%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : RNG111+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:37:48 AM UTC 2026
% Result : Theorem 0.06s 0.28s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 129 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 1398 ( 557 equ; 0 cnn)
% Maximal formula atoms : 15 ( 10 avg)
% Number of connectives : 2403 ( 704 ~; 452 |; 58 &;1138 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 9 con; 0-3 aty)
% Number of variables : 276 ( 0 ^; 263 !; 13 ?; 276 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aDivisorOf0,type,
aDivisorOf0: $i > $i > $o ).
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aGcdOfAnd0,type,
aGcdOfAnd0: $i > $i > $i > $o ).
thf(tp_aIdeal0,type,
aIdeal0: $i > $o ).
thf(tp_aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_doDivides0,type,
doDivides0: $i > $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_misRelativelyPrime0,type,
misRelativelyPrime0: $i > $i > $o ).
thf(tp_sK1_W0,type,
sK1_W0: $i ).
thf(tp_sK2_SX1,type,
sK2_SX1: $i > $i ).
thf(tp_sK3_SY23,type,
sK3_SY23: $i > $i > $i ).
thf(tp_sK4_SY25,type,
sK4_SY25: $i > $i ).
thf(tp_sK5_SY24,type,
sK5_SY24: $i > $i > $i ).
thf(tp_sK6_SY24,type,
sK6_SY24: $i > $i > $i ).
thf(tp_sbrdtbr0,type,
sbrdtbr0: $i > $i ).
thf(tp_sdtasasdt0,type,
sdtasasdt0: $i > $i > $i ).
thf(tp_sdtasdt0,type,
sdtasdt0: $i > $i > $i ).
thf(tp_sdteqdtlpzmzozddtrp0,type,
sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_sdtpldt1,type,
sdtpldt1: $i > $i > $i ).
thf(tp_slsdtgt0,type,
slsdtgt0: $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_xa,type,
xa: $i ).
thf(tp_xb,type,
xb: $i ).
thf(tp_xc,type,
xc: $i ).
thf(3,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatLess) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',mSetEq) ).
thf(12,axiom,
sz10 != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnNeZr) ).
thf(28,axiom,
aElement0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(36,conjecture,
! [W0: $i] :
( ( ( aElementOf0 @ W0 @ xI )
& ( W0 != sz00 ) )
=> ( ! [W1: $i] :
( ( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 ) )
=> ( ( iLess0 @ ( sbrdtbr0 @ W1 ) @ ( sbrdtbr0 @ W0 ) )
=> ? [W2: $i] :
( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 )
& ! [W3: $i] :
( ( ( aElementOf0 @ W3 @ xI )
& ( W3 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W2 ) ) ) ) ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 )
& ! [W2: $i] :
( ( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W2 ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(37,negated_conjecture,
( ( ! [W0: $i] :
( ( ( aElementOf0 @ W0 @ xI )
& ( W0 != sz00 ) )
=> ( ! [W1: $i] :
( ( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 ) )
=> ( ( iLess0 @ ( sbrdtbr0 @ W1 ) @ ( sbrdtbr0 @ W0 ) )
=> ? [W2: $i] :
( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 )
& ! [W3: $i] :
( ( ( aElementOf0 @ W3 @ xI )
& ( W3 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W2 ) ) ) ) ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 )
& ! [W2: $i] :
( ( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W2 ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [W0: $i] :
( ( ( aElementOf0 @ W0 @ xI )
& ( W0 != sz00 ) )
=> ( ! [W1: $i] :
( ( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 ) )
=> ( ( iLess0 @ ( sbrdtbr0 @ W1 ) @ ( sbrdtbr0 @ W0 ) )
=> ? [W2: $i] :
( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 )
& ! [W3: $i] :
( ( ( aElementOf0 @ W3 @ xI )
& ( W3 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W2 ) ) ) ) ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 )
& ! [W2: $i] :
( ( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W2 ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(40,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)],[9]) ).
thf(41,plain,
( ( sz10 != sz00 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(42,plain,
( ( aElement0 @ sz00 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(43,plain,
( ( ( ( aElementOf0 @ sK1_W0 @ xI )
& ( sK1_W0 != sz00 ) )
=> ( ! [SY12: $i] :
( ( ( aElementOf0 @ SY12 @ xI )
& ( SY12 != sz00 ) )
=> ( ( iLess0 @ ( sbrdtbr0 @ SY12 ) @ ( sbrdtbr0 @ sK1_W0 ) )
=> ? [W2: $i] :
( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 )
& ! [W3: $i] :
( ( ( aElementOf0 @ W3 @ xI )
& ( W3 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W2 ) ) ) ) ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 )
& ! [W2: $i] :
( ( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W2 ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(44,plain,
( ( aElementOf0 @ sK1_W0 @ xI )
= $true ),
inference(standard_cnf,[status(thm)],[43]) ).
thf(45,plain,
( ( sK1_W0 != sz00 )
= $true ),
inference(standard_cnf,[status(thm)],[43]) ).
thf(46,plain,
( ( ! [SY12: $i] :
( ( ( aElementOf0 @ SY12 @ xI )
& ( SY12 != sz00 ) )
=> ( ( iLess0 @ ( sbrdtbr0 @ SY12 ) @ ( sbrdtbr0 @ sK1_W0 ) )
=> ? [W2: $i] :
( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 )
& ! [W3: $i] :
( ( ( aElementOf0 @ W3 @ xI )
& ( W3 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W2 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[43]) ).
thf(47,plain,
( ( ? [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 )
& ! [W2: $i] :
( ( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W2 ) @ ( sbrdtbr0 @ W1 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[43]) ).
thf(48,plain,
( ( ~ ? [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 )
& ! [W2: $i] :
( ( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W2 ) @ ( sbrdtbr0 @ W1 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(49,plain,
( ( aElement0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(50,plain,
( ( sz10 != sz00 )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(51,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(copy,[status(thm)],[40]) ).
thf(52,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(53,plain,
( ( ! [SY12: $i] :
( ( ( aElementOf0 @ SY12 @ xI )
& ( SY12 != sz00 ) )
=> ( ( iLess0 @ ( sbrdtbr0 @ SY12 ) @ ( sbrdtbr0 @ sK1_W0 ) )
=> ? [W2: $i] :
( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 )
& ! [W3: $i] :
( ( ( aElementOf0 @ W3 @ xI )
& ( W3 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W2 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(54,plain,
( ( sK1_W0 != sz00 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(55,plain,
( ( aElementOf0 @ sK1_W0 @ xI )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(56,plain,
( ( ~ ? [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
& ( W1 != sz00 )
& ! [W2: $i] :
( ( ( aElementOf0 @ W2 @ xI )
& ( W2 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W2 ) @ ( sbrdtbr0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aSet0 @ SX0 )
| ~ ( aSet0 @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( aElementOf0 @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX1 )
| ( aElementOf0 @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(58,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ( SX0 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX0 ) @ ( sbrdtbr0 @ sK1_W0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(59,plain,
( ( sK1_W0 != sz00 )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(60,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ( SX0 != sz00 ) ) )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX1 ) @ ( sbrdtbr0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( iLess0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(62,plain,
( ( sz10 != sz00 )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(63,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
( ~ ~ ( ~ ( aSet0 @ SV1 )
| ~ ( aSet0 @ SY17 ) )
| ~ ~ ( ~ ! [SY18: $i] :
( ~ ( aElementOf0 @ SY18 @ SV1 )
| ( aElementOf0 @ SY18 @ SY17 ) )
| ~ ! [SY19: $i] :
( ~ ( aElementOf0 @ SY19 @ SY17 )
| ( aElementOf0 @ SY19 @ SV1 ) ) )
| ( SV1 = SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV2 @ xI )
| ~ ( ( SV2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(65,plain,
( ( sK1_W0 = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(66,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ( SX0 != sz00 ) ) )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX1 ) @ ( sbrdtbr0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SY22 ) )
| ~ ( iLess0 @ SV3 @ SY22 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(68,plain,
( ( sz10 = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ~ ( ~ ( aSet0 @ SV1 )
| ~ ( aSet0 @ SV4 ) )
| ~ ~ ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
| ( SV1 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV2 @ xI )
| ~ ( ( SV2 != sz00 ) ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(71,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ( SX0 != sz00 ) ) )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX1 ) @ ( sbrdtbr0 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(72,plain,
! [SV5: $i,SV3: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV5 ) )
| ~ ( iLess0 @ SV3 @ SV5 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aSet0 @ SV1 )
| ~ ( aSet0 @ SV4 ) ) )
= $true )
| ( ( ~ ~ ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
| ( SV1 = SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV2 @ xI )
| ~ ( ( SV2 != sz00 ) ) ) )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV6 @ xI )
| ~ ( ( SV6 != sz00 ) ) )
| ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV5 ) ) )
= $true )
| ( ( ~ ( iLess0 @ SV3 @ SV5 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( ~ ( aSet0 @ SV1 )
| ~ ( aSet0 @ SV4 ) ) )
= $false )
| ( ( ~ ~ ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
| ( SV1 = SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV2: $i] :
( ( ( ~ ( aElementOf0 @ SV2 @ xI )
| ~ ( ( SV2 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV6: $i] :
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV6 @ xI )
| ~ ( ( SV6 != sz00 ) ) )
| ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV5 ) ) )
= $false )
| ( ( ~ ( iLess0 @ SV3 @ SV5 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( aSet0 @ SV1 )
| ~ ( aSet0 @ SV4 ) )
= $true )
| ( ( ~ ~ ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
| ( SV1 = SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(82,plain,
! [SV2: $i] :
( ( ( ~ ( aElementOf0 @ SV2 @ xI ) )
= $true )
| ( ( ~ ( ( SV2 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV6 @ xI )
| ~ ( ( SV6 != sz00 ) ) )
| ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(84,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV5 ) )
= $true )
| ( ( ~ ( iLess0 @ SV3 @ SV5 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(85,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( aSet0 @ SV1 ) )
= $true )
| ( ( ~ ( aSet0 @ SV4 ) )
= $true )
| ( ( ~ ~ ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
| ( SV1 = SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV2: $i] :
( ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( ~ ( ( SV2 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV6 @ xI )
| ~ ( ( SV6 != sz00 ) ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV5 ) )
= $true )
| ( ( ~ ( iLess0 @ SV3 @ SV5 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV4: $i,SV1: $i] :
( ( ( aSet0 @ SV1 )
= $false )
| ( ( ~ ( aSet0 @ SV4 ) )
= $true )
| ( ( ~ ~ ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
| ( SV1 = SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV2: $i] :
( ( ( SV2 != sz00 )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV6 @ xI )
| ~ ( ( SV6 != sz00 ) ) ) )
= $false )
| ( ( ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV5: $i,SV3: $i] :
( ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV5 ) )
= $true )
| ( ( ~ ( iLess0 @ SV3 @ SV5 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(93,plain,
! [SV1: $i,SV4: $i] :
( ( ( aSet0 @ SV4 )
= $false )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( ~ ~ ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
| ( SV1 = SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(94,plain,
! [SV2: $i] :
( ( ( SV2 = sz00 )
= $true )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(95,plain,
! [SV6: $i] :
( ( ( ~ ( aElementOf0 @ SV6 @ xI )
| ~ ( ( SV6 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(96,plain,
! [SV3: $i,SV5: $i] :
( ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( ~ ( iLess0 @ SV3 @ SV5 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(97,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV2: $i] :
( ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) ) )
= $true )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV6: $i] :
( ( ( ~ ( aElementOf0 @ SV6 @ xI ) )
= $true )
| ( ( ~ ( ( SV6 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( iLess0 @ SV3 @ SV5 ) )
= $true )
| ( $true = $true )
| ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(101,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) ) )
= $false )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV2: $i] :
( ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $true )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV6: $i] :
( ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( ~ ( ( SV6 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV5: $i,SV3: $i] :
( ( ( iLess0 @ SV3 @ SV5 )
= $false )
| ( $true = $true )
| ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) )
| ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(106,plain,
! [SV2: $i] :
( ( ( ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xI )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xI )
| ~ ( ( SX2 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX2 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV6: $i] :
( ( ( SV6 != sz00 )
= $false )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(109,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK2_SX1 @ SV2 ) @ xI )
| ~ ( ( ( sK2_SX1 @ SV2 )
!= sz00 ) ) )
| ~ ! [SY26: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY26 @ xI )
| ~ ( ( SY26 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY26 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) ) ) )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[106]) ).
thf(110,plain,
! [SV6: $i] :
( ( ( SV6 = sz00 )
= $true )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( ~ ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(111,plain,
! [SV4: $i,SV1: $i] :
( ( ( ! [SY23: $i] :
( ~ ( aElementOf0 @ SY23 @ SV1 )
| ( aElementOf0 @ SY23 @ SV4 ) ) )
= $false )
| ( ( ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(112,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK2_SX1 @ SV2 ) @ xI )
| ~ ( ( ( sK2_SX1 @ SV2 )
!= sz00 ) ) )
| ~ ! [SY26: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY26 @ xI )
| ~ ( ( SY26 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY26 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(113,plain,
! [SV6: $i] :
( ( ( ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY25 @ xI )
| ~ ( ( SY25 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY25 ) @ ( sbrdtbr0 @ SV6 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(114,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV1 )
| ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV4 ) )
= $false )
| ( ( ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(115,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK2_SX1 @ SV2 ) @ xI )
| ~ ( ( ( sK2_SX1 @ SV2 )
!= sz00 ) ) )
| ~ ! [SY26: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY26 @ xI )
| ~ ( ( SY26 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY26 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) ) )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK4_SY25 @ SV6 ) @ xI )
| ~ ( ( ( sK4_SY25 @ SV6 )
!= sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ ( sK4_SY25 @ SV6 ) ) @ ( sbrdtbr0 @ SV6 ) ) )
= $false )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[113]) ).
thf(117,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV1 ) )
= $false )
| ( ( ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(118,plain,
! [SV1: $i,SV4: $i] :
( ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV4 )
= $false )
| ( ( ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(119,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK2_SX1 @ SV2 ) @ xI )
| ~ ( ( ( sK2_SX1 @ SV2 )
!= sz00 ) ) ) )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(120,plain,
! [SV2: $i] :
( ( ( ~ ! [SY26: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY26 @ xI )
| ~ ( ( SY26 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY26 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) ) )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(121,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK4_SY25 @ SV6 ) @ xI )
| ~ ( ( ( sK4_SY25 @ SV6 )
!= sz00 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV6: $i] :
( ( ( ~ ( iLess0 @ ( sbrdtbr0 @ ( sK4_SY25 @ SV6 ) ) @ ( sbrdtbr0 @ SV6 ) ) )
= $false )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(123,plain,
! [SV1: $i,SV4: $i] :
( ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV1 )
= $true )
| ( ( ~ ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(124,plain,
! [SV1: $i,SV4: $i] :
( ( ( ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
= $false )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV4 )
= $false )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK2_SX1 @ SV2 ) @ xI )
| ~ ( ( ( sK2_SX1 @ SV2 )
!= sz00 ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(126,plain,
! [SV2: $i] :
( ( ( ! [SY26: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SY26 @ xI )
| ~ ( ( SY26 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SY26 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(127,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK4_SY25 @ SV6 ) @ xI )
| ~ ( ( ( sK4_SY25 @ SV6 )
!= sz00 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(128,plain,
! [SV6: $i] :
( ( ( iLess0 @ ( sbrdtbr0 @ ( sK4_SY25 @ SV6 ) ) @ ( sbrdtbr0 @ SV6 ) )
= $true )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(129,plain,
! [SV1: $i,SV4: $i] :
( ( ( ! [SY24: $i] :
( ~ ( aElementOf0 @ SY24 @ SV4 )
| ( aElementOf0 @ SY24 @ SV1 ) ) )
= $false )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( aElementOf0 @ ( sK5_SY24 @ SV1 @ SV4 ) @ SV4 )
| ( aElementOf0 @ ( sK5_SY24 @ SV1 @ SV4 ) @ SV1 ) )
= $false )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV4 )
= $false )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[124]) ).
thf(131,plain,
! [SV2: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_SX1 @ SV2 ) @ xI )
| ~ ( ( ( sK2_SX1 @ SV2 )
!= sz00 ) ) )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV7 @ xI )
| ~ ( ( SV7 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SV7 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV6: $i] :
( ( ( ~ ( aElementOf0 @ ( sK4_SY25 @ SV6 ) @ xI )
| ~ ( ( ( sK4_SY25 @ SV6 )
!= sz00 ) ) )
= $false )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( aElementOf0 @ ( sK6_SY24 @ SV1 @ SV4 ) @ SV4 )
| ( aElementOf0 @ ( sK6_SY24 @ SV1 @ SV4 ) @ SV1 ) )
= $false )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(135,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( aElementOf0 @ ( sK5_SY24 @ SV1 @ SV4 ) @ SV4 ) )
= $false )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV4 )
= $false )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(136,plain,
! [SV4: $i,SV1: $i] :
( ( ( aElementOf0 @ ( sK5_SY24 @ SV1 @ SV4 ) @ SV1 )
= $false )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV4 )
= $false )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(137,plain,
! [SV2: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_SX1 @ SV2 ) @ xI ) )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(138,plain,
! [SV2: $i] :
( ( ( ~ ( ( ( sK2_SX1 @ SV2 )
!= sz00 ) ) )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(139,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV7 @ xI )
| ~ ( ( SV7 != sz00 ) ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV7 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV6: $i] :
( ( ( ~ ( aElementOf0 @ ( sK4_SY25 @ SV6 ) @ xI ) )
= $false )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(141,plain,
! [SV6: $i] :
( ( ( ~ ( ( ( sK4_SY25 @ SV6 )
!= sz00 ) ) )
= $false )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(142,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( aElementOf0 @ ( sK6_SY24 @ SV1 @ SV4 ) @ SV4 ) )
= $false )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(143,plain,
! [SV4: $i,SV1: $i] :
( ( ( aElementOf0 @ ( sK6_SY24 @ SV1 @ SV4 ) @ SV1 )
= $false )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(144,plain,
! [SV4: $i,SV1: $i] :
( ( ( aElementOf0 @ ( sK5_SY24 @ SV1 @ SV4 ) @ SV4 )
= $true )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV4 )
= $false )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(145,plain,
! [SV2: $i] :
( ( ( aElementOf0 @ ( sK2_SX1 @ SV2 ) @ xI )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(146,plain,
! [SV2: $i] :
( ( ( ( sK2_SX1 @ SV2 )
!= sz00 )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(147,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV7 @ xI )
| ~ ( ( SV7 != sz00 ) ) ) )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV7 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV6: $i] :
( ( ( aElementOf0 @ ( sK4_SY25 @ SV6 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(149,plain,
! [SV6: $i] :
( ( ( ( sK4_SY25 @ SV6 )
!= sz00 )
= $true )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(150,plain,
! [SV4: $i,SV1: $i] :
( ( ( aElementOf0 @ ( sK6_SY24 @ SV1 @ SV4 ) @ SV4 )
= $true )
| ( ( aElementOf0 @ ( sK3_SY23 @ SV4 @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = SV4 )
= $true )
| ( ( aSet0 @ SV1 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(151,plain,
! [SV2: $i] :
( ( ( ( sK2_SX1 @ SV2 )
= sz00 )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(152,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( aElementOf0 @ SV7 @ xI )
| ~ ( ( SV7 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV7 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(153,plain,
! [SV6: $i] :
( ( ( ( sK4_SY25 @ SV6 )
= sz00 )
= $false )
| ( ( aElementOf0 @ SV6 @ xI )
= $false )
| ( ( SV6 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(154,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( aElementOf0 @ SV7 @ xI ) )
= $true )
| ( ( ~ ( ( SV7 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV7 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(155,plain,
! [SV2: $i,SV7: $i] :
( ( ( aElementOf0 @ SV7 @ xI )
= $false )
| ( ( ~ ( ( SV7 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV7 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(156,plain,
! [SV2: $i,SV7: $i] :
( ( ( SV7 != sz00 )
= $false )
| ( ( aElementOf0 @ SV7 @ xI )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV7 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(157,plain,
! [SV2: $i,SV7: $i] :
( ( ( SV7 = sz00 )
= $true )
| ( ( aElementOf0 @ SV7 @ xI )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV7 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(158,plain,
! [SV2: $i,SV7: $i] :
( ( ( iLess0 @ ( sbrdtbr0 @ SV7 ) @ ( sbrdtbr0 @ ( sK2_SX1 @ SV2 ) ) )
= $false )
| ( ( aElementOf0 @ SV7 @ xI )
= $false )
| ( ( SV7 = sz00 )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ SV2 ) @ ( sbrdtbr0 @ sK1_W0 ) )
= $false )
| ( ( aElementOf0 @ SV2 @ xI )
= $false )
| ( ( SV2 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(159,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[49,158,153,151,150,148,145,144,143,136,128,104,68,65,55]) ).
thf(160,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG111+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n003.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 14:17:09 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.28
% 0.06/0.28 No.of.Axioms: 4
% 0.06/0.28
% 0.06/0.28 Length.of.Defs: 0
% 0.06/0.28
% 0.06/0.28 Contains.Choice.Funs: false
% 0.06/0.28 ...
% 0.06/0.28
% 0.06/0.28 ********************************
% 0.06/0.28 * All subproblems solved! *
% 0.06/0.28 ********************************
% 0.06/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:159,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.28
% 0.06/0.28 %**** Beginning of derivation protocol ****
% 0.06/0.28 % SZS output start CNFRefutation
% See solution above
% 0.06/0.28
% 0.06/0.28 %**** End of derivation protocol ****
% 0.06/0.28 %**** no. of clauses in derivation: 129 ****
% 0.06/0.28 %**** clause counter: 159 ****
% 0.06/0.28
% 0.06/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:159,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------