%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET677+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n017.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 10:40:49 AM UTC 2026
% Result : Theorem 0.59s 0.33s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 227 ( 83 unt; 0 typ; 0 def)
% Number of atoms : 1950 ( 605 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 3624 ( 560 ~; 597 |; 16 &;2343 @)
% ( 9 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 7 con; 0-3 aty)
% Number of variables : 463 ( 0 ^; 451 !; 12 ?; 463 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binary_relation_type,type,
binary_relation_type: $i ).
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_domain,type,
domain: $i > $i > $i > $i ).
thf(tp_domain_of,type,
domain_of: $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_identity_relation_of,type,
identity_relation_of: $i > $i ).
thf(tp_identity_relation_of_type,type,
identity_relation_of_type: $i > $i ).
thf(tp_ilf_type,type,
ilf_type: $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_member_type,type,
member_type: $i > $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_range,type,
range: $i > $i > $i > $i ).
thf(tp_range_of,type,
range_of: $i > $i ).
thf(tp_relation_like,type,
relation_like: $i > $o ).
thf(tp_relation_type,type,
relation_type: $i > $i > $i ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY32,type,
sK4_SY32: $i > $i ).
thf(tp_sK5_SY37,type,
sK5_SY37: $i > $i ).
thf(tp_sK6_SY47,type,
sK6_SY47: $i > $i > $i ).
thf(tp_sK7_SY50,type,
sK7_SY50: $i > $i > $i ).
thf(tp_set_type,type,
set_type: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_type,type,
subset_type: $i > $i ).
thf(1,axiom,
! [B: $i] : ( ilf_type @ B @ set_type ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
thf(14,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( cross_product @ B @ C ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
thf(15,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( subset @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
thf(16,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
thf(17,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ B @ C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
thf(18,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).
thf(20,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ? [D: $i] : ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
thf(22,axiom,
? [B: $i] : ( ilf_type @ B @ binary_relation_type ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
thf(24,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( ordered_pair @ B @ C ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
thf(27,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
thf(29,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( identity_relation_of_type @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
thf(30,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
<=> ( ilf_type @ C @ ( relation_type @ B @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
thf(31,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( identity_relation_of @ B ) @ binary_relation_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
thf(33,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( subset @ ( identity_relation_of @ C ) @ D )
=> ( ( subset @ C @ ( domain @ B @ C @ D ) )
& ( C
= ( range @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(34,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ C @ B ) )
=> ( ( subset @ ( identity_relation_of @ C ) @ D )
=> ( ( C
= ( domain @ C @ B @ D ) )
& ( subset @ C @ ( range @ C @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(35,conjecture,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
=> ( ( subset @ ( identity_relation_of @ B ) @ C )
=> ( ( B
= ( domain @ B @ B @ C ) )
& ( B
= ( range @ B @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_44) ).
thf(36,negated_conjecture,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
=> ( ( subset @ ( identity_relation_of @ B ) @ C )
=> ( ( B
= ( domain @ B @ B @ C ) )
& ( B
= ( range @ B @ B @ C ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[35]) ).
thf(37,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
=> ( ( subset @ ( identity_relation_of @ B ) @ C )
=> ( ( B
= ( domain @ B @ B @ C ) )
& ( B
= ( range @ B @ B @ C ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(39,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( cross_product @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(40,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(41,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(42,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ B @ C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(43,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(44,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ? [D: $i] : ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ? [B: $i] : ( ilf_type @ B @ binary_relation_type ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(46,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( ordered_pair @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(48,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( identity_relation_of_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(49,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
<=> ( ilf_type @ C @ ( relation_type @ B @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(50,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( identity_relation_of @ B ) @ binary_relation_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(51,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( subset @ ( identity_relation_of @ C ) @ D )
=> ( ( subset @ C @ ( domain @ B @ C @ D ) )
& ( C
= ( range @ B @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(52,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ C @ B ) )
=> ( ( subset @ ( identity_relation_of @ C ) @ D )
=> ( ( C
= ( domain @ C @ B @ D ) )
& ( subset @ C @ ( range @ C @ B @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(53,plain,
( ( ( ilf_type @ sK1_B @ set_type )
=> ! [SY31: $i] :
( ( ilf_type @ SY31 @ ( identity_relation_of_type @ sK1_B ) )
=> ( ( subset @ ( identity_relation_of @ sK1_B ) @ SY31 )
=> ( ( sK1_B
= ( domain @ sK1_B @ sK1_B @ SY31 ) )
& ( sK1_B
= ( range @ sK1_B @ sK1_B @ SY31 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(54,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(55,plain,
( ( ! [SY31: $i] :
( ( ilf_type @ SY31 @ ( identity_relation_of_type @ sK1_B ) )
=> ( ( subset @ ( identity_relation_of @ sK1_B ) @ SY31 )
=> ( ( sK1_B
= ( domain @ sK1_B @ sK1_B @ SY31 ) )
& ( sK1_B
= ( range @ sK1_B @ sK1_B @ SY31 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(56,plain,
( ( ~ ! [SY31: $i] :
( ( ilf_type @ SY31 @ ( identity_relation_of_type @ sK1_B ) )
=> ( ( subset @ ( identity_relation_of @ sK1_B ) @ SY31 )
=> ( ( sK1_B
= ( domain @ sK1_B @ sK1_B @ SY31 ) )
& ( sK1_B
= ( range @ sK1_B @ sK1_B @ SY31 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[55]) ).
thf(57,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ C @ B ) )
=> ( ( subset @ ( identity_relation_of @ C ) @ D )
=> ( ( C
= ( domain @ C @ B @ D ) )
& ( subset @ C @ ( range @ C @ B @ D ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(58,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( subset @ ( identity_relation_of @ C ) @ D )
=> ( ( subset @ C @ ( domain @ B @ C @ D ) )
& ( C
= ( range @ B @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(59,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( identity_relation_of @ B ) @ binary_relation_type ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(60,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
<=> ( ilf_type @ C @ ( relation_type @ B @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(61,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( identity_relation_of_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(62,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(63,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( ordered_pair @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(64,plain,
( ( ? [B: $i] : ( ilf_type @ B @ binary_relation_type ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(65,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ? [D: $i] : ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(66,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(67,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ B @ C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(68,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(69,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(70,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( cross_product @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(71,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(72,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(73,plain,
( ( ~ ! [SY31: $i] :
( ( ilf_type @ SY31 @ ( identity_relation_of_type @ sK1_B ) )
=> ( ( subset @ ( identity_relation_of @ sK1_B ) @ SY31 )
=> ( ( sK1_B
= ( domain @ sK1_B @ sK1_B @ SY31 ) )
& ( sK1_B
= ( range @ sK1_B @ sK1_B @ SY31 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(74,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ! [SX1: $i] :
~ ( ilf_type @ SX1 @ ( subset_type @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(75,plain,
( ( ~ ! [SX0: $i] :
~ ( ilf_type @ SX0 @ binary_relation_type ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(76,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ ( identity_relation_of_type @ sK1_B ) )
| ~ ( subset @ ( identity_relation_of @ sK1_B ) @ SX0 )
| ~ ( ( sK1_B
!= ( domain @ sK1_B @ sK1_B @ SX0 ) )
| ( sK1_B
!= ( range @ sK1_B @ sK1_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(77,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ! [SX2: $i] :
~ ( ilf_type @ SX2 @ ( relation_type @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ~ ( subset @ ( identity_relation_of @ SX1 ) @ SX2 )
| ~ ( ~ ( subset @ SX1 @ ( domain @ SX0 @ SX1 @ SX2 ) )
| ( SX1
!= ( range @ SX0 @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(79,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ! [SX1: $i] :
~ ( ilf_type @ SX1 @ ( identity_relation_of_type @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( ilf_type @ ( identity_relation_of @ SX0 ) @ binary_relation_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(81,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SX1 @ ( identity_relation_of_type @ SX0 ) )
| ( ilf_type @ SX1 @ ( relation_type @ SX0 @ SX0 ) ) )
| ~ ( ~ ( ilf_type @ SX1 @ ( relation_type @ SX0 @ SX0 ) )
| ( ilf_type @ SX1 @ ( identity_relation_of_type @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(83,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( ilf_type @ ( ordered_pair @ SX0 @ SX1 ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(84,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( subset @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(85,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX1 @ SX0 ) )
| ~ ( subset @ ( identity_relation_of @ SX1 ) @ SX2 )
| ~ ( ( SX1
!= ( domain @ SX1 @ SX0 @ SX2 ) )
| ~ ( subset @ SX1 @ ( range @ SX1 @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(86,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( ilf_type @ ( cross_product @ SX0 @ SX1 ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(87,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ( subset @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(88,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(89,plain,
! [SV1: $i] :
( ( ilf_type @ SV1 @ set_type )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(90,plain,
! [SV2: $i] :
( ( ~ ( ilf_type @ SV2 @ set_type )
| ~ ! [SY32: $i] :
~ ( ilf_type @ SY32 @ ( subset_type @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(91,plain,
( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ binary_relation_type ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(92,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ ( identity_relation_of_type @ sK1_B ) )
| ~ ( subset @ ( identity_relation_of @ sK1_B ) @ SX0 )
| ~ ( ( sK1_B
!= ( domain @ sK1_B @ sK1_B @ SX0 ) )
| ( sK1_B
!= ( range @ sK1_B @ sK1_B @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(93,plain,
! [SV3: $i] :
( ( ~ ( ilf_type @ SV3 @ set_type )
| ! [SY33: $i] :
( ~ ( ilf_type @ SY33 @ set_type )
| ~ ! [SY34: $i] :
~ ( ilf_type @ SY34 @ ( relation_type @ SY33 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(94,plain,
! [SV4: $i] :
( ( ~ ( ilf_type @ SV4 @ set_type )
| ! [SY35: $i] :
( ~ ( ilf_type @ SY35 @ set_type )
| ! [SY36: $i] :
( ~ ( ilf_type @ SY36 @ ( relation_type @ SV4 @ SY35 ) )
| ~ ( subset @ ( identity_relation_of @ SY35 ) @ SY36 )
| ~ ( ~ ( subset @ SY35 @ ( domain @ SV4 @ SY35 @ SY36 ) )
| ( SY35
!= ( range @ SV4 @ SY35 @ SY36 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(95,plain,
! [SV5: $i] :
( ( ~ ( ilf_type @ SV5 @ set_type )
| ~ ! [SY37: $i] :
~ ( ilf_type @ SY37 @ ( identity_relation_of_type @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(96,plain,
! [SV6: $i] :
( ( ~ ( ilf_type @ SV6 @ set_type )
| ( ilf_type @ ( identity_relation_of @ SV6 ) @ binary_relation_type ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(97,plain,
! [SV7: $i] :
( ( ~ ( ilf_type @ SV7 @ set_type )
| ! [SY38: $i] :
( ~ ( ilf_type @ SY38 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY38 @ ( identity_relation_of_type @ SV7 ) )
| ( ilf_type @ SY38 @ ( relation_type @ SV7 @ SV7 ) ) )
| ~ ( ~ ( ilf_type @ SY38 @ ( relation_type @ SV7 @ SV7 ) )
| ( ilf_type @ SY38 @ ( identity_relation_of_type @ SV7 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(98,plain,
! [SV8: $i] :
( ( ~ ( ilf_type @ SV8 @ set_type )
| ! [SY39: $i] :
( ~ ( ilf_type @ SY39 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV8 @ SY39 )
| ! [SY40: $i] :
( ~ ( ilf_type @ SY40 @ set_type )
| ~ ( member @ SY40 @ SV8 )
| ( member @ SY40 @ SY39 ) ) )
| ~ ( ~ ! [SY41: $i] :
( ~ ( ilf_type @ SY41 @ set_type )
| ~ ( member @ SY41 @ SV8 )
| ( member @ SY41 @ SY39 ) )
| ( subset @ SV8 @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(99,plain,
! [SV9: $i] :
( ( ~ ( ilf_type @ SV9 @ set_type )
| ! [SY42: $i] :
( ~ ( ilf_type @ SY42 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV9 @ SY42 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(100,plain,
! [SV10: $i] :
( ( ~ ( ilf_type @ SV10 @ set_type )
| ( subset @ SV10 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV11: $i] :
( ( ~ ( ilf_type @ SV11 @ set_type )
| ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ ( relation_type @ SY43 @ SV11 ) )
| ~ ( subset @ ( identity_relation_of @ SY43 ) @ SY44 )
| ~ ( ( SY43
!= ( domain @ SY43 @ SV11 @ SY44 ) )
| ~ ( subset @ SY43 @ ( range @ SY43 @ SV11 @ SY44 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV12: $i] :
( ( ~ ( ilf_type @ SV12 @ set_type )
| ! [SY45: $i] :
( ~ ( ilf_type @ SY45 @ set_type )
| ( ilf_type @ ( cross_product @ SV12 @ SY45 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV13: $i] :
( ( ~ ( ilf_type @ SV13 @ binary_relation_type )
| ( subset @ SV13 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV14: $i] :
( ( ~ ( ilf_type @ SV14 @ set_type )
| ! [SY46: $i] :
( ~ ( ilf_type @ SY46 @ set_type )
| ~ ( ~ ( ( SV14 != SY46 )
| ~ ( ~ ( subset @ SV14 @ SY46 )
| ~ ( subset @ SY46 @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SY46 )
| ~ ( subset @ SY46 @ SV14 ) )
| ( SV14 = SY46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV2: $i] :
( ( ( ~ ( ilf_type @ SV2 @ set_type ) )
= $true )
| ( ( ~ ! [SY32: $i] :
~ ( ilf_type @ SY32 @ ( subset_type @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(106,plain,
( ( ~ ( ilf_type @ sK2_SX0 @ binary_relation_type ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(107,plain,
( ( ~ ( ilf_type @ sK3_SX0 @ ( identity_relation_of_type @ sK1_B ) )
| ~ ( subset @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 )
| ~ ( ( sK1_B
!= ( domain @ sK1_B @ sK1_B @ sK3_SX0 ) )
| ( sK1_B
!= ( range @ sK1_B @ sK1_B @ sK3_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(108,plain,
! [SV3: $i] :
( ( ( ~ ( ilf_type @ SV3 @ set_type ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( ilf_type @ SY33 @ set_type )
| ~ ! [SY34: $i] :
~ ( ilf_type @ SY34 @ ( relation_type @ SY33 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV4: $i] :
( ( ( ~ ( ilf_type @ SV4 @ set_type ) )
= $true )
| ( ( ! [SY35: $i] :
( ~ ( ilf_type @ SY35 @ set_type )
| ! [SY36: $i] :
( ~ ( ilf_type @ SY36 @ ( relation_type @ SV4 @ SY35 ) )
| ~ ( subset @ ( identity_relation_of @ SY35 ) @ SY36 )
| ~ ( ~ ( subset @ SY35 @ ( domain @ SV4 @ SY35 @ SY36 ) )
| ( SY35
!= ( range @ SV4 @ SY35 @ SY36 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV5: $i] :
( ( ( ~ ( ilf_type @ SV5 @ set_type ) )
= $true )
| ( ( ~ ! [SY37: $i] :
~ ( ilf_type @ SY37 @ ( identity_relation_of_type @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV6: $i] :
( ( ( ~ ( ilf_type @ SV6 @ set_type ) )
= $true )
| ( ( ilf_type @ ( identity_relation_of @ SV6 ) @ binary_relation_type )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV7: $i] :
( ( ( ~ ( ilf_type @ SV7 @ set_type ) )
= $true )
| ( ( ! [SY38: $i] :
( ~ ( ilf_type @ SY38 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY38 @ ( identity_relation_of_type @ SV7 ) )
| ( ilf_type @ SY38 @ ( relation_type @ SV7 @ SV7 ) ) )
| ~ ( ~ ( ilf_type @ SY38 @ ( relation_type @ SV7 @ SV7 ) )
| ( ilf_type @ SY38 @ ( identity_relation_of_type @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV8: $i] :
( ( ( ~ ( ilf_type @ SV8 @ set_type ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( ilf_type @ SY39 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV8 @ SY39 )
| ! [SY40: $i] :
( ~ ( ilf_type @ SY40 @ set_type )
| ~ ( member @ SY40 @ SV8 )
| ( member @ SY40 @ SY39 ) ) )
| ~ ( ~ ! [SY41: $i] :
( ~ ( ilf_type @ SY41 @ set_type )
| ~ ( member @ SY41 @ SV8 )
| ( member @ SY41 @ SY39 ) )
| ( subset @ SV8 @ SY39 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV9: $i] :
( ( ( ~ ( ilf_type @ SV9 @ set_type ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ( ilf_type @ SY42 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV9 @ SY42 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV10: $i] :
( ( ( ~ ( ilf_type @ SV10 @ set_type ) )
= $true )
| ( ( subset @ SV10 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV11: $i] :
( ( ( ~ ( ilf_type @ SV11 @ set_type ) )
= $true )
| ( ( ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ ( relation_type @ SY43 @ SV11 ) )
| ~ ( subset @ ( identity_relation_of @ SY43 ) @ SY44 )
| ~ ( ( SY43
!= ( domain @ SY43 @ SV11 @ SY44 ) )
| ~ ( subset @ SY43 @ ( range @ SY43 @ SV11 @ SY44 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV12: $i] :
( ( ( ~ ( ilf_type @ SV12 @ set_type ) )
= $true )
| ( ( ! [SY45: $i] :
( ~ ( ilf_type @ SY45 @ set_type )
| ( ilf_type @ ( cross_product @ SV12 @ SY45 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV13: $i] :
( ( ( ~ ( ilf_type @ SV13 @ binary_relation_type ) )
= $true )
| ( ( subset @ SV13 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV14: $i] :
( ( ( ~ ( ilf_type @ SV14 @ set_type ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( ilf_type @ SY46 @ set_type )
| ~ ( ~ ( ( SV14 != SY46 )
| ~ ( ~ ( subset @ SV14 @ SY46 )
| ~ ( subset @ SY46 @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SY46 )
| ~ ( subset @ SY46 @ SV14 ) )
| ( SV14 = SY46 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV2: $i] :
( ( ( ilf_type @ SV2 @ set_type )
= $false )
| ( ( ~ ! [SY32: $i] :
~ ( ilf_type @ SY32 @ ( subset_type @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(121,plain,
( ( ilf_type @ sK2_SX0 @ binary_relation_type )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(122,plain,
( ( ~ ( ilf_type @ sK3_SX0 @ ( identity_relation_of_type @ sK1_B ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(123,plain,
( ( ~ ( subset @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 )
| ~ ( ( sK1_B
!= ( domain @ sK1_B @ sK1_B @ sK3_SX0 ) )
| ( sK1_B
!= ( range @ sK1_B @ sK1_B @ sK3_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(124,plain,
! [SV3: $i] :
( ( ( ilf_type @ SV3 @ set_type )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( ilf_type @ SY33 @ set_type )
| ~ ! [SY34: $i] :
~ ( ilf_type @ SY34 @ ( relation_type @ SY33 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(125,plain,
! [SV4: $i] :
( ( ( ilf_type @ SV4 @ set_type )
= $false )
| ( ( ! [SY35: $i] :
( ~ ( ilf_type @ SY35 @ set_type )
| ! [SY36: $i] :
( ~ ( ilf_type @ SY36 @ ( relation_type @ SV4 @ SY35 ) )
| ~ ( subset @ ( identity_relation_of @ SY35 ) @ SY36 )
| ~ ( ~ ( subset @ SY35 @ ( domain @ SV4 @ SY35 @ SY36 ) )
| ( SY35
!= ( range @ SV4 @ SY35 @ SY36 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV5: $i] :
( ( ( ilf_type @ SV5 @ set_type )
= $false )
| ( ( ~ ! [SY37: $i] :
~ ( ilf_type @ SY37 @ ( identity_relation_of_type @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV6: $i] :
( ( ( ilf_type @ SV6 @ set_type )
= $false )
| ( ( ilf_type @ ( identity_relation_of @ SV6 ) @ binary_relation_type )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV7: $i] :
( ( ( ilf_type @ SV7 @ set_type )
= $false )
| ( ( ! [SY38: $i] :
( ~ ( ilf_type @ SY38 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY38 @ ( identity_relation_of_type @ SV7 ) )
| ( ilf_type @ SY38 @ ( relation_type @ SV7 @ SV7 ) ) )
| ~ ( ~ ( ilf_type @ SY38 @ ( relation_type @ SV7 @ SV7 ) )
| ( ilf_type @ SY38 @ ( identity_relation_of_type @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV8: $i] :
( ( ( ilf_type @ SV8 @ set_type )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( ilf_type @ SY39 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV8 @ SY39 )
| ! [SY40: $i] :
( ~ ( ilf_type @ SY40 @ set_type )
| ~ ( member @ SY40 @ SV8 )
| ( member @ SY40 @ SY39 ) ) )
| ~ ( ~ ! [SY41: $i] :
( ~ ( ilf_type @ SY41 @ set_type )
| ~ ( member @ SY41 @ SV8 )
| ( member @ SY41 @ SY39 ) )
| ( subset @ SV8 @ SY39 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV9: $i] :
( ( ( ilf_type @ SV9 @ set_type )
= $false )
| ( ( ! [SY42: $i] :
( ~ ( ilf_type @ SY42 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV9 @ SY42 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(131,plain,
! [SV10: $i] :
( ( ( ilf_type @ SV10 @ set_type )
= $false )
| ( ( subset @ SV10 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(132,plain,
! [SV11: $i] :
( ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ ( relation_type @ SY43 @ SV11 ) )
| ~ ( subset @ ( identity_relation_of @ SY43 ) @ SY44 )
| ~ ( ( SY43
!= ( domain @ SY43 @ SV11 @ SY44 ) )
| ~ ( subset @ SY43 @ ( range @ SY43 @ SV11 @ SY44 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(133,plain,
! [SV12: $i] :
( ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ! [SY45: $i] :
( ~ ( ilf_type @ SY45 @ set_type )
| ( ilf_type @ ( cross_product @ SV12 @ SY45 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(134,plain,
! [SV13: $i] :
( ( ( ilf_type @ SV13 @ binary_relation_type )
= $false )
| ( ( subset @ SV13 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV14: $i] :
( ( ( ilf_type @ SV14 @ set_type )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( ilf_type @ SY46 @ set_type )
| ~ ( ~ ( ( SV14 != SY46 )
| ~ ( ~ ( subset @ SV14 @ SY46 )
| ~ ( subset @ SY46 @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SY46 )
| ~ ( subset @ SY46 @ SV14 ) )
| ( SV14 = SY46 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV2: $i] :
( ( ( ! [SY32: $i] :
~ ( ilf_type @ SY32 @ ( subset_type @ SV2 ) ) )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(137,plain,
( ( ilf_type @ sK3_SX0 @ ( identity_relation_of_type @ sK1_B ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(138,plain,
( ( ~ ( subset @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(139,plain,
( ( ~ ( ( sK1_B
!= ( domain @ sK1_B @ sK1_B @ sK3_SX0 ) )
| ( sK1_B
!= ( range @ sK1_B @ sK1_B @ sK3_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(140,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( ilf_type @ SV15 @ set_type )
| ~ ! [SY47: $i] :
~ ( ilf_type @ SY47 @ ( relation_type @ SV15 @ SV3 ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(141,plain,
! [SV4: $i,SV16: $i] :
( ( ( ~ ( ilf_type @ SV16 @ set_type )
| ! [SY48: $i] :
( ~ ( ilf_type @ SY48 @ ( relation_type @ SV4 @ SV16 ) )
| ~ ( subset @ ( identity_relation_of @ SV16 ) @ SY48 )
| ~ ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SY48 ) )
| ( SV16
!= ( range @ SV4 @ SV16 @ SY48 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(142,plain,
! [SV5: $i] :
( ( ( ! [SY37: $i] :
~ ( ilf_type @ SY37 @ ( identity_relation_of_type @ SV5 ) ) )
= $false )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) )
| ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) ) )
| ~ ( ~ ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) )
| ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(144,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( ilf_type @ SV18 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV8 @ SV18 )
| ! [SY49: $i] :
( ~ ( ilf_type @ SY49 @ set_type )
| ~ ( member @ SY49 @ SV8 )
| ( member @ SY49 @ SV18 ) ) )
| ~ ( ~ ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ set_type )
| ~ ( member @ SY50 @ SV8 )
| ( member @ SY50 @ SV18 ) )
| ( subset @ SV8 @ SV18 ) ) ) )
= $true )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(145,plain,
! [SV9: $i,SV19: $i] :
( ( ( ~ ( ilf_type @ SV19 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV9 @ SV19 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(146,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ( ilf_type @ SV20 @ set_type )
| ! [SY51: $i] :
( ~ ( ilf_type @ SY51 @ ( relation_type @ SV20 @ SV11 ) )
| ~ ( subset @ ( identity_relation_of @ SV20 ) @ SY51 )
| ~ ( ( SV20
!= ( domain @ SV20 @ SV11 @ SY51 ) )
| ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SY51 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV12: $i,SV21: $i] :
( ( ( ~ ( ilf_type @ SV21 @ set_type )
| ( ilf_type @ ( cross_product @ SV12 @ SV21 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV14: $i,SV22: $i] :
( ( ( ~ ( ilf_type @ SV22 @ set_type )
| ~ ( ~ ( ( SV14 != SV22 )
| ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) )
| ( SV14 = SV22 ) ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(149,plain,
! [SV2: $i] :
( ( ( ~ ( ilf_type @ ( sK4_SY32 @ SV2 ) @ ( subset_type @ SV2 ) ) )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[136]) ).
thf(150,plain,
( ( subset @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(151,plain,
( ( ( sK1_B
!= ( domain @ sK1_B @ sK1_B @ sK3_SX0 ) )
| ( sK1_B
!= ( range @ sK1_B @ sK1_B @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(152,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( ilf_type @ SV15 @ set_type ) )
= $true )
| ( ( ~ ! [SY47: $i] :
~ ( ilf_type @ SY47 @ ( relation_type @ SV15 @ SV3 ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV4: $i,SV16: $i] :
( ( ( ~ ( ilf_type @ SV16 @ set_type ) )
= $true )
| ( ( ! [SY48: $i] :
( ~ ( ilf_type @ SY48 @ ( relation_type @ SV4 @ SV16 ) )
| ~ ( subset @ ( identity_relation_of @ SV16 ) @ SY48 )
| ~ ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SY48 ) )
| ( SV16
!= ( range @ SV4 @ SV16 @ SY48 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(154,plain,
! [SV5: $i] :
( ( ( ~ ( ilf_type @ ( sK5_SY37 @ SV5 ) @ ( identity_relation_of_type @ SV5 ) ) )
= $false )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[142]) ).
thf(155,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) )
| ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) ) )
| ~ ( ~ ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) )
| ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( ilf_type @ SV18 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV8 @ SV18 )
| ! [SY49: $i] :
( ~ ( ilf_type @ SY49 @ set_type )
| ~ ( member @ SY49 @ SV8 )
| ( member @ SY49 @ SV18 ) ) )
| ~ ( ~ ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ set_type )
| ~ ( member @ SY50 @ SV8 )
| ( member @ SY50 @ SV18 ) )
| ( subset @ SV8 @ SV18 ) ) ) )
= $true )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV9: $i,SV19: $i] :
( ( ( ~ ( ilf_type @ SV19 @ set_type ) )
= $true )
| ( ( ilf_type @ ( ordered_pair @ SV9 @ SV19 ) @ set_type )
= $true )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ( ilf_type @ SV20 @ set_type ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( ilf_type @ SY51 @ ( relation_type @ SV20 @ SV11 ) )
| ~ ( subset @ ( identity_relation_of @ SV20 ) @ SY51 )
| ~ ( ( SV20
!= ( domain @ SV20 @ SV11 @ SY51 ) )
| ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SY51 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(159,plain,
! [SV12: $i,SV21: $i] :
( ( ( ~ ( ilf_type @ SV21 @ set_type ) )
= $true )
| ( ( ilf_type @ ( cross_product @ SV12 @ SV21 ) @ set_type )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(160,plain,
! [SV14: $i,SV22: $i] :
( ( ( ~ ( ilf_type @ SV22 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ( SV14 != SV22 )
| ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) )
| ( SV14 = SV22 ) ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(161,plain,
! [SV2: $i] :
( ( ( ilf_type @ ( sK4_SY32 @ SV2 ) @ ( subset_type @ SV2 ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(162,plain,
( ( ( sK1_B
!= ( domain @ sK1_B @ sK1_B @ sK3_SX0 ) )
= $true )
| ( ( sK1_B
!= ( range @ sK1_B @ sK1_B @ sK3_SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(163,plain,
! [SV3: $i,SV15: $i] :
( ( ( ilf_type @ SV15 @ set_type )
= $false )
| ( ( ~ ! [SY47: $i] :
~ ( ilf_type @ SY47 @ ( relation_type @ SV15 @ SV3 ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(164,plain,
! [SV4: $i,SV16: $i] :
( ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ! [SY48: $i] :
( ~ ( ilf_type @ SY48 @ ( relation_type @ SV4 @ SV16 ) )
| ~ ( subset @ ( identity_relation_of @ SV16 ) @ SY48 )
| ~ ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SY48 ) )
| ( SV16
!= ( range @ SV4 @ SV16 @ SY48 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(165,plain,
! [SV5: $i] :
( ( ( ilf_type @ ( sK5_SY37 @ SV5 ) @ ( identity_relation_of_type @ SV5 ) )
= $true )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(166,plain,
! [SV7: $i,SV17: $i] :
( ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) )
| ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) ) )
| ~ ( ~ ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) )
| ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(167,plain,
! [SV8: $i,SV18: $i] :
( ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV8 @ SV18 )
| ! [SY49: $i] :
( ~ ( ilf_type @ SY49 @ set_type )
| ~ ( member @ SY49 @ SV8 )
| ( member @ SY49 @ SV18 ) ) )
| ~ ( ~ ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ set_type )
| ~ ( member @ SY50 @ SV8 )
| ( member @ SY50 @ SV18 ) )
| ( subset @ SV8 @ SV18 ) ) ) )
= $true )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(168,plain,
! [SV9: $i,SV19: $i] :
( ( ( ilf_type @ SV19 @ set_type )
= $false )
| ( ( ilf_type @ ( ordered_pair @ SV9 @ SV19 ) @ set_type )
= $true )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(169,plain,
! [SV11: $i,SV20: $i] :
( ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( ilf_type @ SY51 @ ( relation_type @ SV20 @ SV11 ) )
| ~ ( subset @ ( identity_relation_of @ SV20 ) @ SY51 )
| ~ ( ( SV20
!= ( domain @ SV20 @ SV11 @ SY51 ) )
| ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SY51 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(170,plain,
! [SV12: $i,SV21: $i] :
( ( ( ilf_type @ SV21 @ set_type )
= $false )
| ( ( ilf_type @ ( cross_product @ SV12 @ SV21 ) @ set_type )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(171,plain,
! [SV14: $i,SV22: $i] :
( ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ~ ( ~ ( ( SV14 != SV22 )
| ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) )
| ( SV14 = SV22 ) ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(172,plain,
( ( ( sK1_B
= ( domain @ sK1_B @ sK1_B @ sK3_SX0 ) )
= $false )
| ( ( sK1_B
!= ( range @ sK1_B @ sK1_B @ sK3_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV3: $i,SV15: $i] :
( ( ( ! [SY47: $i] :
~ ( ilf_type @ SY47 @ ( relation_type @ SV15 @ SV3 ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV16: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) )
| ~ ( subset @ ( identity_relation_of @ SV16 ) @ SV23 )
| ~ ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SV23 ) )
| ( SV16
!= ( range @ SV4 @ SV16 @ SV23 ) ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) )
| ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) ) )
| ~ ( ~ ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) )
| ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) ) ) )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( ~ ( subset @ SV8 @ SV18 )
| ! [SY49: $i] :
( ~ ( ilf_type @ SY49 @ set_type )
| ~ ( member @ SY49 @ SV8 )
| ( member @ SY49 @ SV18 ) ) )
| ~ ( ~ ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ set_type )
| ~ ( member @ SY50 @ SV8 )
| ( member @ SY50 @ SV18 ) )
| ( subset @ SV8 @ SV18 ) ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV11: $i,SV20: $i,SV24: $i] :
( ( ( ~ ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) )
| ~ ( subset @ ( identity_relation_of @ SV20 ) @ SV24 )
| ~ ( ( SV20
!= ( domain @ SV20 @ SV11 @ SV24 ) )
| ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SV24 ) ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ( SV14 != SV22 )
| ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) )
| ( SV14 = SV22 ) ) )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(179,plain,
( ( ( sK1_B
= ( range @ sK1_B @ sK1_B @ sK3_SX0 ) )
= $false )
| ( ( sK1_B
= ( domain @ sK1_B @ sK1_B @ sK3_SX0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(180,plain,
! [SV15: $i,SV3: $i] :
( ( ( ~ ( ilf_type @ ( sK6_SY47 @ SV3 @ SV15 ) @ ( relation_type @ SV15 @ SV3 ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[173]) ).
thf(181,plain,
! [SV16: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) ) )
= $true )
| ( ( ~ ( subset @ ( identity_relation_of @ SV16 ) @ SV23 )
| ~ ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SV23 ) )
| ( SV16
!= ( range @ SV4 @ SV16 @ SV23 ) ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(182,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) )
| ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) ) ) )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(183,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) )
| ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) ) ) )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(184,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( ~ ( subset @ SV8 @ SV18 )
| ! [SY49: $i] :
( ~ ( ilf_type @ SY49 @ set_type )
| ~ ( member @ SY49 @ SV8 )
| ( member @ SY49 @ SV18 ) ) ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(185,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( ~ ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ set_type )
| ~ ( member @ SY50 @ SV8 )
| ( member @ SY50 @ SV18 ) )
| ( subset @ SV8 @ SV18 ) ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(186,plain,
! [SV11: $i,SV20: $i,SV24: $i] :
( ( ( ~ ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) ) )
= $true )
| ( ( ~ ( subset @ ( identity_relation_of @ SV20 ) @ SV24 )
| ~ ( ( SV20
!= ( domain @ SV20 @ SV11 @ SV24 ) )
| ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SV24 ) ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ( SV14 != SV22 )
| ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) ) )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(188,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) )
| ( SV14 = SV22 ) ) )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(189,plain,
! [SV15: $i,SV3: $i] :
( ( ( ilf_type @ ( sK6_SY47 @ SV3 @ SV15 ) @ ( relation_type @ SV15 @ SV3 ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(190,plain,
! [SV16: $i,SV4: $i,SV23: $i] :
( ( ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) )
= $false )
| ( ( ~ ( subset @ ( identity_relation_of @ SV16 ) @ SV23 )
| ~ ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SV23 ) )
| ( SV16
!= ( range @ SV4 @ SV16 @ SV23 ) ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(191,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) )
| ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(192,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) )
| ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(193,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV18 )
| ! [SY49: $i] :
( ~ ( ilf_type @ SY49 @ set_type )
| ~ ( member @ SY49 @ SV8 )
| ( member @ SY49 @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(194,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ set_type )
| ~ ( member @ SY50 @ SV8 )
| ( member @ SY50 @ SV18 ) )
| ( subset @ SV8 @ SV18 ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(195,plain,
! [SV11: $i,SV20: $i,SV24: $i] :
( ( ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) )
= $false )
| ( ( ~ ( subset @ ( identity_relation_of @ SV20 ) @ SV24 )
| ~ ( ( SV20
!= ( domain @ SV20 @ SV11 @ SV24 ) )
| ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SV24 ) ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(196,plain,
! [SV22: $i,SV14: $i] :
( ( ( ( SV14 != SV22 )
| ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(197,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) )
| ( SV14 = SV22 ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(198,plain,
! [SV4: $i,SV23: $i,SV16: $i] :
( ( ( ~ ( subset @ ( identity_relation_of @ SV16 ) @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SV23 ) )
| ( SV16
!= ( range @ SV4 @ SV16 @ SV23 ) ) ) )
= $true )
| ( ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(199,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) ) )
= $true )
| ( ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(200,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) ) )
= $true )
| ( ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV18 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( ilf_type @ SY49 @ set_type )
| ~ ( member @ SY49 @ SV8 )
| ( member @ SY49 @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ set_type )
| ~ ( member @ SY50 @ SV8 )
| ( member @ SY50 @ SV18 ) ) )
= $true )
| ( ( subset @ SV8 @ SV18 )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(203,plain,
! [SV11: $i,SV24: $i,SV20: $i] :
( ( ( ~ ( subset @ ( identity_relation_of @ SV20 ) @ SV24 ) )
= $true )
| ( ( ~ ( ( SV20
!= ( domain @ SV20 @ SV11 @ SV24 ) )
| ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SV24 ) ) ) )
= $true )
| ( ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV22: $i,SV14: $i] :
( ( ( SV14 != SV22 )
= $true )
| ( ( ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(205,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) )
= $true )
| ( ( SV14 = SV22 )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(206,plain,
! [SV4: $i,SV23: $i,SV16: $i] :
( ( ( subset @ ( identity_relation_of @ SV16 ) @ SV23 )
= $false )
| ( ( ~ ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SV23 ) )
| ( SV16
!= ( range @ SV4 @ SV16 @ SV23 ) ) ) )
= $true )
| ( ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(207,plain,
! [SV7: $i,SV17: $i] :
( ( ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) )
= $false )
| ( ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(208,plain,
! [SV7: $i,SV17: $i] :
( ( ( ilf_type @ SV17 @ ( relation_type @ SV7 @ SV7 ) )
= $false )
| ( ( ilf_type @ SV17 @ ( identity_relation_of_type @ SV7 ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(209,plain,
! [SV18: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV18 )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( ilf_type @ SY49 @ set_type )
| ~ ( member @ SY49 @ SV8 )
| ( member @ SY49 @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV18: $i,SV8: $i] :
( ( ( ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ set_type )
| ~ ( member @ SY50 @ SV8 )
| ( member @ SY50 @ SV18 ) ) )
= $false )
| ( ( subset @ SV8 @ SV18 )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(211,plain,
! [SV11: $i,SV24: $i,SV20: $i] :
( ( ( subset @ ( identity_relation_of @ SV20 ) @ SV24 )
= $false )
| ( ( ~ ( ( SV20
!= ( domain @ SV20 @ SV11 @ SV24 ) )
| ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SV24 ) ) ) )
= $true )
| ( ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV22: $i,SV14: $i] :
( ( ( SV14 = SV22 )
= $false )
| ( ( ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(213,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) ) )
= $false )
| ( ( SV14 = SV22 )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(214,plain,
! [SV23: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SV23 ) )
| ( SV16
!= ( range @ SV4 @ SV16 @ SV23 ) ) )
= $false )
| ( ( subset @ ( identity_relation_of @ SV16 ) @ SV23 )
= $false )
| ( ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(215,plain,
! [SV18: $i,SV8: $i,SV25: $i] :
( ( ( ~ ( ilf_type @ SV25 @ set_type )
| ~ ( member @ SV25 @ SV8 )
| ( member @ SV25 @ SV18 ) )
= $true )
| ( ( subset @ SV8 @ SV18 )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(216,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( ilf_type @ ( sK7_SY50 @ SV18 @ SV8 ) @ set_type )
| ~ ( member @ ( sK7_SY50 @ SV18 @ SV8 ) @ SV8 )
| ( member @ ( sK7_SY50 @ SV18 @ SV8 ) @ SV18 ) )
= $false )
| ( ( subset @ SV8 @ SV18 )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[210]) ).
thf(217,plain,
! [SV24: $i,SV11: $i,SV20: $i] :
( ( ( ( SV20
!= ( domain @ SV20 @ SV11 @ SV24 ) )
| ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SV24 ) ) )
= $false )
| ( ( subset @ ( identity_relation_of @ SV20 ) @ SV24 )
= $false )
| ( ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(218,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) )
= $false )
| ( ( SV14 = SV22 )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(219,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV22 )
| ~ ( subset @ SV22 @ SV14 ) )
= $true )
| ( ( SV14 = SV22 )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(220,plain,
! [SV23: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SV23 ) ) )
= $false )
| ( ( subset @ ( identity_relation_of @ SV16 ) @ SV23 )
= $false )
| ( ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(221,plain,
! [SV23: $i,SV4: $i,SV16: $i] :
( ( ( SV16
!= ( range @ SV4 @ SV16 @ SV23 ) )
= $false )
| ( ( subset @ ( identity_relation_of @ SV16 ) @ SV23 )
= $false )
| ( ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(222,plain,
! [SV18: $i,SV8: $i,SV25: $i] :
( ( ( ~ ( ilf_type @ SV25 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV8 )
| ( member @ SV25 @ SV18 ) )
= $true )
| ( ( subset @ SV8 @ SV18 )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(223,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( ilf_type @ ( sK7_SY50 @ SV18 @ SV8 ) @ set_type ) )
= $false )
| ( ( subset @ SV8 @ SV18 )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(224,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( member @ ( sK7_SY50 @ SV18 @ SV8 ) @ SV8 )
| ( member @ ( sK7_SY50 @ SV18 @ SV8 ) @ SV18 ) )
= $false )
| ( ( subset @ SV8 @ SV18 )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(225,plain,
! [SV24: $i,SV11: $i,SV20: $i] :
( ( ( SV20
!= ( domain @ SV20 @ SV11 @ SV24 ) )
= $false )
| ( ( subset @ ( identity_relation_of @ SV20 ) @ SV24 )
= $false )
| ( ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(226,plain,
! [SV24: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SV24 ) ) )
= $false )
| ( ( subset @ ( identity_relation_of @ SV20 ) @ SV24 )
= $false )
| ( ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(227,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV22 ) )
= $false )
| ( ( SV14 = SV22 )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(228,plain,
! [SV14: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV14 ) )
= $false )
| ( ( SV14 = SV22 )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(229,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV22 ) )
= $true )
| ( ( ~ ( subset @ SV22 @ SV14 ) )
= $true )
| ( ( SV14 = SV22 )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(230,plain,
! [SV23: $i,SV4: $i,SV16: $i] :
( ( ( subset @ SV16 @ ( domain @ SV4 @ SV16 @ SV23 ) )
= $true )
| ( ( subset @ ( identity_relation_of @ SV16 ) @ SV23 )
= $false )
| ( ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(231,plain,
! [SV23: $i,SV4: $i,SV16: $i] :
( ( ( SV16
= ( range @ SV4 @ SV16 @ SV23 ) )
= $true )
| ( ( subset @ ( identity_relation_of @ SV16 ) @ SV23 )
= $false )
| ( ( ilf_type @ SV23 @ ( relation_type @ SV4 @ SV16 ) )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(232,plain,
! [SV18: $i,SV8: $i,SV25: $i] :
( ( ( ilf_type @ SV25 @ set_type )
= $false )
| ( ( ~ ( member @ SV25 @ SV8 )
| ( member @ SV25 @ SV18 ) )
= $true )
| ( ( subset @ SV8 @ SV18 )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(233,plain,
! [SV8: $i,SV18: $i] :
( ( ( ilf_type @ ( sK7_SY50 @ SV18 @ SV8 ) @ set_type )
= $true )
| ( ( subset @ SV8 @ SV18 )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(234,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( member @ ( sK7_SY50 @ SV18 @ SV8 ) @ SV8 ) )
= $false )
| ( ( subset @ SV8 @ SV18 )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(235,plain,
! [SV8: $i,SV18: $i] :
( ( ( member @ ( sK7_SY50 @ SV18 @ SV8 ) @ SV18 )
= $false )
| ( ( subset @ SV8 @ SV18 )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(236,plain,
! [SV24: $i,SV11: $i,SV20: $i] :
( ( ( SV20
= ( domain @ SV20 @ SV11 @ SV24 ) )
= $true )
| ( ( subset @ ( identity_relation_of @ SV20 ) @ SV24 )
= $false )
| ( ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(237,plain,
! [SV24: $i,SV11: $i,SV20: $i] :
( ( ( subset @ SV20 @ ( range @ SV20 @ SV11 @ SV24 ) )
= $true )
| ( ( subset @ ( identity_relation_of @ SV20 ) @ SV24 )
= $false )
| ( ( ilf_type @ SV24 @ ( relation_type @ SV20 @ SV11 ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(238,plain,
! [SV22: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV22 )
= $true )
| ( ( SV14 = SV22 )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(239,plain,
! [SV14: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV14 )
= $true )
| ( ( SV14 = SV22 )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(240,plain,
! [SV22: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV22 )
= $false )
| ( ( ~ ( subset @ SV22 @ SV14 ) )
= $true )
| ( ( SV14 = SV22 )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(241,plain,
! [SV18: $i,SV8: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV8 ) )
= $true )
| ( ( member @ SV25 @ SV18 )
= $true )
| ( ( ilf_type @ SV25 @ set_type )
= $false )
| ( ( subset @ SV8 @ SV18 )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(242,plain,
! [SV8: $i,SV18: $i] :
( ( ( member @ ( sK7_SY50 @ SV18 @ SV8 ) @ SV8 )
= $true )
| ( ( subset @ SV8 @ SV18 )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(243,plain,
! [SV14: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV14 )
= $false )
| ( ( subset @ SV14 @ SV22 )
= $false )
| ( ( SV14 = SV22 )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(244,plain,
! [SV18: $i,SV8: $i,SV25: $i] :
( ( ( member @ SV25 @ SV8 )
= $false )
| ( ( member @ SV25 @ SV18 )
= $true )
| ( ( ilf_type @ SV25 @ set_type )
= $false )
| ( ( subset @ SV8 @ SV18 )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(245,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[72,244,243,242,239,238,237,236,235,233,231,230,208,207,189,179,170,168,165,161,150,137,134,131,127,121,89]) ).
thf(246,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET677+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.09/0.17 % Computer : n017.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 14:43:45 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.33
% 0.59/0.33 No.of.Axioms: 15
% 0.59/0.33
% 0.59/0.33 Length.of.Defs: 0
% 0.59/0.33
% 0.59/0.33 Contains.Choice.Funs: false
% 0.59/0.33 .......
% 0.59/0.33
% 0.59/0.33 ********************************
% 0.59/0.33 * All subproblems solved! *
% 0.59/0.33 ********************************
% 0.59/0.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,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:245,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.59/0.33
% 0.59/0.33 %**** Beginning of derivation protocol ****
% 0.59/0.33 % SZS output start CNFRefutation
% See solution above
% 0.59/0.33
% 0.59/0.33 %**** End of derivation protocol ****
% 0.59/0.33 %**** no. of clauses in derivation: 227 ****
% 0.59/0.33 %**** clause counter: 245 ****
% 0.59/0.33
% 0.59/0.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,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:245,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------