TSTP Solution File: RNG088+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG088+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:34:21 EDT 2022
% Result : Theorem 0.48s 0.69s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 52
% Syntax : Number of formulae : 753 ( 468 unt; 26 typ; 0 def)
% Number of atoms : 5030 (1755 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 9944 (2249 ~;1697 |; 156 &;5784 @)
% ( 0 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 17 con; 0-2 aty)
% Number of variables : 1220 ( 0 ^1212 !; 8 ?;1220 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aIdeal0,type,
aIdeal0: $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_sK1_W2,type,
sK1_W2: $i > $i > $i ).
thf(tp_sK2_W2,type,
sK2_W2: $i > $i > $i ).
thf(tp_sK3_W0,type,
sK3_W0: $i ).
thf(tp_sK4_SY43,type,
sK4_SY43: $i ).
thf(tp_sK5_W0,type,
sK5_W0: $i ).
thf(tp_sK6_SY44,type,
sK6_SY44: $i ).
thf(tp_sdtasasdt0,type,
sdtasasdt0: $i > $i > $i ).
thf(tp_sdtasdt0,type,
sdtasdt0: $i > $i > $i ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_sdtpldt1,type,
sdtpldt1: $i > $i > $i ).
thf(tp_smndt0,type,
smndt0: $i > $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_sz10,type,
sz10: $i ).
thf(tp_xI,type,
xI: $i ).
thf(tp_xJ,type,
xJ: $i ).
thf(tp_xk,type,
xk: $i ).
thf(tp_xl,type,
xl: $i ).
thf(tp_xm,type,
xm: $i ).
thf(tp_xn,type,
xn: $i ).
thf(tp_xx,type,
xx: $i ).
thf(tp_xy,type,
xy: $i ).
thf(tp_xz,type,
xz: $i ).
thf(1,axiom,
! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ! [W2: $i] :
( ( aElementOf0 @ W2 @ W0 )
=> ( aElementOf0 @ W2 @ W1 ) )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ W1 )
=> ( aElementOf0 @ W2 @ W0 ) ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).
thf(2,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(3,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(4,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
thf(5,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).
thf(6,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
thf(7,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
= ( smndt0 @ W0 ) )
& ( ( smndt0 @ W0 )
= ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
thf(8,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
thf(9,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
thf(10,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
thf(11,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(12,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
thf(13,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
thf(14,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
thf(15,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(16,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
thf(17,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(18,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( aElement0 @ ( smndt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
thf(19,axiom,
aElement0 @ sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(20,axiom,
aElement0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(21,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(22,axiom,
( ( aElementOf0 @ xm @ xI )
& ( aElementOf0 @ xn @ xJ )
& ( xy
= ( sdtpldt0 @ xm @ xn ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).
thf(23,axiom,
( ( aElementOf0 @ xk @ xI )
& ( aElementOf0 @ xl @ xJ )
& ( xx
= ( sdtpldt0 @ xk @ xl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
thf(24,axiom,
( ? [W0: $i,W1: $i] :
( ( aElementOf0 @ W0 @ xI )
& ( aElementOf0 @ W1 @ xJ )
& ( ( sdtpldt0 @ W0 @ W1 )
= xx ) )
& ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
& ? [W0: $i,W1: $i] :
( ( aElementOf0 @ W0 @ xI )
& ( aElementOf0 @ W1 @ xJ )
& ( ( sdtpldt0 @ W0 @ W1 )
= xy ) )
& ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElement0 @ xz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
thf(25,axiom,
( ( aSet0 @ xI )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xI )
=> ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
=> ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) )
& ! [W1: $i] :
( ( aElement0 @ W1 )
=> ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) ) )
& ( aIdeal0 @ xI )
& ( aSet0 @ xJ )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xJ )
=> ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xJ )
=> ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xJ ) )
& ! [W1: $i] :
( ( aElement0 @ W1 )
=> ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xJ ) ) ) )
& ( aIdeal0 @ xJ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
thf(26,conjecture,
( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
& ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(27,negated_conjecture,
( ( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
& ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) )
= $false ),
inference(negate_conjecture,[status(cth)],[26]) ).
thf(28,plain,
( ( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
& ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) )
= $false ),
inference(unfold_def,[status(thm)],[27]) ).
thf(29,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ! [W2: $i] :
( ( aElementOf0 @ W2 @ W0 )
=> ( aElementOf0 @ W2 @ W1 ) )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ W1 )
=> ( aElementOf0 @ W2 @ W0 ) ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(30,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(31,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(32,plain,
( ( ( sz10 != sz00 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(33,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(34,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(35,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
= ( smndt0 @ W0 ) )
& ( ( smndt0 @ W0 )
= ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(36,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(37,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(38,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(39,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(40,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(42,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(43,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( aElement0 @ ( smndt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,plain,
( ( aElement0 @ sz10 )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(48,plain,
( ( aElement0 @ sz00 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(49,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(50,plain,
( ( ( aElementOf0 @ xm @ xI )
& ( aElementOf0 @ xn @ xJ )
& ( xy
= ( sdtpldt0 @ xm @ xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(51,plain,
( ( ( aElementOf0 @ xk @ xI )
& ( aElementOf0 @ xl @ xJ )
& ( xx
= ( sdtpldt0 @ xk @ xl ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(52,plain,
( ( ? [W0: $i,W1: $i] :
( ( aElementOf0 @ W0 @ xI )
& ( aElementOf0 @ W1 @ xJ )
& ( ( sdtpldt0 @ W0 @ W1 )
= xx ) )
& ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
& ? [W0: $i,W1: $i] :
( ( aElementOf0 @ W0 @ xI )
& ( aElementOf0 @ W1 @ xJ )
& ( ( sdtpldt0 @ W0 @ W1 )
= xy ) )
& ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElement0 @ xz ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(53,plain,
( ( ( aSet0 @ xI )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xI )
=> ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
=> ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) )
& ! [W1: $i] :
( ( aElement0 @ W1 )
=> ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) ) )
& ( aIdeal0 @ xI )
& ( aSet0 @ xJ )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xJ )
=> ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xJ )
=> ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xJ ) )
& ! [W1: $i] :
( ( aElement0 @ W1 )
=> ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xJ ) ) ) )
& ( aIdeal0 @ xJ ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(54,plain,
( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[28]) ).
thf(55,plain,
( ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[28]) ).
thf(56,plain,
( ( ~ ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI ) )
= $true ),
inference(polarity_switch,[status(thm)],[54]) ).
thf(57,plain,
( ( ~ ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) )
= $true ),
inference(polarity_switch,[status(thm)],[55]) ).
thf(58,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( aSet0 @ W1 )
| ( ( aElementOf0 @ ( sK2_W2 @ W1 @ W0 ) @ W0 )
& ~ ( aElementOf0 @ ( sK2_W2 @ W1 @ W0 ) @ W1 ) )
| ( ( aElementOf0 @ ( sK1_W2 @ W1 @ W0 ) @ W1 )
& ~ ( aElementOf0 @ ( sK1_W2 @ W1 @ W0 ) @ W0 ) )
| ( W0 = W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(59,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ W0 )
| ( aElement0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(60,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(61,plain,
( ( ( sz10 != sz00 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(62,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(63,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(64,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
= ( smndt0 @ W0 ) ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( smndt0 @ W0 )
= ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(65,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(66,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz10 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(67,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(68,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(69,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(70,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(71,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(72,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(73,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(74,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(75,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( aElement0 @ ( smndt0 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(76,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(77,plain,
( ( ( aElementOf0 @ sK5_W0 @ xI )
& ( aElementOf0 @ sK6_SY44 @ xJ )
& ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
= xx )
& ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElementOf0 @ sK3_W0 @ xI )
& ( aElementOf0 @ sK4_SY43 @ xJ )
& ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
= xy )
& ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElement0 @ xz ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(78,plain,
( ( ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xJ )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xJ ) ) )
& ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xJ )
| ! [W1: $i] :
( ~ ( aElement0 @ W1 )
| ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xJ ) ) )
& ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xI )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) ) )
& ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xI )
| ! [W1: $i] :
( ~ ( aElement0 @ W1 )
| ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) )
& ( aSet0 @ xI )
& ( aIdeal0 @ xI )
& ( aSet0 @ xJ )
& ( aIdeal0 @ xJ ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(79,plain,
( ( ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xJ )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xJ ) ) )
& ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xJ )
| ! [W1: $i] :
( ~ ( aElement0 @ W1 )
| ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xJ ) ) )
& ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xI )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) ) )
& ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xI )
| ! [W1: $i] :
( ~ ( aElement0 @ W1 )
| ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) )
& ( aSet0 @ xI )
& ( aIdeal0 @ xI )
& ( aSet0 @ xJ )
& ( aIdeal0 @ xJ ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(80,plain,
( ( ( aElementOf0 @ sK5_W0 @ xI )
& ( aElementOf0 @ sK6_SY44 @ xJ )
& ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
= xx )
& ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElementOf0 @ sK3_W0 @ xI )
& ( aElementOf0 @ sK4_SY43 @ xJ )
& ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
= xy )
& ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElement0 @ xz ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(81,plain,
( ( ( aElementOf0 @ xk @ xI )
& ( aElementOf0 @ xl @ xJ )
& ( xx
= ( sdtpldt0 @ xk @ xl ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(82,plain,
( ( ( aElementOf0 @ xm @ xI )
& ( aElementOf0 @ xn @ xJ )
& ( xy
= ( sdtpldt0 @ xm @ xn ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(83,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(84,plain,
( ( aElement0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(85,plain,
( ( aElement0 @ sz10 )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(86,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( aElement0 @ ( smndt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(87,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(88,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(89,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(90,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(91,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(92,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(93,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(94,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(95,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz10 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(96,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(97,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
= ( smndt0 @ W0 ) ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( smndt0 @ W0 )
= ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(98,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(99,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(100,plain,
( ( ( sz10 != sz00 ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(101,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(102,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ W0 )
| ( aElement0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(103,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( aSet0 @ W1 )
| ( ( aElementOf0 @ ( sK2_W2 @ W1 @ W0 ) @ W0 )
& ~ ( aElementOf0 @ ( sK2_W2 @ W1 @ W0 ) @ W1 ) )
| ( ( aElementOf0 @ ( sK1_W2 @ W1 @ W0 ) @ W1 )
& ~ ( aElementOf0 @ ( sK1_W2 @ W1 @ W0 ) @ W0 ) )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(104,plain,
( ( ~ ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(105,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(106,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(107,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
= ( smndt0 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( smndt0 @ SX0 )
= ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(108,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(109,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(110,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) )
| ( xx
!= ( sdtpldt0 @ xk @ xl ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(111,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 )
| ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 )
| ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SX1 @ SX2 ) @ SX0 )
= ( sdtpldt0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ ( sdtasdt0 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(112,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
| ~ ( aIdeal0 @ xJ ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(113,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) )
| ( xy
!= ( sdtpldt0 @ xm @ xn ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aSet0 @ SX0 )
| ~ ( aSet0 @ SX1 )
| ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SX1 @ SX0 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(115,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ( aElement0 @ xz ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(116,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(117,plain,
! [SV2: $i] :
( ( ~ ( aElement0 @ SV2 )
| ( aElement0 @ ( smndt0 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(118,plain,
! [SV3: $i] :
( ( ! [SY45: $i] :
( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SY45 )
| ( aElement0 @ ( sdtpldt0 @ SV3 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(119,plain,
! [SV4: $i] :
( ( ! [SY46: $i] :
( ~ ( aElement0 @ SV4 )
| ~ ( aElement0 @ SY46 )
| ( aElement0 @ ( sdtasdt0 @ SV4 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(120,plain,
! [SV5: $i] :
( ( ! [SY47: $i] :
( ~ ( aElement0 @ SV5 )
| ~ ( aElement0 @ SY47 )
| ( ( sdtpldt0 @ SV5 @ SY47 )
= ( sdtpldt0 @ SY47 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(121,plain,
! [SV6: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SY48 )
| ~ ( aElement0 @ SY49 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SY48 ) @ SY49 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SY48 @ SY49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(122,plain,
! [SV7: $i] :
( ( ! [SY50: $i] :
( ~ ( aElement0 @ SV7 )
| ~ ( aElement0 @ SY50 )
| ( ( sdtasdt0 @ SV7 @ SY50 )
= ( sdtasdt0 @ SY50 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(123,plain,
! [SV8: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ( aElement0 @ SV8 )
| ~ ( aElement0 @ SY51 )
| ~ ( aElement0 @ SY52 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SY51 ) @ SY52 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SY51 @ SY52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(124,plain,
! [SV9: $i] :
( ( ! [SY53: $i] :
( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SY53 )
| ( ( sdtasdt0 @ SV9 @ SY53 )
!= sz00 )
| ( SV9 = sz00 )
| ( SY53 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(125,plain,
( ( sz10 = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(126,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(127,plain,
! [SV11: $i] :
( ( ~ ( aSet0 @ SV11 )
| ! [SY54: $i] :
( ~ ( aElementOf0 @ SY54 @ SV11 )
| ( aElement0 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(128,plain,
( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(129,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(130,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(131,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
= ( smndt0 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( smndt0 @ SX0 )
= ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(132,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(133,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(134,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) )
| ( xx
!= ( sdtpldt0 @ xk @ xl ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(135,plain,
! [SV12: $i] :
( ( ~ ( ~ ! [SY55: $i,SY56: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SY55 )
| ~ ( aElement0 @ SY56 )
| ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SY55 @ SY56 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SY55 ) @ ( sdtasdt0 @ SV12 @ SY56 ) ) ) )
| ~ ! [SY57: $i,SY58: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SY57 )
| ~ ( aElement0 @ SY58 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY57 @ SY58 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY57 @ SV12 ) @ ( sdtasdt0 @ SY58 @ SV12 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(136,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
| ~ ( aIdeal0 @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(137,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) )
| ( xy
!= ( sdtpldt0 @ xm @ xn ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(138,plain,
! [SV13: $i] :
( ( ! [SY59: $i] :
( ~ ( aSet0 @ SV13 )
| ~ ( aSet0 @ SY59 )
| ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SY59 @ SV13 ) @ SV13 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SY59 @ SV13 ) @ SY59 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SY59 @ SV13 ) @ SY59 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SY59 @ SV13 ) @ SV13 ) )
| ( SV13 = SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(139,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ( aElement0 @ xz ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(140,plain,
! [SV2: $i] :
( ( ( ~ ( aElement0 @ SV2 ) )
= $true )
| ( ( aElement0 @ ( smndt0 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(141,plain,
! [SV14: $i,SV3: $i] :
( ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 )
| ( aElement0 @ ( sdtpldt0 @ SV3 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(142,plain,
! [SV15: $i,SV4: $i] :
( ( ~ ( aElement0 @ SV4 )
| ~ ( aElement0 @ SV15 )
| ( aElement0 @ ( sdtasdt0 @ SV4 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(143,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( aElement0 @ SV5 )
| ~ ( aElement0 @ SV16 )
| ( ( sdtpldt0 @ SV5 @ SV16 )
= ( sdtpldt0 @ SV16 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(144,plain,
! [SV17: $i,SV6: $i] :
( ( ! [SY60: $i] :
( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SV17 )
| ~ ( aElement0 @ SY60 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV17 ) @ SY60 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV17 @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(145,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ( aElement0 @ SV7 )
| ~ ( aElement0 @ SV18 )
| ( ( sdtasdt0 @ SV7 @ SV18 )
= ( sdtasdt0 @ SV18 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(146,plain,
! [SV19: $i,SV8: $i] :
( ( ! [SY61: $i] :
( ~ ( aElement0 @ SV8 )
| ~ ( aElement0 @ SV19 )
| ~ ( aElement0 @ SY61 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV19 ) @ SY61 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV19 @ SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(147,plain,
! [SV20: $i,SV9: $i] :
( ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV20 )
| ( ( sdtasdt0 @ SV9 @ SV20 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV20 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(148,plain,
! [SV11: $i] :
( ( ( ~ ( aSet0 @ SV11 ) )
= $true )
| ( ( ! [SY54: $i] :
( ~ ( aElementOf0 @ SY54 @ SV11 )
| ( aElement0 @ SY54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(149,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(150,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(151,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(152,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(153,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
= ( smndt0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(154,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( smndt0 @ SX0 )
= ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(155,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(156,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(157,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(158,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(159,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(160,plain,
( ( ( xx
!= ( sdtpldt0 @ xk @ xl ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(161,plain,
! [SV12: $i] :
( ( ~ ! [SY55: $i,SY56: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SY55 )
| ~ ( aElement0 @ SY56 )
| ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SY55 @ SY56 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SY55 ) @ ( sdtasdt0 @ SV12 @ SY56 ) ) ) )
| ~ ! [SY57: $i,SY58: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SY57 )
| ~ ( aElement0 @ SY58 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY57 @ SY58 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY57 @ SV12 ) @ ( sdtasdt0 @ SY58 @ SV12 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(162,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(163,plain,
( ( ~ ( aIdeal0 @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(164,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(165,plain,
( ( ( xy
!= ( sdtpldt0 @ xm @ xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(166,plain,
! [SV21: $i,SV13: $i] :
( ( ~ ( aSet0 @ SV13 )
| ~ ( aSet0 @ SV21 )
| ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
| ( SV13 = SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(167,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(168,plain,
( ( ~ ( aElement0 @ xz ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(169,plain,
! [SV2: $i] :
( ( ( aElement0 @ SV2 )
= $false )
| ( ( aElement0 @ ( smndt0 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(170,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(171,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( aElement0 @ SV4 )
| ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(172,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( aElement0 @ SV5 )
| ~ ( aElement0 @ SV16 ) )
= $true )
| ( ( ( sdtpldt0 @ SV5 @ SV16 )
= ( sdtpldt0 @ SV16 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(173,plain,
! [SV22: $i,SV17: $i,SV6: $i] :
( ( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SV17 )
| ~ ( aElement0 @ SV22 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV17 ) @ SV22 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV17 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(174,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( aElement0 @ SV7 )
| ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ( sdtasdt0 @ SV7 @ SV18 )
= ( sdtasdt0 @ SV18 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(175,plain,
! [SV23: $i,SV19: $i,SV8: $i] :
( ( ~ ( aElement0 @ SV8 )
| ~ ( aElement0 @ SV19 )
| ~ ( aElement0 @ SV23 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV19 ) @ SV23 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV19 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(176,plain,
! [SV20: $i,SV9: $i] :
( ( ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV20 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV9 @ SV20 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV20 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(177,plain,
! [SV11: $i] :
( ( ( aSet0 @ SV11 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( aElementOf0 @ SY54 @ SV11 )
| ( aElement0 @ SY54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(178,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(179,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(180,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(181,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(182,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
= ( smndt0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(183,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( smndt0 @ SX0 )
= ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(184,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(185,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(186,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(187,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(188,plain,
( ( ~ ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(189,plain,
( ( xx
= ( sdtpldt0 @ xk @ xl ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(190,plain,
! [SV12: $i] :
( ( ~ ! [SY55: $i,SY56: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SY55 )
| ~ ( aElement0 @ SY56 )
| ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SY55 @ SY56 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SY55 ) @ ( sdtasdt0 @ SV12 @ SY56 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(191,plain,
! [SV12: $i] :
( ( ~ ! [SY57: $i,SY58: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SY57 )
| ~ ( aElement0 @ SY58 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY57 @ SY58 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY57 @ SV12 ) @ ( sdtasdt0 @ SY58 @ SV12 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(192,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(193,plain,
( ( aIdeal0 @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(194,plain,
( ( ~ ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(195,plain,
( ( xy
= ( sdtpldt0 @ xm @ xn ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(196,plain,
! [SV21: $i,SV13: $i] :
( ( ( ~ ( aSet0 @ SV13 )
| ~ ( aSet0 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
| ( SV13 = SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(197,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(198,plain,
( ( aElement0 @ xz )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(199,plain,
! [SV14: $i,SV3: $i] :
( ( ( ~ ( aElement0 @ SV3 ) )
= $true )
| ( ( ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(200,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( aElement0 @ SV4 ) )
= $true )
| ( ( ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(201,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( aElement0 @ SV5 ) )
= $true )
| ( ( ~ ( aElement0 @ SV16 ) )
= $true )
| ( ( ( sdtpldt0 @ SV5 @ SV16 )
= ( sdtpldt0 @ SV16 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(202,plain,
! [SV22: $i,SV17: $i,SV6: $i] :
( ( ( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SV17 )
| ~ ( aElement0 @ SV22 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV17 ) @ SV22 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV17 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(203,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( aElement0 @ SV7 ) )
= $true )
| ( ( ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ( sdtasdt0 @ SV7 @ SV18 )
= ( sdtasdt0 @ SV18 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(204,plain,
! [SV23: $i,SV19: $i,SV8: $i] :
( ( ( ~ ( aElement0 @ SV8 )
| ~ ( aElement0 @ SV19 )
| ~ ( aElement0 @ SV23 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV19 ) @ SV23 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV19 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(205,plain,
! [SV20: $i,SV9: $i] :
( ( ( ~ ( aElement0 @ SV9 ) )
= $true )
| ( ( ~ ( aElement0 @ SV20 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV9 @ SV20 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV20 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(206,plain,
! [SV11: $i,SV24: $i] :
( ( ( ~ ( aElementOf0 @ SV24 @ SV11 )
| ( aElement0 @ SV24 ) )
= $true )
| ( ( aSet0 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(207,plain,
! [SV25: $i] :
( ( ~ ( aElement0 @ SV25 )
| ( ( sdtpldt0 @ SV25 @ ( smndt0 @ SV25 ) )
= sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(208,plain,
! [SV26: $i] :
( ( ~ ( aElement0 @ SV26 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SV26 ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(209,plain,
! [SV27: $i] :
( ( ~ ( aElement0 @ SV27 )
| ( ( sdtasdt0 @ SV27 @ sz10 )
= SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(210,plain,
! [SV28: $i] :
( ( ~ ( aElement0 @ SV28 )
| ( SV28
= ( sdtasdt0 @ sz10 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(211,plain,
! [SV29: $i] :
( ( ~ ( aElement0 @ SV29 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV29 )
= ( smndt0 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(212,plain,
! [SV30: $i] :
( ( ~ ( aElement0 @ SV30 )
| ( ( smndt0 @ SV30 )
= ( sdtasdt0 @ SV30 @ ( smndt0 @ sz10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(213,plain,
! [SV31: $i] :
( ( ~ ( aElement0 @ SV31 )
| ( ( sdtpldt0 @ SV31 @ sz00 )
= SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(214,plain,
! [SV32: $i] :
( ( ~ ( aElement0 @ SV32 )
| ( SV32
= ( sdtpldt0 @ sz00 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(215,plain,
! [SV33: $i] :
( ( ~ ( aElement0 @ SV33 )
| ( ( sdtasdt0 @ SV33 @ sz00 )
= sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(216,plain,
! [SV34: $i] :
( ( ~ ( aElement0 @ SV34 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(217,plain,
( ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(218,plain,
! [SV12: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SY55 )
| ~ ( aElement0 @ SY56 )
| ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SY55 @ SY56 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SY55 ) @ ( sdtasdt0 @ SV12 @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(219,plain,
! [SV12: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SY57 )
| ~ ( aElement0 @ SY58 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY57 @ SY58 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY57 @ SV12 ) @ ( sdtasdt0 @ SY58 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(220,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(221,plain,
( ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(222,plain,
! [SV21: $i,SV13: $i] :
( ( ( ~ ( aSet0 @ SV13 ) )
= $true )
| ( ( ~ ( aSet0 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
| ( SV13 = SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(223,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(224,plain,
! [SV14: $i,SV3: $i] :
( ( ( aElement0 @ SV3 )
= $false )
| ( ( ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(225,plain,
! [SV15: $i,SV4: $i] :
( ( ( aElement0 @ SV4 )
= $false )
| ( ( ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(226,plain,
! [SV16: $i,SV5: $i] :
( ( ( aElement0 @ SV5 )
= $false )
| ( ( ~ ( aElement0 @ SV16 ) )
= $true )
| ( ( ( sdtpldt0 @ SV5 @ SV16 )
= ( sdtpldt0 @ SV16 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(227,plain,
! [SV22: $i,SV17: $i,SV6: $i] :
( ( ( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SV17 ) )
= $true )
| ( ( ~ ( aElement0 @ SV22 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV17 ) @ SV22 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV17 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(228,plain,
! [SV18: $i,SV7: $i] :
( ( ( aElement0 @ SV7 )
= $false )
| ( ( ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ( sdtasdt0 @ SV7 @ SV18 )
= ( sdtasdt0 @ SV18 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(229,plain,
! [SV23: $i,SV19: $i,SV8: $i] :
( ( ( ~ ( aElement0 @ SV8 )
| ~ ( aElement0 @ SV19 ) )
= $true )
| ( ( ~ ( aElement0 @ SV23 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV19 ) @ SV23 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV19 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(230,plain,
! [SV20: $i,SV9: $i] :
( ( ( aElement0 @ SV9 )
= $false )
| ( ( ~ ( aElement0 @ SV20 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV9 @ SV20 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV20 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(231,plain,
! [SV11: $i,SV24: $i] :
( ( ( ~ ( aElementOf0 @ SV24 @ SV11 ) )
= $true )
| ( ( aElement0 @ SV24 )
= $true )
| ( ( aSet0 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(232,plain,
! [SV25: $i] :
( ( ( ~ ( aElement0 @ SV25 ) )
= $true )
| ( ( ( sdtpldt0 @ SV25 @ ( smndt0 @ SV25 ) )
= sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(233,plain,
! [SV26: $i] :
( ( ( ~ ( aElement0 @ SV26 ) )
= $true )
| ( ( sz00
= ( sdtpldt0 @ ( smndt0 @ SV26 ) @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(234,plain,
! [SV27: $i] :
( ( ( ~ ( aElement0 @ SV27 ) )
= $true )
| ( ( ( sdtasdt0 @ SV27 @ sz10 )
= SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(235,plain,
! [SV28: $i] :
( ( ( ~ ( aElement0 @ SV28 ) )
= $true )
| ( ( SV28
= ( sdtasdt0 @ sz10 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(236,plain,
! [SV29: $i] :
( ( ( ~ ( aElement0 @ SV29 ) )
= $true )
| ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV29 )
= ( smndt0 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(237,plain,
! [SV30: $i] :
( ( ( ~ ( aElement0 @ SV30 ) )
= $true )
| ( ( ( smndt0 @ SV30 )
= ( sdtasdt0 @ SV30 @ ( smndt0 @ sz10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(238,plain,
! [SV31: $i] :
( ( ( ~ ( aElement0 @ SV31 ) )
= $true )
| ( ( ( sdtpldt0 @ SV31 @ sz00 )
= SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(239,plain,
! [SV32: $i] :
( ( ( ~ ( aElement0 @ SV32 ) )
= $true )
| ( ( SV32
= ( sdtpldt0 @ sz00 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(240,plain,
! [SV33: $i] :
( ( ( ~ ( aElement0 @ SV33 ) )
= $true )
| ( ( ( sdtasdt0 @ SV33 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(241,plain,
! [SV34: $i] :
( ( ( ~ ( aElement0 @ SV34 ) )
= $true )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(242,plain,
( ( ~ ( aElementOf0 @ xk @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(243,plain,
( ( ~ ( aElementOf0 @ xl @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(244,plain,
! [SV35: $i,SV12: $i] :
( ( ! [SY62: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SV35 )
| ~ ( aElement0 @ SY62 )
| ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SV35 @ SY62 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SV35 ) @ ( sdtasdt0 @ SV12 @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(245,plain,
! [SV36: $i,SV12: $i] :
( ( ! [SY63: $i] :
( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SV36 )
| ~ ( aElement0 @ SY63 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV36 @ SY63 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV36 @ SV12 ) @ ( sdtasdt0 @ SY63 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(246,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(247,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(248,plain,
( ( ~ ( aElementOf0 @ xm @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(249,plain,
( ( ~ ( aElementOf0 @ xn @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(250,plain,
! [SV21: $i,SV13: $i] :
( ( ( aSet0 @ SV13 )
= $false )
| ( ( ~ ( aSet0 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
| ( SV13 = SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(251,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(252,plain,
( ( ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(253,plain,
! [SV3: $i,SV14: $i] :
( ( ( aElement0 @ SV14 )
= $false )
| ( ( aElement0 @ SV3 )
= $false )
| ( ( aElement0 @ ( sdtpldt0 @ SV3 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(254,plain,
! [SV4: $i,SV15: $i] :
( ( ( aElement0 @ SV15 )
= $false )
| ( ( aElement0 @ SV4 )
= $false )
| ( ( aElement0 @ ( sdtasdt0 @ SV4 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(255,plain,
! [SV5: $i,SV16: $i] :
( ( ( aElement0 @ SV16 )
= $false )
| ( ( aElement0 @ SV5 )
= $false )
| ( ( ( sdtpldt0 @ SV5 @ SV16 )
= ( sdtpldt0 @ SV16 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(256,plain,
! [SV22: $i,SV17: $i,SV6: $i] :
( ( ( ~ ( aElement0 @ SV6 ) )
= $true )
| ( ( ~ ( aElement0 @ SV17 ) )
= $true )
| ( ( ~ ( aElement0 @ SV22 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV17 ) @ SV22 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV17 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(257,plain,
! [SV7: $i,SV18: $i] :
( ( ( aElement0 @ SV18 )
= $false )
| ( ( aElement0 @ SV7 )
= $false )
| ( ( ( sdtasdt0 @ SV7 @ SV18 )
= ( sdtasdt0 @ SV18 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(258,plain,
! [SV23: $i,SV19: $i,SV8: $i] :
( ( ( ~ ( aElement0 @ SV8 ) )
= $true )
| ( ( ~ ( aElement0 @ SV19 ) )
= $true )
| ( ( ~ ( aElement0 @ SV23 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV19 ) @ SV23 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV19 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(259,plain,
! [SV9: $i,SV20: $i] :
( ( ( aElement0 @ SV20 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( ( ( sdtasdt0 @ SV9 @ SV20 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV20 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(260,plain,
! [SV11: $i,SV24: $i] :
( ( ( aElementOf0 @ SV24 @ SV11 )
= $false )
| ( ( aElement0 @ SV24 )
= $true )
| ( ( aSet0 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(261,plain,
! [SV25: $i] :
( ( ( aElement0 @ SV25 )
= $false )
| ( ( ( sdtpldt0 @ SV25 @ ( smndt0 @ SV25 ) )
= sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(262,plain,
! [SV26: $i] :
( ( ( aElement0 @ SV26 )
= $false )
| ( ( sz00
= ( sdtpldt0 @ ( smndt0 @ SV26 ) @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(263,plain,
! [SV27: $i] :
( ( ( aElement0 @ SV27 )
= $false )
| ( ( ( sdtasdt0 @ SV27 @ sz10 )
= SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(264,plain,
! [SV28: $i] :
( ( ( aElement0 @ SV28 )
= $false )
| ( ( SV28
= ( sdtasdt0 @ sz10 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(265,plain,
! [SV29: $i] :
( ( ( aElement0 @ SV29 )
= $false )
| ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV29 )
= ( smndt0 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(266,plain,
! [SV30: $i] :
( ( ( aElement0 @ SV30 )
= $false )
| ( ( ( smndt0 @ SV30 )
= ( sdtasdt0 @ SV30 @ ( smndt0 @ sz10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(267,plain,
! [SV31: $i] :
( ( ( aElement0 @ SV31 )
= $false )
| ( ( ( sdtpldt0 @ SV31 @ sz00 )
= SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(268,plain,
! [SV32: $i] :
( ( ( aElement0 @ SV32 )
= $false )
| ( ( SV32
= ( sdtpldt0 @ sz00 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(269,plain,
! [SV33: $i] :
( ( ( aElement0 @ SV33 )
= $false )
| ( ( ( sdtasdt0 @ SV33 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(270,plain,
! [SV34: $i] :
( ( ( aElement0 @ SV34 )
= $false )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(271,plain,
( ( aElementOf0 @ xk @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(272,plain,
( ( aElementOf0 @ xl @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(273,plain,
! [SV37: $i,SV35: $i,SV12: $i] :
( ( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SV35 )
| ~ ( aElement0 @ SV37 )
| ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SV35 @ SV37 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SV35 ) @ ( sdtasdt0 @ SV12 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(274,plain,
! [SV38: $i,SV36: $i,SV12: $i] :
( ( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SV36 )
| ~ ( aElement0 @ SV38 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV36 @ SV38 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV36 @ SV12 ) @ ( sdtasdt0 @ SV38 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(275,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(276,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(277,plain,
( ( aElementOf0 @ xm @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(278,plain,
( ( aElementOf0 @ xn @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(279,plain,
! [SV13: $i,SV21: $i] :
( ( ( aSet0 @ SV21 )
= $false )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
| ( SV13 = SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(280,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(281,plain,
( ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(282,plain,
! [SV22: $i,SV17: $i,SV6: $i] :
( ( ( aElement0 @ SV6 )
= $false )
| ( ( ~ ( aElement0 @ SV17 ) )
= $true )
| ( ( ~ ( aElement0 @ SV22 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV17 ) @ SV22 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV17 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(283,plain,
! [SV23: $i,SV19: $i,SV8: $i] :
( ( ( aElement0 @ SV8 )
= $false )
| ( ( ~ ( aElement0 @ SV19 ) )
= $true )
| ( ( ~ ( aElement0 @ SV23 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV19 ) @ SV23 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV19 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(284,plain,
! [SV20: $i,SV9: $i] :
( ( ( ( ( sdtasdt0 @ SV9 @ SV20 )
!= sz00 ) )
= $true )
| ( ( ( SV9 = sz00 )
| ( SV20 = sz00 ) )
= $true )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(285,plain,
! [SV37: $i,SV35: $i,SV12: $i] :
( ( ( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SV35 )
| ~ ( aElement0 @ SV37 ) )
= $true )
| ( ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SV35 @ SV37 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SV35 ) @ ( sdtasdt0 @ SV12 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(286,plain,
! [SV38: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SV36 )
| ~ ( aElement0 @ SV38 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV36 @ SV38 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV36 @ SV12 ) @ ( sdtasdt0 @ SV38 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(287,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(288,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(289,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(290,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(291,plain,
! [SV22: $i,SV6: $i,SV17: $i] :
( ( ( aElement0 @ SV17 )
= $false )
| ( ( aElement0 @ SV6 )
= $false )
| ( ( ~ ( aElement0 @ SV22 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV17 ) @ SV22 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV17 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(292,plain,
! [SV23: $i,SV8: $i,SV19: $i] :
( ( ( aElement0 @ SV19 )
= $false )
| ( ( aElement0 @ SV8 )
= $false )
| ( ( ~ ( aElement0 @ SV23 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV19 ) @ SV23 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV19 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(293,plain,
! [SV20: $i,SV9: $i] :
( ( ( ( sdtasdt0 @ SV9 @ SV20 )
= sz00 )
= $false )
| ( ( ( SV9 = sz00 )
| ( SV20 = sz00 ) )
= $true )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(294,plain,
! [SV37: $i,SV35: $i,SV12: $i] :
( ( ( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SV35 ) )
= $true )
| ( ( ~ ( aElement0 @ SV37 ) )
= $true )
| ( ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SV35 @ SV37 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SV35 ) @ ( sdtasdt0 @ SV12 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(295,plain,
! [SV38: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( aElement0 @ SV12 )
| ~ ( aElement0 @ SV36 ) )
= $true )
| ( ( ~ ( aElement0 @ SV38 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV36 @ SV38 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV36 @ SV12 ) @ ( sdtasdt0 @ SV38 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(296,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(297,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(298,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(299,plain,
( ( ~ ( aSet0 @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(300,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(301,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(302,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(303,plain,
! [SV17: $i,SV6: $i,SV22: $i] :
( ( ( aElement0 @ SV22 )
= $false )
| ( ( aElement0 @ SV6 )
= $false )
| ( ( aElement0 @ SV17 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV17 ) @ SV22 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV17 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(304,plain,
! [SV19: $i,SV8: $i,SV23: $i] :
( ( ( aElement0 @ SV23 )
= $false )
| ( ( aElement0 @ SV8 )
= $false )
| ( ( aElement0 @ SV19 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV19 ) @ SV23 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV19 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(305,plain,
! [SV20: $i,SV9: $i] :
( ( ( SV9 = sz00 )
= $true )
| ( ( SV20 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV9 @ SV20 )
= sz00 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(306,plain,
! [SV37: $i,SV35: $i,SV12: $i] :
( ( ( ~ ( aElement0 @ SV12 ) )
= $true )
| ( ( ~ ( aElement0 @ SV35 ) )
= $true )
| ( ( ~ ( aElement0 @ SV37 ) )
= $true )
| ( ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SV35 @ SV37 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SV35 ) @ ( sdtasdt0 @ SV12 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(307,plain,
! [SV38: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( aElement0 @ SV12 ) )
= $true )
| ( ( ~ ( aElement0 @ SV36 ) )
= $true )
| ( ( ~ ( aElement0 @ SV38 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV36 @ SV38 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV36 @ SV12 ) @ ( sdtasdt0 @ SV38 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(308,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(309,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(310,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(311,plain,
( ( aSet0 @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(312,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(313,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(314,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(315,plain,
! [SV37: $i,SV35: $i,SV12: $i] :
( ( ( aElement0 @ SV12 )
= $false )
| ( ( ~ ( aElement0 @ SV35 ) )
= $true )
| ( ( ~ ( aElement0 @ SV37 ) )
= $true )
| ( ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SV35 @ SV37 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SV35 ) @ ( sdtasdt0 @ SV12 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(316,plain,
! [SV38: $i,SV36: $i,SV12: $i] :
( ( ( aElement0 @ SV12 )
= $false )
| ( ( ~ ( aElement0 @ SV36 ) )
= $true )
| ( ( ~ ( aElement0 @ SV38 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV36 @ SV38 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV36 @ SV12 ) @ ( sdtasdt0 @ SV38 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(317,plain,
! [SV39: $i] :
( ( ~ ( aElementOf0 @ SV39 @ xJ )
| ! [SY64: $i] :
( ~ ( aElementOf0 @ SY64 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SV39 @ SY64 ) @ xJ ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(318,plain,
! [SV40: $i] :
( ( ~ ( aElementOf0 @ SV40 @ xJ )
| ! [SY65: $i] :
( ~ ( aElement0 @ SY65 )
| ( aElementOf0 @ ( sdtasdt0 @ SY65 @ SV40 ) @ xJ ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(319,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(320,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(321,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(322,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(323,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(324,plain,
! [SV37: $i,SV12: $i,SV35: $i] :
( ( ( aElement0 @ SV35 )
= $false )
| ( ( aElement0 @ SV12 )
= $false )
| ( ( ~ ( aElement0 @ SV37 ) )
= $true )
| ( ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SV35 @ SV37 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SV35 ) @ ( sdtasdt0 @ SV12 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(325,plain,
! [SV38: $i,SV12: $i,SV36: $i] :
( ( ( aElement0 @ SV36 )
= $false )
| ( ( aElement0 @ SV12 )
= $false )
| ( ( ~ ( aElement0 @ SV38 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV36 @ SV38 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV36 @ SV12 ) @ ( sdtasdt0 @ SV38 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(326,plain,
! [SV39: $i] :
( ( ( ~ ( aElementOf0 @ SV39 @ xJ ) )
= $true )
| ( ( ! [SY64: $i] :
( ~ ( aElementOf0 @ SY64 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SV39 @ SY64 ) @ xJ ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(327,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ SV40 @ xJ ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( aElement0 @ SY65 )
| ( aElementOf0 @ ( sdtasdt0 @ SY65 @ SV40 ) @ xJ ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(328,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(329,plain,
( ( ~ ( aIdeal0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(330,plain,
! [SV13: $i,SV21: $i] :
( ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(331,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(332,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(333,plain,
( ( ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(334,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(335,plain,
( ( ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(336,plain,
! [SV35: $i,SV12: $i,SV37: $i] :
( ( ( aElement0 @ SV37 )
= $false )
| ( ( aElement0 @ SV12 )
= $false )
| ( ( aElement0 @ SV35 )
= $false )
| ( ( ( sdtasdt0 @ SV12 @ ( sdtpldt0 @ SV35 @ SV37 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV12 @ SV35 ) @ ( sdtasdt0 @ SV12 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(337,plain,
! [SV36: $i,SV12: $i,SV38: $i] :
( ( ( aElement0 @ SV38 )
= $false )
| ( ( aElement0 @ SV12 )
= $false )
| ( ( aElement0 @ SV36 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV36 @ SV38 ) @ SV12 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV36 @ SV12 ) @ ( sdtasdt0 @ SV38 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(338,plain,
! [SV39: $i] :
( ( ( aElementOf0 @ SV39 @ xJ )
= $false )
| ( ( ! [SY64: $i] :
( ~ ( aElementOf0 @ SY64 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SV39 @ SY64 ) @ xJ ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(339,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ SV40 @ xJ )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( aElement0 @ SY65 )
| ( aElementOf0 @ ( sdtasdt0 @ SY65 @ SV40 ) @ xJ ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(340,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(341,plain,
( ( aIdeal0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(342,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(343,plain,
! [SV13: $i,SV21: $i] :
( ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(344,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(345,plain,
( ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(346,plain,
( ( ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(347,plain,
( ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
= xy )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(348,plain,
! [SV39: $i,SV41: $i] :
( ( ( ~ ( aElementOf0 @ SV41 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SV39 @ SV41 ) @ xJ ) )
= $true )
| ( ( aElementOf0 @ SV39 @ xJ )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(349,plain,
! [SV40: $i,SV42: $i] :
( ( ( ~ ( aElement0 @ SV42 )
| ( aElementOf0 @ ( sdtasdt0 @ SV42 @ SV40 ) @ xJ ) )
= $true )
| ( ( aElementOf0 @ SV40 @ xJ )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(350,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(351,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(352,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(353,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 )
= $false )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(354,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(355,plain,
( ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(356,plain,
! [SV39: $i,SV41: $i] :
( ( ( ~ ( aElementOf0 @ SV41 @ xJ ) )
= $true )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV39 @ SV41 ) @ xJ )
= $true )
| ( ( aElementOf0 @ SV39 @ xJ )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(357,plain,
! [SV40: $i,SV42: $i] :
( ( ( ~ ( aElement0 @ SV42 ) )
= $true )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV42 @ SV40 ) @ xJ )
= $true )
| ( ( aElementOf0 @ SV40 @ xJ )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(358,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(359,plain,
( ( ~ ( aSet0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(360,plain,
! [SV13: $i,SV21: $i] :
( ( ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
= $true )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(361,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
= $true )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(362,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 )
= $false )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(363,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 )
= $false )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(364,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(365,plain,
( ( ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(366,plain,
( ( ~ ( aElementOf0 @ sK3_W0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(367,plain,
( ( ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(368,plain,
! [SV39: $i,SV41: $i] :
( ( ( aElementOf0 @ SV41 @ xJ )
= $false )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV39 @ SV41 ) @ xJ )
= $true )
| ( ( aElementOf0 @ SV39 @ xJ )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(369,plain,
! [SV40: $i,SV42: $i] :
( ( ( aElement0 @ SV42 )
= $false )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV42 @ SV40 ) @ xJ )
= $true )
| ( ( aElementOf0 @ SV40 @ xJ )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(370,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(371,plain,
( ( aSet0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(372,plain,
! [SV13: $i,SV21: $i] :
( ( ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(373,plain,
! [SV13: $i,SV21: $i] :
( ( ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV21 )
= $true )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 )
= $false )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(374,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 ) )
= $true )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 )
= $false )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(375,plain,
( ( ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(376,plain,
( ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
= xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(377,plain,
( ( aElementOf0 @ sK3_W0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(378,plain,
( ( aElementOf0 @ sK4_SY43 @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(379,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(380,plain,
! [SV13: $i,SV21: $i] :
( ( ( aElementOf0 @ ( sK1_W2 @ SV21 @ SV13 ) @ SV13 )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV21 @ SV13 ) @ SV21 )
= $false )
| ( ( SV13 = SV21 )
= $true )
| ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(381,plain,
( ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(382,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(383,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(384,plain,
( ( ~ ( aElementOf0 @ sK5_W0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(385,plain,
( ( ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(386,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(387,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(388,plain,
( ( aElementOf0 @ sK5_W0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(389,plain,
( ( aElementOf0 @ sK6_SY44 @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(390,plain,
! [SV43: $i] :
( ( ~ ( aElementOf0 @ SV43 @ xI )
| ! [SY66: $i] :
( ~ ( aElementOf0 @ SY66 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV43 @ SY66 ) @ xI ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(391,plain,
! [SV44: $i] :
( ( ~ ( aElementOf0 @ SV44 @ xI )
| ! [SY67: $i] :
( ~ ( aElement0 @ SY67 )
| ( aElementOf0 @ ( sdtasdt0 @ SY67 @ SV44 ) @ xI ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(392,plain,
! [SV43: $i] :
( ( ( ~ ( aElementOf0 @ SV43 @ xI ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( aElementOf0 @ SY66 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV43 @ SY66 ) @ xI ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(393,plain,
! [SV44: $i] :
( ( ( ~ ( aElementOf0 @ SV44 @ xI ) )
= $true )
| ( ( ! [SY67: $i] :
( ~ ( aElement0 @ SY67 )
| ( aElementOf0 @ ( sdtasdt0 @ SY67 @ SV44 ) @ xI ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(394,plain,
! [SV43: $i] :
( ( ( aElementOf0 @ SV43 @ xI )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( aElementOf0 @ SY66 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV43 @ SY66 ) @ xI ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(395,plain,
! [SV44: $i] :
( ( ( aElementOf0 @ SV44 @ xI )
= $false )
| ( ( ! [SY67: $i] :
( ~ ( aElement0 @ SY67 )
| ( aElementOf0 @ ( sdtasdt0 @ SY67 @ SV44 ) @ xI ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(396,plain,
! [SV43: $i,SV45: $i] :
( ( ( ~ ( aElementOf0 @ SV45 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV43 @ SV45 ) @ xI ) )
= $true )
| ( ( aElementOf0 @ SV43 @ xI )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(397,plain,
! [SV44: $i,SV46: $i] :
( ( ( ~ ( aElement0 @ SV46 )
| ( aElementOf0 @ ( sdtasdt0 @ SV46 @ SV44 ) @ xI ) )
= $true )
| ( ( aElementOf0 @ SV44 @ xI )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(398,plain,
! [SV43: $i,SV45: $i] :
( ( ( ~ ( aElementOf0 @ SV45 @ xI ) )
= $true )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV43 @ SV45 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV43 @ xI )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(399,plain,
! [SV44: $i,SV46: $i] :
( ( ( ~ ( aElement0 @ SV46 ) )
= $true )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV46 @ SV44 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV44 @ xI )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(400,plain,
! [SV43: $i,SV45: $i] :
( ( ( aElementOf0 @ SV45 @ xI )
= $false )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV43 @ SV45 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV43 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(401,plain,
! [SV44: $i,SV46: $i] :
( ( ( aElement0 @ SV46 )
= $false )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV46 @ SV44 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV44 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(402,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[84,401,400,389,388,380,378,377,376,373,372,371,369,368,360,347,345,341,337,336,311,305,304,303,281,278,277,272,271,270,269,268,267,266,265,264,263,262,261,260,257,255,254,253,198,195,193,189,169,128,126,125,116,85]) ).
thf(403,plain,
( ( ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xJ )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xJ ) ) )
& ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xJ )
| ! [W1: $i] :
( ~ ( aElement0 @ W1 )
| ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xJ ) ) )
& ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xI )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) ) )
& ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xI )
| ! [W1: $i] :
( ~ ( aElement0 @ W1 )
| ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) )
& ( aSet0 @ xI )
& ( aIdeal0 @ xI )
& ( aSet0 @ xJ )
& ( aIdeal0 @ xJ ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(404,plain,
( ( ( aElementOf0 @ sK5_W0 @ xI )
& ( aElementOf0 @ sK6_SY44 @ xJ )
& ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
= xx )
& ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElementOf0 @ sK3_W0 @ xI )
& ( aElementOf0 @ sK4_SY43 @ xJ )
& ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
= xy )
& ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElement0 @ xz ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(405,plain,
( ( ( aElementOf0 @ xk @ xI )
& ( aElementOf0 @ xl @ xJ )
& ( xx
= ( sdtpldt0 @ xk @ xl ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(406,plain,
( ( ( aElementOf0 @ xm @ xI )
& ( aElementOf0 @ xn @ xJ )
& ( xy
= ( sdtpldt0 @ xm @ xn ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(407,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(408,plain,
( ( aElement0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(409,plain,
( ( aElement0 @ sz10 )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(410,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( aElement0 @ ( smndt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(411,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(412,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(413,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(414,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(415,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(416,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(417,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(418,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(419,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz10 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(420,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(421,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
= ( smndt0 @ W0 ) ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( smndt0 @ W0 )
= ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(422,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(423,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(424,plain,
( ( ( sz10 != sz00 ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(425,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(426,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ W0 )
| ( aElement0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(427,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( aSet0 @ W1 )
| ( ( aElementOf0 @ ( sK2_W2 @ W1 @ W0 ) @ W0 )
& ~ ( aElementOf0 @ ( sK2_W2 @ W1 @ W0 ) @ W1 ) )
| ( ( aElementOf0 @ ( sK1_W2 @ W1 @ W0 ) @ W1 )
& ~ ( aElementOf0 @ ( sK1_W2 @ W1 @ W0 ) @ W0 ) )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(428,plain,
( ( ~ ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(429,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) )
| ( xy
!= ( sdtpldt0 @ xm @ xn ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(430,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(431,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) )
| ( xx
!= ( sdtpldt0 @ xk @ xl ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(432,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(433,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 )
| ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 )
| ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SX1 @ SX2 ) @ SX0 )
= ( sdtpldt0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ ( sdtasdt0 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(434,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
= ( smndt0 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( smndt0 @ SX0 )
= ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(435,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(436,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(437,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ( aElement0 @ xz ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(438,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
| ~ ( aIdeal0 @ xJ ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(439,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aSet0 @ SX0 )
| ~ ( aSet0 @ SX1 )
| ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SX1 @ SX0 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(440,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(441,plain,
! [SV48: $i] :
( ( ~ ( aElement0 @ SV48 )
| ( aElement0 @ ( smndt0 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(442,plain,
! [SV49: $i] :
( ( ! [SY68: $i] :
( ~ ( aElement0 @ SV49 )
| ~ ( aElement0 @ SY68 )
| ( aElement0 @ ( sdtpldt0 @ SV49 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(443,plain,
! [SV50: $i] :
( ( ! [SY69: $i] :
( ~ ( aElement0 @ SV50 )
| ~ ( aElement0 @ SY69 )
| ( aElement0 @ ( sdtasdt0 @ SV50 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(444,plain,
! [SV51: $i] :
( ( ! [SY70: $i] :
( ~ ( aElement0 @ SV51 )
| ~ ( aElement0 @ SY70 )
| ( ( sdtpldt0 @ SV51 @ SY70 )
= ( sdtpldt0 @ SY70 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(445,plain,
! [SV52: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ( aElement0 @ SV52 )
| ~ ( aElement0 @ SY71 )
| ~ ( aElement0 @ SY72 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV52 @ SY71 ) @ SY72 )
= ( sdtpldt0 @ SV52 @ ( sdtpldt0 @ SY71 @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(446,plain,
! [SV53: $i] :
( ( ! [SY73: $i] :
( ~ ( aElement0 @ SV53 )
| ~ ( aElement0 @ SY73 )
| ( ( sdtasdt0 @ SV53 @ SY73 )
= ( sdtasdt0 @ SY73 @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(447,plain,
! [SV54: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ~ ( aElement0 @ SV54 )
| ~ ( aElement0 @ SY74 )
| ~ ( aElement0 @ SY75 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV54 @ SY74 ) @ SY75 )
= ( sdtasdt0 @ SV54 @ ( sdtasdt0 @ SY74 @ SY75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(448,plain,
! [SV55: $i] :
( ( ! [SY76: $i] :
( ~ ( aElement0 @ SV55 )
| ~ ( aElement0 @ SY76 )
| ( ( sdtasdt0 @ SV55 @ SY76 )
!= sz00 )
| ( SV55 = sz00 )
| ( SY76 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(449,plain,
( ( sz10 = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(450,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(451,plain,
! [SV57: $i] :
( ( ~ ( aSet0 @ SV57 )
| ! [SY77: $i] :
( ~ ( aElementOf0 @ SY77 @ SV57 )
| ( aElement0 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(452,plain,
( ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(453,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) )
| ( xy
!= ( sdtpldt0 @ xm @ xn ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(454,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(455,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) )
| ( xx
!= ( sdtpldt0 @ xk @ xl ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(456,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(457,plain,
! [SV58: $i] :
( ( ~ ( ~ ! [SY78: $i,SY79: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SY78 )
| ~ ( aElement0 @ SY79 )
| ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SY78 @ SY79 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SY78 ) @ ( sdtasdt0 @ SV58 @ SY79 ) ) ) )
| ~ ! [SY80: $i,SY81: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SY80 )
| ~ ( aElement0 @ SY81 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY80 @ SY81 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY80 @ SV58 ) @ ( sdtasdt0 @ SY81 @ SV58 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(458,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
= ( smndt0 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( smndt0 @ SX0 )
= ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(459,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(460,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(461,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ( aElement0 @ xz ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(462,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
| ~ ( aIdeal0 @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(463,plain,
! [SV59: $i] :
( ( ! [SY82: $i] :
( ~ ( aSet0 @ SV59 )
| ~ ( aSet0 @ SY82 )
| ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SY82 @ SV59 ) @ SV59 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SY82 @ SV59 ) @ SY82 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SY82 @ SV59 ) @ SY82 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SY82 @ SV59 ) @ SV59 ) )
| ( SV59 = SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(464,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ SV48 ) )
= $true )
| ( ( aElement0 @ ( smndt0 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(465,plain,
! [SV60: $i,SV49: $i] :
( ( ~ ( aElement0 @ SV49 )
| ~ ( aElement0 @ SV60 )
| ( aElement0 @ ( sdtpldt0 @ SV49 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(466,plain,
! [SV61: $i,SV50: $i] :
( ( ~ ( aElement0 @ SV50 )
| ~ ( aElement0 @ SV61 )
| ( aElement0 @ ( sdtasdt0 @ SV50 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(467,plain,
! [SV62: $i,SV51: $i] :
( ( ~ ( aElement0 @ SV51 )
| ~ ( aElement0 @ SV62 )
| ( ( sdtpldt0 @ SV51 @ SV62 )
= ( sdtpldt0 @ SV62 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(468,plain,
! [SV63: $i,SV52: $i] :
( ( ! [SY83: $i] :
( ~ ( aElement0 @ SV52 )
| ~ ( aElement0 @ SV63 )
| ~ ( aElement0 @ SY83 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV52 @ SV63 ) @ SY83 )
= ( sdtpldt0 @ SV52 @ ( sdtpldt0 @ SV63 @ SY83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(469,plain,
! [SV64: $i,SV53: $i] :
( ( ~ ( aElement0 @ SV53 )
| ~ ( aElement0 @ SV64 )
| ( ( sdtasdt0 @ SV53 @ SV64 )
= ( sdtasdt0 @ SV64 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(470,plain,
! [SV65: $i,SV54: $i] :
( ( ! [SY84: $i] :
( ~ ( aElement0 @ SV54 )
| ~ ( aElement0 @ SV65 )
| ~ ( aElement0 @ SY84 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV54 @ SV65 ) @ SY84 )
= ( sdtasdt0 @ SV54 @ ( sdtasdt0 @ SV65 @ SY84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(471,plain,
! [SV66: $i,SV55: $i] :
( ( ~ ( aElement0 @ SV55 )
| ~ ( aElement0 @ SV66 )
| ( ( sdtasdt0 @ SV55 @ SV66 )
!= sz00 )
| ( SV55 = sz00 )
| ( SV66 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(472,plain,
! [SV57: $i] :
( ( ( ~ ( aSet0 @ SV57 ) )
= $true )
| ( ( ! [SY77: $i] :
( ~ ( aElementOf0 @ SY77 @ SV57 )
| ( aElement0 @ SY77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(473,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(474,plain,
( ( ( xy
!= ( sdtpldt0 @ xm @ xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(475,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(476,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(477,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(478,plain,
( ( ( xx
!= ( sdtpldt0 @ xk @ xl ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(479,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(480,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(481,plain,
! [SV58: $i] :
( ( ~ ! [SY78: $i,SY79: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SY78 )
| ~ ( aElement0 @ SY79 )
| ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SY78 @ SY79 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SY78 ) @ ( sdtasdt0 @ SV58 @ SY79 ) ) ) )
| ~ ! [SY80: $i,SY81: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SY80 )
| ~ ( aElement0 @ SY81 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY80 @ SY81 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY80 @ SV58 ) @ ( sdtasdt0 @ SY81 @ SV58 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(482,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
= ( smndt0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(483,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( smndt0 @ SX0 )
= ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(484,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(485,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(486,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(487,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(488,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(489,plain,
( ( ~ ( aElement0 @ xz ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(490,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(491,plain,
( ( ~ ( aIdeal0 @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(492,plain,
! [SV67: $i,SV59: $i] :
( ( ~ ( aSet0 @ SV59 )
| ~ ( aSet0 @ SV67 )
| ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
| ( SV59 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(493,plain,
! [SV48: $i] :
( ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ ( smndt0 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(494,plain,
! [SV60: $i,SV49: $i] :
( ( ( ~ ( aElement0 @ SV49 )
| ~ ( aElement0 @ SV60 ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV49 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(495,plain,
! [SV61: $i,SV50: $i] :
( ( ( ~ ( aElement0 @ SV50 )
| ~ ( aElement0 @ SV61 ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV50 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(496,plain,
! [SV62: $i,SV51: $i] :
( ( ( ~ ( aElement0 @ SV51 )
| ~ ( aElement0 @ SV62 ) )
= $true )
| ( ( ( sdtpldt0 @ SV51 @ SV62 )
= ( sdtpldt0 @ SV62 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(497,plain,
! [SV68: $i,SV63: $i,SV52: $i] :
( ( ~ ( aElement0 @ SV52 )
| ~ ( aElement0 @ SV63 )
| ~ ( aElement0 @ SV68 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV52 @ SV63 ) @ SV68 )
= ( sdtpldt0 @ SV52 @ ( sdtpldt0 @ SV63 @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(498,plain,
! [SV64: $i,SV53: $i] :
( ( ( ~ ( aElement0 @ SV53 )
| ~ ( aElement0 @ SV64 ) )
= $true )
| ( ( ( sdtasdt0 @ SV53 @ SV64 )
= ( sdtasdt0 @ SV64 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(499,plain,
! [SV69: $i,SV65: $i,SV54: $i] :
( ( ~ ( aElement0 @ SV54 )
| ~ ( aElement0 @ SV65 )
| ~ ( aElement0 @ SV69 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV54 @ SV65 ) @ SV69 )
= ( sdtasdt0 @ SV54 @ ( sdtasdt0 @ SV65 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(500,plain,
! [SV66: $i,SV55: $i] :
( ( ( ~ ( aElement0 @ SV55 )
| ~ ( aElement0 @ SV66 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV55 @ SV66 )
!= sz00 )
| ( SV55 = sz00 )
| ( SV66 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(501,plain,
! [SV57: $i] :
( ( ( aSet0 @ SV57 )
= $false )
| ( ( ! [SY77: $i] :
( ~ ( aElementOf0 @ SY77 @ SV57 )
| ( aElement0 @ SY77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(502,plain,
( ( ~ ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(503,plain,
( ( xy
= ( sdtpldt0 @ xm @ xn ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(504,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(505,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(506,plain,
( ( ~ ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(507,plain,
( ( xx
= ( sdtpldt0 @ xk @ xl ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(508,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(509,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(510,plain,
! [SV58: $i] :
( ( ~ ! [SY78: $i,SY79: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SY78 )
| ~ ( aElement0 @ SY79 )
| ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SY78 @ SY79 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SY78 ) @ ( sdtasdt0 @ SV58 @ SY79 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(511,plain,
! [SV58: $i] :
( ( ~ ! [SY80: $i,SY81: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SY80 )
| ~ ( aElement0 @ SY81 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY80 @ SY81 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY80 @ SV58 ) @ ( sdtasdt0 @ SY81 @ SV58 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(512,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
= ( smndt0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(513,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( smndt0 @ SX0 )
= ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(514,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(515,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(516,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(517,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(518,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(519,plain,
( ( aElement0 @ xz )
= $true ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(520,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(521,plain,
( ( aIdeal0 @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(522,plain,
! [SV67: $i,SV59: $i] :
( ( ( ~ ( aSet0 @ SV59 )
| ~ ( aSet0 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
| ( SV59 = SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(523,plain,
! [SV60: $i,SV49: $i] :
( ( ( ~ ( aElement0 @ SV49 ) )
= $true )
| ( ( ~ ( aElement0 @ SV60 ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV49 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(524,plain,
! [SV61: $i,SV50: $i] :
( ( ( ~ ( aElement0 @ SV50 ) )
= $true )
| ( ( ~ ( aElement0 @ SV61 ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV50 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(525,plain,
! [SV62: $i,SV51: $i] :
( ( ( ~ ( aElement0 @ SV51 ) )
= $true )
| ( ( ~ ( aElement0 @ SV62 ) )
= $true )
| ( ( ( sdtpldt0 @ SV51 @ SV62 )
= ( sdtpldt0 @ SV62 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(526,plain,
! [SV68: $i,SV63: $i,SV52: $i] :
( ( ( ~ ( aElement0 @ SV52 )
| ~ ( aElement0 @ SV63 )
| ~ ( aElement0 @ SV68 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV52 @ SV63 ) @ SV68 )
= ( sdtpldt0 @ SV52 @ ( sdtpldt0 @ SV63 @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(527,plain,
! [SV64: $i,SV53: $i] :
( ( ( ~ ( aElement0 @ SV53 ) )
= $true )
| ( ( ~ ( aElement0 @ SV64 ) )
= $true )
| ( ( ( sdtasdt0 @ SV53 @ SV64 )
= ( sdtasdt0 @ SV64 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(528,plain,
! [SV69: $i,SV65: $i,SV54: $i] :
( ( ( ~ ( aElement0 @ SV54 )
| ~ ( aElement0 @ SV65 )
| ~ ( aElement0 @ SV69 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV54 @ SV65 ) @ SV69 )
= ( sdtasdt0 @ SV54 @ ( sdtasdt0 @ SV65 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(529,plain,
! [SV66: $i,SV55: $i] :
( ( ( ~ ( aElement0 @ SV55 ) )
= $true )
| ( ( ~ ( aElement0 @ SV66 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV55 @ SV66 )
!= sz00 )
| ( SV55 = sz00 )
| ( SV66 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(530,plain,
! [SV57: $i,SV70: $i] :
( ( ( ~ ( aElementOf0 @ SV70 @ SV57 )
| ( aElement0 @ SV70 ) )
= $true )
| ( ( aSet0 @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(531,plain,
( ( ~ ( aElementOf0 @ xm @ xI )
| ~ ( aElementOf0 @ xn @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(532,plain,
! [SV71: $i] :
( ( ~ ( aElement0 @ SV71 )
| ( ( sdtasdt0 @ SV71 @ sz00 )
= sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(533,plain,
! [SV72: $i] :
( ( ~ ( aElement0 @ SV72 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(534,plain,
( ( ~ ( aElementOf0 @ xk @ xI )
| ~ ( aElementOf0 @ xl @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(535,plain,
! [SV73: $i] :
( ( ~ ( aElement0 @ SV73 )
| ( ( sdtasdt0 @ SV73 @ sz10 )
= SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(536,plain,
! [SV74: $i] :
( ( ~ ( aElement0 @ SV74 )
| ( SV74
= ( sdtasdt0 @ sz10 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(537,plain,
! [SV58: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SY78 )
| ~ ( aElement0 @ SY79 )
| ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SY78 @ SY79 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SY78 ) @ ( sdtasdt0 @ SV58 @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(538,plain,
! [SV58: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SY80 )
| ~ ( aElement0 @ SY81 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY80 @ SY81 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY80 @ SV58 ) @ ( sdtasdt0 @ SY81 @ SV58 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(539,plain,
! [SV75: $i] :
( ( ~ ( aElement0 @ SV75 )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV75 )
= ( smndt0 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(540,plain,
! [SV76: $i] :
( ( ~ ( aElement0 @ SV76 )
| ( ( smndt0 @ SV76 )
= ( sdtasdt0 @ SV76 @ ( smndt0 @ sz10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(541,plain,
! [SV77: $i] :
( ( ~ ( aElement0 @ SV77 )
| ( ( sdtpldt0 @ SV77 @ sz00 )
= SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(542,plain,
! [SV78: $i] :
( ( ~ ( aElement0 @ SV78 )
| ( SV78
= ( sdtpldt0 @ sz00 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(543,plain,
! [SV79: $i] :
( ( ~ ( aElement0 @ SV79 )
| ( ( sdtpldt0 @ SV79 @ ( smndt0 @ SV79 ) )
= sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(544,plain,
! [SV80: $i] :
( ( ~ ( aElement0 @ SV80 )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ SV80 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(545,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
| ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(546,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(547,plain,
! [SV67: $i,SV59: $i] :
( ( ( ~ ( aSet0 @ SV59 ) )
= $true )
| ( ( ~ ( aSet0 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
| ( SV59 = SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(548,plain,
! [SV60: $i,SV49: $i] :
( ( ( aElement0 @ SV49 )
= $false )
| ( ( ~ ( aElement0 @ SV60 ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV49 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(549,plain,
! [SV61: $i,SV50: $i] :
( ( ( aElement0 @ SV50 )
= $false )
| ( ( ~ ( aElement0 @ SV61 ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV50 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(550,plain,
! [SV62: $i,SV51: $i] :
( ( ( aElement0 @ SV51 )
= $false )
| ( ( ~ ( aElement0 @ SV62 ) )
= $true )
| ( ( ( sdtpldt0 @ SV51 @ SV62 )
= ( sdtpldt0 @ SV62 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(551,plain,
! [SV68: $i,SV63: $i,SV52: $i] :
( ( ( ~ ( aElement0 @ SV52 )
| ~ ( aElement0 @ SV63 ) )
= $true )
| ( ( ~ ( aElement0 @ SV68 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV52 @ SV63 ) @ SV68 )
= ( sdtpldt0 @ SV52 @ ( sdtpldt0 @ SV63 @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(552,plain,
! [SV64: $i,SV53: $i] :
( ( ( aElement0 @ SV53 )
= $false )
| ( ( ~ ( aElement0 @ SV64 ) )
= $true )
| ( ( ( sdtasdt0 @ SV53 @ SV64 )
= ( sdtasdt0 @ SV64 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(553,plain,
! [SV69: $i,SV65: $i,SV54: $i] :
( ( ( ~ ( aElement0 @ SV54 )
| ~ ( aElement0 @ SV65 ) )
= $true )
| ( ( ~ ( aElement0 @ SV69 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV54 @ SV65 ) @ SV69 )
= ( sdtasdt0 @ SV54 @ ( sdtasdt0 @ SV65 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(554,plain,
! [SV66: $i,SV55: $i] :
( ( ( aElement0 @ SV55 )
= $false )
| ( ( ~ ( aElement0 @ SV66 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV55 @ SV66 )
!= sz00 )
| ( SV55 = sz00 )
| ( SV66 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(555,plain,
! [SV57: $i,SV70: $i] :
( ( ( ~ ( aElementOf0 @ SV70 @ SV57 ) )
= $true )
| ( ( aElement0 @ SV70 )
= $true )
| ( ( aSet0 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(556,plain,
( ( ~ ( aElementOf0 @ xm @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(557,plain,
( ( ~ ( aElementOf0 @ xn @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(558,plain,
! [SV71: $i] :
( ( ( ~ ( aElement0 @ SV71 ) )
= $true )
| ( ( ( sdtasdt0 @ SV71 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(559,plain,
! [SV72: $i] :
( ( ( ~ ( aElement0 @ SV72 ) )
= $true )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(560,plain,
( ( ~ ( aElementOf0 @ xk @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(561,plain,
( ( ~ ( aElementOf0 @ xl @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(562,plain,
! [SV73: $i] :
( ( ( ~ ( aElement0 @ SV73 ) )
= $true )
| ( ( ( sdtasdt0 @ SV73 @ sz10 )
= SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(563,plain,
! [SV74: $i] :
( ( ( ~ ( aElement0 @ SV74 ) )
= $true )
| ( ( SV74
= ( sdtasdt0 @ sz10 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(564,plain,
! [SV81: $i,SV58: $i] :
( ( ! [SY85: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SV81 )
| ~ ( aElement0 @ SY85 )
| ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SV81 @ SY85 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SV81 ) @ ( sdtasdt0 @ SV58 @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(565,plain,
! [SV82: $i,SV58: $i] :
( ( ! [SY86: $i] :
( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SV82 )
| ~ ( aElement0 @ SY86 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV82 @ SY86 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV82 @ SV58 ) @ ( sdtasdt0 @ SY86 @ SV58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(566,plain,
! [SV75: $i] :
( ( ( ~ ( aElement0 @ SV75 ) )
= $true )
| ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV75 )
= ( smndt0 @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(567,plain,
! [SV76: $i] :
( ( ( ~ ( aElement0 @ SV76 ) )
= $true )
| ( ( ( smndt0 @ SV76 )
= ( sdtasdt0 @ SV76 @ ( smndt0 @ sz10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(568,plain,
! [SV77: $i] :
( ( ( ~ ( aElement0 @ SV77 ) )
= $true )
| ( ( ( sdtpldt0 @ SV77 @ sz00 )
= SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(569,plain,
! [SV78: $i] :
( ( ( ~ ( aElement0 @ SV78 ) )
= $true )
| ( ( SV78
= ( sdtpldt0 @ sz00 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(570,plain,
! [SV79: $i] :
( ( ( ~ ( aElement0 @ SV79 ) )
= $true )
| ( ( ( sdtpldt0 @ SV79 @ ( smndt0 @ SV79 ) )
= sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(571,plain,
! [SV80: $i] :
( ( ( ~ ( aElement0 @ SV80 ) )
= $true )
| ( ( sz00
= ( sdtpldt0 @ ( smndt0 @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(572,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(573,plain,
( ( ~ ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(574,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(575,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(576,plain,
! [SV67: $i,SV59: $i] :
( ( ( aSet0 @ SV59 )
= $false )
| ( ( ~ ( aSet0 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
| ( SV59 = SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(577,plain,
! [SV49: $i,SV60: $i] :
( ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( aElement0 @ ( sdtpldt0 @ SV49 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(578,plain,
! [SV50: $i,SV61: $i] :
( ( ( aElement0 @ SV61 )
= $false )
| ( ( aElement0 @ SV50 )
= $false )
| ( ( aElement0 @ ( sdtasdt0 @ SV50 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(579,plain,
! [SV51: $i,SV62: $i] :
( ( ( aElement0 @ SV62 )
= $false )
| ( ( aElement0 @ SV51 )
= $false )
| ( ( ( sdtpldt0 @ SV51 @ SV62 )
= ( sdtpldt0 @ SV62 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(580,plain,
! [SV68: $i,SV63: $i,SV52: $i] :
( ( ( ~ ( aElement0 @ SV52 ) )
= $true )
| ( ( ~ ( aElement0 @ SV63 ) )
= $true )
| ( ( ~ ( aElement0 @ SV68 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV52 @ SV63 ) @ SV68 )
= ( sdtpldt0 @ SV52 @ ( sdtpldt0 @ SV63 @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(581,plain,
! [SV53: $i,SV64: $i] :
( ( ( aElement0 @ SV64 )
= $false )
| ( ( aElement0 @ SV53 )
= $false )
| ( ( ( sdtasdt0 @ SV53 @ SV64 )
= ( sdtasdt0 @ SV64 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(582,plain,
! [SV69: $i,SV65: $i,SV54: $i] :
( ( ( ~ ( aElement0 @ SV54 ) )
= $true )
| ( ( ~ ( aElement0 @ SV65 ) )
= $true )
| ( ( ~ ( aElement0 @ SV69 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV54 @ SV65 ) @ SV69 )
= ( sdtasdt0 @ SV54 @ ( sdtasdt0 @ SV65 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(583,plain,
! [SV55: $i,SV66: $i] :
( ( ( aElement0 @ SV66 )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( ( ( sdtasdt0 @ SV55 @ SV66 )
!= sz00 )
| ( SV55 = sz00 )
| ( SV66 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(584,plain,
! [SV57: $i,SV70: $i] :
( ( ( aElementOf0 @ SV70 @ SV57 )
= $false )
| ( ( aElement0 @ SV70 )
= $true )
| ( ( aSet0 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(585,plain,
( ( aElementOf0 @ xm @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(586,plain,
( ( aElementOf0 @ xn @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(587,plain,
! [SV71: $i] :
( ( ( aElement0 @ SV71 )
= $false )
| ( ( ( sdtasdt0 @ SV71 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(588,plain,
! [SV72: $i] :
( ( ( aElement0 @ SV72 )
= $false )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(589,plain,
( ( aElementOf0 @ xk @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(590,plain,
( ( aElementOf0 @ xl @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(591,plain,
! [SV73: $i] :
( ( ( aElement0 @ SV73 )
= $false )
| ( ( ( sdtasdt0 @ SV73 @ sz10 )
= SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(592,plain,
! [SV74: $i] :
( ( ( aElement0 @ SV74 )
= $false )
| ( ( SV74
= ( sdtasdt0 @ sz10 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(593,plain,
! [SV83: $i,SV81: $i,SV58: $i] :
( ( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SV81 )
| ~ ( aElement0 @ SV83 )
| ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SV81 @ SV83 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SV81 ) @ ( sdtasdt0 @ SV58 @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(594,plain,
! [SV84: $i,SV82: $i,SV58: $i] :
( ( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SV82 )
| ~ ( aElement0 @ SV84 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV82 @ SV84 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV82 @ SV58 ) @ ( sdtasdt0 @ SV84 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(595,plain,
! [SV75: $i] :
( ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV75 )
= ( smndt0 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(596,plain,
! [SV76: $i] :
( ( ( aElement0 @ SV76 )
= $false )
| ( ( ( smndt0 @ SV76 )
= ( sdtasdt0 @ SV76 @ ( smndt0 @ sz10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(597,plain,
! [SV77: $i] :
( ( ( aElement0 @ SV77 )
= $false )
| ( ( ( sdtpldt0 @ SV77 @ sz00 )
= SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(598,plain,
! [SV78: $i] :
( ( ( aElement0 @ SV78 )
= $false )
| ( ( SV78
= ( sdtpldt0 @ sz00 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(599,plain,
! [SV79: $i] :
( ( ( aElement0 @ SV79 )
= $false )
| ( ( ( sdtpldt0 @ SV79 @ ( smndt0 @ SV79 ) )
= sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(600,plain,
! [SV80: $i] :
( ( ( aElement0 @ SV80 )
= $false )
| ( ( sz00
= ( sdtpldt0 @ ( smndt0 @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(601,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(602,plain,
( ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(603,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(604,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(605,plain,
! [SV59: $i,SV67: $i] :
( ( ( aSet0 @ SV67 )
= $false )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
| ( SV59 = SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(606,plain,
! [SV68: $i,SV63: $i,SV52: $i] :
( ( ( aElement0 @ SV52 )
= $false )
| ( ( ~ ( aElement0 @ SV63 ) )
= $true )
| ( ( ~ ( aElement0 @ SV68 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV52 @ SV63 ) @ SV68 )
= ( sdtpldt0 @ SV52 @ ( sdtpldt0 @ SV63 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(607,plain,
! [SV69: $i,SV65: $i,SV54: $i] :
( ( ( aElement0 @ SV54 )
= $false )
| ( ( ~ ( aElement0 @ SV65 ) )
= $true )
| ( ( ~ ( aElement0 @ SV69 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV54 @ SV65 ) @ SV69 )
= ( sdtasdt0 @ SV54 @ ( sdtasdt0 @ SV65 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(608,plain,
! [SV66: $i,SV55: $i] :
( ( ( ( ( sdtasdt0 @ SV55 @ SV66 )
!= sz00 ) )
= $true )
| ( ( ( SV55 = sz00 )
| ( SV66 = sz00 ) )
= $true )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(609,plain,
! [SV83: $i,SV81: $i,SV58: $i] :
( ( ( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SV81 )
| ~ ( aElement0 @ SV83 ) )
= $true )
| ( ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SV81 @ SV83 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SV81 ) @ ( sdtasdt0 @ SV58 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(610,plain,
! [SV84: $i,SV82: $i,SV58: $i] :
( ( ( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SV82 )
| ~ ( aElement0 @ SV84 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV82 @ SV84 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV82 @ SV58 ) @ ( sdtasdt0 @ SV84 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(611,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
| ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(612,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(613,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ( aSet0 @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(614,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) )
| ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(615,plain,
! [SV68: $i,SV52: $i,SV63: $i] :
( ( ( aElement0 @ SV63 )
= $false )
| ( ( aElement0 @ SV52 )
= $false )
| ( ( ~ ( aElement0 @ SV68 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV52 @ SV63 ) @ SV68 )
= ( sdtpldt0 @ SV52 @ ( sdtpldt0 @ SV63 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(616,plain,
! [SV69: $i,SV54: $i,SV65: $i] :
( ( ( aElement0 @ SV65 )
= $false )
| ( ( aElement0 @ SV54 )
= $false )
| ( ( ~ ( aElement0 @ SV69 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV54 @ SV65 ) @ SV69 )
= ( sdtasdt0 @ SV54 @ ( sdtasdt0 @ SV65 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(617,plain,
! [SV66: $i,SV55: $i] :
( ( ( ( sdtasdt0 @ SV55 @ SV66 )
= sz00 )
= $false )
| ( ( ( SV55 = sz00 )
| ( SV66 = sz00 ) )
= $true )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(618,plain,
! [SV83: $i,SV81: $i,SV58: $i] :
( ( ( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SV81 ) )
= $true )
| ( ( ~ ( aElement0 @ SV83 ) )
= $true )
| ( ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SV81 @ SV83 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SV81 ) @ ( sdtasdt0 @ SV58 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(619,plain,
! [SV84: $i,SV82: $i,SV58: $i] :
( ( ( ~ ( aElement0 @ SV58 )
| ~ ( aElement0 @ SV82 ) )
= $true )
| ( ( ~ ( aElement0 @ SV84 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV82 @ SV84 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV82 @ SV58 ) @ ( sdtasdt0 @ SV84 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(620,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(621,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(622,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(623,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(624,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(625,plain,
( ( ~ ( aSet0 @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(626,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(627,plain,
! [SV63: $i,SV52: $i,SV68: $i] :
( ( ( aElement0 @ SV68 )
= $false )
| ( ( aElement0 @ SV52 )
= $false )
| ( ( aElement0 @ SV63 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV52 @ SV63 ) @ SV68 )
= ( sdtpldt0 @ SV52 @ ( sdtpldt0 @ SV63 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(628,plain,
! [SV65: $i,SV54: $i,SV69: $i] :
( ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV54 )
= $false )
| ( ( aElement0 @ SV65 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV54 @ SV65 ) @ SV69 )
= ( sdtasdt0 @ SV54 @ ( sdtasdt0 @ SV65 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(629,plain,
! [SV66: $i,SV55: $i] :
( ( ( SV55 = sz00 )
= $true )
| ( ( SV66 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV55 @ SV66 )
= sz00 )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(630,plain,
! [SV83: $i,SV81: $i,SV58: $i] :
( ( ( ~ ( aElement0 @ SV58 ) )
= $true )
| ( ( ~ ( aElement0 @ SV81 ) )
= $true )
| ( ( ~ ( aElement0 @ SV83 ) )
= $true )
| ( ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SV81 @ SV83 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SV81 ) @ ( sdtasdt0 @ SV58 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(631,plain,
! [SV84: $i,SV82: $i,SV58: $i] :
( ( ( ~ ( aElement0 @ SV58 ) )
= $true )
| ( ( ~ ( aElement0 @ SV82 ) )
= $true )
| ( ( ~ ( aElement0 @ SV84 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV82 @ SV84 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV82 @ SV58 ) @ ( sdtasdt0 @ SV84 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(632,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(633,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(634,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(635,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xJ )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xJ ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(636,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(637,plain,
( ( aSet0 @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(638,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
| ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(639,plain,
! [SV83: $i,SV81: $i,SV58: $i] :
( ( ( aElement0 @ SV58 )
= $false )
| ( ( ~ ( aElement0 @ SV81 ) )
= $true )
| ( ( ~ ( aElement0 @ SV83 ) )
= $true )
| ( ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SV81 @ SV83 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SV81 ) @ ( sdtasdt0 @ SV58 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(640,plain,
! [SV84: $i,SV82: $i,SV58: $i] :
( ( ( aElement0 @ SV58 )
= $false )
| ( ( ~ ( aElement0 @ SV82 ) )
= $true )
| ( ( ~ ( aElement0 @ SV84 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV82 @ SV84 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV82 @ SV58 ) @ ( sdtasdt0 @ SV84 @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(641,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
| ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(642,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
| ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(643,plain,
! [SV85: $i] :
( ( ~ ( aElementOf0 @ SV85 @ xJ )
| ! [SY87: $i] :
( ~ ( aElementOf0 @ SY87 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SV85 @ SY87 ) @ xJ ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(644,plain,
! [SV86: $i] :
( ( ~ ( aElementOf0 @ SV86 @ xJ )
| ! [SY88: $i] :
( ~ ( aElement0 @ SY88 )
| ( aElementOf0 @ ( sdtasdt0 @ SY88 @ SV86 ) @ xJ ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(645,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
| ~ ( aIdeal0 @ xI ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(646,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 ) )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(647,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(648,plain,
! [SV83: $i,SV58: $i,SV81: $i] :
( ( ( aElement0 @ SV81 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( ~ ( aElement0 @ SV83 ) )
= $true )
| ( ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SV81 @ SV83 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SV81 ) @ ( sdtasdt0 @ SV58 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(649,plain,
! [SV84: $i,SV58: $i,SV82: $i] :
( ( ( aElement0 @ SV82 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( ~ ( aElement0 @ SV84 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV82 @ SV84 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV82 @ SV58 ) @ ( sdtasdt0 @ SV84 @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(650,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(651,plain,
( ( ~ ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(652,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(653,plain,
( ( ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
!= xy ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(654,plain,
! [SV85: $i] :
( ( ( ~ ( aElementOf0 @ SV85 @ xJ ) )
= $true )
| ( ( ! [SY87: $i] :
( ~ ( aElementOf0 @ SY87 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SV85 @ SY87 ) @ xJ ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(655,plain,
! [SV86: $i] :
( ( ( ~ ( aElementOf0 @ SV86 @ xJ ) )
= $true )
| ( ( ! [SY88: $i] :
( ~ ( aElement0 @ SY88 )
| ( aElementOf0 @ ( sdtasdt0 @ SY88 @ SV86 ) @ xJ ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(656,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(657,plain,
( ( ~ ( aIdeal0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(658,plain,
! [SV59: $i,SV67: $i] :
( ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[646]) ).
thf(659,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(660,plain,
! [SV81: $i,SV58: $i,SV83: $i] :
( ( ( aElement0 @ SV83 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElement0 @ SV81 )
= $false )
| ( ( ( sdtasdt0 @ SV58 @ ( sdtpldt0 @ SV81 @ SV83 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV58 @ SV81 ) @ ( sdtasdt0 @ SV58 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(661,plain,
! [SV82: $i,SV58: $i,SV84: $i] :
( ( ( aElement0 @ SV84 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElement0 @ SV82 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV82 @ SV84 ) @ SV58 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV82 @ SV58 ) @ ( sdtasdt0 @ SV84 @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(662,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(663,plain,
( ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(664,plain,
( ( ~ ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(665,plain,
( ( ( sdtpldt0 @ sK3_W0 @ sK4_SY43 )
= xy )
= $true ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(666,plain,
! [SV85: $i] :
( ( ( aElementOf0 @ SV85 @ xJ )
= $false )
| ( ( ! [SY87: $i] :
( ~ ( aElementOf0 @ SY87 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SV85 @ SY87 ) @ xJ ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(667,plain,
! [SV86: $i] :
( ( ( aElementOf0 @ SV86 @ xJ )
= $false )
| ( ( ! [SY88: $i] :
( ~ ( aElement0 @ SY88 )
| ( aElementOf0 @ ( sdtasdt0 @ SY88 @ SV86 ) @ xJ ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(668,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(669,plain,
( ( aIdeal0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(670,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(671,plain,
! [SV59: $i,SV67: $i] :
( ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(672,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
| ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(673,plain,
( ( ~ ( aElementOf0 @ sK3_W0 @ xI )
| ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(674,plain,
! [SV85: $i,SV87: $i] :
( ( ( ~ ( aElementOf0 @ SV87 @ xJ )
| ( aElementOf0 @ ( sdtpldt0 @ SV85 @ SV87 ) @ xJ ) )
= $true )
| ( ( aElementOf0 @ SV85 @ xJ )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(675,plain,
! [SV86: $i,SV88: $i] :
( ( ( ~ ( aElement0 @ SV88 )
| ( aElementOf0 @ ( sdtasdt0 @ SV88 @ SV86 ) @ xJ ) )
= $true )
| ( ( aElementOf0 @ SV86 @ xJ )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(676,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
| ~ ( aSet0 @ xI ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(677,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(678,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(679,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
| ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 )
= $false )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(680,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(681,plain,
( ( ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
!= xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(682,plain,
( ( ~ ( aElementOf0 @ sK3_W0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(683,plain,
( ( ~ ( aElementOf0 @ sK4_SY43 @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(684,plain,
! [SV85: $i,SV87: $i] :
( ( ( ~ ( aElementOf0 @ SV87 @ xJ ) )
= $true )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV85 @ SV87 ) @ xJ )
= $true )
| ( ( aElementOf0 @ SV85 @ xJ )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(685,plain,
! [SV86: $i,SV88: $i] :
( ( ( ~ ( aElement0 @ SV88 ) )
= $true )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV88 @ SV86 ) @ xJ )
= $true )
| ( ( aElementOf0 @ SV86 @ xJ )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(686,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(687,plain,
( ( ~ ( aSet0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(688,plain,
! [SV59: $i,SV67: $i] :
( ( ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
= $true )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(689,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
= $true )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(690,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 )
= $false )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(691,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 )
= $false )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(692,plain,
( ( ~ ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[680]) ).
thf(693,plain,
( ( ( sdtpldt0 @ sK5_W0 @ sK6_SY44 )
= xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[681]) ).
thf(694,plain,
( ( aElementOf0 @ sK3_W0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(695,plain,
( ( aElementOf0 @ sK4_SY43 @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(696,plain,
! [SV85: $i,SV87: $i] :
( ( ( aElementOf0 @ SV87 @ xJ )
= $false )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV85 @ SV87 ) @ xJ )
= $true )
| ( ( aElementOf0 @ SV85 @ xJ )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(697,plain,
! [SV86: $i,SV88: $i] :
( ( ( aElement0 @ SV88 )
= $false )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV88 @ SV86 ) @ xJ )
= $true )
| ( ( aElementOf0 @ SV86 @ xJ )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(698,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(699,plain,
( ( aSet0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(700,plain,
! [SV59: $i,SV67: $i] :
( ( ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV59 )
= $true )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(701,plain,
! [SV59: $i,SV67: $i] :
( ( ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV67 )
= $true )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 )
= $false )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(702,plain,
! [SV59: $i,SV67: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 ) )
= $true )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 )
= $false )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(703,plain,
( ( ~ ( aElementOf0 @ sK5_W0 @ xI )
| ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(704,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(705,plain,
! [SV59: $i,SV67: $i] :
( ( ( aElementOf0 @ ( sK1_W2 @ SV67 @ SV59 ) @ SV59 )
= $false )
| ( ( aElementOf0 @ ( sK2_W2 @ SV67 @ SV59 ) @ SV67 )
= $false )
| ( ( SV59 = SV67 )
= $true )
| ( ( aSet0 @ SV59 )
= $false )
| ( ( aSet0 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(706,plain,
( ( ~ ( aElementOf0 @ sK5_W0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(707,plain,
( ( ~ ( aElementOf0 @ sK6_SY44 @ xJ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(708,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(709,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(710,plain,
( ( aElementOf0 @ sK5_W0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(711,plain,
( ( aElementOf0 @ sK6_SY44 @ xJ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(712,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(713,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(714,plain,
! [SV89: $i] :
( ( ~ ( aElementOf0 @ SV89 @ xI )
| ! [SY89: $i] :
( ~ ( aElementOf0 @ SY89 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV89 @ SY89 ) @ xI ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(715,plain,
! [SV90: $i] :
( ( ~ ( aElementOf0 @ SV90 @ xI )
| ! [SY90: $i] :
( ~ ( aElement0 @ SY90 )
| ( aElementOf0 @ ( sdtasdt0 @ SY90 @ SV90 ) @ xI ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(716,plain,
! [SV89: $i] :
( ( ( ~ ( aElementOf0 @ SV89 @ xI ) )
= $true )
| ( ( ! [SY89: $i] :
( ~ ( aElementOf0 @ SY89 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV89 @ SY89 ) @ xI ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(717,plain,
! [SV90: $i] :
( ( ( ~ ( aElementOf0 @ SV90 @ xI ) )
= $true )
| ( ( ! [SY90: $i] :
( ~ ( aElement0 @ SY90 )
| ( aElementOf0 @ ( sdtasdt0 @ SY90 @ SV90 ) @ xI ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(718,plain,
! [SV89: $i] :
( ( ( aElementOf0 @ SV89 @ xI )
= $false )
| ( ( ! [SY89: $i] :
( ~ ( aElementOf0 @ SY89 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV89 @ SY89 ) @ xI ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(719,plain,
! [SV90: $i] :
( ( ( aElementOf0 @ SV90 @ xI )
= $false )
| ( ( ! [SY90: $i] :
( ~ ( aElement0 @ SY90 )
| ( aElementOf0 @ ( sdtasdt0 @ SY90 @ SV90 ) @ xI ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(720,plain,
! [SV89: $i,SV91: $i] :
( ( ( ~ ( aElementOf0 @ SV91 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV89 @ SV91 ) @ xI ) )
= $true )
| ( ( aElementOf0 @ SV89 @ xI )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(721,plain,
! [SV90: $i,SV92: $i] :
( ( ( ~ ( aElement0 @ SV92 )
| ( aElementOf0 @ ( sdtasdt0 @ SV92 @ SV90 ) @ xI ) )
= $true )
| ( ( aElementOf0 @ SV90 @ xI )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(722,plain,
! [SV89: $i,SV91: $i] :
( ( ( ~ ( aElementOf0 @ SV91 @ xI ) )
= $true )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV89 @ SV91 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV89 @ xI )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(723,plain,
! [SV90: $i,SV92: $i] :
( ( ( ~ ( aElement0 @ SV92 ) )
= $true )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV92 @ SV90 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV90 @ xI )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(724,plain,
! [SV89: $i,SV91: $i] :
( ( ( aElementOf0 @ SV91 @ xI )
= $false )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV89 @ SV91 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV89 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(725,plain,
! [SV90: $i,SV92: $i] :
( ( ( aElement0 @ SV92 )
= $false )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV92 @ SV90 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV90 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(726,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[408,725,724,711,710,705,701,700,699,697,696,695,694,693,688,669,665,663,661,660,637,629,628,627,602,600,599,598,597,596,595,592,591,590,589,588,587,586,585,584,581,579,578,577,521,519,507,503,493,452,450,449,440,409]) ).
thf(727,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[726,402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG088+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon May 30 08:21:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.38
% 0.14/0.38 No.of.Axioms: 25
% 0.14/0.38
% 0.14/0.38 Length.of.Defs: 0
% 0.14/0.38
% 0.14/0.38 Contains.Choice.Funs: false
% 0.14/0.40 .
% 0.14/0.40 (rf:0,axioms:25,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:27,loop_count:0,foatp_calls:0,translation:fof_full)....................................
% 0.48/0.69
% 0.48/0.69 ********************************
% 0.48/0.69 * All subproblems solved! *
% 0.48/0.69 ********************************
% 0.48/0.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:726,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.70/0.89
% 0.70/0.89 %**** Beginning of derivation protocol ****
% 0.70/0.89 % SZS output start CNFRefutation
% See solution above
% 0.70/0.89
% 0.70/0.89 %**** End of derivation protocol ****
% 0.70/0.89 %**** no. of clauses in derivation: 727 ****
% 0.70/0.89 %**** clause counter: 726 ****
% 0.70/0.89
% 0.70/0.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:726,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------