%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU500^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:37 AM UTC 2026
% Result : Theorem 274.64s 46.15s
% Output : CNFRefutation 274.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 19
% Syntax : Number of formulae : 675 ( 166 unt; 0 typ; 18 def)
% Number of atoms : 6212 (2188 equ; 0 cnn)
% Maximal formula atoms : 17 ( 9 avg)
% Number of connectives : 14291 (3458 ~;2362 |; 20 &;8380 @)
% ( 6 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 343 ( 343 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 53 usr; 23 con; 0-4 aty)
% Number of variables : 2851 ( 489 ^;2349 !; 13 ?;2851 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK10_SY67,type,
sK10_SY67: $i > $i > $i ).
thf(tp_sK11_SY99,type,
sK11_SY99: $i > ( $i > $o ) > $i ).
thf(tp_sK12_SY100,type,
sK12_SY100: $i > ( $i > $o ) > $i ).
thf(tp_sK13_SY101,type,
sK13_SY101: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK14_SY30,type,
sK14_SY30: $i > ( $i > $o ) > $i ).
thf(tp_sK15_SY103,type,
sK15_SY103: $i > $i > $i ).
thf(tp_sK16_SY30,type,
sK16_SY30: $i > ( $i > $o ) > $i ).
thf(tp_sK17_SY61,type,
sK17_SY61: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK18_SY113,type,
sK18_SY113: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK19_SY61,type,
sK19_SY61: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK1_Xphi,type,
sK1_Xphi: $o ).
thf(tp_sK20_SY105,type,
sK20_SY105: $i > $i > $i > $i ).
thf(tp_sK21_SY105,type,
sK21_SY105: $i > $i > $i > $i ).
thf(tp_sK22_SY125,type,
sK22_SY125: $i > $i > $i > $i ).
thf(tp_sK23_SY136,type,
sK23_SY136: $i > $i > $i > $i ).
thf(tp_sK24_SY140,type,
sK24_SY140: $i > $i > $i > $i ).
thf(tp_sK25_SY132,type,
sK25_SY132: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK26_SY134,type,
sK26_SY134: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK27_E,type,
sK27_E: $i ).
thf(tp_sK2_SY0,type,
sK2_SY0: $i ).
thf(tp_sK3_SY35,type,
sK3_SY35: $i > $i ).
thf(tp_sK4_SY58,type,
sK4_SY58: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK5_SY66,type,
sK5_SY66: $i > $i > $i ).
thf(tp_sK6_SY26,type,
sK6_SY26: $i > $i > $i ).
thf(tp_sK7_SY74,type,
sK7_SY74: $i > $i > $i ).
thf(tp_sK8_SY53,type,
sK8_SY53: $i > $i ).
thf(tp_sK9_SY61,type,
sK9_SY61: ( $i > $i > $o ) > $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(prop2set,definition,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(2,negated_conjecture,
( ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
setextAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
emptysetAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
setadjoinAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
powersetAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(7,plain,
setunionAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(8,plain,
omega0Ax = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(9,plain,
omegaSAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(10,plain,
omegaIndAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(11,plain,
replAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(12,plain,
foundationAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(13,plain,
wellorderingAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(14,plain,
descrp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(15,plain,
dsetconstrI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(16,plain,
dsetconstrEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(17,plain,
dsetconstrER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(18,plain,
exuE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(20,plain,
( ( ~ ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(21,plain,
( ( ( in @ sK2_SY0 @ ( prop2set @ sK1_Xphi ) )
& ~ sK1_Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(22,plain,
exuE1 = $true,
inference(copy,[status(thm)],[18]) ).
thf(23,plain,
dsetconstrER = $true,
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
dsetconstrEL = $true,
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
dsetconstrI = $true,
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
descrp = $true,
inference(copy,[status(thm)],[14]) ).
thf(27,plain,
wellorderingAx = $true,
inference(copy,[status(thm)],[13]) ).
thf(28,plain,
foundationAx = $true,
inference(copy,[status(thm)],[12]) ).
thf(29,plain,
replAx = $true,
inference(copy,[status(thm)],[11]) ).
thf(30,plain,
omegaIndAx = $true,
inference(copy,[status(thm)],[10]) ).
thf(31,plain,
omegaSAx = $true,
inference(copy,[status(thm)],[9]) ).
thf(32,plain,
omega0Ax = $true,
inference(copy,[status(thm)],[8]) ).
thf(33,plain,
setunionAx = $true,
inference(copy,[status(thm)],[7]) ).
thf(34,plain,
powersetAx = $true,
inference(copy,[status(thm)],[6]) ).
thf(35,plain,
setadjoinAx = $true,
inference(copy,[status(thm)],[5]) ).
thf(36,plain,
emptysetAx = $true,
inference(copy,[status(thm)],[4]) ).
thf(37,plain,
setextAx = $true,
inference(copy,[status(thm)],[3]) ).
thf(38,plain,
( ( ( in @ sK2_SY0 @ ( prop2set @ sK1_Xphi ) )
& ~ sK1_Xphi )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(39,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( SX0 @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( SX0 @ SX2 @ SX4 )
| ( SX3 = SX4 ) ) ) )
| ~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) )
| ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(40,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(41,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(42,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[36,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(43,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(46,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(47,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(48,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(49,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(50,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(51,plain,
( ( ~ ( ~ ( in @ sK2_SY0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi ) )
| ~ ~ sK1_Xphi ) )
= $true ),
inference(unfold_def,[status(thm)],[38,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(52,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX4 )
| ( in @ SX3 @ SX4 ) )
| ~ ( ~ ( in @ SX3 @ SX4 )
| ( in @ SX2 @ SX4 ) ) ) )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX2 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SX2 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(53,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( in @ emptyset @ SX0 )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ( in @ SX1 @ omega )
| ~ ( in @ SX1 @ SX0 ) )
| ( in @ ( setadjoin @ SX1 @ SX1 ) @ SX0 ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(54,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(55,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(unfold_def,[status(thm)],[32,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptysetAx,exu,exuE1,foundationAx,omega0Ax,omegaIndAx,omegaSAx,powersetAx,prop2set,replAx,setadjoinAx,setextAx,setunionAx,wellorderingAx]) ).
thf(56,plain,
! [SV1: $i > $i > $o] :
( ( ! [SY1: $i] :
( ~ ! [SY2: $i] :
( ~ ( in @ SY2 @ SY1 )
| ~ ! [SY3: $i] :
~ ~ ( ~ ( SV1 @ SY2 @ SY3 )
| ~ ! [SY4: $i] :
( ~ ( SV1 @ SY2 @ SY4 )
| ( SY3 = SY4 ) ) ) )
| ~ ! [SY5: $i] :
~ ! [SY6: $i] :
~ ( ~ ( ~ ( in @ SY6 @ SY5 )
| ~ ! [SY7: $i] :
~ ~ ( ~ ( in @ SY7 @ SY1 )
| ~ ( SV1 @ SY7 @ SY6 ) ) )
| ~ ( ~ ~ ! [SY8: $i] :
~ ~ ( ~ ( in @ SY8 @ SY1 )
| ~ ( SV1 @ SY8 @ SY6 ) )
| ( in @ SY6 @ SY5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(57,plain,
! [SV2: $i] :
( ( ! [SY9: $i,SY10: $i] :
~ ( ~ ( ~ ( in @ SY10 @ ( setadjoin @ SV2 @ SY9 ) )
| ( SY10 = SV2 )
| ( in @ SY10 @ SY9 ) )
| ~ ( ~ ( ( SY10 = SV2 )
| ( in @ SY10 @ SY9 ) )
| ( in @ SY10 @ ( setadjoin @ SV2 @ SY9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(58,plain,
! [SV3: $i > $o] :
( ( ~ ~ ! [SY11: $i] :
~ ~ ( ~ ( SV3 @ SY11 )
| ~ ! [SY12: $i] :
( ~ ( SV3 @ SY12 )
| ( SY11 = SY12 ) ) )
| ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(59,plain,
! [SV4: $i] :
( ( ~ ( in @ SV4 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(60,plain,
! [SV5: $i] :
( ( ! [SY14: $i] :
( ~ ! [SY15: $i] :
~ ( ~ ( ~ ( in @ SY15 @ SV5 )
| ( in @ SY15 @ SY14 ) )
| ~ ( ~ ( in @ SY15 @ SY14 )
| ( in @ SY15 @ SV5 ) ) )
| ( SV5 = SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(61,plain,
! [SV6: $i] :
( ( ! [SY16: $i] :
~ ( ~ ( ~ ( in @ SY16 @ ( setunion @ SV6 ) )
| ~ ! [SY17: $i] :
~ ~ ( ~ ( in @ SY16 @ SY17 )
| ~ ( in @ SY17 @ SV6 ) ) )
| ~ ( ~ ~ ! [SY18: $i] :
~ ~ ( ~ ( in @ SY16 @ SY18 )
| ~ ( in @ SY18 @ SV6 ) )
| ( in @ SY16 @ ( setunion @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(62,plain,
! [SV7: $i] :
( ( ! [SY19: $i > $o,SY20: $i] :
( ~ ( in @ SY20
@ ( dsetconstr @ SV7
@ ^ [SX3: $i] : ( SY19 @ SX3 ) ) )
| ( in @ SY20 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(63,plain,
! [SV8: $i] :
( ( ! [SY22: $i > $o,SY23: $i] :
( ~ ( in @ SY23
@ ( dsetconstr @ SV8
@ ^ [SX3: $i] : ( SY22 @ SX3 ) ) )
| ( SY22 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(64,plain,
! [SV9: $i] :
( ( ~ ~ ! [SY25: $i] :
~ ( in @ SY25 @ SV9 )
| ~ ! [SY26: $i] :
~ ~ ( ~ ( in @ SY26 @ SV9 )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ( in @ SY27 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(65,plain,
! [SV10: $i > $o] :
( ( ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( SV10 @ SY28 )
| ~ ! [SY29: $i] :
( ~ ( SV10 @ SY29 )
| ( SY28 = SY29 ) ) )
| ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(66,plain,
! [SV11: $i] :
( ( ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ ( powerset @ SV11 ) )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SY32 )
| ( in @ SY33 @ SV11 ) ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SY32 )
| ( in @ SY34 @ SV11 ) )
| ( in @ SY32 @ ( powerset @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(67,plain,
! [SV12: $i] :
( ( ~ ( in @ SV12 @ omega )
| ( in @ ( setadjoin @ SV12 @ SV12 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(68,plain,
( ( ~ ( in @ sK2_SY0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi ) )
| ~ ~ sK1_Xphi )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV13: $i] :
( ( ~ ! [SY35: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SY35 )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY36 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ~ ( ~ ( in @ SY38 @ SV13 )
| ~ ( in @ SY39 @ SV13 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY35 )
| ~ ( ~ ( ~ ( in @ SY38 @ SX4 )
| ( in @ SY39 @ SX4 ) )
| ~ ( ~ ( in @ SY39 @ SX4 )
| ( in @ SY38 @ SX4 ) ) ) )
| ( SY38 = SY39 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY35 )
| ~ ( in @ SX3 @ SY35 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY45: $i] :
( ~ ~ ( ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY45 )
| ( in @ SY46 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY45 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY35 )
| ~ ( in @ SX4 @ SY45 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY45 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY35 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(70,plain,
! [SV14: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV14 )
| ~ ! [SY53: $i] :
( ~ ~ ( ~ ( in @ SY53 @ omega )
| ~ ( in @ SY53 @ SV14 ) )
| ( in @ ( setadjoin @ SY53 @ SY53 ) @ SV14 ) ) )
| ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(71,plain,
! [SV15: $i] :
( ( ! [SY55: $i > $o,SY56: $i] :
( ~ ( in @ SY56 @ SV15 )
| ~ ( SY55 @ SY56 )
| ( in @ SY56
@ ( dsetconstr @ SV15
@ ^ [SX3: $i] : ( SY55 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(72,plain,
! [SV1: $i > $i > $o,SV16: $i] :
( ( ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ SV16 )
| ~ ! [SY3: $i] :
~ ~ ( ~ ( SV1 @ SY58 @ SY3 )
| ~ ! [SY4: $i] :
( ~ ( SV1 @ SY58 @ SY4 )
| ( SY3 = SY4 ) ) ) )
| ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(73,plain,
! [SV17: $i,SV2: $i] :
( ( ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ ( setadjoin @ SV2 @ SV17 ) )
| ( SY65 = SV2 )
| ( in @ SY65 @ SV17 ) )
| ~ ( ~ ( ( SY65 = SV2 )
| ( in @ SY65 @ SV17 ) )
| ( in @ SY65 @ ( setadjoin @ SV2 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(74,plain,
! [SV3: $i > $o] :
( ( ( ~ ~ ! [SY11: $i] :
~ ~ ( ~ ( SV3 @ SY11 )
| ~ ! [SY12: $i] :
( ~ ( SV3 @ SY12 )
| ( SY11 = SY12 ) ) ) )
= $true )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(75,plain,
! [SV4: $i] :
( ( in @ SV4 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(76,plain,
! [SV18: $i,SV5: $i] :
( ( ~ ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ SV5 )
| ( in @ SY66 @ SV18 ) )
| ~ ( ~ ( in @ SY66 @ SV18 )
| ( in @ SY66 @ SV5 ) ) )
| ( SV5 = SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(77,plain,
! [SV6: $i,SV19: $i] :
( ( ~ ( ~ ( ~ ( in @ SV19 @ ( setunion @ SV6 ) )
| ~ ! [SY67: $i] :
~ ~ ( ~ ( in @ SV19 @ SY67 )
| ~ ( in @ SY67 @ SV6 ) ) )
| ~ ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( in @ SV19 @ SY68 )
| ~ ( in @ SY68 @ SV6 ) )
| ( in @ SV19 @ ( setunion @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
! [SV20: $i > $o,SV7: $i] :
( ( ! [SY69: $i] :
( ~ ( in @ SY69
@ ( dsetconstr @ SV7
@ ^ [SY70: $i] : ( SV20 @ SY70 ) ) )
| ( in @ SY69 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(79,plain,
! [SV21: $i > $o,SV8: $i] :
( ( ! [SY71: $i] :
( ~ ( in @ SY71
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) )
| ( SV21 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(80,plain,
! [SV9: $i] :
( ( ( ~ ~ ! [SY25: $i] :
~ ( in @ SY25 @ SV9 ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( in @ SY26 @ SV9 )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ( in @ SY27 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(81,plain,
! [SV10: $i > $o] :
( ( ( ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( SV10 @ SY28 )
| ~ ! [SY29: $i] :
( ~ ( SV10 @ SY29 )
| ( SY28 = SY29 ) ) ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(82,plain,
! [SV11: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( in @ SV22 @ ( powerset @ SV11 ) )
| ! [SY73: $i] :
( ~ ( in @ SY73 @ SV22 )
| ( in @ SY73 @ SV11 ) ) )
| ~ ( ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV22 )
| ( in @ SY74 @ SV11 ) )
| ( in @ SV22 @ ( powerset @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(83,plain,
! [SV12: $i] :
( ( ( ~ ( in @ SV12 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV12 @ SV12 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(84,plain,
( ( ~ ( in @ sK2_SY0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(85,plain,
( ( ~ ~ sK1_Xphi )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(86,plain,
! [SV13: $i] :
( ( ! [SY35: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SY35 )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY36 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ~ ( ~ ( in @ SY38 @ SV13 )
| ~ ( in @ SY39 @ SV13 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY35 )
| ~ ( ~ ( ~ ( in @ SY38 @ SX4 )
| ( in @ SY39 @ SX4 ) )
| ~ ( ~ ( in @ SY39 @ SX4 )
| ( in @ SY38 @ SX4 ) ) ) )
| ( SY38 = SY39 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY35 )
| ~ ( in @ SX3 @ SY35 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY45: $i] :
( ~ ~ ( ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY45 )
| ( in @ SY46 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY45 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY35 )
| ~ ( in @ SX4 @ SY45 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY45 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY35 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(87,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV14 )
| ~ ! [SY53: $i] :
( ~ ~ ( ~ ( in @ SY53 @ omega )
| ~ ( in @ SY53 @ SV14 ) )
| ( in @ ( setadjoin @ SY53 @ SY53 ) @ SV14 ) ) ) )
= $true )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(88,plain,
! [SV23: $i > $o,SV15: $i] :
( ( ! [SY75: $i] :
( ~ ( in @ SY75 @ SV15 )
| ~ ( SV23 @ SY75 )
| ( in @ SY75
@ ( dsetconstr @ SV15
@ ^ [SY76: $i] : ( SV23 @ SY76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(89,plain,
! [SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ SV16 )
| ~ ! [SY3: $i] :
~ ~ ( ~ ( SV1 @ SY58 @ SY3 )
| ~ ! [SY4: $i] :
( ~ ( SV1 @ SY58 @ SY4 )
| ( SY3 = SY4 ) ) ) ) )
= $true )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(90,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ~ ( ~ ( ~ ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
| ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
| ~ ( ~ ( ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
| ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(91,plain,
! [SV3: $i > $o] :
( ( ( ~ ! [SY11: $i] :
~ ~ ( ~ ( SV3 @ SY11 )
| ~ ! [SY12: $i] :
( ~ ( SV3 @ SY12 )
| ( SY11 = SY12 ) ) ) )
= $false )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(92,plain,
! [SV18: $i,SV5: $i] :
( ( ( ~ ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ SV5 )
| ( in @ SY66 @ SV18 ) )
| ~ ( ~ ( in @ SY66 @ SV18 )
| ( in @ SY66 @ SV5 ) ) ) )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(93,plain,
! [SV6: $i,SV19: $i] :
( ( ~ ( ~ ( in @ SV19 @ ( setunion @ SV6 ) )
| ~ ! [SY67: $i] :
~ ~ ( ~ ( in @ SV19 @ SY67 )
| ~ ( in @ SY67 @ SV6 ) ) )
| ~ ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( in @ SV19 @ SY68 )
| ~ ( in @ SY68 @ SV6 ) )
| ( in @ SV19 @ ( setunion @ SV6 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(94,plain,
! [SV20: $i > $o,SV7: $i,SV25: $i] :
( ( ~ ( in @ SV25
@ ( dsetconstr @ SV7
@ ^ [SY70: $i] : ( SV20 @ SY70 ) ) )
| ( in @ SV25 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(95,plain,
! [SV21: $i > $o,SV8: $i,SV26: $i] :
( ( ~ ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) )
| ( SV21 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(96,plain,
! [SV9: $i] :
( ( ( ~ ! [SY25: $i] :
~ ( in @ SY25 @ SV9 ) )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( in @ SY26 @ SV9 )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ( in @ SY27 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(97,plain,
! [SV10: $i > $o] :
( ( ( ~ ! [SY28: $i] :
~ ~ ( ~ ( SV10 @ SY28 )
| ~ ! [SY29: $i] :
( ~ ( SV10 @ SY29 )
| ( SY28 = SY29 ) ) ) )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(98,plain,
! [SV11: $i,SV22: $i] :
( ( ~ ( ~ ( in @ SV22 @ ( powerset @ SV11 ) )
| ! [SY73: $i] :
( ~ ( in @ SY73 @ SV22 )
| ( in @ SY73 @ SV11 ) ) )
| ~ ( ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV22 )
| ( in @ SY74 @ SV11 ) )
| ( in @ SV22 @ ( powerset @ SV11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(99,plain,
! [SV12: $i] :
( ( ( in @ SV12 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV12 @ SV12 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(100,plain,
( ( in @ sK2_SY0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(101,plain,
( ( ~ sK1_Xphi ) = $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(102,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) )
| ~ ! [SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ SY84 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY85 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY84 )
| ( in @ SX4 @ SY85 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY85 )
| ( in @ SX4 @ SY84 ) ) ) )
| ~ ! [SY88: $i] :
( ~ ~ ( ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY88 )
| ( in @ SY46 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY88 ) )
| ~ ! [SY91: $i] :
~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY91 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY92 @ SY88 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY91 )
| ~ ( in @ SX5 @ SY88 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY91 ) )
| ( in @ SY92 @ SY94 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(103,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV14 )
| ~ ! [SY53: $i] :
( ~ ~ ( ~ ( in @ SY53 @ omega )
| ~ ( in @ SY53 @ SV14 ) )
| ( in @ ( setadjoin @ SY53 @ SY53 ) @ SV14 ) ) ) )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV23: $i > $o,SV15: $i,SV27: $i] :
( ( ~ ( in @ SV27 @ SV15 )
| ~ ( SV23 @ SV27 )
| ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SY76: $i] : ( SV23 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY58: $i] :
( ~ ( in @ SY58 @ SV16 )
| ~ ! [SY3: $i] :
~ ~ ( ~ ( SV1 @ SY58 @ SY3 )
| ~ ! [SY4: $i] :
( ~ ( SV1 @ SY58 @ SY4 )
| ( SY3 = SY4 ) ) ) ) )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ~ ( ~ ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
| ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
| ~ ( ~ ( ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
| ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(107,plain,
! [SV3: $i > $o] :
( ( ( ! [SY11: $i] :
~ ~ ( ~ ( SV3 @ SY11 )
| ~ ! [SY12: $i] :
( ~ ( SV3 @ SY12 )
| ( SY11 = SY12 ) ) ) )
= $true )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(108,plain,
! [SV18: $i,SV5: $i] :
( ( ( ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ SV5 )
| ( in @ SY66 @ SV18 ) )
| ~ ( ~ ( in @ SY66 @ SV18 )
| ( in @ SY66 @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(109,plain,
! [SV6: $i,SV19: $i] :
( ( ~ ( ~ ( in @ SV19 @ ( setunion @ SV6 ) )
| ~ ! [SY67: $i] :
~ ~ ( ~ ( in @ SV19 @ SY67 )
| ~ ( in @ SY67 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(110,plain,
! [SV6: $i,SV19: $i] :
( ( ~ ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( in @ SV19 @ SY68 )
| ~ ( in @ SY68 @ SV6 ) )
| ( in @ SV19 @ ( setunion @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(111,plain,
! [SV20: $i > $o,SV7: $i,SV25: $i] :
( ( ( ~ ( in @ SV25
@ ( dsetconstr @ SV7
@ ^ [SY70: $i] : ( SV20 @ SY70 ) ) ) )
= $true )
| ( ( in @ SV25 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(112,plain,
! [SV21: $i > $o,SV8: $i,SV26: $i] :
( ( ( ~ ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) ) )
= $true )
| ( ( SV21 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(113,plain,
! [SV9: $i] :
( ( ( ! [SY25: $i] :
~ ( in @ SY25 @ SV9 ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( in @ SY26 @ SV9 )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ( in @ SY27 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(114,plain,
! [SV10: $i > $o] :
( ( ( ! [SY28: $i] :
~ ~ ( ~ ( SV10 @ SY28 )
| ~ ! [SY29: $i] :
( ~ ( SV10 @ SY29 )
| ( SY28 = SY29 ) ) ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(115,plain,
! [SV11: $i,SV22: $i] :
( ( ~ ( ~ ( in @ SV22 @ ( powerset @ SV11 ) )
| ! [SY73: $i] :
( ~ ( in @ SY73 @ SV22 )
| ( in @ SY73 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(116,plain,
! [SV11: $i,SV22: $i] :
( ( ~ ( ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV22 )
| ( in @ SY74 @ SV11 ) )
| ( in @ SV22 @ ( powerset @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(117,plain,
sK1_Xphi = $false,
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(118,plain,
! [SV13: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) )
| ~ ! [SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ SY84 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY85 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY84 )
| ( in @ SX4 @ SY85 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY85 )
| ( in @ SX4 @ SY84 ) ) ) )
| ~ ! [SY88: $i] :
( ~ ~ ( ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY88 )
| ( in @ SY46 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY88 ) )
| ~ ! [SY91: $i] :
~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY91 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY92 @ SY88 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY91 )
| ~ ( in @ SX5 @ SY88 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY91 ) )
| ( in @ SY92 @ SY94 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(119,plain,
! [SV14: $i] :
( ( ( ~ ( in @ emptyset @ SV14 )
| ~ ! [SY53: $i] :
( ~ ~ ( ~ ( in @ SY53 @ omega )
| ~ ( in @ SY53 @ SV14 ) )
| ( in @ ( setadjoin @ SY53 @ SY53 ) @ SV14 ) ) )
= $true )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(120,plain,
! [SV23: $i > $o,SV15: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV15 ) )
= $true )
| ( ( ~ ( SV23 @ SV27 )
| ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SY76: $i] : ( SV23 @ SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
| ~ ! [SY97: $i] :
~ ~ ( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY97 )
| ~ ! [SY98: $i] :
( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY98 )
| ( SY97 = SY98 ) ) ) )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(122,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ~ ( ~ ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
| ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(123,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ~ ( ~ ( ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
| ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(124,plain,
! [SV28: $i,SV3: $i > $o] :
( ( ( ~ ~ ( ~ ( SV3 @ SV28 )
| ~ ! [SY99: $i] :
( ~ ( SV3 @ SY99 )
| ( SV28 = SY99 ) ) ) )
= $true )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(125,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 ) )
| ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(126,plain,
! [SV6: $i,SV19: $i] :
( ( ~ ( in @ SV19 @ ( setunion @ SV6 ) )
| ~ ! [SY67: $i] :
~ ~ ( ~ ( in @ SV19 @ SY67 )
| ~ ( in @ SY67 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(127,plain,
! [SV6: $i,SV19: $i] :
( ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( in @ SV19 @ SY68 )
| ~ ( in @ SY68 @ SV6 ) )
| ( in @ SV19 @ ( setunion @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(128,plain,
! [SV20: $i > $o,SV7: $i,SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ SV7
@ ^ [SY70: $i] : ( SV20 @ SY70 ) ) )
= $false )
| ( ( in @ SV25 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(129,plain,
! [SV21: $i > $o,SV8: $i,SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) )
= $false )
| ( ( SV21 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(130,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV9 ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( in @ SY26 @ SV9 )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ( in @ SY27 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(131,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ SV30 )
| ~ ! [SY100: $i] :
( ~ ( SV10 @ SY100 )
| ( SV30 = SY100 ) ) ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(132,plain,
! [SV11: $i,SV22: $i] :
( ( ~ ( in @ SV22 @ ( powerset @ SV11 ) )
| ! [SY73: $i] :
( ~ ( in @ SY73 @ SV22 )
| ( in @ SY73 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(133,plain,
! [SV11: $i,SV22: $i] :
( ( ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV22 )
| ( in @ SY74 @ SV11 ) )
| ( in @ SV22 @ ( powerset @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(134,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) )
| ~ ! [SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ SY84 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY85 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY84 )
| ( in @ SX4 @ SY85 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY85 )
| ( in @ SX4 @ SY84 ) ) ) )
| ~ ! [SY88: $i] :
( ~ ~ ( ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY88 )
| ( in @ SY46 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY88 ) )
| ~ ! [SY91: $i] :
~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY91 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY92 @ SY88 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY91 )
| ~ ( in @ SX5 @ SY88 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY91 ) )
| ( in @ SY92 @ SY94 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV14: $i] :
( ( ( ~ ( in @ emptyset @ SV14 ) )
= $true )
| ( ( ~ ! [SY53: $i] :
( ~ ~ ( ~ ( in @ SY53 @ omega )
| ~ ( in @ SY53 @ SV14 ) )
| ( in @ ( setadjoin @ SY53 @ SY53 ) @ SV14 ) ) )
= $true )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV23: $i > $o,SV15: $i,SV27: $i] :
( ( ( in @ SV27 @ SV15 )
= $false )
| ( ( ~ ( SV23 @ SV27 )
| ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SY76: $i] : ( SV23 @ SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 ) )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(138,plain,
! [SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ! [SY97: $i] :
~ ~ ( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY97 )
| ~ ! [SY98: $i] :
( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY98 )
| ( SY97 = SY98 ) ) ) )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(139,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ~ ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
| ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(140,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ~ ( ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
| ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(141,plain,
! [SV28: $i,SV3: $i > $o] :
( ( ( ~ ( ~ ( SV3 @ SV28 )
| ~ ! [SY99: $i] :
( ~ ( SV3 @ SY99 )
| ( SV28 = SY99 ) ) ) )
= $false )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(142,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 ) )
| ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(143,plain,
! [SV6: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( setunion @ SV6 ) ) )
= $true )
| ( ( ~ ! [SY67: $i] :
~ ~ ( ~ ( in @ SV19 @ SY67 )
| ~ ( in @ SY67 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(144,plain,
! [SV6: $i,SV19: $i] :
( ( ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( in @ SV19 @ SY68 )
| ~ ( in @ SY68 @ SV6 ) ) )
= $true )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(145,plain,
! [SV9: $i,SV29: $i] :
( ( ( in @ SV29 @ SV9 )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( in @ SY26 @ SV9 )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ( in @ SY27 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(146,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ SV30 )
| ~ ! [SY100: $i] :
( ~ ( SV10 @ SY100 )
| ( SV30 = SY100 ) ) ) )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(147,plain,
! [SV11: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( in @ SY73 @ SV22 )
| ( in @ SY73 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV11: $i,SV22: $i] :
( ( ( ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV22 )
| ( in @ SY74 @ SV11 ) ) )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(149,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) )
| ~ ! [SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ SY84 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY85 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY84 )
| ( in @ SX4 @ SY85 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY85 )
| ( in @ SX4 @ SY84 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(150,plain,
! [SV13: $i] :
( ( ~ ! [SY88: $i] :
( ~ ~ ( ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY88 )
| ( in @ SY46 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY88 ) )
| ~ ! [SY91: $i] :
~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY91 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY92 @ SY88 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY91 )
| ~ ( in @ SX5 @ SY88 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY91 ) )
| ( in @ SY92 @ SY94 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(151,plain,
! [SV14: $i] :
( ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ~ ! [SY53: $i] :
( ~ ~ ( ~ ( in @ SY53 @ omega )
| ~ ( in @ SY53 @ SV14 ) )
| ( in @ ( setadjoin @ SY53 @ SY53 ) @ SV14 ) ) )
= $true )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV15: $i,SV27: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ SV27 ) )
= $true )
| ( ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SY76: $i] : ( SV23 @ SY76 ) ) )
= $true )
| ( ( in @ SV27 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV16: $i,SV1: $i > $i > $o] :
( ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(154,plain,
! [SV16: $i,SV1: $i > $i > $o] :
( ( ( ! [SY97: $i] :
~ ~ ( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY97 )
| ~ ! [SY98: $i] :
( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY98 )
| ( SY97 = SY98 ) ) ) )
= $true )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(155,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) ) )
= $true )
| ( ( ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ( ~ ( ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) ) )
= $true )
| ( ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(157,plain,
! [SV28: $i,SV3: $i > $o] :
( ( ( ~ ( SV3 @ SV28 )
| ~ ! [SY99: $i] :
( ~ ( SV3 @ SY99 )
| ( SV28 = SY99 ) ) )
= $true )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(158,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(159,plain,
! [SV6: $i,SV19: $i] :
( ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $false )
| ( ( ~ ! [SY67: $i] :
~ ~ ( ~ ( in @ SV19 @ SY67 )
| ~ ( in @ SY67 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(160,plain,
! [SV6: $i,SV19: $i] :
( ( ( ~ ! [SY68: $i] :
~ ~ ( ~ ( in @ SV19 @ SY68 )
| ~ ( in @ SY68 @ SV6 ) ) )
= $false )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(161,plain,
! [SV29: $i,SV9: $i] :
( ( ( ! [SY26: $i] :
~ ~ ( ~ ( in @ SY26 @ SV9 )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ( in @ SY27 @ SV9 ) ) ) )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(162,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV30 )
| ~ ! [SY100: $i] :
( ~ ( SV10 @ SY100 )
| ( SV30 = SY100 ) ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(163,plain,
! [SV11: $i,SV22: $i] :
( ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $false )
| ( ( ! [SY73: $i] :
( ~ ( in @ SY73 @ SV22 )
| ( in @ SY73 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(164,plain,
! [SV11: $i,SV22: $i] :
( ( ( ! [SY74: $i] :
( ~ ( in @ SY74 @ SV22 )
| ( in @ SY74 @ SV11 ) ) )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(165,plain,
! [SV13: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) )
| ~ ! [SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ SY84 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY85 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY84 )
| ( in @ SX4 @ SY85 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY85 )
| ( in @ SX4 @ SY84 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(166,plain,
! [SV13: $i] :
( ( ! [SY88: $i] :
( ~ ~ ( ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY88 )
| ( in @ SY46 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY88 ) )
| ~ ! [SY91: $i] :
~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY91 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY92 @ SY88 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY91 )
| ~ ( in @ SX5 @ SY88 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY91 ) )
| ( in @ SY92 @ SY94 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(167,plain,
! [SV14: $i] :
( ( ( ! [SY53: $i] :
( ~ ~ ( ~ ( in @ SY53 @ omega )
| ~ ( in @ SY53 @ SV14 ) )
| ( in @ ( setadjoin @ SY53 @ SY53 ) @ SV14 ) ) )
= $false )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(168,plain,
! [SV15: $i,SV27: $i,SV23: $i > $o] :
( ( ( SV23 @ SV27 )
= $false )
| ( ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SY76: $i] : ( SV23 @ SY76 ) ) )
= $true )
| ( ( in @ SV27 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(169,plain,
! [SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(170,plain,
! [SV31: $i,SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
| ~ ! [SY101: $i] :
( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY101 )
| ( SV31 = SY101 ) ) ) )
= $true )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(171,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
= $false )
| ( ( ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(172,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ( ( SV24 = SV2 )
| ( in @ SV24 @ SV17 ) )
= $false )
| ( ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(173,plain,
! [SV28: $i,SV3: $i > $o] :
( ( ( ~ ( SV3 @ SV28 ) )
= $true )
| ( ( ~ ! [SY99: $i] :
( ~ ( SV3 @ SY99 )
| ( SV28 = SY99 ) ) )
= $true )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(174,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(175,plain,
! [SV6: $i,SV19: $i] :
( ( ( ! [SY67: $i] :
~ ~ ( ~ ( in @ SV19 @ SY67 )
| ~ ( in @ SY67 @ SV6 ) ) )
= $false )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(176,plain,
! [SV6: $i,SV19: $i] :
( ( ( ! [SY68: $i] :
~ ~ ( ~ ( in @ SV19 @ SY68 )
| ~ ( in @ SY68 @ SV6 ) ) )
= $true )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(177,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY26 @ SV29 @ SV9 ) @ SV9 )
| ~ ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY102 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SY102 @ SV9 ) ) ) )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[161]) ).
thf(178,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV30 ) )
= $true )
| ( ( ~ ! [SY100: $i] :
( ~ ( SV10 @ SY100 )
| ( SV30 = SY100 ) ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(179,plain,
! [SV11: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV22 )
| ( in @ SV32 @ SV11 ) )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(180,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 )
| ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV11 ) )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[164]) ).
thf(181,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) )
| ~ ! [SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ SY84 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY85 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY84 )
| ( in @ SX4 @ SY85 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY85 )
| ( in @ SX4 @ SY84 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(182,plain,
! [SV13: $i,SV33: $i] :
( ( ~ ~ ( ~ ! [SY103: $i] :
( ~ ( in @ SY103 @ SV33 )
| ( in @ SY103 @ SV13 ) )
| ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
| ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(183,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY53 @ SV14 ) @ omega )
| ~ ( in @ ( sK8_SY53 @ SV14 ) @ SV14 ) )
| ( in @ ( setadjoin @ ( sK8_SY53 @ SV14 ) @ ( sK8_SY53 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[167]) ).
thf(184,plain,
! [SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ! [SY110: $i] :
~ ( ~ ( ~ ( in @ SY110 @ ( sK9_SY61 @ SV1 @ SV16 ) )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY110 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY110 ) )
| ( in @ SY110 @ ( sK9_SY61 @ SV1 @ SV16 ) ) ) ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[169]) ).
thf(185,plain,
! [SV31: $i,SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
| ~ ! [SY101: $i] :
( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY101 )
| ( SV31 = SY101 ) ) ) )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(186,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ( SV24 = SV2 )
= $true )
| ( ( in @ SV24 @ SV17 )
= $true )
| ( ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(187,plain,
! [SV17: $i,SV2: $i,SV24: $i] :
( ( ( SV24 = SV2 )
= $false )
| ( ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(188,plain,
! [SV2: $i,SV17: $i,SV24: $i] :
( ( ( in @ SV24 @ SV17 )
= $false )
| ( ( in @ SV24 @ ( setadjoin @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(189,plain,
! [SV28: $i,SV3: $i > $o] :
( ( ( SV3 @ SV28 )
= $false )
| ( ( ~ ! [SY99: $i] :
( ~ ( SV3 @ SY99 )
| ( SV28 = SY99 ) ) )
= $true )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(191,plain,
! [SV5: $i,SV18: $i] :
( ( ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(192,plain,
! [SV6: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( in @ SV19 @ ( sK10_SY67 @ SV6 @ SV19 ) )
| ~ ( in @ ( sK10_SY67 @ SV6 @ SV19 ) @ SV6 ) ) )
= $false )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[175]) ).
thf(193,plain,
! [SV6: $i,SV34: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( in @ SV19 @ SV34 )
| ~ ( in @ SV34 @ SV6 ) ) )
= $true )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY26 @ SV29 @ SV9 ) @ SV9 )
| ~ ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY102 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SY102 @ SV9 ) ) ) )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(195,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( SV10 @ SV30 )
= $false )
| ( ( ~ ! [SY100: $i] :
( ~ ( SV10 @ SY100 )
| ( SV30 = SY100 ) ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(196,plain,
! [SV11: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV22 ) )
= $true )
| ( ( in @ SV32 @ SV11 )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(197,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(198,plain,
! [SV22: $i,SV11: $i] :
( ( ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV11 )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(199,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(200,plain,
! [SV13: $i] :
( ( ~ ! [SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ SY84 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY85 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY84 )
| ( in @ SX4 @ SY85 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY85 )
| ( in @ SX4 @ SY84 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(201,plain,
! [SV13: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ! [SY103: $i] :
( ~ ( in @ SY103 @ SV33 )
| ( in @ SY103 @ SV13 ) )
| ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) ) )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(202,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY53 @ SV14 ) @ omega )
| ~ ( in @ ( sK8_SY53 @ SV14 ) @ SV14 ) ) )
= $false )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(203,plain,
! [SV14: $i] :
( ( ( in @ ( setadjoin @ ( sK8_SY53 @ SV14 ) @ ( sK8_SY53 @ SV14 ) ) @ SV14 )
= $false )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(204,plain,
! [SV16: $i,SV1: $i > $i > $o] :
( ( ( ! [SY110: $i] :
~ ( ~ ( ~ ( in @ SY110 @ ( sK9_SY61 @ SV1 @ SV16 ) )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY110 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY110 ) )
| ( in @ SY110 @ ( sK9_SY61 @ SV1 @ SV16 ) ) ) ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(205,plain,
! [SV31: $i,SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
| ~ ! [SY101: $i] :
( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY101 )
| ( SV31 = SY101 ) ) )
= $true )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(206,plain,
! [SV28: $i,SV3: $i > $o] :
( ( ( ! [SY99: $i] :
( ~ ( SV3 @ SY99 )
| ( SV28 = SY99 ) ) )
= $false )
| ( ( SV3 @ SV28 )
= $false )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(207,plain,
! [SV5: $i,SV18: $i] :
( ( ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(208,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
= $false )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(209,plain,
! [SV6: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ ( sK10_SY67 @ SV6 @ SV19 ) )
| ~ ( in @ ( sK10_SY67 @ SV6 @ SV19 ) @ SV6 ) ) )
= $true )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(210,plain,
! [SV6: $i,SV34: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ SV34 )
| ~ ( in @ SV34 @ SV6 ) ) )
= $false )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(211,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ( in @ ( sK6_SY26 @ SV29 @ SV9 ) @ SV9 )
| ~ ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY102 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SY102 @ SV9 ) ) )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(212,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ! [SY100: $i] :
( ~ ( SV10 @ SY100 )
| ( SV30 = SY100 ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(213,plain,
! [SV11: $i,SV22: $i,SV32: $i] :
( ( ( in @ SV32 @ SV22 )
= $false )
| ( ( in @ SV32 @ SV11 )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(214,plain,
! [SV22: $i,SV11: $i] :
( ( ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(215,plain,
! [SV13: $i] :
( ( ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(216,plain,
! [SV13: $i] :
( ( ! [SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ SY84 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY85 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY84 )
| ( in @ SX4 @ SY85 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY85 )
| ( in @ SX4 @ SY84 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(217,plain,
! [SV13: $i,SV33: $i] :
( ( ( ~ ( ~ ! [SY103: $i] :
( ~ ( in @ SY103 @ SV33 )
| ( in @ SY103 @ SV13 ) )
| ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) ) )
= $false )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(218,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY53 @ SV14 ) @ omega )
| ~ ( in @ ( sK8_SY53 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(219,plain,
! [SV14: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ omega )
| ( in @ SV35 @ SV14 ) )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( in @ ( setadjoin @ ( sK8_SY53 @ SV14 ) @ ( sK8_SY53 @ SV14 ) ) @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(220,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
| ~ ! [SY113: $i] :
~ ~ ( ~ ( in @ SY113 @ SV16 )
| ~ ( SV1 @ SY113 @ SV36 ) ) )
| ~ ( ~ ~ ! [SY114: $i] :
~ ~ ( ~ ( in @ SY114 @ SV16 )
| ~ ( SV1 @ SY114 @ SV36 ) )
| ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) ) ) ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV31: $i,SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 ) )
= $true )
| ( ( ~ ! [SY101: $i] :
( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY101 )
| ( SV31 = SY101 ) ) )
= $true )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(222,plain,
! [SV28: $i,SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( sK11_SY99 @ SV28 @ SV3 ) )
| ( SV28
= ( sK11_SY99 @ SV28 @ SV3 ) ) )
= $false )
| ( ( SV3 @ SV28 )
= $false )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[206]) ).
thf(223,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
| ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(225,plain,
! [SV5: $i,SV18: $i] :
( ( ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 )
= $false )
| ( ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
= $false )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(226,plain,
! [SV6: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( sK10_SY67 @ SV6 @ SV19 ) )
| ~ ( in @ ( sK10_SY67 @ SV6 @ SV19 ) @ SV6 ) )
= $false )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(227,plain,
! [SV6: $i,SV34: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV34 )
| ~ ( in @ SV34 @ SV6 ) )
= $true )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(228,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ( in @ ( sK6_SY26 @ SV29 @ SV9 ) @ SV9 ) )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(229,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY102 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SY102 @ SV9 ) ) )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(230,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
| ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[212]) ).
thf(231,plain,
! [SV13: $i] :
( ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(232,plain,
! [SV13: $i,SV37: $i] :
( ( ! [SY115: $i] :
( ~ ~ ( ~ ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY115 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SY116: $i] :
( ~ ( in @ SY116 @ SV37 )
| ( in @ SY116 @ SY115 ) )
| ! [SY117: $i] :
( ~ ( in @ SY117 @ SY115 )
| ( in @ SY117 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(233,plain,
! [SV13: $i,SV33: $i] :
( ( ( ~ ! [SY103: $i] :
( ~ ( in @ SY103 @ SV33 )
| ( in @ SY103 @ SV13 ) )
| ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(234,plain,
! [SV14: $i] :
( ( ( ~ ( in @ ( sK8_SY53 @ SV14 ) @ omega )
| ~ ( in @ ( sK8_SY53 @ SV14 ) @ SV14 ) )
= $false )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(235,plain,
! [SV14: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ omega ) )
= $true )
| ( ( in @ SV35 @ SV14 )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( in @ ( setadjoin @ ( sK8_SY53 @ SV14 ) @ ( sK8_SY53 @ SV14 ) ) @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(236,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( ~ ( ~ ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
| ~ ! [SY113: $i] :
~ ~ ( ~ ( in @ SY113 @ SV16 )
| ~ ( SV1 @ SY113 @ SV36 ) ) )
| ~ ( ~ ~ ! [SY114: $i] :
~ ~ ( ~ ( in @ SY114 @ SV16 )
| ~ ( SV1 @ SY114 @ SV36 ) )
| ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(237,plain,
! [SV31: $i,SV16: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( ~ ! [SY101: $i] :
( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY101 )
| ( SV31 = SY101 ) ) )
= $true )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(238,plain,
! [SV28: $i,SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( sK11_SY99 @ SV28 @ SV3 ) ) )
= $false )
| ( ( SV3 @ SV28 )
= $false )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(239,plain,
! [SV3: $i > $o,SV28: $i] :
( ( ( SV28
= ( sK11_SY99 @ SV28 @ SV3 ) )
= $false )
| ( ( SV3 @ SV28 )
= $false )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(240,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 ) )
= $false )
| ( ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(243,plain,
! [SV6: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( sK10_SY67 @ SV6 @ SV19 ) ) )
= $false )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(244,plain,
! [SV19: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK10_SY67 @ SV6 @ SV19 ) @ SV6 ) )
= $false )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(245,plain,
! [SV6: $i,SV34: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV34 ) )
= $true )
| ( ( ~ ( in @ SV34 @ SV6 ) )
= $true )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(246,plain,
! [SV9: $i,SV29: $i] :
( ( ( in @ ( sK6_SY26 @ SV29 @ SV9 ) @ SV9 )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(247,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY102 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SY102 @ SV9 ) ) )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(248,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(249,plain,
! [SV10: $i > $o,SV30: $i] :
( ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(250,plain,
! [SV13: $i] :
( ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(251,plain,
! [SV13: $i] :
( ( ~ ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(252,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ~ ~ ( ~ ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SV38 @ ( sK3_SY35 @ SV13 ) ) )
| ! [SY118: $i] :
( ~ ( in @ SY118 @ SV37 )
| ( in @ SY118 @ SV38 ) )
| ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(253,plain,
! [SV13: $i,SV33: $i] :
( ( ( ~ ! [SY103: $i] :
( ~ ( in @ SY103 @ SV33 )
| ( in @ SY103 @ SV13 ) ) )
= $true )
| ( ( ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(254,plain,
! [SV14: $i] :
( ( ( ~ ( in @ ( sK8_SY53 @ SV14 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(255,plain,
! [SV14: $i] :
( ( ( ~ ( in @ ( sK8_SY53 @ SV14 ) @ SV14 ) )
= $false )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(256,plain,
! [SV14: $i,SV35: $i] :
( ( ( in @ SV35 @ omega )
= $false )
| ( ( in @ SV35 @ SV14 )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( in @ ( setadjoin @ ( sK8_SY53 @ SV14 ) @ ( sK8_SY53 @ SV14 ) ) @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(257,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( ~ ( ~ ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
| ~ ! [SY113: $i] :
~ ~ ( ~ ( in @ SY113 @ SV16 )
| ~ ( SV1 @ SY113 @ SV36 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(258,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ( ~ ( in @ SY114 @ SV16 )
| ~ ( SV1 @ SY114 @ SV36 ) )
| ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(259,plain,
! [SV31: $i,SV16: $i,SV1: $i > $i > $o] :
( ( ( ! [SY101: $i] :
( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SY101 )
| ( SV31 = SY101 ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(260,plain,
! [SV28: $i,SV3: $i > $o] :
( ( ( SV3 @ ( sK11_SY99 @ SV28 @ SV3 ) )
= $true )
| ( ( SV3 @ SV28 )
= $false )
| ( ( SV3
@ ( descr
@ ^ [SY13: $i] : ( SV3 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(261,plain,
! [SV5: $i,SV18: $i] :
( ( ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV18 )
= $true )
| ( ( in @ ( sK5_SY66 @ SV18 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(262,plain,
! [SV6: $i,SV19: $i] :
( ( ( in @ SV19 @ ( sK10_SY67 @ SV6 @ SV19 ) )
= $true )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(263,plain,
! [SV19: $i,SV6: $i] :
( ( ( in @ ( sK10_SY67 @ SV6 @ SV19 ) @ SV6 )
= $true )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(264,plain,
! [SV6: $i,SV34: $i,SV19: $i] :
( ( ( in @ SV19 @ SV34 )
= $false )
| ( ( ~ ( in @ SV34 @ SV6 ) )
= $true )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(265,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY102 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SY102 @ SV9 ) ) )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(266,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(267,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(268,plain,
! [SV13: $i] :
( ( ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK3_SY35 @ SV13 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SY79 )
| ( in @ SY37 @ SV13 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(269,plain,
! [SV13: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ SY81 @ SV13 )
| ~ ( in @ SY82 @ SV13 ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY81 @ SY83 )
| ( in @ SY82 @ SY83 ) )
| ~ ( ~ ( in @ SY82 @ SY83 )
| ( in @ SY81 @ SY83 ) ) ) )
| ( SY81 = SY82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(270,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SV38 @ ( sK3_SY35 @ SV13 ) ) ) )
= $true )
| ( ( ! [SY118: $i] :
( ~ ( in @ SY118 @ SV37 )
| ( in @ SY118 @ SV38 ) )
| ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(271,plain,
! [SV13: $i,SV33: $i] :
( ( ( ! [SY103: $i] :
( ~ ( in @ SY103 @ SV33 )
| ( in @ SY103 @ SV13 ) ) )
= $false )
| ( ( ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(272,plain,
! [SV14: $i] :
( ( ( in @ ( sK8_SY53 @ SV14 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(273,plain,
! [SV14: $i] :
( ( ( in @ ( sK8_SY53 @ SV14 ) @ SV14 )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ omega )
| ( in @ SY54 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(274,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( ~ ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
| ~ ! [SY113: $i] :
~ ~ ( ~ ( in @ SY113 @ SV16 )
| ~ ( SV1 @ SY113 @ SV36 ) ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(275,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ~ ! [SY114: $i] :
~ ~ ( ~ ( in @ SY114 @ SV16 )
| ~ ( SV1 @ SY114 @ SV36 ) )
| ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(276,plain,
! [SV31: $i,SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
| ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[259]) ).
thf(277,plain,
! [SV19: $i,SV6: $i,SV34: $i] :
( ( ( in @ SV34 @ SV6 )
= $false )
| ( ( in @ SV19 @ SV34 )
= $false )
| ( ( in @ SV19 @ ( setunion @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(278,plain,
! [SV9: $i,SV29: $i] :
( ( ( ! [SY102: $i] :
~ ~ ( ~ ( in @ SY102 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SY102 @ SV9 ) ) )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(279,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ! [SY30: $i] :
~ ~ ( ~ ( SV10 @ SY30 )
| ~ ! [SY31: $i] :
( ~ ( SV10 @ SY31 )
| ( SY30 = SY31 ) ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(280,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK14_SY30 @ SV30 @ SV10 ) )
| ~ ! [SY120: $i] :
( ~ ( SV10 @ SY120 )
| ( ( sK14_SY30 @ SV30 @ SV10 )
= SY120 ) ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[267]) ).
thf(281,plain,
! [SV13: $i,SV39: $i] :
( ( ~ ( in @ SV39 @ ( sK3_SY35 @ SV13 ) )
| ! [SY121: $i] :
( ~ ( in @ SY121 @ SV39 )
| ( in @ SY121 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(282,plain,
! [SV13: $i,SV40: $i] :
( ( ! [SY122: $i] :
( ~ ~ ( ~ ( in @ SV40 @ SV13 )
| ~ ( in @ SY122 @ SV13 ) )
| ~ ! [SY123: $i] :
( ~ ( in @ SY123 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY123 )
| ( in @ SY122 @ SY123 ) )
| ~ ( ~ ( in @ SY122 @ SY123 )
| ( in @ SV40 @ SY123 ) ) ) )
| ( SV40 = SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(283,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( ~ ( ~ ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SV38 @ ( sK3_SY35 @ SV13 ) ) ) )
= $false )
| ( ( ! [SY118: $i] :
( ~ ( in @ SY118 @ SV37 )
| ( in @ SY118 @ SV38 ) )
| ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(284,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
| ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 ) )
= $false )
| ( ( ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[271]) ).
thf(285,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ omega )
| ( in @ SV41 @ SV14 ) )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( in @ ( sK8_SY53 @ SV14 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(286,plain,
! [SV14: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ omega )
| ( in @ SV42 @ SV14 ) )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( in @ ( sK8_SY53 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(287,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( ~ ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY113: $i] :
~ ~ ( ~ ( in @ SY113 @ SV16 )
| ~ ( SV1 @ SY113 @ SV36 ) ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(288,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ~ ! [SY114: $i] :
~ ~ ( ~ ( in @ SY114 @ SV16 )
| ~ ( SV1 @ SY114 @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(289,plain,
! [SV31: $i,SV16: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(290,plain,
! [SV1: $i > $i > $o,SV16: $i,SV31: $i] :
( ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(291,plain,
! [SV9: $i,SV29: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ SV43 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SV43 @ SV9 ) ) )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(292,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK16_SY30 @ SV30 @ SV10 ) )
| ~ ! [SY124: $i] :
( ~ ( SV10 @ SY124 )
| ( ( sK16_SY30 @ SV30 @ SV10 )
= SY124 ) ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[279]) ).
thf(293,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK14_SY30 @ SV30 @ SV10 ) )
| ~ ! [SY120: $i] :
( ~ ( SV10 @ SY120 )
| ( ( sK14_SY30 @ SV30 @ SV10 )
= SY120 ) ) ) )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(294,plain,
! [SV13: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( sK3_SY35 @ SV13 ) ) )
= $true )
| ( ( ! [SY121: $i] :
( ~ ( in @ SY121 @ SV39 )
| ( in @ SY121 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(295,plain,
! [SV44: $i,SV13: $i,SV40: $i] :
( ( ~ ~ ( ~ ( in @ SV40 @ SV13 )
| ~ ( in @ SV44 @ SV13 ) )
| ~ ! [SY125: $i] :
( ~ ( in @ SY125 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY125 )
| ( in @ SV44 @ SY125 ) )
| ~ ( ~ ( in @ SV44 @ SY125 )
| ( in @ SV40 @ SY125 ) ) ) )
| ( SV40 = SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(296,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SV38 @ ( sK3_SY35 @ SV13 ) ) )
= $true )
| ( ( ! [SY118: $i] :
( ~ ( in @ SY118 @ SV37 )
| ( in @ SY118 @ SV38 ) )
| ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(297,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 ) )
= $false )
| ( ( ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(298,plain,
! [SV33: $i,SV13: $i] :
( ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(299,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ omega ) )
= $true )
| ( ( in @ SV41 @ SV14 )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( in @ ( sK8_SY53 @ SV14 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(300,plain,
! [SV14: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ omega ) )
= $true )
| ( ( in @ SV42 @ SV14 )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( in @ ( sK8_SY53 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(301,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $false )
| ( ( ~ ! [SY113: $i] :
~ ~ ( ~ ( in @ SY113 @ SV16 )
| ~ ( SV1 @ SY113 @ SV36 ) ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(302,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ! [SY114: $i] :
~ ~ ( ~ ( in @ SY114 @ SV16 )
| ~ ( SV1 @ SY114 @ SV36 ) ) )
= $false )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(303,plain,
! [SV31: $i,SV16: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(304,plain,
! [SV31: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(305,plain,
! [SV9: $i,SV29: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SV43 @ SV9 ) ) )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(306,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK16_SY30 @ SV30 @ SV10 ) )
| ~ ! [SY124: $i] :
( ~ ( SV10 @ SY124 )
| ( ( sK16_SY30 @ SV30 @ SV10 )
= SY124 ) ) ) )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(307,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK14_SY30 @ SV30 @ SV10 ) )
| ~ ! [SY120: $i] :
( ~ ( SV10 @ SY120 )
| ( ( sK14_SY30 @ SV30 @ SV10 )
= SY120 ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(308,plain,
! [SV13: $i,SV39: $i] :
( ( ( in @ SV39 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( ! [SY121: $i] :
( ~ ( in @ SY121 @ SV39 )
| ( in @ SY121 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(309,plain,
! [SV44: $i,SV13: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ( in @ SV40 @ SV13 )
| ~ ( in @ SV44 @ SV13 ) ) )
= $true )
| ( ( ~ ! [SY125: $i] :
( ~ ( in @ SY125 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY125 )
| ( in @ SV44 @ SY125 ) )
| ~ ( ~ ( in @ SV44 @ SY125 )
| ( in @ SV40 @ SY125 ) ) ) )
| ( SV40 = SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(310,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ ( sK3_SY35 @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV38 @ ( sK3_SY35 @ SV13 ) ) )
= $true )
| ( ( ! [SY118: $i] :
( ~ ( in @ SY118 @ SV37 )
| ( in @ SY118 @ SV38 ) )
| ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(311,plain,
! [SV33: $i,SV13: $i] :
( ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( ~ ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(312,plain,
! [SV13: $i,SV33: $i] :
( ( ( ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(313,plain,
! [SV14: $i,SV41: $i] :
( ( ( in @ SV41 @ omega )
= $false )
| ( ( in @ SV41 @ SV14 )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( in @ ( sK8_SY53 @ SV14 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(314,plain,
! [SV14: $i,SV42: $i] :
( ( ( in @ SV42 @ omega )
= $false )
| ( ( in @ SV42 @ SV14 )
= $true )
| ( ( in @ emptyset @ SV14 )
= $false )
| ( ( in @ ( sK8_SY53 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(315,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY113: $i] :
~ ~ ( ~ ( in @ SY113 @ SV16 )
| ~ ( SV1 @ SY113 @ SV36 ) ) )
= $false )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(316,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY114: $i] :
~ ~ ( ~ ( in @ SY114 @ SV16 )
| ~ ( SV1 @ SY114 @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(317,plain,
! [SV31: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY62 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY62 ) )
| ( in @ SY62 @ SY61 ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(318,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i] :
( ( ( ~ ! [SY126: $i] :
~ ( ~ ( ~ ( in @ SY126 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY126 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY126 ) )
| ( in @ SY126 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[304]) ).
thf(319,plain,
! [SV9: $i,SV29: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( sK6_SY26 @ SV29 @ SV9 ) )
| ~ ( in @ SV43 @ SV9 ) )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(320,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK16_SY30 @ SV30 @ SV10 ) )
| ~ ! [SY124: $i] :
( ~ ( SV10 @ SY124 )
| ( ( sK16_SY30 @ SV30 @ SV10 )
= SY124 ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(321,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK14_SY30 @ SV30 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(322,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ! [SY120: $i] :
( ~ ( SV10 @ SY120 )
| ( ( sK14_SY30 @ SV30 @ SV10 )
= SY120 ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(323,plain,
! [SV13: $i,SV39: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV39 )
| ( in @ SV45 @ SV13 ) )
= $true )
| ( ( in @ SV39 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(324,plain,
! [SV44: $i,SV13: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ SV40 @ SV13 )
| ~ ( in @ SV44 @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY125: $i] :
( ~ ( in @ SY125 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY125 )
| ( in @ SV44 @ SY125 ) )
| ~ ( ~ ( in @ SV44 @ SY125 )
| ( in @ SV40 @ SY125 ) ) ) )
| ( SV40 = SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(325,plain,
! [SV38: $i,SV13: $i,SV37: $i] :
( ( ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV38 @ ( sK3_SY35 @ SV13 ) ) )
= $true )
| ( ( ! [SY118: $i] :
( ~ ( in @ SY118 @ SV37 )
| ( in @ SY118 @ SV38 ) )
| ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(326,plain,
! [SV13: $i,SV33: $i] :
( ( ( ~ ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(327,plain,
! [SV13: $i,SV33: $i] :
( ( ( ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(328,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV16 )
| ~ ( SV1 @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV36 ) ) )
= $false )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[315]) ).
thf(329,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( in @ SV46 @ SV16 )
| ~ ( SV1 @ SV46 @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(330,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i] :
( ( ( ~ ! [SY129: $i] :
~ ( ~ ( ~ ( in @ SY129 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY129 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY129 ) )
| ( in @ SY129 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[317]) ).
thf(331,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i] :
( ( ( ! [SY126: $i] :
~ ( ~ ( ~ ( in @ SY126 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY126 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY126 ) )
| ( in @ SY126 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) ) ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(332,plain,
! [SV9: $i,SV29: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( sK6_SY26 @ SV29 @ SV9 ) ) )
= $true )
| ( ( ~ ( in @ SV43 @ SV9 ) )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(333,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK16_SY30 @ SV30 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(334,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ~ ! [SY124: $i] :
( ~ ( SV10 @ SY124 )
| ( ( sK16_SY30 @ SV30 @ SV10 )
= SY124 ) ) )
= $false )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(335,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK14_SY30 @ SV30 @ SV10 ) )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(336,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ! [SY120: $i] :
( ~ ( SV10 @ SY120 )
| ( ( sK14_SY30 @ SV30 @ SV10 )
= SY120 ) ) )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(337,plain,
! [SV13: $i,SV39: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV39 ) )
= $true )
| ( ( in @ SV45 @ SV13 )
= $true )
| ( ( in @ SV39 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(338,plain,
! [SV44: $i,SV13: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV13 )
| ~ ( in @ SV44 @ SV13 ) )
= $true )
| ( ( ~ ! [SY125: $i] :
( ~ ( in @ SY125 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY125 )
| ( in @ SV44 @ SY125 ) )
| ~ ( ~ ( in @ SV44 @ SY125 )
| ( in @ SV40 @ SY125 ) ) ) )
| ( SV40 = SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(339,plain,
! [SV37: $i,SV13: $i,SV38: $i] :
( ( ( in @ SV38 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( ! [SY118: $i] :
( ~ ( in @ SY118 @ SV37 )
| ( in @ SY118 @ SV38 ) )
| ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(340,plain,
! [SV13: $i,SV33: $i] :
( ( ( ! [SY104: $i] :
~ ( in @ SY104 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(341,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(342,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV16 )
| ~ ( SV1 @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(343,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i,SV46: $i] :
( ( ( ~ ( ~ ( in @ SV46 @ SV16 )
| ~ ( SV1 @ SV46 @ SV36 ) ) )
= $false )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(344,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i] :
( ( ( ! [SY129: $i] :
~ ( ~ ( ~ ( in @ SY129 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( in @ SY63 @ SV16 )
| ~ ( SV1 @ SY63 @ SY129 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( in @ SY64 @ SV16 )
| ~ ( SV1 @ SY64 @ SY129 ) )
| ( in @ SY129 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) ) ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(345,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV48: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV16 )
| ~ ( SV1 @ SY132 @ SV48 ) ) )
| ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( in @ SY133 @ SV16 )
| ~ ( SV1 @ SY133 @ SV48 ) )
| ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) ) ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(346,plain,
! [SV9: $i,SV29: $i,SV43: $i] :
( ( ( in @ SV43 @ ( sK6_SY26 @ SV29 @ SV9 ) )
= $false )
| ( ( ~ ( in @ SV43 @ SV9 ) )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(347,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK16_SY30 @ SV30 @ SV10 ) )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(348,plain,
! [SV30: $i,SV10: $i > $o] :
( ( ( ! [SY124: $i] :
( ~ ( SV10 @ SY124 )
| ( ( sK16_SY30 @ SV30 @ SV10 )
= SY124 ) ) )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(349,plain,
! [SV30: $i,SV49: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV49 )
| ( ( sK14_SY30 @ SV30 @ SV10 )
= SV49 ) )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(350,plain,
! [SV13: $i,SV39: $i,SV45: $i] :
( ( ( in @ SV45 @ SV39 )
= $false )
| ( ( in @ SV45 @ SV13 )
= $true )
| ( ( in @ SV39 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(351,plain,
! [SV44: $i,SV13: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV13 ) )
= $true )
| ( ( ~ ( in @ SV44 @ SV13 ) )
= $true )
| ( ( ~ ! [SY125: $i] :
( ~ ( in @ SY125 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY125 )
| ( in @ SV44 @ SY125 ) )
| ~ ( ~ ( in @ SV44 @ SY125 )
| ( in @ SV40 @ SY125 ) ) ) )
| ( SV40 = SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(352,plain,
! [SV13: $i,SV38: $i,SV37: $i] :
( ( ( ! [SY118: $i] :
( ~ ( in @ SY118 @ SV37 )
| ( in @ SY118 @ SV38 ) ) )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(353,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(354,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( in @ SV47 @ SV33 )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(355,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( ~ ( in @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV16 )
| ~ ( SV1 @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV36 ) )
= $false )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(356,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV16 )
| ~ ( SV1 @ SV46 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(357,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV51: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ( in @ SY134 @ SV16 )
| ~ ( SV1 @ SY134 @ SV51 ) ) )
| ~ ( ~ ~ ! [SY135: $i] :
~ ~ ( ~ ( in @ SY135 @ SV16 )
| ~ ( SV1 @ SY135 @ SV51 ) )
| ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) ) ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(358,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV48: $i] :
( ( ( ~ ( ~ ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV16 )
| ~ ( SV1 @ SY132 @ SV48 ) ) )
| ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( in @ SY133 @ SV16 )
| ~ ( SV1 @ SY133 @ SV48 ) )
| ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(359,plain,
! [SV29: $i,SV9: $i,SV43: $i] :
( ( ( in @ SV43 @ SV9 )
= $false )
| ( ( in @ SV43 @ ( sK6_SY26 @ SV29 @ SV9 ) )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(360,plain,
! [SV30: $i,SV52: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV52 )
| ( ( sK16_SY30 @ SV30 @ SV10 )
= SV52 ) )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(361,plain,
! [SV30: $i,SV49: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV49 ) )
= $true )
| ( ( ( sK14_SY30 @ SV30 @ SV10 )
= SV49 )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(362,plain,
! [SV44: $i,SV13: $i,SV40: $i] :
( ( ( in @ SV40 @ SV13 )
= $false )
| ( ( ~ ( in @ SV44 @ SV13 ) )
= $true )
| ( ( ~ ! [SY125: $i] :
( ~ ( in @ SY125 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY125 )
| ( in @ SV44 @ SY125 ) )
| ~ ( ~ ( in @ SV44 @ SY125 )
| ( in @ SV40 @ SY125 ) ) ) )
| ( SV40 = SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(363,plain,
! [SV13: $i,SV38: $i,SV37: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV37 )
| ( in @ SV53 @ SV38 ) )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(364,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( in @ SV50 @ SV33 )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( ~ ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(365,plain,
! [SV47: $i,SV33: $i,SV13: $i] :
( ( ( ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(366,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( ~ ( in @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV16 ) )
= $false )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(367,plain,
! [SV16: $i,SV36: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV36 ) )
= $false )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(368,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV16 ) )
= $true )
| ( ( ~ ( SV1 @ SV46 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(369,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV51: $i] :
( ( ( ~ ( ~ ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ( in @ SY134 @ SV16 )
| ~ ( SV1 @ SY134 @ SV51 ) ) )
| ~ ( ~ ~ ! [SY135: $i] :
~ ~ ( ~ ( in @ SY135 @ SV16 )
| ~ ( SV1 @ SY135 @ SV51 ) )
| ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(370,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV48: $i] :
( ( ( ~ ( ~ ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV16 )
| ~ ( SV1 @ SY132 @ SV48 ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(371,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( in @ SY133 @ SV16 )
| ~ ( SV1 @ SY133 @ SV48 ) )
| ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(372,plain,
! [SV30: $i,SV52: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV52 ) )
= $true )
| ( ( ( sK16_SY30 @ SV30 @ SV10 )
= SV52 )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(373,plain,
! [SV30: $i,SV49: $i,SV10: $i > $o] :
( ( ( SV10 @ SV49 )
= $false )
| ( ( ( sK14_SY30 @ SV30 @ SV10 )
= SV49 )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(374,plain,
! [SV40: $i,SV13: $i,SV44: $i] :
( ( ( in @ SV44 @ SV13 )
= $false )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( ~ ! [SY125: $i] :
( ~ ( in @ SY125 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY125 )
| ( in @ SV44 @ SY125 ) )
| ~ ( ~ ( in @ SV44 @ SY125 )
| ( in @ SV40 @ SY125 ) ) ) )
| ( SV40 = SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(375,plain,
! [SV13: $i,SV38: $i,SV37: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV37 ) )
= $true )
| ( ( in @ SV53 @ SV38 )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(376,plain,
! [SV50: $i,SV33: $i,SV13: $i] :
( ( ( ! [SY105: $i] :
~ ~ ! [SY106: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY105 @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY106 @ SV33 ) )
| ~ ~ ~ ! [SY107: $i] :
~ ~ ( ~ ( in @ SY107 @ SY105 )
| ~ ( in @ SY107 @ SV33 ) ) )
| ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( sK3_SY35 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY94 )
| ( in @ SX6 @ SY105 ) )
| ( in @ SY106 @ SY94 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(377,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY136 @ SV33 ) )
| ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
| ~ ! [SY138: $i] :
( ~ ( in @ SY138 @ ( sK3_SY35 @ SV13 ) )
| ! [SY139: $i] :
( ~ ( in @ SY139 @ SY138 )
| ( in @ SY139 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ SY136 @ SY138 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[365]) ).
thf(378,plain,
! [SV16: $i,SV1: $i > $i > $o,SV36: $i] :
( ( ( in @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV16 )
= $true )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(379,plain,
! [SV16: $i,SV36: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK18_SY113 @ SV36 @ SV1 @ SV16 ) @ SV36 )
= $true )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $false )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(380,plain,
! [SV36: $i,SV1: $i > $i > $o,SV16: $i,SV46: $i] :
( ( ( in @ SV46 @ SV16 )
= $false )
| ( ( ~ ( SV1 @ SV46 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(381,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV51: $i] :
( ( ( ~ ( ~ ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ( in @ SY134 @ SV16 )
| ~ ( SV1 @ SY134 @ SV51 ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(382,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY135: $i] :
~ ~ ( ~ ( in @ SY135 @ SV16 )
| ~ ( SV1 @ SY135 @ SV51 ) )
| ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) ) ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(383,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV16 )
| ~ ( SV1 @ SY132 @ SV48 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(384,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( in @ SY133 @ SV16 )
| ~ ( SV1 @ SY133 @ SV48 ) )
| ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(385,plain,
! [SV30: $i,SV52: $i,SV10: $i > $o] :
( ( ( SV10 @ SV52 )
= $false )
| ( ( ( sK16_SY30 @ SV30 @ SV10 )
= SV52 )
= $true )
| ( ( SV10 @ SV30 )
= $false )
| ( ( SV10 @ ( sK12_SY100 @ SV30 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(386,plain,
! [SV44: $i,SV40: $i,SV13: $i] :
( ( ( ~ ! [SY125: $i] :
( ~ ( in @ SY125 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY125 )
| ( in @ SV44 @ SY125 ) )
| ~ ( ~ ( in @ SV44 @ SY125 )
| ( in @ SV40 @ SY125 ) ) ) ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(387,plain,
! [SV13: $i,SV38: $i,SV37: $i,SV53: $i] :
( ( ( in @ SV53 @ SV37 )
= $false )
| ( ( in @ SV53 @ SV38 )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ SV38 )
| ( in @ SY119 @ SV37 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(388,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ~ ! [SY140: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY140 @ SV33 ) )
| ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
| ~ ! [SY142: $i] :
( ~ ( in @ SY142 @ ( sK3_SY35 @ SV13 ) )
| ! [SY143: $i] :
( ~ ( in @ SY143 @ SY142 )
| ( in @ SY143 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ SY140 @ SY142 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[376]) ).
thf(389,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ! [SY136: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY136 @ SV33 ) )
| ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
| ~ ! [SY138: $i] :
( ~ ( in @ SY138 @ ( sK3_SY35 @ SV13 ) )
| ! [SY139: $i] :
( ~ ( in @ SY139 @ SY138 )
| ( in @ SY139 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ SY136 @ SY138 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(390,plain,
! [SV16: $i,SV36: $i,SV46: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ SV46 @ SV36 )
= $false )
| ( ( in @ SV46 @ SV16 )
= $false )
| ( ( in @ SV36 @ ( sK9_SY61 @ SV1 @ SV16 ) )
= $true )
| ( ( in @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(391,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ( in @ SY134 @ SV16 )
| ~ ( SV1 @ SY134 @ SV51 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(392,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ~ ! [SY135: $i] :
~ ~ ( ~ ( in @ SY135 @ SV16 )
| ~ ( SV1 @ SY135 @ SV51 ) )
| ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(393,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV16 )
| ~ ( SV1 @ SY132 @ SV48 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(394,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ( in @ SY133 @ SV16 )
| ~ ( SV1 @ SY133 @ SV48 ) ) )
= $true )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(395,plain,
! [SV44: $i,SV40: $i,SV13: $i] :
( ( ( ! [SY125: $i] :
( ~ ( in @ SY125 @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ SY125 )
| ( in @ SV44 @ SY125 ) )
| ~ ( ~ ( in @ SV44 @ SY125 )
| ( in @ SV40 @ SY125 ) ) ) ) )
= $false )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(396,plain,
! [SV13: $i,SV53: $i,SV37: $i,SV38: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV38 )
| ( in @ SV54 @ SV37 ) )
= $true )
| ( ( in @ SV53 @ SV38 )
= $true )
| ( ( in @ SV53 @ SV37 )
= $false )
| ( ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(397,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ! [SY140: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY140 @ SV33 ) )
| ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
| ~ ! [SY142: $i] :
( ~ ( in @ SY142 @ ( sK3_SY35 @ SV13 ) )
| ! [SY143: $i] :
( ~ ( in @ SY143 @ SY142 )
| ( in @ SY143 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ SY140 @ SY142 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(398,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ! [SY136: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY136 @ SV33 ) )
| ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
| ~ ! [SY138: $i] :
( ~ ( in @ SY138 @ ( sK3_SY35 @ SV13 ) )
| ! [SY139: $i] :
( ~ ( in @ SY139 @ SY138 )
| ( in @ SY139 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ SY136 @ SY138 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(399,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY134: $i] :
~ ~ ( ~ ( in @ SY134 @ SV16 )
| ~ ( SV1 @ SY134 @ SV51 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(400,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ~ ! [SY135: $i] :
~ ~ ( ~ ( in @ SY135 @ SV16 )
| ~ ( SV1 @ SY135 @ SV51 ) ) )
= $true )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(401,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV48: $i] :
( ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV16 )
| ~ ( SV1 @ SY132 @ SV48 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(402,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ! [SY133: $i] :
~ ~ ( ~ ( in @ SY133 @ SV16 )
| ~ ( SV1 @ SY133 @ SV48 ) ) )
= $false )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(403,plain,
! [SV13: $i,SV40: $i,SV44: $i] :
( ( ( ~ ( in @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) )
| ~ ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) ) ) )
= $false )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[395]) ).
thf(404,plain,
! [SV13: $i,SV53: $i,SV37: $i,SV38: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV38 ) )
= $true )
| ( ( in @ SV54 @ SV37 )
= $true )
| ( ( in @ SV53 @ SV38 )
= $true )
| ( ( in @ SV53 @ SV37 )
= $false )
| ( ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(405,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ! [SY140: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ SY140 @ SV33 ) )
| ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
| ~ ! [SY142: $i] :
( ~ ( in @ SY142 @ ( sK3_SY35 @ SV13 ) )
| ! [SY143: $i] :
( ~ ( in @ SY143 @ SY142 )
| ( in @ SY143 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ SY140 @ SY142 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(406,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) )
| ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
| ~ ! [SY145: $i] :
( ~ ( in @ SY145 @ ( sK3_SY35 @ SV13 ) )
| ! [SY139: $i] :
( ~ ( in @ SY139 @ SY145 )
| ( in @ SY139 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SY145 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[398]) ).
thf(407,plain,
! [SV16: $i,SV1: $i > $i > $o,SV31: $i,SV51: $i] :
( ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( ~ ! [SY134: $i] :
~ ~ ( ~ ( in @ SY134 @ SV16 )
| ~ ( SV1 @ SY134 @ SV51 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(408,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ~ ! [SY135: $i] :
~ ~ ( ~ ( in @ SY135 @ SV16 )
| ~ ( SV1 @ SY135 @ SV51 ) ) )
= $false )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(409,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV16 )
| ~ ( SV1 @ SY132 @ SV48 ) ) )
= $false )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(410,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY133: $i] :
~ ~ ( ~ ( in @ SY133 @ SV16 )
| ~ ( SV1 @ SY133 @ SV48 ) ) )
= $true )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(411,plain,
! [SV13: $i,SV40: $i,SV44: $i] :
( ( ( ~ ( in @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) @ ( sK3_SY35 @ SV13 ) ) )
= $false )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(412,plain,
! [SV13: $i,SV44: $i,SV40: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) )
| ~ ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) ) ) )
= $false )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(413,plain,
! [SV13: $i,SV53: $i,SV37: $i,SV38: $i,SV54: $i] :
( ( ( in @ SV54 @ SV38 )
= $false )
| ( ( in @ SV54 @ SV37 )
= $true )
| ( ( in @ SV53 @ SV38 )
= $true )
| ( ( in @ SV53 @ SV37 )
= $false )
| ( ( in @ SV37 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ SV38 @ ( sK3_SY35 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(414,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) )
| ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
| ~ ! [SY148: $i] :
( ~ ( in @ SY148 @ ( sK3_SY35 @ SV13 ) )
| ! [SY143: $i] :
( ~ ( in @ SY143 @ SY148 )
| ( in @ SY143 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SY148 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[405]) ).
thf(415,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) )
| ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
| ~ ! [SY145: $i] :
( ~ ( in @ SY145 @ ( sK3_SY35 @ SV13 ) )
| ! [SY139: $i] :
( ~ ( in @ SY139 @ SY145 )
| ( in @ SY139 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SY145 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(416,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY134: $i] :
~ ~ ( ~ ( in @ SY134 @ SV16 )
| ~ ( SV1 @ SY134 @ SV51 ) ) )
= $false )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(417,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i] :
( ( ( ! [SY135: $i] :
~ ~ ( ~ ( in @ SY135 @ SV16 )
| ~ ( SV1 @ SY135 @ SV51 ) ) )
= $true )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(418,plain,
! [SV16: $i,SV1: $i > $i > $o,SV48: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV16 )
| ~ ( SV1 @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV48 ) ) )
= $false )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[409]) ).
thf(419,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( in @ SV55 @ SV16 )
| ~ ( SV1 @ SV55 @ SV48 ) ) )
= $true )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(420,plain,
! [SV13: $i,SV40: $i,SV44: $i] :
( ( ( in @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(421,plain,
! [SV13: $i,SV44: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) )
| ~ ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(422,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) )
| ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
| ~ ! [SY148: $i] :
( ~ ( in @ SY148 @ ( sK3_SY35 @ SV13 ) )
| ! [SY143: $i] :
( ~ ( in @ SY143 @ SY148 )
| ( in @ SY143 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SY148 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(423,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) )
| ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
| ~ ! [SY145: $i] :
( ~ ( in @ SY145 @ ( sK3_SY35 @ SV13 ) )
| ! [SY139: $i] :
( ~ ( in @ SY139 @ SY145 )
| ( in @ SY139 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SY145 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(424,plain,
! [SV16: $i,SV1: $i > $i > $o,SV51: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV16 )
| ~ ( SV1 @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV51 ) ) )
= $false )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[416]) ).
thf(425,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( in @ SV56 @ SV16 )
| ~ ( SV1 @ SV56 @ SV51 ) ) )
= $true )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(426,plain,
! [SV16: $i,SV1: $i > $i > $o,SV48: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV16 )
| ~ ( SV1 @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV48 ) ) )
= $true )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(427,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ SV55 @ SV16 )
| ~ ( SV1 @ SV55 @ SV48 ) ) )
= $false )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(428,plain,
! [SV13: $i,SV44: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(429,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) )
| ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
| ~ ! [SY148: $i] :
( ~ ( in @ SY148 @ ( sK3_SY35 @ SV13 ) )
| ! [SY143: $i] :
( ~ ( in @ SY143 @ SY148 )
| ( in @ SY143 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SY148 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(430,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) )
| ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(431,plain,
! [SV33: $i,SV47: $i,SV13: $i] :
( ( ( ~ ! [SY145: $i] :
( ~ ( in @ SY145 @ ( sK3_SY35 @ SV13 ) )
| ! [SY139: $i] :
( ~ ( in @ SY139 @ SY145 )
| ( in @ SY139 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SY145 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(432,plain,
! [SV16: $i,SV1: $i > $i > $o,SV51: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV16 )
| ~ ( SV1 @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV51 ) ) )
= $true )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(433,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i,SV56: $i] :
( ( ( ~ ( ~ ( in @ SV56 @ SV16 )
| ~ ( SV1 @ SV56 @ SV51 ) ) )
= $false )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(434,plain,
! [SV16: $i,SV1: $i > $i > $o,SV48: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV16 )
| ~ ( SV1 @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV48 ) )
= $false )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(435,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV16 )
| ~ ( SV1 @ SV55 @ SV48 ) )
= $true )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(436,plain,
! [SV13: $i,SV44: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(437,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) )
| ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(438,plain,
! [SV33: $i,SV50: $i,SV13: $i] :
( ( ( ~ ! [SY148: $i] :
( ~ ( in @ SY148 @ ( sK3_SY35 @ SV13 ) )
| ! [SY143: $i] :
( ~ ( in @ SY143 @ SY148 )
| ( in @ SY143 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SY148 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(439,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) )
| ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(440,plain,
! [SV33: $i,SV47: $i,SV13: $i] :
( ( ( ! [SY145: $i] :
( ~ ( in @ SY145 @ ( sK3_SY35 @ SV13 ) )
| ! [SY139: $i] :
( ~ ( in @ SY139 @ SY145 )
| ( in @ SY139 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SY145 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(441,plain,
! [SV16: $i,SV1: $i > $i > $o,SV51: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV16 )
| ~ ( SV1 @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV51 ) )
= $false )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(442,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV16 )
| ~ ( SV1 @ SV56 @ SV51 ) )
= $true )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(443,plain,
! [SV16: $i,SV1: $i > $i > $o,SV48: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV16 ) )
= $false )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(444,plain,
! [SV16: $i,SV48: $i,SV31: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV48 ) )
= $false )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(445,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV16 ) )
= $true )
| ( ( ~ ( SV1 @ SV55 @ SV48 ) )
= $true )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(446,plain,
! [SV13: $i,SV44: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(447,plain,
! [SV13: $i,SV40: $i,SV44: $i] :
( ( ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(448,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) )
| ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(449,plain,
! [SV33: $i,SV50: $i,SV13: $i] :
( ( ( ! [SY148: $i] :
( ~ ( in @ SY148 @ ( sK3_SY35 @ SV13 ) )
| ! [SY143: $i] :
( ~ ( in @ SY143 @ SY148 )
| ( in @ SY143 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SY148 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(450,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) )
| ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(451,plain,
! [SV33: $i,SV47: $i,SV13: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ ( sK3_SY35 @ SV13 ) )
| ! [SY150: $i] :
( ~ ( in @ SY150 @ SV57 )
| ( in @ SY150 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV57 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(452,plain,
! [SV16: $i,SV1: $i > $i > $o,SV51: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV16 ) )
= $false )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(453,plain,
! [SV16: $i,SV51: $i,SV31: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV51 ) )
= $false )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(454,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV16 ) )
= $true )
| ( ( ~ ( SV1 @ SV56 @ SV51 ) )
= $true )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(455,plain,
! [SV16: $i,SV1: $i > $i > $o,SV48: $i,SV31: $i] :
( ( ( in @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV16 )
= $true )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(456,plain,
! [SV16: $i,SV48: $i,SV31: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK25_SY132 @ SV31 @ SV48 @ SV1 @ SV16 ) @ SV48 )
= $true )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(457,plain,
! [SV31: $i,SV48: $i,SV1: $i > $i > $o,SV16: $i,SV55: $i] :
( ( ( in @ SV55 @ SV16 )
= $false )
| ( ( ~ ( SV1 @ SV55 @ SV48 ) )
= $true )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(458,plain,
! [SV13: $i,SV44: $i,SV40: $i] :
( ( ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(459,plain,
! [SV13: $i,SV40: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) )
= $false )
| ( ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
= $false )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(460,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) )
| ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(461,plain,
! [SV33: $i,SV50: $i,SV13: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ ( sK3_SY35 @ SV13 ) )
| ! [SY151: $i] :
( ~ ( in @ SY151 @ SV58 )
| ( in @ SY151 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV58 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(462,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(463,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(464,plain,
! [SV33: $i,SV47: $i,SV13: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ ( sK3_SY35 @ SV13 ) ) )
= $true )
| ( ( ! [SY150: $i] :
( ~ ( in @ SY150 @ SV57 )
| ( in @ SY150 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV57 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(465,plain,
! [SV16: $i,SV1: $i > $i > $o,SV51: $i,SV31: $i] :
( ( ( in @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV16 )
= $true )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(466,plain,
! [SV16: $i,SV51: $i,SV31: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK26_SY134 @ SV31 @ SV51 @ SV1 @ SV16 ) @ SV51 )
= $true )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(467,plain,
! [SV31: $i,SV51: $i,SV1: $i > $i > $o,SV16: $i,SV56: $i] :
( ( ( in @ SV56 @ SV16 )
= $false )
| ( ( ~ ( SV1 @ SV56 @ SV51 ) )
= $true )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(468,plain,
! [SV31: $i,SV16: $i,SV48: $i,SV55: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ SV55 @ SV48 )
= $false )
| ( ( in @ SV55 @ SV16 )
= $false )
| ( ( in @ SV48 @ ( sK17_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(469,plain,
! [SV13: $i,SV40: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
| ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) )
= $false )
| ( ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(471,plain,
! [SV13: $i,SV44: $i,SV40: $i] :
( ( ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
= $false )
| ( ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
= $false )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(472,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(473,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(474,plain,
! [SV33: $i,SV50: $i,SV13: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ ( sK3_SY35 @ SV13 ) ) )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( in @ SY151 @ SV58 )
| ( in @ SY151 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV58 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(475,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(476,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(477,plain,
! [SV33: $i,SV47: $i,SV13: $i,SV57: $i] :
( ( ( in @ SV57 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( ! [SY150: $i] :
( ~ ( in @ SY150 @ SV57 )
| ( in @ SY150 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
| ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV57 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(478,plain,
! [SV31: $i,SV16: $i,SV51: $i,SV56: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ SV56 @ SV51 )
= $false )
| ( ( in @ SV56 @ SV16 )
= $false )
| ( ( in @ SV51 @ ( sK19_SY61 @ SV31 @ SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ SV31 )
= $false )
| ( ( SV1 @ ( sK4_SY58 @ SV1 @ SV16 ) @ ( sK13_SY101 @ SV31 @ SV16 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(479,plain,
! [SV13: $i,SV40: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) ) )
= $false )
| ( ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(482,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(483,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(484,plain,
! [SV33: $i,SV50: $i,SV13: $i,SV58: $i] :
( ( ( in @ SV58 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( ! [SY151: $i] :
( ~ ( in @ SY151 @ SV58 )
| ( in @ SY151 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
| ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV58 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(485,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(486,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(487,plain,
! [SV13: $i,SV33: $i,SV47: $i,SV57: $i] :
( ( ( ! [SY150: $i] :
( ~ ( in @ SY150 @ SV57 )
| ( in @ SY150 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) ) )
= $true )
| ( ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV57 )
= $true )
| ( ( in @ SV57 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(488,plain,
! [SV13: $i,SV40: $i,SV44: $i] :
( ( ( in @ SV44 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
= $true )
| ( ( in @ SV40 @ ( sK22_SY125 @ SV44 @ SV40 @ SV13 ) )
= $true )
| ( ( SV40 = SV44 )
= $true )
| ( ( in @ SV40 @ SV13 )
= $false )
| ( ( in @ SV44 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(489,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
| ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(490,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(491,plain,
! [SV13: $i,SV33: $i,SV50: $i,SV58: $i] :
( ( ( ! [SY151: $i] :
( ~ ( in @ SY151 @ SV58 )
| ( in @ SY151 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) ) )
= $true )
| ( ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV58 )
= $true )
| ( ( in @ SV58 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(492,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(493,plain,
! [SV47: $i,SV33: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(494,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SY137 @ SV33 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(495,plain,
! [SV13: $i,SV33: $i,SV47: $i,SV57: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV57 )
| ( in @ SV59 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
= $true )
| ( ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV57 )
= $true )
| ( ( in @ SV57 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(496,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(497,plain,
! [SV50: $i,SV33: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(498,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( ! [SY141: $i] :
~ ~ ( ~ ( in @ SY141 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SY141 @ SV33 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(499,plain,
! [SV13: $i,SV33: $i,SV50: $i,SV58: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ SV58 )
| ( in @ SV60 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
= $true )
| ( ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV58 )
= $true )
| ( ( in @ SV58 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(500,plain,
! [SV13: $i,SV33: $i,SV47: $i] :
( ( ( in @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(501,plain,
! [SV47: $i,SV33: $i,SV13: $i] :
( ( ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV33 )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(502,plain,
! [SV13: $i,SV33: $i,SV47: $i,SV61: $i] :
( ( ( ~ ~ ( ~ ( in @ SV61 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SV61 @ SV33 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(503,plain,
! [SV13: $i,SV33: $i,SV47: $i,SV57: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV57 ) )
= $true )
| ( ( in @ SV59 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
= $true )
| ( ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV57 )
= $true )
| ( ( in @ SV57 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(504,plain,
! [SV13: $i,SV33: $i,SV50: $i] :
( ( ( in @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) @ ( sK3_SY35 @ SV13 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(505,plain,
! [SV50: $i,SV33: $i,SV13: $i] :
( ( ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV33 )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(506,plain,
! [SV13: $i,SV33: $i,SV50: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( in @ SV62 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SV62 @ SV33 ) ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(507,plain,
! [SV13: $i,SV33: $i,SV50: $i,SV58: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ SV58 ) )
= $true )
| ( ( in @ SV60 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
= $true )
| ( ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV58 )
= $true )
| ( ( in @ SV58 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(508,plain,
! [SV13: $i,SV33: $i,SV47: $i,SV61: $i] :
( ( ( ~ ( ~ ( in @ SV61 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SV61 @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(509,plain,
! [SV13: $i,SV33: $i,SV47: $i,SV57: $i,SV59: $i] :
( ( ( in @ SV59 @ SV57 )
= $false )
| ( ( in @ SV59 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
= $true )
| ( ( in @ ( sK23_SY136 @ SV13 @ SV33 @ SV47 ) @ SV57 )
= $true )
| ( ( in @ SV57 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(510,plain,
! [SV13: $i,SV33: $i,SV50: $i,SV62: $i] :
( ( ( ~ ( ~ ( in @ SV62 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SV62 @ SV33 ) ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(511,plain,
! [SV13: $i,SV33: $i,SV50: $i,SV58: $i,SV60: $i] :
( ( ( in @ SV60 @ SV58 )
= $false )
| ( ( in @ SV60 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
= $true )
| ( ( in @ ( sK24_SY140 @ SV13 @ SV33 @ SV50 ) @ SV58 )
= $true )
| ( ( in @ SV58 @ ( sK3_SY35 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(512,plain,
! [SV13: $i,SV33: $i,SV47: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
| ~ ( in @ SV61 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(513,plain,
! [SV13: $i,SV33: $i,SV50: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
| ~ ( in @ SV62 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(514,plain,
! [SV13: $i,SV33: $i,SV47: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV61 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(515,plain,
! [SV13: $i,SV33: $i,SV50: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV62 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(516,plain,
! [SV13: $i,SV33: $i,SV47: $i,SV61: $i] :
( ( ( in @ SV61 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV61 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(517,plain,
! [SV13: $i,SV33: $i,SV50: $i,SV62: $i] :
( ( ( in @ SV62 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV62 @ SV33 ) )
= $true )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(518,plain,
! [SV13: $i,SV47: $i,SV33: $i,SV61: $i] :
( ( ( in @ SV61 @ SV33 )
= $false )
| ( ( in @ SV61 @ ( sK20_SY105 @ SV47 @ SV33 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV13 )
= $false )
| ( ( in @ SV47 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(519,plain,
! [SV13: $i,SV50: $i,SV33: $i,SV62: $i] :
( ( ( in @ SV62 @ SV33 )
= $false )
| ( ( in @ SV62 @ ( sK21_SY105 @ SV50 @ SV33 @ SV13 ) )
= $false )
| ( ( in @ ( sK15_SY103 @ SV13 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ SV50 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(521,plain,
! [SV8: $i,SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SX0: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[129:[bind(SV21,$thf( ^ [SV98: $i] : $false ))]]) ).
thf(522,plain,
! [SV97: $i > $o,SV8: $i,SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SX0: $i] :
~ ( SV97 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV97 @ SV26 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[129:[bind(SV21,$thf( ^ [SV96: $i] : ~ ( SV97 @ SV96 ) ))]]) ).
thf(523,plain,
! [SV8: $i,SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SX0: $i] : ( SX0 = omega ) ) )
= $false )
| ( ( SV26 = omega )
= $true ) ),
inference(prim_subst,[status(thm)],[129:[bind(SV21,$thf( ^ [SV93: $i] : ( SV93 = omega ) ))]]) ).
thf(524,plain,
! [SV8: $i,SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) ) )
= $false )
| ( ( SV26 = sK2_SY0 )
= $true ) ),
inference(prim_subst,[status(thm)],[129:[bind(SV21,$thf( ^ [SV94: $i] : ( SV94 = sK2_SY0 ) ))]]) ).
thf(525,plain,
! [SV8: $i,SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(prim_subst,[status(thm)],[129:[bind(SV21,$thf( ^ [SV95: $i] : ( SV95 = emptyset ) ))]]) ).
thf(526,plain,
! [SV15: $i,SV27: $i] :
( ( $true = $false )
| ( ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV27 @ SV15 )
= $false ) ),
inference(prim_subst,[status(thm)],[168:[bind(SV23,$thf( ^ [SV92: $i] : $true ))]]) ).
thf(528,plain,
! [SV15: $i,SV27: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV27 ) )
= $false )
| ( ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] :
~ ( SV90 @ SX0 ) ) )
= $true )
| ( ( in @ SV27 @ SV15 )
= $false ) ),
inference(prim_subst,[status(thm)],[168:[bind(SV23,$thf( ^ [SV89: $i] : ~ ( SV90 @ SV89 ) ))]]) ).
thf(529,plain,
! [SV15: $i,SV27: $i] :
( ( ( SV27 = omega )
= $false )
| ( ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] : ( SX0 = omega ) ) )
= $true )
| ( ( in @ SV27 @ SV15 )
= $false ) ),
inference(prim_subst,[status(thm)],[168:[bind(SV23,$thf( ^ [SV86: $i] : ( SV86 = omega ) ))]]) ).
thf(530,plain,
! [SV15: $i,SV27: $i] :
( ( ( SV27 = sK2_SY0 )
= $false )
| ( ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) ) )
= $true )
| ( ( in @ SV27 @ SV15 )
= $false ) ),
inference(prim_subst,[status(thm)],[168:[bind(SV23,$thf( ^ [SV87: $i] : ( SV87 = sK2_SY0 ) ))]]) ).
thf(531,plain,
! [SV15: $i,SV27: $i] :
( ( ( SV27 = emptyset )
= $false )
| ( ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true )
| ( ( in @ SV27 @ SV15 )
= $false ) ),
inference(prim_subst,[status(thm)],[168:[bind(SV23,$thf( ^ [SV88: $i] : ( SV88 = emptyset ) ))]]) ).
thf(540,plain,
! [SV28: $i,SV83: $i > $o] :
( ( ( ~ ( SV83
@ ( sK11_SY99 @ SV28
@ ^ [SX0: $i] :
~ ( SV83 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV83 @ SV28 ) )
= $false )
| ( ( ~ ( SV83
@ ( descr
@ ^ [SX0: $i] :
~ ( SV83 @ SX0 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[260:[bind(SV3,$thf( ^ [SV82: $i] : ~ ( SV83 @ SV82 ) ))]]) ).
thf(541,plain,
! [SV28: $i] :
( ( ( ( sK11_SY99 @ SV28
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true )
| ( ( SV28 = omega )
= $false )
| ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true ) ),
inference(prim_subst,[status(thm)],[260:[bind(SV3,$thf( ^ [SV79: $i] : ( SV79 = omega ) ))]]) ).
thf(542,plain,
! [SV28: $i] :
( ( ( ( sK11_SY99 @ SV28
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true )
| ( ( SV28 = sK2_SY0 )
= $false )
| ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true ) ),
inference(prim_subst,[status(thm)],[260:[bind(SV3,$thf( ^ [SV80: $i] : ( SV80 = sK2_SY0 ) ))]]) ).
thf(543,plain,
! [SV28: $i] :
( ( ( ( sK11_SY99 @ SV28
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true )
| ( ( SV28 = emptyset )
= $false )
| ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true ) ),
inference(prim_subst,[status(thm)],[260:[bind(SV3,$thf( ^ [SV81: $i] : ( SV81 = emptyset ) ))]]) ).
thf(547,plain,
! [SV30: $i] :
( ( ( ( sK14_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true )
| ( ( SV30 = emptyset )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[335:[bind(SV10,$thf( ^ [SV72: $i] : ( SV72 = emptyset ) ))]]) ).
thf(548,plain,
! [SV30: $i] :
( ( ( ( sK14_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true )
| ( ( SV30 = omega )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = omega ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[335:[bind(SV10,$thf( ^ [SV73: $i] : ( SV73 = omega ) ))]]) ).
thf(549,plain,
! [SV30: $i] :
( ( ( ( sK14_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true )
| ( ( SV30 = sK2_SY0 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[335:[bind(SV10,$thf( ^ [SV74: $i] : ( SV74 = sK2_SY0 ) ))]]) ).
thf(552,plain,
! [SV30: $i,SV76: $i > $o] :
( ( ( ~ ( SV76
@ ( sK16_SY30 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV76 @ SV30 ) )
= $false )
| ( ( ~ ( SV76
@ ( sK12_SY100 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[347:[bind(SV10,$thf( ^ [SV75: $i] : ~ ( SV76 @ SV75 ) ))]]) ).
thf(553,plain,
! [SV30: $i] :
( ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true )
| ( ( SV30 = emptyset )
= $false )
| ( ( ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true ) ),
inference(prim_subst,[status(thm)],[347:[bind(SV10,$thf( ^ [SV72: $i] : ( SV72 = emptyset ) ))]]) ).
thf(554,plain,
! [SV30: $i] :
( ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true )
| ( ( SV30 = omega )
= $false )
| ( ( ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true ) ),
inference(prim_subst,[status(thm)],[347:[bind(SV10,$thf( ^ [SV73: $i] : ( SV73 = omega ) ))]]) ).
thf(555,plain,
! [SV30: $i] :
( ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true )
| ( ( SV30 = sK2_SY0 )
= $false )
| ( ( ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true ) ),
inference(prim_subst,[status(thm)],[347:[bind(SV10,$thf( ^ [SV74: $i] : ( SV74 = sK2_SY0 ) ))]]) ).
thf(559,plain,
! [SV30: $i,SV49: $i] :
( ( ( SV49 = emptyset )
= $false )
| ( ( ( sK14_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= SV49 )
= $true )
| ( ( SV30 = emptyset )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[373:[bind(SV10,$thf( ^ [SV72: $i] : ( SV72 = emptyset ) ))]]) ).
thf(560,plain,
! [SV30: $i,SV49: $i] :
( ( ( SV49 = omega )
= $false )
| ( ( ( sK14_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = omega ) )
= SV49 )
= $true )
| ( ( SV30 = omega )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = omega ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[373:[bind(SV10,$thf( ^ [SV73: $i] : ( SV73 = omega ) ))]]) ).
thf(561,plain,
! [SV30: $i,SV49: $i] :
( ( ( SV49 = sK2_SY0 )
= $false )
| ( ( ( sK14_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= SV49 )
= $true )
| ( ( SV30 = sK2_SY0 )
= $false )
| ( ( SV30
= ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[373:[bind(SV10,$thf( ^ [SV74: $i] : ( SV74 = sK2_SY0 ) ))]]) ).
thf(562,plain,
! [SV16: $i,SV36: $i] :
( ( ( in
@ ( sK18_SY113 @ SV36
@ ^ [SX0: $i,SX1: $i] : $true
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : $true
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : $true
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[378:[bind(SV1,$thf( ^ [SV70: $i] : ^ [SV71: $i] : $true ))]]) ).
thf(563,plain,
! [SV16: $i,SV36: $i] :
( ( ( in
@ ( sK18_SY113 @ SV36
@ ^ [SX0: $i,SX1: $i] : $false
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : $false
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : $false
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[378:[bind(SV1,$thf( ^ [SV68: $i] : ^ [SV69: $i] : $false ))]]) ).
thf(564,plain,
! [SV16: $i,SV67: $i > $i > $o,SV36: $i] :
( ( ( in
@ ( sK18_SY113 @ SV36
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[378:[bind(SV1,$thf( ^ [SV65: $i] : ^ [SV66: $i] : ~ ( SV67 @ SV65 @ SV66 ) ))]]) ).
thf(565,plain,
! [SV16: $i,SV36: $i] :
( ( ( in
@ ( sK18_SY113 @ SV36
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[378:[bind(SV1,$thf( ^ [SY152: $i] : ^ [SY153: $i] : ( SY152 != SY153 ) ))]]) ).
thf(566,plain,
! [SV16: $i,SV36: $i] :
( ( ( in
@ ( sK18_SY113 @ SV36
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[378:[bind(SV1,$thf( ^ [SV64: $i] : ^ [SV63: $i] : ( SV64 = SV63 ) ))]]) ).
thf(568,plain,
! [SV16: $i,SV36: $i] :
( ( $false = $true )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : $false
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : $false
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[379:[bind(SV1,$thf( ^ [SV68: $i] : ^ [SV69: $i] : $false ))]]) ).
thf(569,plain,
! [SV16: $i,SV36: $i,SV67: $i > $i > $o] :
( ( ( ~ ( SV67
@ ( sK18_SY113 @ SV36
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV36 ) )
= $true )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[379:[bind(SV1,$thf( ^ [SV65: $i] : ^ [SV66: $i] : ~ ( SV67 @ SV65 @ SV66 ) ))]]) ).
thf(571,plain,
! [SV16: $i,SV36: $i] :
( ( ( ( sK18_SY113 @ SV36
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV36 )
= $true )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[379:[bind(SV1,$thf( ^ [SV64: $i] : ^ [SV63: $i] : ( SV64 = SV63 ) ))]]) ).
thf(574,plain,
! [SV30: $i,SV52: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV52 ) )
= $false )
| ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) )
= SV52 )
= $true )
| ( ( ~ ( SV76 @ SV30 ) )
= $false )
| ( ( ~ ( SV76
@ ( sK12_SY100 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[385:[bind(SV10,$thf( ^ [SV75: $i] : ~ ( SV76 @ SV75 ) ))]]) ).
thf(575,plain,
! [SV30: $i,SV52: $i] :
( ( ( SV52 = emptyset )
= $false )
| ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= SV52 )
= $true )
| ( ( SV30 = emptyset )
= $false )
| ( ( ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true ) ),
inference(prim_subst,[status(thm)],[385:[bind(SV10,$thf( ^ [SV72: $i] : ( SV72 = emptyset ) ))]]) ).
thf(576,plain,
! [SV30: $i,SV52: $i] :
( ( ( SV52 = omega )
= $false )
| ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = omega ) )
= SV52 )
= $true )
| ( ( SV30 = omega )
= $false )
| ( ( ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true ) ),
inference(prim_subst,[status(thm)],[385:[bind(SV10,$thf( ^ [SV73: $i] : ( SV73 = omega ) ))]]) ).
thf(577,plain,
! [SV30: $i,SV52: $i] :
( ( ( SV52 = sK2_SY0 )
= $false )
| ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= SV52 )
= $true )
| ( ( SV30 = sK2_SY0 )
= $false )
| ( ( ( sK12_SY100 @ SV30
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true ) ),
inference(prim_subst,[status(thm)],[385:[bind(SV10,$thf( ^ [SV74: $i] : ( SV74 = sK2_SY0 ) ))]]) ).
thf(578,plain,
! [SV36: $i,SV16: $i,SV46: $i] :
( ( $true = $false )
| ( ( in @ SV46 @ SV16 )
= $false )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : $true
@ SV16 ) )
= $true )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : $true
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[390:[bind(SV1,$thf( ^ [SV70: $i] : ^ [SV71: $i] : $true ))]]) ).
thf(580,plain,
! [SV16: $i,SV36: $i,SV46: $i,SV67: $i > $i > $o] :
( ( ( ~ ( SV67 @ SV46 @ SV36 ) )
= $false )
| ( ( in @ SV46 @ SV16 )
= $false )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $true )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[390:[bind(SV1,$thf( ^ [SV65: $i] : ^ [SV66: $i] : ~ ( SV67 @ SV65 @ SV66 ) ))]]) ).
thf(581,plain,
! [SV16: $i,SV36: $i,SV46: $i] :
( ( ( SV46 != SV36 )
= $false )
| ( ( in @ SV46 @ SV16 )
= $false )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ SV16 ) )
= $true )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[390:[bind(SV1,$thf( ^ [SY152: $i] : ^ [SY153: $i] : ( SY152 != SY153 ) ))]]) ).
thf(582,plain,
! [SV16: $i,SV36: $i,SV46: $i] :
( ( ( SV46 = SV36 )
= $false )
| ( ( in @ SV46 @ SV16 )
= $false )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $true )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[390:[bind(SV1,$thf( ^ [SV64: $i] : ^ [SV63: $i] : ( SV64 = SV63 ) ))]]) ).
thf(587,plain,
! [SV16: $i,SV48: $i,SV31: $i] :
( ( ( in
@ ( sK25_SY132 @ SV31 @ SV48
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV48
@ ( sK17_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[455:[bind(SV1,$thf( ^ [SV64: $i] : ^ [SV63: $i] : ( SV64 = SV63 ) ))]]) ).
thf(592,plain,
! [SV16: $i,SV48: $i,SV31: $i] :
( ( ( ( sK25_SY132 @ SV31 @ SV48
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV48 )
= $true )
| ( ( in @ SV48
@ ( sK17_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[456:[bind(SV1,$thf( ^ [SV64: $i] : ^ [SV63: $i] : ( SV64 = SV63 ) ))]]) ).
thf(595,plain,
! [SV16: $i,SV67: $i > $i > $o,SV51: $i,SV31: $i] :
( ( ( in
@ ( sK26_SY134 @ SV31 @ SV51
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 ) )
= $false )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[465:[bind(SV1,$thf( ^ [SV65: $i] : ^ [SV66: $i] : ~ ( SV67 @ SV65 @ SV66 ) ))]]) ).
thf(597,plain,
! [SV16: $i,SV51: $i,SV31: $i] :
( ( ( in
@ ( sK26_SY134 @ SV31 @ SV51
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV31 )
= $false )
| ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[465:[bind(SV1,$thf( ^ [SV64: $i] : ^ [SV63: $i] : ( SV64 = SV63 ) ))]]) ).
thf(600,plain,
! [SV16: $i,SV51: $i,SV31: $i,SV67: $i > $i > $o] :
( ( ( ~ ( SV67
@ ( sK26_SY134 @ SV31 @ SV51
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV51 ) )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 ) )
= $false )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[466:[bind(SV1,$thf( ^ [SV65: $i] : ^ [SV66: $i] : ~ ( SV67 @ SV65 @ SV66 ) ))]]) ).
thf(602,plain,
! [SV16: $i,SV51: $i,SV31: $i] :
( ( ( ( sK26_SY134 @ SV31 @ SV51
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV51 )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV31 )
= $false )
| ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[466:[bind(SV1,$thf( ^ [SV64: $i] : ^ [SV63: $i] : ( SV64 = SV63 ) ))]]) ).
thf(607,plain,
! [SV31: $i,SV16: $i,SV48: $i,SV55: $i] :
( ( ( SV55 = SV48 )
= $false )
| ( ( in @ SV55 @ SV16 )
= $false )
| ( ( in @ SV48
@ ( sK17_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $true )
| ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV31 )
= $false )
| ( ( SV31
= ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[468:[bind(SV1,$thf( ^ [SV64: $i] : ^ [SV63: $i] : ( SV64 = SV63 ) ))]]) ).
thf(610,plain,
! [SV31: $i,SV16: $i,SV51: $i,SV56: $i,SV67: $i > $i > $o] :
( ( ( ~ ( SV67 @ SV56 @ SV51 ) )
= $false )
| ( ( in @ SV56 @ SV16 )
= $false )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $true )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 ) )
= $false )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[478:[bind(SV1,$thf( ^ [SV65: $i] : ^ [SV66: $i] : ~ ( SV67 @ SV65 @ SV66 ) ))]]) ).
thf(612,plain,
! [SV31: $i,SV16: $i,SV51: $i,SV56: $i] :
( ( ( SV56 = SV51 )
= $false )
| ( ( in @ SV56 @ SV16 )
= $false )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $true )
| ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV31 )
= $false )
| ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[478:[bind(SV1,$thf( ^ [SV64: $i] : ^ [SV63: $i] : ( SV64 = SV63 ) ))]]) ).
thf(613,plain,
! [SV21: $i > $o,SV8: $i,SV26: $i] :
( ( ( SV21 @ SV26 )
= $true )
| ( ( ( SV21 @ SV26 )
= ( ~ ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[129]) ).
thf(614,plain,
! [SV22: $i,SV11: $i] :
( ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true )
| ( ( ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 )
= ( in @ SV22 @ ( powerset @ SV11 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[214]) ).
thf(615,plain,
! [SV8: $i,SV26: $i,SV21: $i > $o] :
( ( ( ~ ( ( SV21 @ SV26 )
| ~ ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) ) )
| ~ ( ~ ( SV21 @ SV26 )
| ~ ~ ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) ) ) )
= $false )
| ( ( SV21 @ SV26 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[613]) ).
thf(617,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 )
| ( in @ SV22 @ ( powerset @ SV11 ) ) )
| ~ ( ~ ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 )
| ~ ( in @ SV22 @ ( powerset @ SV11 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[614]) ).
thf(619,plain,
! [SV8: $i,SV26: $i,SV21: $i > $o] :
( ( ( ~ ( ( SV21 @ SV26 )
| ~ ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) ) ) )
= $false )
| ( ( SV21 @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(621,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 )
| ( in @ SV22 @ ( powerset @ SV11 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(623,plain,
! [SV8: $i,SV26: $i,SV21: $i > $o] :
( ( ( ( SV21 @ SV26 )
| ~ ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) ) )
= $true )
| ( ( SV21 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(625,plain,
! [SV22: $i,SV11: $i] :
( ( ( ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 )
| ( in @ SV22 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(627,plain,
! [SV8: $i,SV26: $i,SV21: $i > $o] :
( ( ( SV21 @ SV26 )
= $true )
| ( ( ~ ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) ) )
= $true )
| ( ( SV21 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(629,plain,
! [SV22: $i,SV11: $i] :
( ( ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(631,plain,
! [SV21: $i > $o,SV8: $i,SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) )
= $false )
| ( ( SV21 @ SV26 )
= $true )
| ( ( SV21 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(637,plain,
! [SV17: $i,SV2: $i] :
( ( in @ SV2 @ ( setadjoin @ SV2 @ SV17 ) )
= $true ),
inference(extuni,[status(esa)],[187:[bind(SV24,$thf( SV2 ))]]) ).
thf(638,plain,
! [SV8: $i,SV26: $i,SV97: $i > $o] :
( ( ( SV97 @ SV26 )
= $false )
| ( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SX0: $i] :
~ ( SV97 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(639,plain,
! [SV15: $i,SV27: $i,SV90: $i > $o] :
( ( ( SV90 @ SV27 )
= $true )
| ( ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] :
~ ( SV90 @ SX0 ) ) )
= $true )
| ( ( in @ SV27 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(641,plain,
! [SV28: $i,SV83: $i > $o] :
( ( ( SV83
@ ( sK11_SY99 @ SV28
@ ^ [SX0: $i] :
~ ( SV83 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV83 @ SV28 ) )
= $false )
| ( ( ~ ( SV83
@ ( descr
@ ^ [SX0: $i] :
~ ( SV83 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(643,plain,
! [SV30: $i,SV76: $i > $o] :
( ( ( SV76
@ ( sK16_SY30 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV76 @ SV30 ) )
= $false )
| ( ( ~ ( SV76
@ ( sK12_SY100 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(645,plain,
! [SV16: $i,SV36: $i,SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK18_SY113 @ SV36
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV36 )
= $false )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(647,plain,
! [SV30: $i,SV52: $i,SV76: $i > $o] :
( ( ( SV76 @ SV52 )
= $true )
| ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) )
= SV52 )
= $true )
| ( ( ~ ( SV76 @ SV30 ) )
= $false )
| ( ( ~ ( SV76
@ ( sK12_SY100 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(648,plain,
! [SV16: $i,SV36: $i,SV46: $i,SV67: $i > $i > $o] :
( ( ( SV67 @ SV46 @ SV36 )
= $true )
| ( ( in @ SV46 @ SV16 )
= $false )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $true )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(649,plain,
! [SV16: $i,SV36: $i,SV46: $i] :
( ( ( SV46 = SV36 )
= $true )
| ( ( in @ SV46 @ SV16 )
= $false )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ SV16 ) )
= $true )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(654,plain,
! [SV51: $i,SV31: $i,SV16: $i,SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( in
@ ( sK26_SY134 @ SV31 @ SV51
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV16 )
= $true )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(656,plain,
! [SV16: $i,SV51: $i,SV31: $i,SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK26_SY134 @ SV31 @ SV51
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV51 )
= $false )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 ) )
= $false )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(660,plain,
! [SV31: $i,SV16: $i,SV51: $i,SV56: $i,SV67: $i > $i > $o] :
( ( ( SV67 @ SV56 @ SV51 )
= $true )
| ( ( in @ SV56 @ SV16 )
= $false )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $true )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 ) )
= $false )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(663,plain,
! [SV28: $i,SV83: $i > $o] :
( ( ( SV83 @ SV28 )
= $true )
| ( ( SV83
@ ( sK11_SY99 @ SV28
@ ^ [SX0: $i] :
~ ( SV83 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV83
@ ( descr
@ ^ [SX0: $i] :
~ ( SV83 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(665,plain,
! [SV30: $i,SV76: $i > $o] :
( ( ( SV76 @ SV30 )
= $true )
| ( ( SV76
@ ( sK16_SY30 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV76
@ ( sK12_SY100 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(667,plain,
! [SV52: $i,SV30: $i,SV76: $i > $o] :
( ( ( SV76 @ SV30 )
= $true )
| ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) )
= SV52 )
= $true )
| ( ( SV76 @ SV52 )
= $true )
| ( ( ~ ( SV76
@ ( sK12_SY100 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(670,plain,
! [SV51: $i,SV31: $i,SV16: $i,SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) )
= $false )
| ( ( in
@ ( sK26_SY134 @ SV31 @ SV51
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(672,plain,
! [SV51: $i,SV31: $i,SV16: $i,SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( SV67
@ ( sK26_SY134 @ SV31 @ SV51
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV51 )
= $false )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(676,plain,
! [SV56: $i,SV51: $i,SV31: $i,SV16: $i,SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $true )
| ( ( in @ SV56 @ SV16 )
= $false )
| ( ( SV67 @ SV56 @ SV51 )
= $true )
| ( ( ~ ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(678,plain,
! [SV28: $i,SV83: $i > $o] :
( ( ( SV83
@ ( descr
@ ^ [SX0: $i] :
~ ( SV83 @ SX0 ) ) )
= $false )
| ( ( SV83
@ ( sK11_SY99 @ SV28
@ ^ [SX0: $i] :
~ ( SV83 @ SX0 ) ) )
= $false )
| ( ( SV83 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(679,plain,
! [SV30: $i,SV76: $i > $o] :
( ( ( SV76
@ ( sK12_SY100 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) )
= $false )
| ( ( SV76
@ ( sK16_SY30 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) )
= $false )
| ( ( SV76 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(680,plain,
! [SV52: $i,SV30: $i,SV76: $i > $o] :
( ( ( SV76
@ ( sK12_SY100 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) ) )
= $false )
| ( ( SV76 @ SV52 )
= $true )
| ( ( ( sK16_SY30 @ SV30
@ ^ [SX0: $i] :
~ ( SV76 @ SX0 ) )
= SV52 )
= $true )
| ( ( SV76 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(681,plain,
! [SV51: $i,SV31: $i,SV16: $i,SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV67
@ ( sK26_SY134 @ SV31 @ SV51
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV51 )
= $false )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(683,plain,
! [SV51: $i,SV56: $i,SV31: $i,SV16: $i,SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ ( sK13_SY101 @ SV31 @ SV16
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV67 @ SV56 @ SV51 )
= $true )
| ( ( in @ SV56 @ SV16 )
= $false )
| ( ( in @ SV51
@ ( sK19_SY61 @ SV31
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 ) )
= $true )
| ( ( SV67
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 )
@ SV16 )
@ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(685,plain,
! [SV15: $i] :
( ( ( in @ omega @ SV15 )
= $false )
| ( ( in @ omega
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] : ( SX0 = omega ) ) )
= $true ) ),
inference(extuni,[status(esa)],[529:[bind(SV27,$thf( omega ))]]) ).
thf(686,plain,
! [SV15: $i] :
( ( ( in @ sK2_SY0 @ SV15 )
= $false )
| ( ( in @ sK2_SY0
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[530:[bind(SV27,$thf( sK2_SY0 ))]]) ).
thf(687,plain,
! [SV15: $i] :
( ( ( in @ emptyset @ SV15 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(extuni,[status(esa)],[531:[bind(SV27,$thf( emptyset ))]]) ).
thf(688,plain,
( ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true )
| ( ( ( sK11_SY99 @ omega
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true ) ),
inference(extuni,[status(esa)],[541:[bind(SV28,$thf( omega ))]]) ).
thf(689,plain,
( ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true )
| ( ( ( sK11_SY99 @ sK2_SY0
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[542:[bind(SV28,$thf( sK2_SY0 ))]]) ).
thf(690,plain,
( ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true )
| ( ( ( sK11_SY99 @ emptyset
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true ) ),
inference(extuni,[status(esa)],[543:[bind(SV28,$thf( emptyset ))]]) ).
thf(691,plain,
( ( ( emptyset
= ( sK12_SY100 @ emptyset
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $false )
| ( ( ( sK14_SY30 @ emptyset
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true ) ),
inference(extuni,[status(esa)],[547:[bind(SV30,$thf( emptyset ))]]) ).
thf(692,plain,
( ( ( omega
= ( sK12_SY100 @ omega
@ ^ [SX0: $i] : ( SX0 = omega ) ) )
= $false )
| ( ( ( sK14_SY30 @ omega
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true ) ),
inference(extuni,[status(esa)],[548:[bind(SV30,$thf( omega ))]]) ).
thf(693,plain,
( ( ( sK2_SY0
= ( sK12_SY100 @ sK2_SY0
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) ) )
= $false )
| ( ( ( sK14_SY30 @ sK2_SY0
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[549:[bind(SV30,$thf( sK2_SY0 ))]]) ).
thf(694,plain,
( ( ( ( sK12_SY100 @ emptyset
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true )
| ( ( ( sK16_SY30 @ emptyset
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true ) ),
inference(extuni,[status(esa)],[553:[bind(SV30,$thf( emptyset ))]]) ).
thf(695,plain,
( ( ( ( sK12_SY100 @ omega
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true )
| ( ( ( sK16_SY30 @ omega
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true ) ),
inference(extuni,[status(esa)],[554:[bind(SV30,$thf( omega ))]]) ).
thf(696,plain,
( ( ( ( sK12_SY100 @ sK2_SY0
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true )
| ( ( ( sK16_SY30 @ sK2_SY0
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[555:[bind(SV30,$thf( sK2_SY0 ))]]) ).
thf(697,plain,
( ( ( emptyset
= ( sK12_SY100 @ emptyset
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $false )
| ( ( ( sK14_SY30 @ emptyset
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true ) ),
inference(extuni,[status(esa)],[559:[bind(SV30,$thf( emptyset )),bind(SV49,$thf( emptyset ))]]) ).
thf(698,plain,
( ( ( omega
= ( sK12_SY100 @ omega
@ ^ [SX0: $i] : ( SX0 = omega ) ) )
= $false )
| ( ( ( sK14_SY30 @ omega
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true ) ),
inference(extuni,[status(esa)],[560:[bind(SV30,$thf( omega )),bind(SV49,$thf( omega ))]]) ).
thf(699,plain,
( ( ( sK2_SY0
= ( sK12_SY100 @ sK2_SY0
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) ) )
= $false )
| ( ( ( sK14_SY30 @ sK2_SY0
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[561:[bind(SV30,$thf( sK2_SY0 )),bind(SV49,$thf( sK2_SY0 ))]]) ).
thf(700,plain,
( ( ( ( sK12_SY100 @ emptyset
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true )
| ( ( ( sK16_SY30 @ emptyset
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $true ) ),
inference(extuni,[status(esa)],[575:[bind(SV30,$thf( emptyset )),bind(SV52,$thf( emptyset ))]]) ).
thf(701,plain,
( ( ( ( sK12_SY100 @ omega
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true )
| ( ( ( sK16_SY30 @ omega
@ ^ [SX0: $i] : ( SX0 = omega ) )
= omega )
= $true ) ),
inference(extuni,[status(esa)],[576:[bind(SV30,$thf( omega )),bind(SV52,$thf( omega ))]]) ).
thf(702,plain,
( ( ( ( sK12_SY100 @ sK2_SY0
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true )
| ( ( ( sK16_SY30 @ sK2_SY0
@ ^ [SX0: $i] : ( SX0 = sK2_SY0 ) )
= sK2_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[577:[bind(SV30,$thf( sK2_SY0 )),bind(SV52,$thf( sK2_SY0 ))]]) ).
thf(703,plain,
! [SV36: $i,SV16: $i] :
( ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16 )
= $true )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $true )
| ( ( in @ SV36 @ SV16 )
= $false ) ),
inference(extuni,[status(esa)],[582:[bind(SV46,$thf( SV36 ))]]) ).
thf(704,plain,
! [SV48: $i,SV16: $i] :
( ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= ( sK13_SY101
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false )
| ( ( in @ SV48
@ ( sK17_SY61
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( in
@ ( sK25_SY132
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV48
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(extuni,[status(esa)],[587:[bind(SV31,$thf( sK4_SY58 @ ^ [SX0: $i] : ^ [SX1: $i] : ( SX0 = SX1 ) @ SV16 ))]]) ).
thf(705,plain,
! [SV48: $i,SV16: $i] :
( ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= ( sK13_SY101
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false )
| ( ( in @ SV48
@ ( sK17_SY61
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( ( sK25_SY132
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV48
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV48 )
= $true ) ),
inference(extuni,[status(esa)],[592:[bind(SV31,$thf( sK4_SY58 @ ^ [SX0: $i] : ^ [SX1: $i] : ( SX0 = SX1 ) @ SV16 ))]]) ).
thf(706,plain,
! [SV51: $i,SV16: $i] :
( ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= ( sK13_SY101
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( in
@ ( sK26_SY134
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV51
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16 )
= $true ) ),
inference(extuni,[status(esa)],[597:[bind(SV31,$thf( sK4_SY58 @ ^ [SX0: $i] : ^ [SX1: $i] : ( SX0 = SX1 ) @ SV16 ))]]) ).
thf(707,plain,
! [SV51: $i,SV16: $i] :
( ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= ( sK13_SY101
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $false )
| ( ( ( sK26_SY134
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV51
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= SV51 )
= $true ) ),
inference(extuni,[status(esa)],[602:[bind(SV31,$thf( sK4_SY58 @ ^ [SX0: $i] : ^ [SX1: $i] : ( SX0 = SX1 ) @ SV16 ))]]) ).
thf(708,plain,
! [SV48: $i,SV16: $i] :
( ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= ( sK13_SY101
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false )
| ( ( in @ SV48
@ ( sK17_SY61
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $true )
| ( ( in @ SV48 @ SV16 )
= $false ) ),
inference(extuni,[status(esa)],[607:[bind(SV31,$thf( sK4_SY58 @ ^ [SX0: $i] : ^ [SX1: $i] : ( SX0 = SX1 ) @ SV16 )),bind(SV55,$thf( SV48 ))]]) ).
thf(709,plain,
! [SV51: $i,SV16: $i] :
( ( ( ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
= ( sK13_SY101
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ SV16
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true )
| ( ( in @ SV51
@ ( sK19_SY61
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 )
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV16 ) )
= $true )
| ( ( in @ SV51 @ SV16 )
= $false ) ),
inference(extuni,[status(esa)],[612:[bind(SV31,$thf( sK4_SY58 @ ^ [SX0: $i] : ^ [SX1: $i] : ( SX0 = SX1 ) @ SV16 )),bind(SV56,$thf( SV51 ))]]) ).
thf(710,plain,
! [SV21: $i > $o,SV8: $i,SV26: $i] :
( ( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SY72: $i] : ( SV21 @ SY72 ) ) )
= $false )
| ( ( SV21 @ SV26 )
= $true ) ),
inference(sim,[status(thm)],[631]) ).
thf(711,plain,
! [SV22: $i,SV11: $i] :
( ( ( in @ ( sK7_SY74 @ SV11 @ SV22 ) @ SV22 )
= $true )
| ( ( in @ SV22 @ ( powerset @ SV11 ) )
= $true ) ),
inference(sim,[status(thm)],[629]) ).
thf(712,plain,
! [SV8: $i,SV26: $i] :
( ( in @ SV26
@ ( dsetconstr @ SV8
@ ^ [SX0: $i] : $false ) )
= $false ),
inference(sim,[status(thm)],[521]) ).
thf(713,plain,
! [SV15: $i,SV27: $i] :
( ( ( in @ SV27
@ ( dsetconstr @ SV15
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV27 @ SV15 )
= $false ) ),
inference(sim,[status(thm)],[526]) ).
thf(714,plain,
! [SV16: $i,SV36: $i] :
( ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : $false
@ SV16 ) )
= $false )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : $false
@ SV16 )
@ SV16 )
= $true ) ),
inference(sim,[status(thm)],[568]) ).
thf(715,plain,
! [SV36: $i,SV16: $i,SV46: $i] :
( ( ( in @ SV46 @ SV16 )
= $false )
| ( ( in @ SV36
@ ( sK9_SY61
@ ^ [SX0: $i,SX1: $i] : $true
@ SV16 ) )
= $true )
| ( ( in
@ ( sK4_SY58
@ ^ [SX0: $i,SX1: $i] : $true
@ SV16 )
@ SV16 )
= $true ) ),
inference(sim,[status(thm)],[578]) ).
thf(716,plain,
! [SV103: $i] :
( ( in @ SV103 @ emptyset )
= $false ),
inference(rename,[status(thm)],[75]) ).
thf(717,plain,
! [SV103: $i] :
( ( ( in @ SV103 @ emptyset )
= ( in @ emptyset @ omega ) )
= $false ),
inference(res,[status(thm)],[716,55]) ).
thf(718,plain,
( ( emptyset = omega )
= $false ),
inference(extuni,[status(esa)],[717:[bind(SV103,$thf( emptyset ))]]) ).
thf(719,plain,
! [SV103: $i] :
( ( ( in @ sK2_SY0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi ) )
= ( in @ SV103 @ emptyset ) )
= $false ),
inference(res,[status(thm)],[100,716]) ).
thf(720,plain,
( ( ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi )
= emptyset )
= $false ),
inference(extuni,[status(esa)],[719:[bind(SV103,$thf( sK2_SY0 ))]]) ).
thf(723,plain,
! [SV104: $i] :
( ( ( in @ SV104 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV104 @ SV104 ) @ omega )
= $true ) ),
inference(rename,[status(thm)],[99]) ).
thf(726,plain,
! [SV104: $i,SV103: $i] :
( ( ( ( in @ ( setadjoin @ SV104 @ SV104 ) @ omega )
= ( in @ SV103 @ emptyset ) )
= $false )
| ( ( in @ SV104 @ omega )
= $false ) ),
inference(res,[status(thm)],[723,716]) ).
thf(728,plain,
! [SV104: $i] :
( ( ( ( in @ SV104 @ omega )
= ( in @ sK2_SY0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi ) ) )
= $false )
| ( ( in @ ( setadjoin @ SV104 @ SV104 ) @ omega )
= $true ) ),
inference(res,[status(thm)],[723,100]) ).
thf(729,plain,
! [SV104: $i] :
( ( ( ( in @ SV104 @ omega )
= ( in @ emptyset @ omega ) )
= $false )
| ( ( in @ ( setadjoin @ SV104 @ SV104 ) @ omega )
= $true ) ),
inference(res,[status(thm)],[723,55]) ).
thf(730,plain,
( ( in @ ( setadjoin @ emptyset @ emptyset ) @ omega )
= $true ),
inference(extuni,[status(esa)],[729:[bind(SV104,$thf( emptyset ))]]) ).
thf(731,plain,
( ( ( in @ ( setadjoin @ sK2_SY0 @ sK2_SY0 ) @ omega )
= $true )
| ( ( omega
= ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi ) )
= $false ) ),
inference(extuni,[status(esa)],[728:[bind(SV104,$thf( sK2_SY0 ))]]) ).
thf(732,plain,
! [SV104: $i] :
( ( ( in @ SV104 @ omega )
= $false )
| ( ( omega = emptyset )
= $false ) ),
inference(extuni,[status(esa)],[726:[bind(SV103,$thf( setadjoin @ SV104 @ SV104 ))]]) ).
thf(733,plain,
! [SV105: $i,SV106: $i] :
( ( in @ SV106 @ ( setadjoin @ SV106 @ SV105 ) )
= $true ),
inference(rename,[status(thm)],[637]) ).
thf(734,plain,
! [SV105: $i,SV106: $i,SV104: $i] :
( ( ( ( in @ SV106 @ ( setadjoin @ SV106 @ SV105 ) )
= ( in @ SV104 @ omega ) )
= $false )
| ( ( in @ ( setadjoin @ SV104 @ SV104 ) @ omega )
= $true ) ),
inference(res,[status(thm)],[733,723]) ).
thf(735,plain,
! [SV105: $i,SV106: $i,SV103: $i] :
( ( ( in @ SV106 @ ( setadjoin @ SV106 @ SV105 ) )
= ( in @ SV103 @ emptyset ) )
= $false ),
inference(res,[status(thm)],[733,716]) ).
thf(737,plain,
! [SV105: $i,SV103: $i] :
( ( ( setadjoin @ SV103 @ SV105 )
= emptyset )
= $false ),
inference(extuni,[status(esa)],[735:[bind(SV106,$thf( SV103 ))]]) ).
thf(738,plain,
! [SV105: $i,SV104: $i] :
( ( ( in @ ( setadjoin @ SV104 @ SV104 ) @ omega )
= $true )
| ( ( ( setadjoin @ SV104 @ SV105 )
= omega )
= $false ) ),
inference(extuni,[status(esa)],[734:[bind(SV106,$thf( SV104 ))]]) ).
thf(739,plain,
! [SV107: $i,SV108: $i] :
( ( in @ SV108
@ ( dsetconstr @ SV107
@ ^ [SX0: $i] : $false ) )
= $false ),
inference(rename,[status(thm)],[712]) ).
thf(740,plain,
! [SV107: $i,SV108: $i,SV105: $i,SV106: $i] :
( ( ( in @ SV108
@ ( dsetconstr @ SV107
@ ^ [SX0: $i] : $false ) )
= ( in @ SV106 @ ( setadjoin @ SV106 @ SV105 ) ) )
= $false ),
inference(res,[status(thm)],[739,733]) ).
thf(741,plain,
! [SV107: $i,SV108: $i,SV104: $i] :
( ( ( ( in @ SV108
@ ( dsetconstr @ SV107
@ ^ [SX0: $i] : $false ) )
= ( in @ ( setadjoin @ SV104 @ SV104 ) @ omega ) )
= $false )
| ( ( in @ SV104 @ omega )
= $false ) ),
inference(res,[status(thm)],[739,723]) ).
thf(742,plain,
! [SV107: $i,SV108: $i] :
( ( ( in @ SV108
@ ( dsetconstr @ SV107
@ ^ [SX0: $i] : $false ) )
= ( in @ sK2_SY0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi ) ) )
= $false ),
inference(res,[status(thm)],[739,100]) ).
thf(743,plain,
! [SV107: $i,SV108: $i] :
( ( ( in @ SV108
@ ( dsetconstr @ SV107
@ ^ [SX0: $i] : $false ) )
= ( in @ emptyset @ omega ) )
= $false ),
inference(res,[status(thm)],[739,55]) ).
thf(744,plain,
! [SV107: $i] :
( ( ( dsetconstr @ SV107
@ ^ [SX0: $i] : $false )
= omega )
= $false ),
inference(extuni,[status(esa)],[743:[bind(SV108,$thf( emptyset ))]]) ).
thf(745,plain,
( ( $false = $true )
| ( sK1_Xphi = $true ) ),
inference(extuni,[status(esa)],[742:[bind(SV107,$thf( powerset @ emptyset )),bind(SV108,$thf( sK2_SY0 ))]]) ).
thf(747,plain,
! [SV107: $i] :
( ( ( dsetconstr @ SV107
@ ^ [SX0: $i] : $false )
= ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX0: $i] : sK1_Xphi ) )
= $false ),
inference(extuni,[status(esa)],[742:[bind(SV108,$thf( sK2_SY0 ))]]) ).
thf(748,plain,
! [SV107: $i,SV104: $i] :
( ( ( in @ SV104 @ omega )
= $false )
| ( ( ( dsetconstr @ SV107
@ ^ [SX0: $i] : $false )
= omega )
= $false ) ),
inference(extuni,[status(esa)],[741:[bind(SV108,$thf( setadjoin @ SV104 @ SV104 ))]]) ).
thf(749,plain,
! [SV105: $i,SV106: $i,SV107: $i] :
( ( ( dsetconstr @ SV107
@ ^ [SX0: $i] : $false )
= ( setadjoin @ SV106 @ SV105 ) )
= $false ),
inference(extuni,[status(esa)],[740:[bind(SV108,$thf( SV106 ))]]) ).
thf(750,plain,
sK1_Xphi = $true,
inference(sim,[status(thm)],[745]) ).
thf(759,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,750,749,748,747,744,739,738,737,733,732,731,730,723,720,718,716,715,714,713,711,710,709,708,707,706,705,704,703,702,701,700,699,698,697,696,695,694,693,692,691,690,689,688,687,686,685,683,681,680,679,678,670,649,648,645,639,638,571,566,565,564,563,562,525,524,523,519,518,511,509,505,504,501,500,488,478,471,468,466,465,456,455,420,413,390,385,379,378,373,359,350,347,335,314,313,277,263,262,261,260,256,246,239,225,214,213,198,188,187,186,168,129,128,117,100]) ).
thf(760,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[759]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU500^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n026.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 15:29:02 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 274.64/46.15
% 274.64/46.15 No.of.Axioms: 0
% 274.64/46.15
% 274.64/46.15 Length.of.Defs: 4160
% 274.64/46.15
% 274.64/46.15 Contains.Choice.Funs: true
% 274.64/46.15 ..................eprover: CPU time limit exceeded, terminating
% 274.64/46.15 .......eprover: CPU time limit exceeded, terminating
% 274.64/46.15 eprover: CPU time limit exceeded, terminating
% 274.64/46.15 .
% 274.64/46.15
% 274.64/46.15 ********************************
% 274.64/46.15 * All subproblems solved! *
% 274.64/46.15 ********************************
% 274.64/46.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:759,loop_count:10,foatp_calls:4,translation:fof_full)
% 274.64/46.15
% 274.64/46.15 %**** Beginning of derivation protocol ****
% 274.64/46.15 % SZS output start CNFRefutation
% See solution above
% 274.64/46.16
% 274.64/46.16 %**** End of derivation protocol ****
% 274.64/46.16 %**** no. of clauses in derivation: 657 ****
% 274.64/46.16 %**** clause counter: 759 ****
% 274.64/46.16
% 274.64/46.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:759,loop_count:10,foatp_calls:4,translation:fof_full)
%------------------------------------------------------------------------------