ) )
| ~ ! [SY87: $i] :
( ~ ( mem @ SY87 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY87 ) )
| ( SV38 = SY87 ) ) )
= $false )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(248,plain,
! [SV21: $i,SV45: $i] :
( ( ( ~ ( mem @ SV45 @ ( arr @ SV21 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SV45 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SV45 @ ( sK3_X @ SV45 @ SV21 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) ) )
= $true )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(249,plain,
! [SV21: $i,SV46: $i] :
( ( ( ~ ( mem @ SV46 @ ( arr @ SV21 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV46 ) )
| ! [SY88: $i] :
( ~ ( mem @ SY88 @ SV21 )
| ( p @ ( ap @ SV46 @ SY88 ) ) ) )
= $true )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(250,plain,
! [SV22: $i,SV26: $i,SV2: $i,SV40: $i] :
( ( ( mem @ SV40 @ SV2 )
= $false )
| ( ( mem @ ( ap @ SV26 @ SV40 ) @ SV22 )
= $true )
| ( ( mem @ SV26 @ ( arr @ SV2 @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(251,plain,
! [SV36: $i,SV15: $i,SV42: $i] :
( ( ( ~ ( mem @ SV42 @ ( ty_2Ebinary__ieee_2Efloat @ SV15 @ SV36 ) ) )
= $true )
| ( ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV15 @ SV36 ) @ SV42 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ SV42 ) ) )
= $true )
| ( ( ne @ SV36 )
= $false )
| ( ( ne @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(252,plain,
! [SV28: $i,SV25: $i,SV18: $i,SV41: $i] :
( ( ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) )
= $false )
| ( ( ~ ( ~ ( mem @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SV28 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SV41 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) ) ) ) )
| ( SV28 = SV41 ) )
= $true )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(253,plain,
! [SV19: $i,SV43: $i] :
( ( ( ~ ( mem @ SV43 @ bool ) )
= $true )
| ( ( ~ ( p @ SV19 )
| ~ ( p @ SV43 )
| ( SV19 = SV43 ) )
= $true )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(254,plain,
! [SV19: $i,SV44: $i] :
( ( ( ~ ( mem @ SV44 @ bool ) )
= $true )
| ( ( ( p @ SV19 )
| ( p @ SV44 )
| ( SV19 = SV44 ) )
= $true )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(255,plain,
! [SV38: $i,SV20: $i] :
( ( ( ~ ! [SY86: $i] :
( ~ ( mem @ SY86 @ SV20 )
| ( SV38 != SY86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY86 ) ) ) )
= $false )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(256,plain,
! [SV38: $i,SV20: $i] :
( ( ( ~ ! [SY87: $i] :
( ~ ( mem @ SY87 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY87 ) )
| ( SV38 = SY87 ) ) )
= $false )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(257,plain,
! [SV21: $i,SV45: $i] :
( ( ( ~ ( mem @ SV45 @ ( arr @ SV21 @ bool ) ) )
= $true )
| ( ( ~ ( ~ ( mem @ ( sK3_X @ SV45 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SV45 @ ( sK3_X @ SV45 @ SV21 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) ) )
= $true )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(258,plain,
! [SV21: $i,SV46: $i] :
( ( ( ~ ( mem @ SV46 @ ( arr @ SV21 @ bool ) ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV46 ) )
| ! [SY88: $i] :
( ~ ( mem @ SY88 @ SV21 )
| ( p @ ( ap @ SV46 @ SY88 ) ) ) )
= $true )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(259,plain,
! [SV36: $i,SV15: $i,SV42: $i] :
( ( ( mem @ SV42 @ ( ty_2Ebinary__ieee_2Efloat @ SV15 @ SV36 ) )
= $false )
| ( ( ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV15 @ SV36 ) @ SV42 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV15 @ SV36 ) @ SV42 ) ) )
= $true )
| ( ( ne @ SV36 )
= $false )
| ( ( ne @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(260,plain,
! [SV18: $i,SV25: $i,SV28: $i,SV41: $i] :
( ( ( ~ ( ~ ( mem @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SV28 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SV41 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) ) ) ) ) )
= $true )
| ( ( SV28 = SV41 )
= $true )
| ( ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) )
= $false )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(261,plain,
! [SV19: $i,SV43: $i] :
( ( ( mem @ SV43 @ bool )
= $false )
| ( ( ~ ( p @ SV19 )
| ~ ( p @ SV43 )
| ( SV19 = SV43 ) )
= $true )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(262,plain,
! [SV19: $i,SV44: $i] :
( ( ( mem @ SV44 @ bool )
= $false )
| ( ( ( p @ SV19 )
| ( p @ SV44 )
| ( SV19 = SV44 ) )
= $true )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(263,plain,
! [SV38: $i,SV20: $i] :
( ( ( ! [SY86: $i] :
( ~ ( mem @ SY86 @ SV20 )
| ( SV38 != SY86 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY86 ) ) ) )
= $true )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(264,plain,
! [SV38: $i,SV20: $i] :
( ( ( ! [SY87: $i] :
( ~ ( mem @ SY87 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SY87 ) )
| ( SV38 = SY87 ) ) )
= $true )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(265,plain,
! [SV21: $i,SV45: $i] :
( ( ( mem @ SV45 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ~ ( ~ ( mem @ ( sK3_X @ SV45 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SV45 @ ( sK3_X @ SV45 @ SV21 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) ) )
= $true )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(266,plain,
! [SV21: $i,SV46: $i] :
( ( ( mem @ SV46 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV46 ) )
| ! [SY88: $i] :
( ~ ( mem @ SY88 @ SV21 )
| ( p @ ( ap @ SV46 @ SY88 ) ) ) )
= $true )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(267,plain,
! [SV18: $i,SV25: $i,SV28: $i,SV41: $i] :
( ( ( ~ ( mem @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) @ SV18 )
| ~ ( ( ( ap @ SV28 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SV41 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) ) ) ) )
= $false )
| ( ( SV28 = SV41 )
= $true )
| ( ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) )
= $false )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(268,plain,
! [SV43: $i,SV19: $i] :
( ( ( ~ ( p @ SV19 )
| ~ ( p @ SV43 ) )
= $true )
| ( ( SV19 = SV43 )
= $true )
| ( ( mem @ SV43 @ bool )
= $false )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(269,plain,
! [SV44: $i,SV19: $i] :
( ( ( ( p @ SV19 )
| ( p @ SV44 ) )
= $true )
| ( ( SV19 = SV44 )
= $true )
| ( ( mem @ SV44 @ bool )
= $false )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(270,plain,
! [SV38: $i,SV20: $i,SV47: $i] :
( ( ( ~ ( mem @ SV47 @ SV20 )
| ( SV38 != SV47 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV47 ) ) )
= $true )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(271,plain,
! [SV38: $i,SV20: $i,SV48: $i] :
( ( ( ~ ( mem @ SV48 @ SV20 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV48 ) )
| ( SV38 = SV48 ) )
= $true )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(272,plain,
! [SV21: $i,SV45: $i] :
( ( ( ~ ( ~ ( mem @ ( sK3_X @ SV45 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SV45 @ ( sK3_X @ SV45 @ SV21 ) ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(273,plain,
! [SV46: $i,SV21: $i] :
( ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV46 ) ) )
= $true )
| ( ( ! [SY88: $i] :
( ~ ( mem @ SY88 @ SV21 )
| ( p @ ( ap @ SV46 @ SY88 ) ) ) )
= $true )
| ( ( mem @ SV46 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(274,plain,
! [SV18: $i,SV25: $i,SV28: $i,SV41: $i] :
( ( ( ~ ( mem @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) @ SV18 ) )
= $false )
| ( ( SV28 = SV41 )
= $true )
| ( ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) )
= $false )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(275,plain,
! [SV18: $i,SV25: $i,SV41: $i,SV28: $i] :
( ( ( ~ ( ( ( ap @ SV28 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SV41 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) ) ) ) )
= $false )
| ( ( SV28 = SV41 )
= $true )
| ( ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) )
= $false )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(276,plain,
! [SV43: $i,SV19: $i] :
( ( ( ~ ( p @ SV19 ) )
= $true )
| ( ( ~ ( p @ SV43 ) )
= $true )
| ( ( SV19 = SV43 )
= $true )
| ( ( mem @ SV43 @ bool )
= $false )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(277,plain,
! [SV44: $i,SV19: $i] :
( ( ( p @ SV19 )
= $true )
| ( ( p @ SV44 )
= $true )
| ( ( SV19 = SV44 )
= $true )
| ( ( mem @ SV44 @ bool )
= $false )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(278,plain,
! [SV38: $i,SV20: $i,SV47: $i] :
( ( ( ~ ( mem @ SV47 @ SV20 ) )
= $true )
| ( ( ( SV38 != SV47 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV47 ) ) )
= $true )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(279,plain,
! [SV38: $i,SV20: $i,SV48: $i] :
( ( ( ~ ( mem @ SV48 @ SV20 ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV48 ) )
| ( SV38 = SV48 ) )
= $true )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(280,plain,
! [SV21: $i,SV45: $i] :
( ( ( ~ ( mem @ ( sK3_X @ SV45 @ SV21 ) @ SV21 )
| ~ ~ ( p @ ( ap @ SV45 @ ( sK3_X @ SV45 @ SV21 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(281,plain,
! [SV46: $i,SV21: $i] :
( ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV46 ) )
= $false )
| ( ( ! [SY88: $i] :
( ~ ( mem @ SY88 @ SV21 )
| ( p @ ( ap @ SV46 @ SY88 ) ) ) )
= $true )
| ( ( mem @ SV46 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(282,plain,
! [SV18: $i,SV25: $i,SV28: $i,SV41: $i] :
( ( ( mem @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) @ SV18 )
= $true )
| ( ( SV28 = SV41 )
= $true )
| ( ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) )
= $false )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(283,plain,
! [SV18: $i,SV25: $i,SV41: $i,SV28: $i] :
( ( ( ( ( ap @ SV28 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) )
!= ( ap @ SV41 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) ) ) )
= $true )
| ( ( SV28 = SV41 )
= $true )
| ( ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) )
= $false )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(284,plain,
! [SV43: $i,SV19: $i] :
( ( ( p @ SV19 )
= $false )
| ( ( ~ ( p @ SV43 ) )
= $true )
| ( ( SV19 = SV43 )
= $true )
| ( ( mem @ SV43 @ bool )
= $false )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(285,plain,
! [SV38: $i,SV20: $i,SV47: $i] :
( ( ( mem @ SV47 @ SV20 )
= $false )
| ( ( ( SV38 != SV47 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV47 ) ) )
= $true )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(286,plain,
! [SV38: $i,SV20: $i,SV48: $i] :
( ( ( mem @ SV48 @ SV20 )
= $false )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV48 ) )
| ( SV38 = SV48 ) )
= $true )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(287,plain,
! [SV21: $i,SV45: $i] :
( ( ( ~ ( mem @ ( sK3_X @ SV45 @ SV21 ) @ SV21 ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(288,plain,
! [SV21: $i,SV45: $i] :
( ( ( ~ ~ ( p @ ( ap @ SV45 @ ( sK3_X @ SV45 @ SV21 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(289,plain,
! [SV46: $i,SV21: $i,SV49: $i] :
( ( ( ~ ( mem @ SV49 @ SV21 )
| ( p @ ( ap @ SV46 @ SV49 ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV46 ) )
= $false )
| ( ( mem @ SV46 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(290,plain,
! [SV18: $i,SV25: $i,SV41: $i,SV28: $i] :
( ( ( ( ap @ SV28 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) )
= ( ap @ SV41 @ ( sK4_X @ SV41 @ SV28 @ SV25 @ SV18 ) ) )
= $false )
| ( ( SV28 = SV41 )
= $true )
| ( ( mem @ SV41 @ ( arr @ SV18 @ SV25 ) )
= $false )
| ( ( mem @ SV28 @ ( arr @ SV18 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(291,plain,
! [SV19: $i,SV43: $i] :
( ( ( p @ SV43 )
= $false )
| ( ( p @ SV19 )
= $false )
| ( ( SV19 = SV43 )
= $true )
| ( ( mem @ SV43 @ bool )
= $false )
| ( ( mem @ SV19 @ bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(292,plain,
! [SV20: $i,SV47: $i,SV38: $i] :
( ( ( ( SV38 != SV47 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV47 ) )
= $true )
| ( ( mem @ SV47 @ SV20 )
= $false )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(293,plain,
! [SV48: $i,SV38: $i,SV20: $i] :
( ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV48 ) ) )
= $true )
| ( ( SV38 = SV48 )
= $true )
| ( ( mem @ SV48 @ SV20 )
= $false )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(294,plain,
! [SV21: $i,SV45: $i] :
( ( ( mem @ ( sK3_X @ SV45 @ SV21 ) @ SV21 )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(295,plain,
! [SV21: $i,SV45: $i] :
( ( ( ~ ( p @ ( ap @ SV45 @ ( sK3_X @ SV45 @ SV21 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(296,plain,
! [SV46: $i,SV21: $i,SV49: $i] :
( ( ( ~ ( mem @ SV49 @ SV21 ) )
= $true )
| ( ( p @ ( ap @ SV46 @ SV49 ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV46 ) )
= $false )
| ( ( mem @ SV46 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(297,plain,
! [SV20: $i,SV47: $i,SV38: $i] :
( ( ( SV38 = SV47 )
= $false )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV47 ) )
= $true )
| ( ( mem @ SV47 @ SV20 )
= $false )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(298,plain,
! [SV48: $i,SV38: $i,SV20: $i] :
( ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV20 ) @ SV38 ) @ SV48 ) )
= $false )
| ( ( SV38 = SV48 )
= $true )
| ( ( mem @ SV48 @ SV20 )
= $false )
| ( ( mem @ SV38 @ SV20 )
= $false )
| ( ( ne @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(299,plain,
! [SV21: $i,SV45: $i] :
( ( ( p @ ( ap @ SV45 @ ( sK3_X @ SV45 @ SV21 ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV45 ) )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(300,plain,
! [SV46: $i,SV21: $i,SV49: $i] :
( ( ( mem @ SV49 @ SV21 )
= $false )
| ( ( p @ ( ap @ SV46 @ SV49 ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV21 ) @ SV46 ) )
= $false )
| ( ( mem @ SV46 @ ( arr @ SV21 @ bool ) )
= $false )
| ( ( ne @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(301,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[86,300,299,298,297,294,291,290,282,277,259,250,235,234,232,231,230,229,228,227,225,209,202,192,183,179,178,176,173,114,112,105,104,95,94,87]) ).
thf(302,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP018+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 2 13:00:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 28
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 .
% 0.13/0.37 (rf:0,axioms:28,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:0,foatp_calls:0,translation:fof_full)...................
% 0.39/0.62
% 0.39/0.62 ********************************
% 0.39/0.62 * All subproblems solved! *
% 0.39/0.62 ********************************
% 0.39/0.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:29,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:301,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.47/0.66
% 0.47/0.66 %**** Beginning of derivation protocol ****
% 0.47/0.66 % SZS output start CNFRefutation
% See solution above
% 0.47/0.66
% 0.47/0.66 %**** End of derivation protocol ****
% 0.47/0.66 %**** no. of clauses in derivation: 302 ****
% 0.47/0.66 %**** clause counter: 301 ****
% 0.47/0.66
% 0.47/0.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:29,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:301,loop_count:0,foatp_calls:1,translation:fof_full)
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