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 : n025.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 0.65s 0.83s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 59
% Syntax : Number of formulae : 303 ( 151 unt; 31 typ; 0 def)
% Number of atoms : 1552 ( 532 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 3506 ( 384 ~; 388 |; 10 &;2684 @)
% ( 6 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 9 con; 0-4 aty)
% Number of variables : 531 ( 0 ^ 531 !; 0 ?; 531 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_del,type,
del: $tType ).
thf(tp_tp__ty_2Erealax_2Ereal,type,
tp__ty_2Erealax_2Ereal: $tType ).
thf(tp_ap,type,
ap: $i > $i > $i ).
thf(tp_arr,type,
arr: del > del > del ).
thf(tp_bool,type,
bool: del ).
thf(tp_c_2Ebinary__ieee_2Efloat__negate,type,
c_2Ebinary__ieee_2Efloat__negate: del > del > $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__min,type,
c_2Ebinary__ieee_2Efloat__plus__min: del > del > $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__to__real,type,
c_2Ebinary__ieee_2Efloat__to__real: del > del > $i ).
thf(tp_c_2Ebinary__ieee_2Eulp,type,
c_2Ebinary__ieee_2Eulp: del > del > $i ).
thf(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
thf(tp_c_2Ebool_2E_21,type,
c_2Ebool_2E_21: del > $i ).
thf(tp_c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value: del > $i ).
thf(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
thf(tp_c_2Erealax_2Ereal__neg,type,
c_2Erealax_2Ereal__neg: $i ).
thf(tp_fo__c_2Erealax_2Ereal__neg,type,
fo__c_2Erealax_2Ereal__neg: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
thf(tp_ind,type,
ind: del ).
thf(tp_inj__o,type,
inj__o: $o > $i ).
thf(tp_inj__ty_2Erealax_2Ereal,type,
inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
thf(tp_lam,type,
lam: del > ( $i > $i ) > $i ).
thf(tp_mem,type,
mem: $i > del > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_sK1_A_27t,type,
sK1_A_27t: del ).
thf(tp_sK2_SY49,type,
sK2_SY49: del ).
thf(tp_sK3_X,type,
sK3_X: $i > del > $i ).
thf(tp_sK4_X,type,
sK4_X: $i > $i > del > del > $i ).
thf(tp_sK5_X,type,
sK5_X: ( $i > $i ) > del > del > $i ).
thf(tp_surj__ty_2Erealax_2Ereal,type,
surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).
thf(tp_ty_2Ebinary__ieee_2Efloat,type,
ty_2Ebinary__ieee_2Efloat: del > del > del ).
thf(tp_ty_2Ebool_2Eitself,type,
ty_2Ebool_2Eitself: del > del ).
thf(tp_ty_2Epair_2Eprod,type,
ty_2Epair_2Eprod: del > del > del ).
thf(tp_ty_2Erealax_2Ereal,type,
ty_2Erealax_2Ereal: del ).
thf(1,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( V0x = V0x )
<=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EREFL__CLAUSE) ).
thf(2,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(3,axiom,
! [A_27t: del,A_27w: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eulp) ).
thf(4,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) )
=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b ) @ V0x ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ V0x ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(5,axiom,
! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
<=> ! [X: $i] :
( ( mem @ X @ A )
=> ( p @ ( ap @ Q @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p) ).
thf(6,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(7,axiom,
! [A: del,X: $i] :
( ( mem @ X @ A )
=> ! [Y: $i] :
( ( mem @ Y @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
<=> ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).
thf(8,axiom,
! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(9,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
thf(10,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(11,axiom,
! [A_27t: del,A_27w: del] : ( 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/sandbox/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Eulp) ).
thf(12,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2Ethe__value) ).
thf(13,axiom,
! [A_27t: del,A_27w: del] : ( 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/sandbox/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__to__real) ).
thf(14,axiom,
! [A_27t: del,A_27w: del] : ( 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/sandbox/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__plus__min) ).
thf(15,axiom,
! [A_27t: del,A_27w: del] : ( 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/sandbox/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__negate) ).
thf(16,axiom,
! [X0: tp__ty_2Erealax_2Ereal] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Ereal__neg @ X0 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Erealax_2Ereal__neg) ).
thf(17,axiom,
mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Erealax_2Ereal__neg) ).
thf(18,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Erealax_2Ereal )
=> ( X
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Erealax_2Ereal) ).
thf(19,axiom,
! [X: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ X ) @ ty_2Erealax_2Ereal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Erealax_2Ereal) ).
thf(20,axiom,
! [X: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Erealax_2Ereal) ).
thf(21,axiom,
! [A: del,F: $i > $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta) ).
thf(22,axiom,
! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [G: $i] :
( ( mem @ G @ ( arr @ A @ B ) )
=> ( ! [X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ F @ X )
= ( ap @ G @ X ) ) )
=> ( F = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(23,axiom,
! [A: del,B: del,F: $i > $i] :
( ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( F @ X ) @ B ) )
=> ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam_tp) ).
thf(24,axiom,
! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
thf(25,axiom,
! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(26,axiom,
! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(27,axiom,
! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(28,conjecture,
! [A_27t: del,A_27w: del] :
( ( surj__ty_2Erealax_2Ereal @ ( 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 ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eneg__ulp) ).
thf(29,negated_conjecture,
( ( ! [A_27t: del,A_27w: del] :
( ( surj__ty_2Erealax_2Ereal @ ( 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 ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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)],[28]) ).
thf(30,plain,
( ( ! [A_27t: del,A_27w: del] :
( ( surj__ty_2Erealax_2Ereal @ ( 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 ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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)],[29]) ).
thf(31,plain,
( ( ! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( V0x = V0x )
<=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(32,plain,
$true = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(33,plain,
( ( ! [A_27t: del,A_27w: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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(34,plain,
( ( ! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) )
=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b ) @ V0x ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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(35,plain,
( ( ! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
<=> ! [X: $i] :
( ( mem @ X @ A )
=> ( p @ ( ap @ Q @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(36,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(37,plain,
( ( ! [A: del,X: $i] :
( ( mem @ X @ A )
=> ! [Y: $i] :
( ( mem @ Y @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
<=> ( X = Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(38,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(39,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(40,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(41,plain,
( ( ! [A_27t: del,A_27w: del] : ( 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(42,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(43,plain,
( ( ! [A_27t: del,A_27w: del] : ( 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(44,plain,
( ( ! [A_27t: del,A_27w: del] : ( 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(45,plain,
( ( ! [A_27t: del,A_27w: del] : ( 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)],[15]) ).
thf(46,plain,
( ( ! [X0: tp__ty_2Erealax_2Ereal] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Ereal__neg @ X0 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(47,plain,
( ( mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(48,plain,
( ( ! [X: $i] :
( ( mem @ X @ ty_2Erealax_2Ereal )
=> ( X
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(49,plain,
( ( ! [X: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ X ) @ ty_2Erealax_2Ereal ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(50,plain,
( ( ! [X: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(51,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(52,plain,
( ( ! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [G: $i] :
( ( mem @ G @ ( arr @ A @ B ) )
=> ( ! [X: $i] :
( ( mem @ X @ A )
=> ( ( ap @ F @ X )
= ( ap @ G @ X ) ) )
=> ( F = G ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(53,plain,
( ( ! [A: del,B: del,F: $i > $i] :
( ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( F @ X ) @ B ) )
=> ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(54,plain,
( ( ! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(55,plain,
( ( ! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(56,plain,
( ( ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(57,plain,
( ( ! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(58,plain,
( ( ! [SY49: del] :
( ( surj__ty_2Erealax_2Ereal @ ( 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 ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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)],[30]) ).
thf(59,plain,
( ( ( surj__ty_2Erealax_2Ereal @ ( 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 ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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_forall_neg,[status(esa)],[58]) ).
thf(60,plain,
( ( ( ( surj__ty_2Erealax_2Ereal @ ( 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 ) ) ) ) )
!= ( surj__ty_2Erealax_2Ereal @ ( 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(polarity_switch,[status(thm)],[59]) ).
thf(61,plain,
( ( ! [A_27a: del,V0x: $i] :
~ ( mem @ V0x @ A_27a )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(62,plain,
( ( ! [A_27a: del,A_27b: del,V0x: $i] :
( ~ ( mem @ V0x @ ( ty_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) )
| ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b ) @ V0x ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ V0x ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(63,plain,
( ( ! [A: del,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 ) ) )
& ! [A: del,Q: $i] :
( ~ ( mem @ Q @ ( arr @ A @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( p @ ( ap @ Q @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(64,plain,
( ( ! [A: del,X: $i] :
( ~ ( mem @ X @ A )
| ( ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ( X != Y )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) ) )
& ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
| ( X = Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(65,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ ty_2Erealax_2Ereal )
| ( X
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(66,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(67,plain,
( ( ! [A: del,B: del,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)],[52]) ).
thf(68,plain,
( ( ! [A: del,B: del,F: $i > $i] :
( ( ( mem @ ( sK5_X @ F @ B @ A ) @ A )
& ~ ( mem @ ( F @ ( sK5_X @ F @ B @ A ) ) @ B ) )
| ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(69,plain,
( ( ! [A: del,B: del,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(70,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ bool )
| ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(71,plain,
( ( ! [X: $o] :
( ( p @ ( inj__o @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(72,plain,
( ( ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(73,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ bool )
| ( X
= ( inj__o @ ( p @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(74,plain,
( ( ! [A: del,B: del,F: $i] :
( ~ ( mem @ F @ ( arr @ A @ B ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( mem @ ( ap @ F @ X ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(75,plain,
( ( ! [A: del,B: del,F: $i > $i] :
( ( ( mem @ ( sK5_X @ F @ B @ A ) @ A )
& ~ ( mem @ ( F @ ( sK5_X @ F @ B @ A ) ) @ B ) )
| ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(76,plain,
( ( ! [A: del,B: del,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)],[67]) ).
thf(77,plain,
( ( ! [A: del,F: $i > $i,X: $i] :
( ~ ( mem @ X @ A )
| ( ( ap @ ( lam @ A @ F ) @ X )
= ( F @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(78,plain,
( ( ! [X: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(79,plain,
( ( ! [X: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ X ) @ ty_2Erealax_2Ereal ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(80,plain,
( ( ! [X: $i] :
( ~ ( mem @ X @ ty_2Erealax_2Ereal )
| ( X
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(81,plain,
( ( mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(82,plain,
( ( ! [X0: tp__ty_2Erealax_2Ereal] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Ereal__neg @ X0 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(83,plain,
( ( ! [A_27t: del,A_27w: del] : ( 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)],[45]) ).
thf(84,plain,
( ( ! [A_27t: del,A_27w: del] : ( 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)],[44]) ).
thf(85,plain,
( ( ! [A_27t: del,A_27w: del] : ( 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)],[43]) ).
thf(86,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(87,plain,
( ( ! [A_27t: del,A_27w: del] : ( 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)],[41]) ).
thf(88,plain,
( ( mem @ c_2Ebool_2ET @ bool )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(89,plain,
( ( p @ c_2Ebool_2ET )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(90,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(91,plain,
( ( ! [A: del,X: $i] :
( ~ ( mem @ X @ A )
| ( ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ( X != Y )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) ) )
& ! [Y: $i] :
( ~ ( mem @ Y @ A )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
| ( X = Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(92,plain,
( ( ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(93,plain,
( ( ! [A: del,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 ) ) )
& ! [A: del,Q: $i] :
( ~ ( mem @ Q @ ( arr @ A @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
| ! [X: $i] :
( ~ ( mem @ X @ A )
| ( p @ ( ap @ Q @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(94,plain,
( ( ! [A_27a: del,A_27b: del,V0x: $i] :
( ~ ( mem @ V0x @ ( ty_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) )
| ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A_27a @ A_27b ) @ V0x ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A_27a @ A_27b ) @ V0x ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(95,plain,
( ( ! [A_27t: del,A_27w: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A_27t @ A_27w ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A_27t @ A_27w ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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)],[33]) ).
thf(96,plain,
$true = $true,
inference(copy,[status(thm)],[32]) ).
thf(97,plain,
( ( ! [A_27a: del,V0x: $i] :
~ ( mem @ V0x @ A_27a )
| $true )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(98,plain,
( ( ( ( surj__ty_2Erealax_2Ereal @ ( 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 ) ) ) ) )
!= ( surj__ty_2Erealax_2Ereal @ ( 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)],[60]) ).
thf(99,plain,
( ( ~ ( ~ ! [SX0: del,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 ) ) )
| ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(100,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( SX1 != SX2 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SX0 ) @ SX1 ) @ SX2 ) )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(101,plain,
( ( ! [SX0: del,SX1: del,SX2: $i > $i] :
( ~ ( ~ ( mem @ ( sK5_X @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( mem @ ( SX2 @ ( sK5_X @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( mem @ ( lam @ SX0 @ SX2 ) @ ( arr @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(102,plain,
( ( ! [SX0: del,SX1: del,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)],[76]) ).
thf(103,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[71]) ).
thf(104,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[71]) ).
thf(105,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[71]) ).
thf(106,plain,
! [SV2: $o] :
( ( mem @ ( inj__o @ SV2 ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[72]) ).
thf(107,plain,
( ( mem @ ( inj__o @ $true ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[72]) ).
thf(108,plain,
( ( mem @ ( inj__o @ $false ) @ bool )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[72]) ).
thf(109,plain,
! [SV3: $i] :
( ( ~ ( mem @ SV3 @ bool )
| ( SV3
= ( inj__o @ ( p @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(110,plain,
! [SV4: del] :
( ( ! [SY50: del,SY51: $i] :
( ~ ( mem @ SY51 @ ( arr @ SV4 @ SY50 ) )
| ! [SY52: $i] :
( ~ ( mem @ SY52 @ SV4 )
| ( mem @ ( ap @ SY51 @ SY52 ) @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(111,plain,
! [SV5: del] :
( ( ! [SY53: $i > $i,SY54: $i] :
( ~ ( mem @ SY54 @ SV5 )
| ( ( ap @ ( lam @ SV5 @ SY53 ) @ SY54 )
= ( SY53 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(112,plain,
! [SV6: tp__ty_2Erealax_2Ereal] :
( ( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ SV6 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(113,plain,
! [SV7: tp__ty_2Erealax_2Ereal] :
( ( mem @ ( inj__ty_2Erealax_2Ereal @ SV7 ) @ ty_2Erealax_2Ereal )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(114,plain,
! [SV8: $i] :
( ( ~ ( mem @ SV8 @ ty_2Erealax_2Ereal )
| ( SV8
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(115,plain,
! [SV9: tp__ty_2Erealax_2Ereal] :
( ( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Ereal__neg @ SV9 ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(116,plain,
! [SV10: del] :
( ( ! [SY55: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ SV10 @ SY55 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SY55 ) @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(117,plain,
! [SV11: del] :
( ( ! [SY56: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV11 @ SY56 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV11 @ SY56 ) ) @ ( ty_2Ebinary__ieee_2Efloat @ SV11 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(118,plain,
! [SV12: del] :
( ( ! [SY57: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV12 @ SY57 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV12 @ SY57 ) @ ty_2Erealax_2Ereal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(119,plain,
! [SV13: del] :
( ( mem @ ( c_2Ebool_2Ethe__value @ SV13 ) @ ( ty_2Ebool_2Eitself @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(120,plain,
! [SV14: del] :
( ( ! [SY58: del] : ( mem @ ( c_2Ebinary__ieee_2Eulp @ SV14 @ SY58 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV14 @ SY58 ) ) @ ty_2Erealax_2Ereal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(121,plain,
! [SV15: del] :
( ( mem @ ( c_2Emin_2E_3D @ SV15 ) @ ( arr @ SV15 @ ( arr @ SV15 @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(122,plain,
! [SV16: del] :
( ( mem @ ( c_2Ebool_2E_21 @ SV16 ) @ ( arr @ ( arr @ SV16 @ bool ) @ bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(123,plain,
! [SV17: del] :
( ( ! [SY59: del,SY60: $i] :
( ~ ( mem @ SY60 @ ( ty_2Ebinary__ieee_2Efloat @ SV17 @ SY59 ) )
| ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SY59 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV17 @ SY59 ) @ SY60 ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SY59 ) @ SY60 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(124,plain,
! [SV18: del] :
( ( ! [SY61: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ SV18 @ SY61 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV18 @ SY61 ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV18 @ SY61 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV18 @ SY61 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV18 @ SY61 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(125,plain,
( ( ( ! [A_27a: del,V0x: $i] :
~ ( mem @ V0x @ A_27a ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(126,plain,
( ( ( surj__ty_2Erealax_2Ereal @ ( 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 ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( 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)],[98]) ).
thf(127,plain,
( ( ~ ! [SX0: del,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 ) ) )
| ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(128,plain,
! [SV19: del] :
( ( ! [SY62: $i] :
( ~ ( mem @ SY62 @ SV19 )
| ~ ( ~ ! [SY63: $i] :
( ~ ( mem @ SY63 @ SV19 )
| ( SY62 != SY63 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SY62 ) @ SY63 ) ) )
| ~ ! [SY64: $i] :
( ~ ( mem @ SY64 @ SV19 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SY62 ) @ SY64 ) )
| ( SY62 = SY64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(129,plain,
! [SV20: del] :
( ( ! [SY65: del,SY66: $i > $i] :
( ~ ( ~ ( mem @ ( sK5_X @ SY66 @ SY65 @ SV20 ) @ SV20 )
| ~ ~ ( mem @ ( SY66 @ ( sK5_X @ SY66 @ SY65 @ SV20 ) ) @ SY65 ) )
| ( mem @ ( lam @ SV20 @ SY66 ) @ ( arr @ SV20 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(130,plain,
! [SV21: del] :
( ( ! [SY67: del,SY68: $i] :
( ~ ( mem @ SY68 @ ( arr @ SV21 @ SY67 ) )
| ! [SY69: $i] :
( ~ ( mem @ SY69 @ ( arr @ SV21 @ SY67 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY69 @ SY68 @ SY67 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SY68 @ ( sK4_X @ SY69 @ SY68 @ SY67 @ SV21 ) )
!= ( ap @ SY69 @ ( sK4_X @ SY69 @ SY68 @ SY67 @ SV21 ) ) ) ) )
| ( SY68 = SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(131,plain,
! [SV1: $o] :
( ( ~ ( ( p @ ( inj__o @ SV1 ) )
| SV1 )
| ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[103]) ).
thf(132,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[103]) ).
thf(133,plain,
( ( ~ ( ( p @ ( inj__o @ $true ) )
| $true )
| ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[104]) ).
thf(134,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[104]) ).
thf(135,plain,
( ( ~ ( ( p @ ( inj__o @ $false ) )
| $false )
| ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[105]) ).
thf(136,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[105]) ).
thf(137,plain,
! [SV3: $i] :
( ( ( ~ ( mem @ SV3 @ bool ) )
= $true )
| ( ( SV3
= ( inj__o @ ( p @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(138,plain,
! [SV22: del,SV4: del] :
( ( ! [SY70: $i] :
( ~ ( mem @ SY70 @ ( arr @ SV4 @ SV22 ) )
| ! [SY71: $i] :
( ~ ( mem @ SY71 @ SV4 )
| ( mem @ ( ap @ SY70 @ SY71 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(139,plain,
! [SV23: $i > $i,SV5: del] :
( ( ! [SY72: $i] :
( ~ ( mem @ SY72 @ SV5 )
| ( ( ap @ ( lam @ SV5 @ SV23 ) @ SY72 )
= ( SV23 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(140,plain,
! [SV8: $i] :
( ( ( ~ ( mem @ SV8 @ ty_2Erealax_2Ereal ) )
= $true )
| ( ( SV8
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(141,plain,
! [SV24: del,SV10: del] :
( ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ SV10 @ SV24 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SV24 ) @ ( ty_2Ebinary__ieee_2Efloat @ SV10 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(142,plain,
! [SV25: del,SV11: del] :
( ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV11 @ SV25 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV11 @ SV25 ) ) @ ( ty_2Ebinary__ieee_2Efloat @ SV11 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(143,plain,
! [SV26: del,SV12: del] :
( ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV12 @ SV26 ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ SV12 @ SV26 ) @ ty_2Erealax_2Ereal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(144,plain,
! [SV27: del,SV14: del] :
( ( mem @ ( c_2Ebinary__ieee_2Eulp @ SV14 @ SV27 ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ SV14 @ SV27 ) ) @ ty_2Erealax_2Ereal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(145,plain,
! [SV28: del,SV17: del] :
( ( ! [SY73: $i] :
( ~ ( mem @ SY73 @ ( ty_2Ebinary__ieee_2Efloat @ SV17 @ SV28 ) )
| ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SV28 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV17 @ SV28 ) @ SY73 ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SV28 ) @ SY73 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(146,plain,
! [SV29: del,SV18: del] :
( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ SV18 @ SV29 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV18 @ SV29 ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV18 @ SV29 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ SV18 @ SV29 ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ SV18 @ SV29 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(147,plain,
! [SV30: del] :
( ( ( ! [SY74: $i] :
~ ( mem @ SY74 @ SV30 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(148,plain,
( ( ~ ! [SX0: del,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 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(149,plain,
( ( ~ ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(150,plain,
! [SV19: del,SV31: $i] :
( ( ~ ( mem @ SV31 @ SV19 )
| ~ ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ SV19 )
| ( SV31 != SY75 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY75 ) ) )
| ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ SV19 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY76 ) )
| ( SV31 = SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(151,plain,
! [SV20: del,SV32: del] :
( ( ! [SY77: $i > $i] :
( ~ ( ~ ( mem @ ( sK5_X @ SY77 @ SV32 @ SV20 ) @ SV20 )
| ~ ~ ( mem @ ( SY77 @ ( sK5_X @ SY77 @ SV32 @ SV20 ) ) @ SV32 ) )
| ( mem @ ( lam @ SV20 @ SY77 ) @ ( arr @ SV20 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(152,plain,
! [SV33: del,SV21: del] :
( ( ! [SY78: $i] :
( ~ ( mem @ SY78 @ ( arr @ SV21 @ SV33 ) )
| ! [SY79: $i] :
( ~ ( mem @ SY79 @ ( arr @ SV21 @ SV33 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY79 @ SY78 @ SV33 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SY78 @ ( sK4_X @ SY79 @ SY78 @ SV33 @ SV21 ) )
!= ( ap @ SY79 @ ( sK4_X @ SY79 @ SY78 @ SV33 @ SV21 ) ) ) ) )
| ( SY78 = SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(153,plain,
! [SV1: $o] :
( ( ( ~ ( ( p @ ( inj__o @ SV1 ) )
| SV1 ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(154,plain,
( ( ( ~ ( ( p @ ( inj__o @ $true ) )
| $true ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(155,plain,
( ( ( ~ ( ( p @ ( inj__o @ $false ) )
| $false ) )
= $true )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(156,plain,
! [SV3: $i] :
( ( ( mem @ SV3 @ bool )
= $false )
| ( ( SV3
= ( inj__o @ ( p @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV22: del,SV4: del,SV34: $i] :
( ( ~ ( mem @ SV34 @ ( arr @ SV4 @ SV22 ) )
| ! [SY80: $i] :
( ~ ( mem @ SY80 @ SV4 )
| ( mem @ ( ap @ SV34 @ SY80 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV23: $i > $i,SV5: del,SV35: $i] :
( ( ~ ( mem @ SV35 @ SV5 )
| ( ( ap @ ( lam @ SV5 @ SV23 ) @ SV35 )
= ( SV23 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(159,plain,
! [SV8: $i] :
( ( ( mem @ SV8 @ ty_2Erealax_2Ereal )
= $false )
| ( ( SV8
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(160,plain,
! [SV28: del,SV17: del,SV36: $i] :
( ( ~ ( mem @ SV36 @ ( ty_2Ebinary__ieee_2Efloat @ SV17 @ SV28 ) )
| ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SV28 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV17 @ SV28 ) @ SV36 ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SV28 ) @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV30: del,SV37: $i] :
( ( ( ~ ( mem @ SV37 @ SV30 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(162,plain,
( ( ! [SX0: del,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 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(163,plain,
( ( ! [SX0: del,SX1: $i] :
( ~ ( mem @ SX1 @ ( arr @ SX0 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( mem @ SX2 @ SX0 )
| ( p @ ( ap @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(164,plain,
! [SV19: del,SV31: $i] :
( ( ( ~ ( mem @ SV31 @ SV19 ) )
= $true )
| ( ( ~ ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ SV19 )
| ( SV31 != SY75 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY75 ) ) )
| ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ SV19 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY76 ) )
| ( SV31 = SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(165,plain,
! [SV20: del,SV32: del,SV38: $i > $i] :
( ( ~ ( ~ ( mem @ ( sK5_X @ SV38 @ SV32 @ SV20 ) @ SV20 )
| ~ ~ ( mem @ ( SV38 @ ( sK5_X @ SV38 @ SV32 @ SV20 ) ) @ SV32 ) )
| ( mem @ ( lam @ SV20 @ SV38 ) @ ( arr @ SV20 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(166,plain,
! [SV33: del,SV21: del,SV39: $i] :
( ( ~ ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
| ! [SY81: $i] :
( ~ ( mem @ SY81 @ ( arr @ SV21 @ SV33 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY81 @ SV39 @ SV33 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SV39 @ ( sK4_X @ SY81 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SY81 @ ( sK4_X @ SY81 @ SV39 @ SV33 @ SV21 ) ) ) ) )
| ( SV39 = SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(167,plain,
! [SV1: $o] :
( ( ( ( p @ ( inj__o @ SV1 ) )
| SV1 )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(168,plain,
( ( ( ( p @ ( inj__o @ $true ) )
| $true )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(169,plain,
( ( ( ( p @ ( inj__o @ $false ) )
| $false )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(170,plain,
! [SV22: del,SV4: del,SV34: $i] :
( ( ( ~ ( mem @ SV34 @ ( arr @ SV4 @ SV22 ) ) )
= $true )
| ( ( ! [SY80: $i] :
( ~ ( mem @ SY80 @ SV4 )
| ( mem @ ( ap @ SV34 @ SY80 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV23: $i > $i,SV5: del,SV35: $i] :
( ( ( ~ ( mem @ SV35 @ SV5 ) )
= $true )
| ( ( ( ap @ ( lam @ SV5 @ SV23 ) @ SV35 )
= ( SV23 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV28: del,SV17: del,SV36: $i] :
( ( ( ~ ( mem @ SV36 @ ( ty_2Ebinary__ieee_2Efloat @ SV17 @ SV28 ) ) )
= $true )
| ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SV28 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV17 @ SV28 ) @ SV36 ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SV28 ) @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(173,plain,
! [SV30: del,SV37: $i] :
( ( ( mem @ SV37 @ SV30 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV40: del] :
( ( ! [SY82: $i] :
( ~ ( mem @ SY82 @ ( arr @ SV40 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SY82 @ SV40 ) @ SV40 )
| ~ ~ ( p @ ( ap @ SY82 @ ( sK3_X @ SY82 @ SV40 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV41: del] :
( ( ! [SY83: $i] :
( ~ ( mem @ SY83 @ ( arr @ SV41 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV41 ) @ SY83 ) )
| ! [SY84: $i] :
( ~ ( mem @ SY84 @ SV41 )
| ( p @ ( ap @ SY83 @ SY84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV19: del,SV31: $i] :
( ( ( mem @ SV31 @ SV19 )
= $false )
| ( ( ~ ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ SV19 )
| ( SV31 != SY75 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY75 ) ) )
| ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ SV19 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY76 ) )
| ( SV31 = SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV20: del,SV32: del,SV38: $i > $i] :
( ( ( ~ ( ~ ( mem @ ( sK5_X @ SV38 @ SV32 @ SV20 ) @ SV20 )
| ~ ~ ( mem @ ( SV38 @ ( sK5_X @ SV38 @ SV32 @ SV20 ) ) @ SV32 ) ) )
= $true )
| ( ( mem @ ( lam @ SV20 @ SV38 ) @ ( arr @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV33: del,SV21: del,SV39: $i] :
( ( ( ~ ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) ) )
= $true )
| ( ( ! [SY81: $i] :
( ~ ( mem @ SY81 @ ( arr @ SV21 @ SV33 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY81 @ SV39 @ SV33 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SV39 @ ( sK4_X @ SY81 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SY81 @ ( sK4_X @ SY81 @ SV39 @ SV33 @ SV21 ) ) ) ) )
| ( SV39 = SY81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(180,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(181,plain,
( ( ( p @ ( inj__o @ $true ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(182,plain,
( ( $true = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(183,plain,
( ( ( p @ ( inj__o @ $false ) )
= $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(184,plain,
( ( $false = $false )
| ( ( ~ ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(185,plain,
! [SV22: del,SV4: del,SV34: $i] :
( ( ( mem @ SV34 @ ( arr @ SV4 @ SV22 ) )
= $false )
| ( ( ! [SY80: $i] :
( ~ ( mem @ SY80 @ SV4 )
| ( mem @ ( ap @ SV34 @ SY80 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(186,plain,
! [SV23: $i > $i,SV5: del,SV35: $i] :
( ( ( mem @ SV35 @ SV5 )
= $false )
| ( ( ( ap @ ( lam @ SV5 @ SV23 ) @ SV35 )
= ( SV23 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(187,plain,
! [SV28: del,SV17: del,SV36: $i] :
( ( ( mem @ SV36 @ ( ty_2Ebinary__ieee_2Efloat @ SV17 @ SV28 ) )
= $false )
| ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SV28 ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ SV17 @ SV28 ) @ SV36 ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ SV17 @ SV28 ) @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(188,plain,
! [SV40: del,SV42: $i] :
( ( ~ ( mem @ SV42 @ ( arr @ SV40 @ bool ) )
| ~ ( ~ ( mem @ ( sK3_X @ SV42 @ SV40 ) @ SV40 )
| ~ ~ ( p @ ( ap @ SV42 @ ( sK3_X @ SV42 @ SV40 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(189,plain,
! [SV41: del,SV43: $i] :
( ( ~ ( mem @ SV43 @ ( arr @ SV41 @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV41 ) @ SV43 ) )
| ! [SY85: $i] :
( ~ ( mem @ SY85 @ SV41 )
| ( p @ ( ap @ SV43 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(190,plain,
! [SV31: $i,SV19: del] :
( ( ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ SV19 )
| ( SV31 != SY75 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY75 ) ) )
| ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ SV19 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY76 ) )
| ( SV31 = SY76 ) ) )
= $false )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(191,plain,
! [SV20: del,SV32: del,SV38: $i > $i] :
( ( ( ~ ( mem @ ( sK5_X @ SV38 @ SV32 @ SV20 ) @ SV20 )
| ~ ~ ( mem @ ( SV38 @ ( sK5_X @ SV38 @ SV32 @ SV20 ) ) @ SV32 ) )
= $false )
| ( ( mem @ ( lam @ SV20 @ SV38 ) @ ( arr @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(192,plain,
! [SV33: del,SV21: del,SV39: $i] :
( ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false )
| ( ( ! [SY81: $i] :
( ~ ( mem @ SY81 @ ( arr @ SV21 @ SV33 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SY81 @ SV39 @ SV33 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SV39 @ ( sK4_X @ SY81 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SY81 @ ( sK4_X @ SY81 @ SV39 @ SV33 @ SV21 ) ) ) ) )
| ( SV39 = SY81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(193,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 )
= $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(194,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) )
| ~ SV1 )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(195,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true )
= $false )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(196,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) )
| ~ $true )
= $false )
| ( $true = $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(197,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false )
= $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(198,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) )
| ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(199,plain,
! [SV22: del,SV34: $i,SV4: del,SV44: $i] :
( ( ( ~ ( mem @ SV44 @ SV4 )
| ( mem @ ( ap @ SV34 @ SV44 ) @ SV22 ) )
= $true )
| ( ( mem @ SV34 @ ( arr @ SV4 @ SV22 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(200,plain,
! [SV40: del,SV42: $i] :
( ( ( ~ ( mem @ SV42 @ ( arr @ SV40 @ bool ) ) )
= $true )
| ( ( ~ ( ~ ( mem @ ( sK3_X @ SV42 @ SV40 ) @ SV40 )
| ~ ~ ( p @ ( ap @ SV42 @ ( sK3_X @ SV42 @ SV40 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(201,plain,
! [SV41: del,SV43: $i] :
( ( ( ~ ( mem @ SV43 @ ( arr @ SV41 @ bool ) ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV41 ) @ SV43 ) )
| ! [SY85: $i] :
( ~ ( mem @ SY85 @ SV41 )
| ( p @ ( ap @ SV43 @ SY85 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV31: $i,SV19: del] :
( ( ( ~ ! [SY75: $i] :
( ~ ( mem @ SY75 @ SV19 )
| ( SV31 != SY75 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY75 ) ) ) )
= $false )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(203,plain,
! [SV31: $i,SV19: del] :
( ( ( ~ ! [SY76: $i] :
( ~ ( mem @ SY76 @ SV19 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY76 ) )
| ( SV31 = SY76 ) ) )
= $false )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(204,plain,
! [SV20: del,SV32: del,SV38: $i > $i] :
( ( ( ~ ( mem @ ( sK5_X @ SV38 @ SV32 @ SV20 ) @ SV20 ) )
= $false )
| ( ( mem @ ( lam @ SV20 @ SV38 ) @ ( arr @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(205,plain,
! [SV20: del,SV32: del,SV38: $i > $i] :
( ( ( ~ ~ ( mem @ ( SV38 @ ( sK5_X @ SV38 @ SV32 @ SV20 ) ) @ SV32 ) )
= $false )
| ( ( mem @ ( lam @ SV20 @ SV38 ) @ ( arr @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(206,plain,
! [SV39: $i,SV33: del,SV21: del,SV45: $i] :
( ( ( ~ ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) )
| ~ ( ~ ( mem @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SV39 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SV45 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) ) ) ) )
| ( SV39 = SV45 ) )
= $true )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(207,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) ) )
= $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(208,plain,
! [SV1: $o] :
( ( ( ~ SV1 )
= $false )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(209,plain,
! [SV1: $o] :
( ( ( ~ ( p @ ( inj__o @ SV1 ) ) )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(210,plain,
! [SV1: $o] :
( ( ( ~ SV1 )
= $false )
| ( SV1 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(211,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) ) )
= $false )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(212,plain,
( ( ( ~ $true )
= $false )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(213,plain,
( ( ( ~ ( p @ ( inj__o @ $true ) ) )
= $false )
| ( $true = $false ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(214,plain,
( ( ( ~ $true )
= $false )
| ( $true = $false ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(215,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) ) )
= $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(216,plain,
( ( ( ~ $false )
= $false )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(217,plain,
( ( ( ~ ( p @ ( inj__o @ $false ) ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(218,plain,
( ( ( ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(219,plain,
! [SV22: del,SV34: $i,SV4: del,SV44: $i] :
( ( ( ~ ( mem @ SV44 @ SV4 ) )
= $true )
| ( ( mem @ ( ap @ SV34 @ SV44 ) @ SV22 )
= $true )
| ( ( mem @ SV34 @ ( arr @ SV4 @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(220,plain,
! [SV40: del,SV42: $i] :
( ( ( mem @ SV42 @ ( arr @ SV40 @ bool ) )
= $false )
| ( ( ~ ( ~ ( mem @ ( sK3_X @ SV42 @ SV40 ) @ SV40 )
| ~ ~ ( p @ ( ap @ SV42 @ ( sK3_X @ SV42 @ SV40 ) ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(221,plain,
! [SV41: del,SV43: $i] :
( ( ( mem @ SV43 @ ( arr @ SV41 @ bool ) )
= $false )
| ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV41 ) @ SV43 ) )
| ! [SY85: $i] :
( ~ ( mem @ SY85 @ SV41 )
| ( p @ ( ap @ SV43 @ SY85 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(222,plain,
! [SV31: $i,SV19: del] :
( ( ( ! [SY75: $i] :
( ~ ( mem @ SY75 @ SV19 )
| ( SV31 != SY75 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY75 ) ) ) )
= $true )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(223,plain,
! [SV31: $i,SV19: del] :
( ( ( ! [SY76: $i] :
( ~ ( mem @ SY76 @ SV19 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SY76 ) )
| ( SV31 = SY76 ) ) )
= $true )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(224,plain,
! [SV20: del,SV32: del,SV38: $i > $i] :
( ( ( mem @ ( sK5_X @ SV38 @ SV32 @ SV20 ) @ SV20 )
= $true )
| ( ( mem @ ( lam @ SV20 @ SV38 ) @ ( arr @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(225,plain,
! [SV20: del,SV32: del,SV38: $i > $i] :
( ( ( ~ ( mem @ ( SV38 @ ( sK5_X @ SV38 @ SV32 @ SV20 ) ) @ SV32 ) )
= $true )
| ( ( mem @ ( lam @ SV20 @ SV38 ) @ ( arr @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(226,plain,
! [SV39: $i,SV33: del,SV21: del,SV45: $i] :
( ( ( ~ ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) ) )
= $true )
| ( ( ~ ( ~ ( mem @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SV39 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SV45 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) ) ) ) )
| ( SV39 = SV45 ) )
= $true )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(227,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(228,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( ( p @ ( inj__o @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(229,plain,
! [SV1: $o] :
( ( ( p @ ( inj__o @ SV1 ) )
= $true )
| ( SV1 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(230,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( SV1 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(231,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(232,plain,
( ( $true = $true )
| ( ( p @ ( inj__o @ $true ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(233,plain,
( ( ( p @ ( inj__o @ $true ) )
= $true )
| ( $true = $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(234,plain,
( ( $true = $true )
| ( $true = $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(235,plain,
( ( ( p @ ( inj__o @ $false ) )
= $true )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(236,plain,
( ( $false = $true )
| ( ( p @ ( inj__o @ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(237,plain,
( ( ( p @ ( inj__o @ $false ) )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(238,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(239,plain,
! [SV22: del,SV34: $i,SV4: del,SV44: $i] :
( ( ( mem @ SV44 @ SV4 )
= $false )
| ( ( mem @ ( ap @ SV34 @ SV44 ) @ SV22 )
= $true )
| ( ( mem @ SV34 @ ( arr @ SV4 @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(240,plain,
! [SV40: del,SV42: $i] :
( ( ( ~ ( ~ ( mem @ ( sK3_X @ SV42 @ SV40 ) @ SV40 )
| ~ ~ ( p @ ( ap @ SV42 @ ( sK3_X @ SV42 @ SV40 ) ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) )
= $true )
| ( ( mem @ SV42 @ ( arr @ SV40 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(241,plain,
! [SV43: $i,SV41: del] :
( ( ( ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV41 ) @ SV43 ) ) )
= $true )
| ( ( ! [SY85: $i] :
( ~ ( mem @ SY85 @ SV41 )
| ( p @ ( ap @ SV43 @ SY85 ) ) ) )
= $true )
| ( ( mem @ SV43 @ ( arr @ SV41 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(242,plain,
! [SV31: $i,SV19: del,SV46: $i] :
( ( ( ~ ( mem @ SV46 @ SV19 )
| ( SV31 != SV46 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV46 ) ) )
= $true )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(243,plain,
! [SV31: $i,SV19: del,SV47: $i] :
( ( ( ~ ( mem @ SV47 @ SV19 )
| ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV47 ) )
| ( SV31 = SV47 ) )
= $true )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(244,plain,
! [SV20: del,SV32: del,SV38: $i > $i] :
( ( ( mem @ ( SV38 @ ( sK5_X @ SV38 @ SV32 @ SV20 ) ) @ SV32 )
= $false )
| ( ( mem @ ( lam @ SV20 @ SV38 ) @ ( arr @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(245,plain,
! [SV39: $i,SV33: del,SV21: del,SV45: $i] :
( ( ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) )
= $false )
| ( ( ~ ( ~ ( mem @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SV39 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SV45 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) ) ) ) )
| ( SV39 = SV45 ) )
= $true )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(246,plain,
! [SV40: del,SV42: $i] :
( ( ( ~ ( mem @ ( sK3_X @ SV42 @ SV40 ) @ SV40 )
| ~ ~ ( p @ ( ap @ SV42 @ ( sK3_X @ SV42 @ SV40 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) )
= $true )
| ( ( mem @ SV42 @ ( arr @ SV40 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(247,plain,
! [SV43: $i,SV41: del] :
( ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV41 ) @ SV43 ) )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( mem @ SY85 @ SV41 )
| ( p @ ( ap @ SV43 @ SY85 ) ) ) )
= $true )
| ( ( mem @ SV43 @ ( arr @ SV41 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(248,plain,
! [SV31: $i,SV19: del,SV46: $i] :
( ( ( ~ ( mem @ SV46 @ SV19 ) )
= $true )
| ( ( ( SV31 != SV46 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV46 ) ) )
= $true )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(249,plain,
! [SV31: $i,SV19: del,SV47: $i] :
( ( ( ~ ( mem @ SV47 @ SV19 ) )
= $true )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV47 ) )
| ( SV31 = SV47 ) )
= $true )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(250,plain,
! [SV21: del,SV33: del,SV39: $i,SV45: $i] :
( ( ( ~ ( ~ ( mem @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SV39 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SV45 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) ) ) ) ) )
= $true )
| ( ( SV39 = SV45 )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) )
= $false )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(251,plain,
! [SV40: del,SV42: $i] :
( ( ( ~ ( mem @ ( sK3_X @ SV42 @ SV40 ) @ SV40 ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) )
= $true )
| ( ( mem @ SV42 @ ( arr @ SV40 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(252,plain,
! [SV40: del,SV42: $i] :
( ( ( ~ ~ ( p @ ( ap @ SV42 @ ( sK3_X @ SV42 @ SV40 ) ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) )
= $true )
| ( ( mem @ SV42 @ ( arr @ SV40 @ bool ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(253,plain,
! [SV43: $i,SV41: del,SV48: $i] :
( ( ( ~ ( mem @ SV48 @ SV41 )
| ( p @ ( ap @ SV43 @ SV48 ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV41 ) @ SV43 ) )
= $false )
| ( ( mem @ SV43 @ ( arr @ SV41 @ bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(254,plain,
! [SV31: $i,SV19: del,SV46: $i] :
( ( ( mem @ SV46 @ SV19 )
= $false )
| ( ( ( SV31 != SV46 )
| ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV46 ) ) )
= $true )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(255,plain,
! [SV31: $i,SV19: del,SV47: $i] :
( ( ( mem @ SV47 @ SV19 )
= $false )
| ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV47 ) )
| ( SV31 = SV47 ) )
= $true )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(256,plain,
! [SV21: del,SV33: del,SV39: $i,SV45: $i] :
( ( ( ~ ( mem @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) @ SV21 )
| ~ ( ( ( ap @ SV39 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SV45 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) ) ) ) )
= $false )
| ( ( SV39 = SV45 )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) )
= $false )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(257,plain,
! [SV40: del,SV42: $i] :
( ( ( mem @ ( sK3_X @ SV42 @ SV40 ) @ SV40 )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) )
= $true )
| ( ( mem @ SV42 @ ( arr @ SV40 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(258,plain,
! [SV40: del,SV42: $i] :
( ( ( ~ ( p @ ( ap @ SV42 @ ( sK3_X @ SV42 @ SV40 ) ) ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) )
= $true )
| ( ( mem @ SV42 @ ( arr @ SV40 @ bool ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(259,plain,
! [SV43: $i,SV41: del,SV48: $i] :
( ( ( ~ ( mem @ SV48 @ SV41 ) )
= $true )
| ( ( p @ ( ap @ SV43 @ SV48 ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV41 ) @ SV43 ) )
= $false )
| ( ( mem @ SV43 @ ( arr @ SV41 @ bool ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(260,plain,
! [SV19: del,SV46: $i,SV31: $i] :
( ( ( ( SV31 != SV46 ) )
= $true )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV46 ) )
= $true )
| ( ( mem @ SV46 @ SV19 )
= $false )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(261,plain,
! [SV47: $i,SV31: $i,SV19: del] :
( ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV47 ) ) )
= $true )
| ( ( SV31 = SV47 )
= $true )
| ( ( mem @ SV47 @ SV19 )
= $false )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(262,plain,
! [SV21: del,SV33: del,SV39: $i,SV45: $i] :
( ( ( ~ ( mem @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) @ SV21 ) )
= $false )
| ( ( SV39 = SV45 )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) )
= $false )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(263,plain,
! [SV21: del,SV33: del,SV45: $i,SV39: $i] :
( ( ( ~ ( ( ( ap @ SV39 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SV45 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) ) ) ) )
= $false )
| ( ( SV39 = SV45 )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) )
= $false )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(264,plain,
! [SV40: del,SV42: $i] :
( ( ( p @ ( ap @ SV42 @ ( sK3_X @ SV42 @ SV40 ) ) )
= $false )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV40 ) @ SV42 ) )
= $true )
| ( ( mem @ SV42 @ ( arr @ SV40 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(265,plain,
! [SV43: $i,SV41: del,SV48: $i] :
( ( ( mem @ SV48 @ SV41 )
= $false )
| ( ( p @ ( ap @ SV43 @ SV48 ) )
= $true )
| ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ SV41 ) @ SV43 ) )
= $false )
| ( ( mem @ SV43 @ ( arr @ SV41 @ bool ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(266,plain,
! [SV19: del,SV46: $i,SV31: $i] :
( ( ( SV31 = SV46 )
= $false )
| ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV46 ) )
= $true )
| ( ( mem @ SV46 @ SV19 )
= $false )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(267,plain,
! [SV47: $i,SV31: $i,SV19: del] :
( ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ SV19 ) @ SV31 ) @ SV47 ) )
= $false )
| ( ( SV31 = SV47 )
= $true )
| ( ( mem @ SV47 @ SV19 )
= $false )
| ( ( mem @ SV31 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(268,plain,
! [SV21: del,SV33: del,SV39: $i,SV45: $i] :
( ( ( mem @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) @ SV21 )
= $true )
| ( ( SV39 = SV45 )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) )
= $false )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(269,plain,
! [SV21: del,SV33: del,SV45: $i,SV39: $i] :
( ( ( ( ( ap @ SV39 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) )
!= ( ap @ SV45 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) ) ) )
= $true )
| ( ( SV39 = SV45 )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) )
= $false )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(270,plain,
! [SV21: del,SV33: del,SV45: $i,SV39: $i] :
( ( ( ( ap @ SV39 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) )
= ( ap @ SV45 @ ( sK4_X @ SV45 @ SV39 @ SV33 @ SV21 ) ) )
= $false )
| ( ( SV39 = SV45 )
= $true )
| ( ( mem @ SV45 @ ( arr @ SV21 @ SV33 ) )
= $false )
| ( ( mem @ SV39 @ ( arr @ SV21 @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(271,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[81,270,268,267,266,265,264,257,244,239,238,237,236,235,234,233,232,231,230,229,228,227,224,187,186,173,159,156,146,144,143,142,141,136,134,132,126,122,121,119,115,113,112,108,107,106,96,89,88]) ).
thf(272,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP018^2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 21:21:15 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.37
% 0.20/0.37 No.of.Axioms: 27
% 0.20/0.37
% 0.20/0.37 Length.of.Defs: 0
% 0.20/0.37
% 0.20/0.37 Contains.Choice.Funs: false
% 0.20/0.39 .
% 0.20/0.39 (rf:0,axioms:27,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:29,loop_count:0,foatp_calls:0,translation:fof_full)..............
% 0.65/0.83
% 0.65/0.83 ********************************
% 0.65/0.83 * All subproblems solved! *
% 0.65/0.83 ********************************
% 0.65/0.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:27,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:271,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.69/0.86
% 0.69/0.86 %**** Beginning of derivation protocol ****
% 0.69/0.86 % SZS output start CNFRefutation
% See solution above
% 0.69/0.86
% 0.69/0.86 %**** End of derivation protocol ****
% 0.69/0.86 %**** no. of clauses in derivation: 272 ****
% 0.69/0.86 %**** clause counter: 271 ****
% 0.69/0.86
% 0.69/0.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:27,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:271,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------