%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET988+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 10:42:42 AM UTC 2026
% Result : Theorem 0.55s 0.36s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 366 ( 212 unt; 0 typ; 0 def)
% Number of atoms : 1978 ( 708 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 3258 ( 914 ~; 462 |; 51 &;1792 @)
% ( 8 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 12 con; 0-2 aty)
% Number of variables : 789 ( 0 ^; 773 !; 16 ?; 789 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_sK10_SY64,type,
sK10_SY64: $i > $i ).
thf(tp_sK11_SY66,type,
sK11_SY66: $i > $i ).
thf(tp_sK12_SY60,type,
sK12_SY60: $i > $i > $i ).
thf(tp_sK13_SY68,type,
sK13_SY68: $i > $i > $i ).
thf(tp_sK14_SX0,type,
sK14_SX0: $i ).
thf(tp_sK15_SX0,type,
sK15_SX0: $i ).
thf(tp_sK16_SX0,type,
sK16_SX0: $i ).
thf(tp_sK17_SX0,type,
sK17_SX0: $i ).
thf(tp_sK18_SY74,type,
sK18_SY74: $i > $i ).
thf(tp_sK19_SY78,type,
sK19_SY78: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY86,type,
sK20_SY86: $i > $i ).
thf(tp_sK21_SY94,type,
sK21_SY94: $i > $i ).
thf(tp_sK22_SY97,type,
sK22_SY97: $i > $i ).
thf(tp_sK23_SY100,type,
sK23_SY100: $i > $i ).
thf(tp_sK24_SY90,type,
sK24_SY90: $i > $i > $i ).
thf(tp_sK25_SY102,type,
sK25_SY102: $i > $i > $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SY39,type,
sK6_SY39: $i > $i ).
thf(tp_sK7_SY48,type,
sK7_SY48: $i > $i ).
thf(tp_sK8_SY53,type,
sK8_SY53: $i > $i ).
thf(tp_sK9_SY58,type,
sK9_SY58: $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(2,axiom,
! [A: $i] :
( ( function @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(9,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(10,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(11,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(14,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(22,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(26,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(33,conjecture,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( relation @ A )
& ( function @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
thf(34,negated_conjecture,
( ( ! [A: $i] :
( ( ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( relation @ A )
& ( function @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[33]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( relation @ A )
& ( function @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[34]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( function @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(41,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(42,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(43,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(44,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(48,plain,
( ( ( ! [SY29: $i] :
~ ( ( in @ SY29 @ sK1_A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= SY29 ) )
& ! [SY32: $i,SY33: $i,SY34: $i] :
( ( ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY32 @ SY34 ) @ sK1_A ) )
=> ( SY33 = SY34 ) ) )
=> ( ( relation @ sK1_A )
& ( function @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(49,plain,
( ( ! [SY29: $i] :
~ ( ( in @ SY29 @ sK1_A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= SY29 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(50,plain,
( ( ! [SY32: $i,SY33: $i,SY34: $i] :
( ( ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY32 @ SY34 ) @ sK1_A ) )
=> ( SY33 = SY34 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(51,plain,
( ( ( relation @ sK1_A )
& ( function @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(52,plain,
( ( relation @ sK1_A )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[51]) ).
thf(53,plain,
( ( function @ sK1_A )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[51]) ).
thf(54,plain,
( ( ~ ( relation @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[52]) ).
thf(55,plain,
( ( ~ ( function @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[53]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(59,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(60,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(61,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(62,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( function @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(68,plain,
( ( ! [SY32: $i,SY33: $i,SY34: $i] :
( ( ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY32 @ SY34 ) @ sK1_A ) )
=> ( SY33 = SY34 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(69,plain,
( ( ! [SY29: $i] :
~ ( ( in @ SY29 @ sK1_A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= SY29 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(70,plain,
( ( ~ ( relation @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(71,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) )
| ( SX2 = SX3 ) ) )
| ~ ( ~ ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) )
| ( SX2 = SX3 ) )
| ( function @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(75,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(76,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(77,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(78,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SX0 @ SX2 ) @ sK1_A ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(81,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( in @ SX0 @ sK1_A )
| ~ ! [SX1: $i,SX2: $i] :
( ( ordered_pair @ SX1 @ SX2 )
!= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(83,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(84,plain,
! [SV1: $i] :
( ( ! [SY35: $i] :
~ ( empty @ ( ordered_pair @ SV1 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(85,plain,
( ( relation @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV2: $i] :
( ( ~ ( ~ ( ~ ( function @ SV2 )
| ! [SY36: $i,SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY36 @ SY37 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY36 @ SY38 ) @ SV2 ) )
| ( SY37 = SY38 ) ) )
| ~ ( ~ ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY39 @ SY40 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY39 @ SY41 ) @ SV2 ) )
| ( SY40 = SY41 ) )
| ( function @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV3: $i] :
( ( ! [SY42: $i] :
( ~ ( in @ SV3 @ SY42 )
| ( element @ SV3 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV4: $i] :
( ( ! [SY43: $i] :
~ ~ ( ~ ( in @ SV4 @ SY43 )
| ~ ( empty @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV5: $i] :
( ( ! [SY44: $i] :
( ~ ( in @ SV5 @ SY44 )
| ~ ( in @ SY44 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(90,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(91,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(92,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(93,plain,
! [SV6: $i] :
( ( ~ ( ~ ( ~ ( relation @ SV6 )
| ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY45
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ SY48 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY48
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(94,plain,
! [SV7: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SY51 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV7 @ SY52 ) @ sK1_A ) )
| ( SY51 = SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV8: $i] :
( ( ~ ( empty @ SV8 )
| ( relation @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ( in @ SV9 @ sK1_A )
| ~ ! [SY53: $i,SY54: $i] :
( ( ordered_pair @ SY53 @ SY54 )
!= SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
! [SV10: $i] :
( ( ~ ( empty @ SV10 )
| ( function @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(98,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV11: $i,SV1: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV1 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV2: $i] :
( ( ~ ( ~ ( function @ SV2 )
| ! [SY36: $i,SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY36 @ SY37 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY36 @ SY38 ) @ SV2 ) )
| ( SY37 = SY38 ) ) )
| ~ ( ~ ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY39 @ SY40 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY39 @ SY41 ) @ SV2 ) )
| ( SY40 = SY41 ) )
| ( function @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV12: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV12 )
| ( element @ SV3 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV13: $i,SV4: $i] :
( ( ~ ~ ( ~ ( in @ SV4 @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV14: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV14 )
| ~ ( in @ SV14 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(104,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(105,plain,
( ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(106,plain,
( ( ~ ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(107,plain,
! [SV6: $i] :
( ( ~ ( ~ ( relation @ SV6 )
| ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY45
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ SY48 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY48
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV15: $i,SV7: $i] :
( ( ! [SY55: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SV15 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV7 @ SY55 ) @ sK1_A ) )
| ( SV15 = SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV9: $i] :
( ( ~ ( ~ ( in @ SV9 @ sK1_A )
| ~ ! [SY53: $i,SY54: $i] :
( ( ordered_pair @ SY53 @ SY54 )
!= SV9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(111,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $true )
| ( ( function @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(112,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_empty_yielding @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(113,plain,
! [SV11: $i,SV1: $i] :
( ( empty @ ( ordered_pair @ SV1 @ SV11 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(114,plain,
! [SV2: $i] :
( ( ~ ( ~ ( function @ SV2 )
| ! [SY36: $i,SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY36 @ SY37 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY36 @ SY38 ) @ SV2 ) )
| ( SY37 = SY38 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(115,plain,
! [SV2: $i] :
( ( ~ ( ~ ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY39 @ SY40 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY39 @ SY41 ) @ SV2 ) )
| ( SY40 = SY41 ) )
| ( function @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(116,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV12 ) )
= $true )
| ( ( element @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV13: $i,SV4: $i] :
( ( ~ ( ~ ( in @ SV4 @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV14 ) )
= $true )
| ( ( ~ ( in @ SV14 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(119,plain,
( ( ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(120,plain,
( ( ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(121,plain,
( ( ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(122,plain,
! [SV6: $i] :
( ( ~ ( ~ ( relation @ SV6 )
| ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY45
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(123,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ SY48 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY48
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(124,plain,
! [SV16: $i,SV15: $i,SV7: $i] :
( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SV15 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV7 @ SV16 ) @ sK1_A ) )
| ( SV15 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(125,plain,
! [SV8: $i] :
( ( ( empty @ SV8 )
= $false )
| ( ( relation @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV9: $i] :
( ( ~ ( in @ SV9 @ sK1_A )
| ~ ! [SY53: $i,SY54: $i] :
( ( ordered_pair @ SY53 @ SY54 )
!= SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(127,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $false )
| ( ( function @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(128,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_empty_yielding @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(129,plain,
! [SV2: $i] :
( ( ~ ( function @ SV2 )
| ! [SY36: $i,SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY36 @ SY37 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY36 @ SY38 ) @ SV2 ) )
| ( SY37 = SY38 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(130,plain,
! [SV2: $i] :
( ( ~ ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY39 @ SY40 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY39 @ SY41 ) @ SV2 ) )
| ( SY40 = SY41 ) )
| ( function @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(131,plain,
! [SV12: $i,SV3: $i] :
( ( ( in @ SV3 @ SV12 )
= $false )
| ( ( element @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(132,plain,
! [SV13: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV13 )
| ~ ( empty @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(133,plain,
! [SV14: $i,SV5: $i] :
( ( ( in @ SV5 @ SV14 )
= $false )
| ( ( ~ ( in @ SV14 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(134,plain,
( ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(135,plain,
( ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(136,plain,
( ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(137,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY45
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(138,plain,
! [SV6: $i] :
( ( ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ SY48 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY48
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(139,plain,
! [SV16: $i,SV15: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SV15 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV7 @ SV16 ) @ sK1_A ) ) )
= $true )
| ( ( SV15 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(140,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ sK1_A ) )
= $true )
| ( ( ~ ! [SY53: $i,SY54: $i] :
( ( ordered_pair @ SY53 @ SY54 )
!= SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(141,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_empty_yielding @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(142,plain,
! [SV2: $i] :
( ( ( ~ ( function @ SV2 ) )
= $true )
| ( ( ! [SY36: $i,SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY36 @ SY37 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY36 @ SY38 ) @ SV2 ) )
| ( SY37 = SY38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(143,plain,
! [SV2: $i] :
( ( ( ~ ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY39 @ SY40 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY39 @ SY41 ) @ SV2 ) )
| ( SY40 = SY41 ) ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(144,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( empty @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV5: $i,SV14: $i] :
( ( ( in @ SV14 @ SV5 )
= $false )
| ( ( in @ SV5 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(146,plain,
( ( ~ ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(147,plain,
( ( ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(148,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(149,plain,
( ( ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(150,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(151,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(152,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY45
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(153,plain,
! [SV6: $i] :
( ( ( ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ SY48 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY48
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(154,plain,
! [SV16: $i,SV15: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SV15 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV7 @ SV16 ) @ sK1_A ) ) )
= $false )
| ( ( SV15 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(155,plain,
! [SV9: $i] :
( ( ( in @ SV9 @ sK1_A )
= $false )
| ( ( ~ ! [SY53: $i,SY54: $i] :
( ( ordered_pair @ SY53 @ SY54 )
!= SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(156,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(157,plain,
( ( ~ ( relation_empty_yielding @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(158,plain,
! [SV2: $i] :
( ( ( function @ SV2 )
= $false )
| ( ( ! [SY36: $i,SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY36 @ SY37 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY36 @ SY38 ) @ SV2 ) )
| ( SY37 = SY38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(159,plain,
! [SV2: $i] :
( ( ( ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY39 @ SY40 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SY39 @ SY41 ) @ SV2 ) )
| ( SY40 = SY41 ) ) )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(160,plain,
! [SV13: $i,SV4: $i] :
( ( ( in @ SV4 @ SV13 )
= $false )
| ( ( ~ ( empty @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(161,plain,
( ( ~ ( empty @ sK2_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(162,plain,
( ( relation @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(163,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(164,plain,
( ( function @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(165,plain,
( ( empty @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(166,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(167,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY45
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV6: $i] :
( ( ( ! [SY48: $i] :
~ ~ ( ~ ( in @ SY48 @ SV6 )
| ~ ! [SX2: $i,SX3: $i] :
( SY48
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV16: $i,SV15: $i,SV7: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV7 @ SV15 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV7 @ SV16 ) @ sK1_A ) )
= $true )
| ( ( SV15 = SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(170,plain,
! [SV9: $i] :
( ( ( ! [SY53: $i,SY54: $i] :
( ( ordered_pair @ SY53 @ SY54 )
!= SV9 ) )
= $false )
| ( ( in @ SV9 @ sK1_A )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(171,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(172,plain,
( ( relation_empty_yielding @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(173,plain,
! [SV2: $i,SV17: $i] :
( ( ( ! [SY56: $i,SY57: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SV17 @ SY56 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY57 ) @ SV2 ) )
| ( SY56 = SY57 ) ) )
= $true )
| ( ( function @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV2: $i] :
( ( ( ! [SY58: $i,SY59: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ SY58 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ SY59 ) @ SV2 ) )
| ( SY58 = SY59 ) ) )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[159]) ).
thf(175,plain,
! [SV4: $i,SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( in @ SV4 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(176,plain,
( ( empty @ sK2_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV6: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ SV18 @ SV6 )
| ~ ! [SY60: $i,SY61: $i] :
( SV18
!= ( ordered_pair @ SY60 @ SY61 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY48 @ SV6 ) @ SV6 )
| ~ ! [SY62: $i,SY63: $i] :
( ( sK7_SY48 @ SV6 )
!= ( ordered_pair @ SY62 @ SY63 ) ) ) )
= $false )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[168]) ).
thf(179,plain,
! [SV16: $i,SV15: $i,SV7: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV7 @ SV15 ) @ sK1_A ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV7 @ SV16 ) @ sK1_A ) )
= $true )
| ( ( SV15 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV9: $i] :
( ( ( ! [SY64: $i] :
( ( ordered_pair @ ( sK8_SY53 @ SV9 ) @ SY64 )
!= SV9 ) )
= $false )
| ( ( in @ SV9 @ sK1_A )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[170]) ).
thf(181,plain,
! [SV2: $i,SV19: $i,SV17: $i] :
( ( ( ! [SY65: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SV17 @ SV19 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY65 ) @ SV2 ) )
| ( SV19 = SY65 ) ) )
= $true )
| ( ( function @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV2: $i] :
( ( ( ! [SY66: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK9_SY58 @ SV2 ) ) @ SV2 )
| ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ SY66 ) @ SV2 ) )
| ( ( sK9_SY58 @ SV2 )
= SY66 ) ) )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[174]) ).
thf(183,plain,
! [SV6: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ SV6 )
| ~ ! [SY60: $i,SY61: $i] :
( SV18
!= ( ordered_pair @ SY60 @ SY61 ) ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(184,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY48 @ SV6 ) @ SV6 )
| ~ ! [SY62: $i,SY63: $i] :
( ( sK7_SY48 @ SV6 )
!= ( ordered_pair @ SY62 @ SY63 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(185,plain,
! [SV16: $i,SV15: $i,SV7: $i] :
( ( ( in @ ( ordered_pair @ SV7 @ SV15 ) @ sK1_A )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV7 @ SV16 ) @ sK1_A ) )
= $true )
| ( ( SV15 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(186,plain,
! [SV9: $i] :
( ( ( ( ordered_pair @ ( sK8_SY53 @ SV9 ) @ ( sK10_SY64 @ SV9 ) )
!= SV9 )
= $false )
| ( ( in @ SV9 @ sK1_A )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[180]) ).
thf(187,plain,
! [SV20: $i,SV2: $i,SV19: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV17 @ SV19 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SV17 @ SV20 ) @ SV2 ) )
| ( SV19 = SV20 ) )
= $true )
| ( ( function @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(188,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK9_SY58 @ SV2 ) ) @ SV2 )
| ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK11_SY66 @ SV2 ) ) @ SV2 ) )
| ( ( sK9_SY58 @ SV2 )
= ( sK11_SY66 @ SV2 ) ) )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[182]) ).
thf(189,plain,
! [SV6: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV6 )
| ~ ! [SY60: $i,SY61: $i] :
( SV18
!= ( ordered_pair @ SY60 @ SY61 ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(190,plain,
! [SV6: $i] :
( ( ( ~ ( in @ ( sK7_SY48 @ SV6 ) @ SV6 )
| ~ ! [SY62: $i,SY63: $i] :
( ( sK7_SY48 @ SV6 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
= $false )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(191,plain,
! [SV15: $i,SV16: $i,SV7: $i] :
( ( ( in @ ( ordered_pair @ SV7 @ SV16 ) @ sK1_A )
= $false )
| ( ( in @ ( ordered_pair @ SV7 @ SV15 ) @ sK1_A )
= $false )
| ( ( SV15 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(192,plain,
! [SV9: $i] :
( ( ( ( ordered_pair @ ( sK8_SY53 @ SV9 ) @ ( sK10_SY64 @ SV9 ) )
= SV9 )
= $true )
| ( ( in @ SV9 @ sK1_A )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(193,plain,
! [SV20: $i,SV2: $i,SV19: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV17 @ SV19 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SV17 @ SV20 ) @ SV2 ) ) )
= $true )
| ( ( SV19 = SV20 )
= $true )
| ( ( function @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(194,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK9_SY58 @ SV2 ) ) @ SV2 )
| ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK11_SY66 @ SV2 ) ) @ SV2 ) ) )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(195,plain,
! [SV2: $i] :
( ( ( ( sK9_SY58 @ SV2 )
= ( sK11_SY66 @ SV2 ) )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(196,plain,
! [SV6: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV6 ) )
= $true )
| ( ( ~ ! [SY60: $i,SY61: $i] :
( SV18
!= ( ordered_pair @ SY60 @ SY61 ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(197,plain,
! [SV6: $i] :
( ( ( ~ ( in @ ( sK7_SY48 @ SV6 ) @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(198,plain,
! [SV6: $i] :
( ( ( ~ ! [SY62: $i,SY63: $i] :
( ( sK7_SY48 @ SV6 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
= $false )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(199,plain,
! [SV20: $i,SV2: $i,SV19: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV17 @ SV19 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SV17 @ SV20 ) @ SV2 ) ) )
= $false )
| ( ( SV19 = SV20 )
= $true )
| ( ( function @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(200,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK9_SY58 @ SV2 ) ) @ SV2 )
| ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK11_SY66 @ SV2 ) ) @ SV2 ) ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(201,plain,
! [SV6: $i,SV18: $i] :
( ( ( in @ SV18 @ SV6 )
= $false )
| ( ( ~ ! [SY60: $i,SY61: $i] :
( SV18
!= ( ordered_pair @ SY60 @ SY61 ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(202,plain,
! [SV6: $i] :
( ( ( in @ ( sK7_SY48 @ SV6 ) @ SV6 )
= $true )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(203,plain,
! [SV6: $i] :
( ( ( ! [SY62: $i,SY63: $i] :
( ( sK7_SY48 @ SV6 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
= $true )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(204,plain,
! [SV20: $i,SV2: $i,SV19: $i,SV17: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV19 ) @ SV2 )
| ~ ( in @ ( ordered_pair @ SV17 @ SV20 ) @ SV2 ) )
= $true )
| ( ( SV19 = SV20 )
= $true )
| ( ( function @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(205,plain,
! [SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK9_SY58 @ SV2 ) ) @ SV2 )
| ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK11_SY66 @ SV2 ) ) @ SV2 ) )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(206,plain,
! [SV6: $i,SV18: $i] :
( ( ( ! [SY60: $i,SY61: $i] :
( SV18
!= ( ordered_pair @ SY60 @ SY61 ) ) )
= $false )
| ( ( in @ SV18 @ SV6 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(207,plain,
! [SV21: $i,SV6: $i] :
( ( ( ! [SY67: $i] :
( ( sK7_SY48 @ SV6 )
!= ( ordered_pair @ SV21 @ SY67 ) ) )
= $true )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(208,plain,
! [SV20: $i,SV2: $i,SV19: $i,SV17: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV19 ) @ SV2 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV20 ) @ SV2 ) )
= $true )
| ( ( SV19 = SV20 )
= $true )
| ( ( function @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(209,plain,
! [SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK9_SY58 @ SV2 ) ) @ SV2 ) )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(210,plain,
! [SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK11_SY66 @ SV2 ) ) @ SV2 ) )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(211,plain,
! [SV6: $i,SV18: $i] :
( ( ( ! [SY68: $i] :
( SV18
!= ( ordered_pair @ ( sK12_SY60 @ SV6 @ SV18 ) @ SY68 ) ) )
= $false )
| ( ( in @ SV18 @ SV6 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[206]) ).
thf(212,plain,
! [SV22: $i,SV21: $i,SV6: $i] :
( ( ( ( sK7_SY48 @ SV6 )
!= ( ordered_pair @ SV21 @ SV22 ) )
= $true )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(213,plain,
! [SV20: $i,SV2: $i,SV19: $i,SV17: $i] :
( ( ( in @ ( ordered_pair @ SV17 @ SV19 ) @ SV2 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV20 ) @ SV2 ) )
= $true )
| ( ( SV19 = SV20 )
= $true )
| ( ( function @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(214,plain,
! [SV2: $i] :
( ( ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK9_SY58 @ SV2 ) ) @ SV2 )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(215,plain,
! [SV2: $i] :
( ( ( in @ ( ordered_pair @ ( sK6_SY39 @ SV2 ) @ ( sK11_SY66 @ SV2 ) ) @ SV2 )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(216,plain,
! [SV6: $i,SV18: $i] :
( ( ( SV18
!= ( ordered_pair @ ( sK12_SY60 @ SV6 @ SV18 ) @ ( sK13_SY68 @ SV6 @ SV18 ) ) )
= $false )
| ( ( in @ SV18 @ SV6 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[211]) ).
thf(217,plain,
! [SV22: $i,SV21: $i,SV6: $i] :
( ( ( ( sK7_SY48 @ SV6 )
= ( ordered_pair @ SV21 @ SV22 ) )
= $false )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(218,plain,
! [SV19: $i,SV2: $i,SV20: $i,SV17: $i] :
( ( ( in @ ( ordered_pair @ SV17 @ SV20 ) @ SV2 )
= $false )
| ( ( in @ ( ordered_pair @ SV17 @ SV19 ) @ SV2 )
= $false )
| ( ( SV19 = SV20 )
= $true )
| ( ( function @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(219,plain,
! [SV6: $i,SV18: $i] :
( ( ( SV18
= ( ordered_pair @ ( sK12_SY60 @ SV6 @ SV18 ) @ ( sK13_SY68 @ SV6 @ SV18 ) ) )
= $true )
| ( ( in @ SV18 @ SV6 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(220,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[85,219,218,217,215,214,202,195,192,191,176,175,172,171,166,165,164,163,162,145,131,127,125,113]) ).
thf(221,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(222,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(224,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(225,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(226,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(227,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(231,plain,
( ( ! [A: $i] :
( ( function @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(232,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(233,plain,
( ( ! [SY32: $i,SY33: $i,SY34: $i] :
( ( ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY32 @ SY34 ) @ sK1_A ) )
=> ( SY33 = SY34 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(234,plain,
( ( ! [SY29: $i] :
~ ( ( in @ SY29 @ sK1_A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= SY29 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(235,plain,
( ( ~ ( function @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(236,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(237,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(238,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(239,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( in @ SX0 @ sK1_A )
| ~ ! [SX1: $i,SX2: $i] :
( ( ordered_pair @ SX1 @ SX2 )
!= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(240,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(241,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(242,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SX0 @ SX2 ) @ sK1_A ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(243,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(244,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(245,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(246,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(247,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) )
| ( SX2 = SX3 ) ) )
| ~ ( ~ ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) )
| ( SX2 = SX3 ) )
| ( function @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(248,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(249,plain,
! [SV23: $i] :
( ( ! [SY69: $i] :
~ ( empty @ ( ordered_pair @ SV23 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(250,plain,
( ( function @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(251,plain,
! [SV24: $i] :
( ( ! [SY70: $i] :
( ~ ( in @ SV24 @ SY70 )
| ( element @ SV24 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(252,plain,
! [SV25: $i] :
( ( ~ ( ~ ( ~ ( relation @ SV25 )
| ! [SY71: $i] :
~ ~ ( ~ ( in @ SY71 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY71
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY74: $i] :
~ ~ ( ~ ( in @ SY74 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY74
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(253,plain,
! [SV26: $i] :
( ( ! [SY77: $i] :
~ ~ ( ~ ( in @ SV26 @ SY77 )
| ~ ( empty @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(254,plain,
! [SV27: $i] :
( ( ~ ~ ( ~ ( in @ SV27 @ sK1_A )
| ~ ! [SY78: $i,SY79: $i] :
( ( ordered_pair @ SY78 @ SY79 )
!= SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(255,plain,
! [SV28: $i] :
( ( ! [SY80: $i] :
( ~ ( in @ SV28 @ SY80 )
| ~ ( in @ SY80 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(256,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(257,plain,
! [SV29: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SY81 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV29 @ SY82 ) @ sK1_A ) )
| ( SY81 = SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(258,plain,
! [SV30: $i] :
( ( ~ ( empty @ SV30 )
| ( relation @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(259,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(260,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(261,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(262,plain,
! [SV31: $i] :
( ( ~ ( ~ ( ~ ( function @ SV31 )
| ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY83 @ SY85 ) @ SV31 ) )
| ( SY84 = SY85 ) ) )
| ~ ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY86 @ SY87 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY86 @ SY88 ) @ SV31 ) )
| ( SY87 = SY88 ) )
| ( function @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(263,plain,
! [SV32: $i] :
( ( ~ ( empty @ SV32 )
| ( function @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(264,plain,
! [SV33: $i,SV23: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV23 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(265,plain,
! [SV34: $i,SV24: $i] :
( ( ~ ( in @ SV24 @ SV34 )
| ( element @ SV24 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(266,plain,
! [SV25: $i] :
( ( ~ ( ~ ( relation @ SV25 )
| ! [SY71: $i] :
~ ~ ( ~ ( in @ SY71 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY71
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY74: $i] :
~ ~ ( ~ ( in @ SY74 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY74
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(267,plain,
! [SV35: $i,SV26: $i] :
( ( ~ ~ ( ~ ( in @ SV26 @ SV35 )
| ~ ( empty @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(268,plain,
! [SV27: $i] :
( ( ~ ( ~ ( in @ SV27 @ sK1_A )
| ~ ! [SY78: $i,SY79: $i] :
( ( ordered_pair @ SY78 @ SY79 )
!= SV27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(269,plain,
! [SV36: $i,SV28: $i] :
( ( ~ ( in @ SV28 @ SV36 )
| ~ ( in @ SV36 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(270,plain,
( ( ~ ~ ( ~ ( relation @ sK14_SX0 )
| ~ ( function @ sK14_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[256]) ).
thf(271,plain,
! [SV37: $i,SV29: $i] :
( ( ! [SY89: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SV37 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV29 @ SY89 ) @ sK1_A ) )
| ( SV37 = SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(272,plain,
! [SV30: $i] :
( ( ( ~ ( empty @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(273,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK15_SX0 )
| ~ ( relation @ sK15_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[259]) ).
thf(274,plain,
( ( ~ ~ ( ~ ( relation @ sK16_SX0 )
| ~ ( relation_empty_yielding @ sK16_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[260]) ).
thf(275,plain,
( ( ~ ~ ( ~ ( empty @ sK17_SX0 )
| ~ ( relation @ sK17_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[261]) ).
thf(276,plain,
! [SV31: $i] :
( ( ~ ( ~ ( function @ SV31 )
| ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY83 @ SY85 ) @ SV31 ) )
| ( SY84 = SY85 ) ) )
| ~ ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY86 @ SY87 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY86 @ SY88 ) @ SV31 ) )
| ( SY87 = SY88 ) )
| ( function @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(277,plain,
! [SV32: $i] :
( ( ( ~ ( empty @ SV32 ) )
= $true )
| ( ( function @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(278,plain,
! [SV33: $i,SV23: $i] :
( ( empty @ ( ordered_pair @ SV23 @ SV33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(279,plain,
! [SV34: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV34 ) )
= $true )
| ( ( element @ SV24 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(280,plain,
! [SV25: $i] :
( ( ~ ( ~ ( relation @ SV25 )
| ! [SY71: $i] :
~ ~ ( ~ ( in @ SY71 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY71
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(281,plain,
! [SV25: $i] :
( ( ~ ( ~ ! [SY74: $i] :
~ ~ ( ~ ( in @ SY74 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY74
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(282,plain,
! [SV35: $i,SV26: $i] :
( ( ~ ( ~ ( in @ SV26 @ SV35 )
| ~ ( empty @ SV35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(283,plain,
! [SV27: $i] :
( ( ~ ( in @ SV27 @ sK1_A )
| ~ ! [SY78: $i,SY79: $i] :
( ( ordered_pair @ SY78 @ SY79 )
!= SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(284,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV36 ) )
= $true )
| ( ( ~ ( in @ SV36 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(285,plain,
( ( ~ ( ~ ( relation @ sK14_SX0 )
| ~ ( function @ sK14_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(286,plain,
! [SV38: $i,SV37: $i,SV29: $i] :
( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SV37 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV29 @ SV38 ) @ sK1_A ) )
| ( SV37 = SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(287,plain,
! [SV30: $i] :
( ( ( empty @ SV30 )
= $false )
| ( ( relation @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(288,plain,
( ( ~ ( ~ ~ ( empty @ sK15_SX0 )
| ~ ( relation @ sK15_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(289,plain,
( ( ~ ( ~ ( relation @ sK16_SX0 )
| ~ ( relation_empty_yielding @ sK16_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(290,plain,
( ( ~ ( ~ ( empty @ sK17_SX0 )
| ~ ( relation @ sK17_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(291,plain,
! [SV31: $i] :
( ( ~ ( ~ ( function @ SV31 )
| ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY83 @ SY85 ) @ SV31 ) )
| ( SY84 = SY85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(292,plain,
! [SV31: $i] :
( ( ~ ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY86 @ SY87 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY86 @ SY88 ) @ SV31 ) )
| ( SY87 = SY88 ) )
| ( function @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(293,plain,
! [SV32: $i] :
( ( ( empty @ SV32 )
= $false )
| ( ( function @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(294,plain,
! [SV34: $i,SV24: $i] :
( ( ( in @ SV24 @ SV34 )
= $false )
| ( ( element @ SV24 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(295,plain,
! [SV25: $i] :
( ( ~ ( relation @ SV25 )
| ! [SY71: $i] :
~ ~ ( ~ ( in @ SY71 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY71
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(296,plain,
! [SV25: $i] :
( ( ~ ! [SY74: $i] :
~ ~ ( ~ ( in @ SY74 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY74
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(297,plain,
! [SV35: $i,SV26: $i] :
( ( ~ ( in @ SV26 @ SV35 )
| ~ ( empty @ SV35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(298,plain,
! [SV27: $i] :
( ( ( ~ ( in @ SV27 @ sK1_A ) )
= $true )
| ( ( ~ ! [SY78: $i,SY79: $i] :
( ( ordered_pair @ SY78 @ SY79 )
!= SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(299,plain,
! [SV36: $i,SV28: $i] :
( ( ( in @ SV28 @ SV36 )
= $false )
| ( ( ~ ( in @ SV36 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(300,plain,
( ( ~ ( relation @ sK14_SX0 )
| ~ ( function @ sK14_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(301,plain,
! [SV38: $i,SV37: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SV37 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV29 @ SV38 ) @ sK1_A ) ) )
= $true )
| ( ( SV37 = SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(302,plain,
( ( ~ ~ ( empty @ sK15_SX0 )
| ~ ( relation @ sK15_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(303,plain,
( ( ~ ( relation @ sK16_SX0 )
| ~ ( relation_empty_yielding @ sK16_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(304,plain,
( ( ~ ( empty @ sK17_SX0 )
| ~ ( relation @ sK17_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(305,plain,
! [SV31: $i] :
( ( ~ ( function @ SV31 )
| ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY83 @ SY85 ) @ SV31 ) )
| ( SY84 = SY85 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(306,plain,
! [SV31: $i] :
( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY86 @ SY87 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY86 @ SY88 ) @ SV31 ) )
| ( SY87 = SY88 ) )
| ( function @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(307,plain,
! [SV25: $i] :
( ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( ! [SY71: $i] :
~ ~ ( ~ ( in @ SY71 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY71
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(308,plain,
! [SV25: $i] :
( ( ( ~ ! [SY74: $i] :
~ ~ ( ~ ( in @ SY74 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY74
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(309,plain,
! [SV35: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV35 ) )
= $true )
| ( ( ~ ( empty @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(310,plain,
! [SV27: $i] :
( ( ( in @ SV27 @ sK1_A )
= $false )
| ( ( ~ ! [SY78: $i,SY79: $i] :
( ( ordered_pair @ SY78 @ SY79 )
!= SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(311,plain,
! [SV28: $i,SV36: $i] :
( ( ( in @ SV36 @ SV28 )
= $false )
| ( ( in @ SV28 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(312,plain,
( ( ~ ( relation @ sK14_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(313,plain,
( ( ~ ( function @ sK14_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(314,plain,
! [SV38: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SV37 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV29 @ SV38 ) @ sK1_A ) ) )
= $false )
| ( ( SV37 = SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(315,plain,
( ( ~ ~ ( empty @ sK15_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(316,plain,
( ( ~ ( relation @ sK15_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(317,plain,
( ( ~ ( relation @ sK16_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(318,plain,
( ( ~ ( relation_empty_yielding @ sK16_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(319,plain,
( ( ~ ( empty @ sK17_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(320,plain,
( ( ~ ( relation @ sK17_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(321,plain,
! [SV31: $i] :
( ( ( ~ ( function @ SV31 ) )
= $true )
| ( ( ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY83 @ SY85 ) @ SV31 ) )
| ( SY84 = SY85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(322,plain,
! [SV31: $i] :
( ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY86 @ SY87 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY86 @ SY88 ) @ SV31 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(323,plain,
! [SV25: $i] :
( ( ( relation @ SV25 )
= $false )
| ( ( ! [SY71: $i] :
~ ~ ( ~ ( in @ SY71 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY71
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(324,plain,
! [SV25: $i] :
( ( ( ! [SY74: $i] :
~ ~ ( ~ ( in @ SY74 @ SV25 )
| ~ ! [SX2: $i,SX3: $i] :
( SY74
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(325,plain,
! [SV35: $i,SV26: $i] :
( ( ( in @ SV26 @ SV35 )
= $false )
| ( ( ~ ( empty @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(326,plain,
! [SV27: $i] :
( ( ( ! [SY78: $i,SY79: $i] :
( ( ordered_pair @ SY78 @ SY79 )
!= SV27 ) )
= $false )
| ( ( in @ SV27 @ sK1_A )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(327,plain,
( ( relation @ sK14_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(328,plain,
( ( function @ sK14_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(329,plain,
! [SV38: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV29 @ SV37 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV29 @ SV38 ) @ sK1_A ) )
= $true )
| ( ( SV37 = SV38 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(330,plain,
( ( ~ ( empty @ sK15_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(331,plain,
( ( relation @ sK15_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(332,plain,
( ( relation @ sK16_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(333,plain,
( ( relation_empty_yielding @ sK16_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(334,plain,
( ( empty @ sK17_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(335,plain,
( ( relation @ sK17_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(336,plain,
! [SV31: $i] :
( ( ( function @ SV31 )
= $false )
| ( ( ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY83 @ SY85 ) @ SV31 ) )
| ( SY84 = SY85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(337,plain,
! [SV31: $i] :
( ( ( ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SY86 @ SY87 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SY86 @ SY88 ) @ SV31 ) )
| ( SY87 = SY88 ) ) )
= $false )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(338,plain,
! [SV25: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ( in @ SV39 @ SV25 )
| ~ ! [SY90: $i,SY91: $i] :
( SV39
!= ( ordered_pair @ SY90 @ SY91 ) ) ) )
= $true )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(339,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY74 @ SV25 ) @ SV25 )
| ~ ! [SY92: $i,SY93: $i] :
( ( sK18_SY74 @ SV25 )
!= ( ordered_pair @ SY92 @ SY93 ) ) ) )
= $false )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[324]) ).
thf(340,plain,
! [SV26: $i,SV35: $i] :
( ( ( empty @ SV35 )
= $false )
| ( ( in @ SV26 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(341,plain,
! [SV27: $i] :
( ( ( ! [SY94: $i] :
( ( ordered_pair @ ( sK19_SY78 @ SV27 ) @ SY94 )
!= SV27 ) )
= $false )
| ( ( in @ SV27 @ sK1_A )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[326]) ).
thf(342,plain,
! [SV38: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV29 @ SV37 ) @ sK1_A ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV29 @ SV38 ) @ sK1_A ) )
= $true )
| ( ( SV37 = SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(343,plain,
( ( empty @ sK15_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(344,plain,
! [SV31: $i,SV40: $i] :
( ( ( ! [SY95: $i,SY96: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SV40 @ SY95 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SV40 @ SY96 ) @ SV31 ) )
| ( SY95 = SY96 ) ) )
= $true )
| ( ( function @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(345,plain,
! [SV31: $i] :
( ( ( ! [SY97: $i,SY98: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ SY97 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ SY98 ) @ SV31 ) )
| ( SY97 = SY98 ) ) )
= $false )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[337]) ).
thf(346,plain,
! [SV25: $i,SV39: $i] :
( ( ( ~ ( ~ ( in @ SV39 @ SV25 )
| ~ ! [SY90: $i,SY91: $i] :
( SV39
!= ( ordered_pair @ SY90 @ SY91 ) ) ) )
= $false )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(347,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY74 @ SV25 ) @ SV25 )
| ~ ! [SY92: $i,SY93: $i] :
( ( sK18_SY74 @ SV25 )
!= ( ordered_pair @ SY92 @ SY93 ) ) ) )
= $true )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(348,plain,
! [SV27: $i] :
( ( ( ( ordered_pair @ ( sK19_SY78 @ SV27 ) @ ( sK21_SY94 @ SV27 ) )
!= SV27 )
= $false )
| ( ( in @ SV27 @ sK1_A )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[341]) ).
thf(349,plain,
! [SV38: $i,SV37: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ SV29 @ SV37 ) @ sK1_A )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV29 @ SV38 ) @ sK1_A ) )
= $true )
| ( ( SV37 = SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(350,plain,
! [SV31: $i,SV41: $i,SV40: $i] :
( ( ( ! [SY99: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ SV40 @ SV41 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SV40 @ SY99 ) @ SV31 ) )
| ( SV41 = SY99 ) ) )
= $true )
| ( ( function @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(351,plain,
! [SV31: $i] :
( ( ( ! [SY100: $i] :
( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK22_SY97 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ SY100 ) @ SV31 ) )
| ( ( sK22_SY97 @ SV31 )
= SY100 ) ) )
= $false )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[345]) ).
thf(352,plain,
! [SV25: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV25 )
| ~ ! [SY90: $i,SY91: $i] :
( SV39
!= ( ordered_pair @ SY90 @ SY91 ) ) )
= $true )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(353,plain,
! [SV25: $i] :
( ( ( ~ ( in @ ( sK18_SY74 @ SV25 ) @ SV25 )
| ~ ! [SY92: $i,SY93: $i] :
( ( sK18_SY74 @ SV25 )
!= ( ordered_pair @ SY92 @ SY93 ) ) )
= $false )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(354,plain,
! [SV27: $i] :
( ( ( ( ordered_pair @ ( sK19_SY78 @ SV27 ) @ ( sK21_SY94 @ SV27 ) )
= SV27 )
= $true )
| ( ( in @ SV27 @ sK1_A )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(355,plain,
! [SV37: $i,SV38: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ SV29 @ SV38 ) @ sK1_A )
= $false )
| ( ( in @ ( ordered_pair @ SV29 @ SV37 ) @ sK1_A )
= $false )
| ( ( SV37 = SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(356,plain,
! [SV42: $i,SV31: $i,SV41: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV40 @ SV41 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SV40 @ SV42 ) @ SV31 ) )
| ( SV41 = SV42 ) )
= $true )
| ( ( function @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(357,plain,
! [SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK22_SY97 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK23_SY100 @ SV31 ) ) @ SV31 ) )
| ( ( sK22_SY97 @ SV31 )
= ( sK23_SY100 @ SV31 ) ) )
= $false )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[351]) ).
thf(358,plain,
! [SV25: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV25 ) )
= $true )
| ( ( ~ ! [SY90: $i,SY91: $i] :
( SV39
!= ( ordered_pair @ SY90 @ SY91 ) ) )
= $true )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(359,plain,
! [SV25: $i] :
( ( ( ~ ( in @ ( sK18_SY74 @ SV25 ) @ SV25 ) )
= $false )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(360,plain,
! [SV25: $i] :
( ( ( ~ ! [SY92: $i,SY93: $i] :
( ( sK18_SY74 @ SV25 )
!= ( ordered_pair @ SY92 @ SY93 ) ) )
= $false )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(361,plain,
! [SV42: $i,SV31: $i,SV41: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV40 @ SV41 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SV40 @ SV42 ) @ SV31 ) ) )
= $true )
| ( ( SV41 = SV42 )
= $true )
| ( ( function @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(362,plain,
! [SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK22_SY97 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK23_SY100 @ SV31 ) ) @ SV31 ) ) )
= $false )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(363,plain,
! [SV31: $i] :
( ( ( ( sK22_SY97 @ SV31 )
= ( sK23_SY100 @ SV31 ) )
= $false )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(364,plain,
! [SV25: $i,SV39: $i] :
( ( ( in @ SV39 @ SV25 )
= $false )
| ( ( ~ ! [SY90: $i,SY91: $i] :
( SV39
!= ( ordered_pair @ SY90 @ SY91 ) ) )
= $true )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(365,plain,
! [SV25: $i] :
( ( ( in @ ( sK18_SY74 @ SV25 ) @ SV25 )
= $true )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(366,plain,
! [SV25: $i] :
( ( ( ! [SY92: $i,SY93: $i] :
( ( sK18_SY74 @ SV25 )
!= ( ordered_pair @ SY92 @ SY93 ) ) )
= $true )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(367,plain,
! [SV42: $i,SV31: $i,SV41: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV40 @ SV41 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SV40 @ SV42 ) @ SV31 ) ) )
= $false )
| ( ( SV41 = SV42 )
= $true )
| ( ( function @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(368,plain,
! [SV31: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK22_SY97 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK23_SY100 @ SV31 ) ) @ SV31 ) ) )
= $true )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(369,plain,
! [SV25: $i,SV39: $i] :
( ( ( ! [SY90: $i,SY91: $i] :
( SV39
!= ( ordered_pair @ SY90 @ SY91 ) ) )
= $false )
| ( ( in @ SV39 @ SV25 )
= $false )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(370,plain,
! [SV43: $i,SV25: $i] :
( ( ( ! [SY101: $i] :
( ( sK18_SY74 @ SV25 )
!= ( ordered_pair @ SV43 @ SY101 ) ) )
= $true )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(371,plain,
! [SV42: $i,SV31: $i,SV41: $i,SV40: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV40 @ SV41 ) @ SV31 )
| ~ ( in @ ( ordered_pair @ SV40 @ SV42 ) @ SV31 ) )
= $true )
| ( ( SV41 = SV42 )
= $true )
| ( ( function @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(372,plain,
! [SV31: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK22_SY97 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK23_SY100 @ SV31 ) ) @ SV31 ) )
= $false )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(373,plain,
! [SV25: $i,SV39: $i] :
( ( ( ! [SY102: $i] :
( SV39
!= ( ordered_pair @ ( sK24_SY90 @ SV25 @ SV39 ) @ SY102 ) ) )
= $false )
| ( ( in @ SV39 @ SV25 )
= $false )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[369]) ).
thf(374,plain,
! [SV44: $i,SV43: $i,SV25: $i] :
( ( ( ( sK18_SY74 @ SV25 )
!= ( ordered_pair @ SV43 @ SV44 ) )
= $true )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(375,plain,
! [SV42: $i,SV31: $i,SV41: $i,SV40: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV40 @ SV41 ) @ SV31 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV40 @ SV42 ) @ SV31 ) )
= $true )
| ( ( SV41 = SV42 )
= $true )
| ( ( function @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(376,plain,
! [SV31: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK22_SY97 @ SV31 ) ) @ SV31 ) )
= $false )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(377,plain,
! [SV31: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK23_SY100 @ SV31 ) ) @ SV31 ) )
= $false )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(378,plain,
! [SV25: $i,SV39: $i] :
( ( ( SV39
!= ( ordered_pair @ ( sK24_SY90 @ SV25 @ SV39 ) @ ( sK25_SY102 @ SV25 @ SV39 ) ) )
= $false )
| ( ( in @ SV39 @ SV25 )
= $false )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[373]) ).
thf(379,plain,
! [SV44: $i,SV43: $i,SV25: $i] :
( ( ( ( sK18_SY74 @ SV25 )
= ( ordered_pair @ SV43 @ SV44 ) )
= $false )
| ( ( relation @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(380,plain,
! [SV42: $i,SV31: $i,SV41: $i,SV40: $i] :
( ( ( in @ ( ordered_pair @ SV40 @ SV41 ) @ SV31 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV40 @ SV42 ) @ SV31 ) )
= $true )
| ( ( SV41 = SV42 )
= $true )
| ( ( function @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(381,plain,
! [SV31: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK22_SY97 @ SV31 ) ) @ SV31 )
= $true )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(382,plain,
! [SV31: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY86 @ SV31 ) @ ( sK23_SY100 @ SV31 ) ) @ SV31 )
= $true )
| ( ( function @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(383,plain,
! [SV25: $i,SV39: $i] :
( ( ( SV39
= ( ordered_pair @ ( sK24_SY90 @ SV25 @ SV39 ) @ ( sK25_SY102 @ SV25 @ SV39 ) ) )
= $true )
| ( ( in @ SV39 @ SV25 )
= $false )
| ( ( relation @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(384,plain,
! [SV41: $i,SV31: $i,SV42: $i,SV40: $i] :
( ( ( in @ ( ordered_pair @ SV40 @ SV42 ) @ SV31 )
= $false )
| ( ( in @ ( ordered_pair @ SV40 @ SV41 ) @ SV31 )
= $false )
| ( ( SV41 = SV42 )
= $true )
| ( ( function @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(385,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[250,384,383,382,381,379,365,363,355,354,343,340,335,334,333,332,331,328,327,311,294,293,287,278]) ).
thf(386,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[385,220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET988+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 14:57:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.36
% 0.55/0.36 No.of.Axioms: 12
% 0.55/0.36
% 0.55/0.36 Length.of.Defs: 0
% 0.55/0.36
% 0.55/0.36 Contains.Choice.Funs: false
% 0.55/0.36 .........
% 0.55/0.36
% 0.55/0.36 ********************************
% 0.55/0.36 * All subproblems solved! *
% 0.55/0.36 ********************************
% 0.55/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,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:385,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.55/0.36
% 0.55/0.36 %**** Beginning of derivation protocol ****
% 0.55/0.36 % SZS output start CNFRefutation
% See solution above
% 0.55/0.36
% 0.55/0.36 %**** End of derivation protocol ****
% 0.55/0.36 %**** no. of clauses in derivation: 366 ****
% 0.55/0.36 %**** clause counter: 385 ****
% 0.55/0.36
% 0.55/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,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:385,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------