%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 10:39:26 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 244 ( 115 unt; 0 typ; 0 def)
% Number of atoms : 1497 ( 461 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 2941 ( 739 ~; 459 |; 21 &;1685 @)
% ( 21 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 8 con; 0-3 aty)
% Number of variables : 572 ( 0 ^; 566 !; 6 ?; 572 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_complement,type,
complement: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_domain_of,type,
domain_of: $i > $i ).
thf(tp_element_relation,type,
element_relation: $i ).
thf(tp_first,type,
first: $i > $i ).
thf(tp_flip,type,
flip: $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_identity_relation,type,
identity_relation: $i ).
thf(tp_image,type,
image: $i > $i > $i ).
thf(tp_inductive,type,
inductive: $i > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_null_class,type,
null_class: $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_power_class,type,
power_class: $i > $i ).
thf(tp_range_of,type,
range_of: $i > $i ).
thf(tp_restrict,type,
restrict: $i > $i > $i > $i ).
thf(tp_rotate,type,
rotate: $i > $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY47,type,
sK2_SY47: $i > $i ).
thf(tp_sK3_SY50,type,
sK3_SY50: $i > $i > $i ).
thf(tp_sK4_SY56,type,
sK4_SY56: $i > $i > $i ).
thf(tp_sK5_SY51,type,
sK5_SY51: $i > $i > $i ).
thf(tp_second,type,
second: $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subclass,type,
subclass: $i > $i > $o ).
thf(tp_successor,type,
successor: $i > $i ).
thf(tp_successor_relation,type,
successor_relation: $i ).
thf(tp_sum_class,type,
sum_class: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_universal_class,type,
universal_class: $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(3,axiom,
! [X: $i] :
( ( X != null_class )
=> ? [U: $i] :
( ( member @ U @ universal_class )
& ( member @ U @ X )
& ( disjoint @ U @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
thf(10,axiom,
! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class) ).
thf(12,axiom,
! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class) ).
thf(13,axiom,
! [U: $i,X: $i] :
( ( member @ U @ ( sum_class @ X ) )
<=> ? [Y: $i] :
( ( member @ U @ Y )
& ( member @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_defn) ).
thf(22,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( union @ X @ Y ) )
<=> ( ( member @ Z @ X )
| ( member @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(28,axiom,
! [X: $i] :
~ ( member @ X @ null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
thf(30,axiom,
! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(31,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
<=> ( ( member @ Z @ X )
& ( member @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(38,axiom,
! [X: $i] :
( ( singleton @ X )
= ( unordered_pair @ X @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
thf(39,axiom,
! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(40,axiom,
! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( unordered_pair @ X @ Y ) )
<=> ( ( member @ U @ universal_class )
& ( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(42,axiom,
! [X: $i] : ( subclass @ X @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(43,axiom,
! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
thf(44,conjecture,
! [X: $i] :
( ~ ( member @ X @ universal_class )
=> ( ( singleton @ X )
= null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
thf(45,negated_conjecture,
( ( ! [X: $i] :
( ~ ( member @ X @ universal_class )
=> ( ( singleton @ X )
= null_class ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ universal_class )
=> ( ( singleton @ X )
= null_class ) ) )
= $false ),
inference(unfold_def,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( X != null_class )
=> ? [U: $i] :
( ( member @ U @ universal_class )
& ( member @ U @ X )
& ( disjoint @ U @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(49,plain,
( ( ! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(50,plain,
( ( ! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(51,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( sum_class @ X ) )
<=> ? [Y: $i] :
( ( member @ U @ Y )
& ( member @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( union @ X @ Y ) )
<=> ( ( member @ Z @ X )
| ( member @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(53,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(54,plain,
( ( ! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
<=> ( ( member @ Z @ X )
& ( member @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(56,plain,
( ( ! [X: $i] :
( ( singleton @ X )
= ( unordered_pair @ X @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( unordered_pair @ X @ Y ) )
<=> ( ( member @ U @ universal_class )
& ( ( U = X )
| ( U = Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(59,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(61,plain,
( ( ~ ( member @ sK1_X @ universal_class )
=> ( ( singleton @ sK1_X )
= null_class ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(62,plain,
( ( ~ ( member @ sK1_X @ universal_class ) )
= $true ),
inference(standard_cnf,[status(thm)],[61]) ).
thf(63,plain,
( ( ( singleton @ sK1_X )
= null_class )
= $false ),
inference(standard_cnf,[status(thm)],[61]) ).
thf(64,plain,
( ( ( singleton @ sK1_X )
!= null_class )
= $true ),
inference(polarity_switch,[status(thm)],[63]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(66,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(67,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( unordered_pair @ X @ Y ) )
<=> ( ( member @ U @ universal_class )
& ( ( U = X )
| ( U = Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(69,plain,
( ( ! [X: $i] :
( ( singleton @ X )
= ( unordered_pair @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
<=> ( ( member @ Z @ X )
& ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(71,plain,
( ( ! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(72,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( union @ X @ Y ) )
<=> ( ( member @ Z @ X )
| ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(74,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( sum_class @ X ) )
<=> ? [Y: $i] :
( ( member @ U @ Y )
& ( member @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(75,plain,
( ( ! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(76,plain,
( ( ! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(78,plain,
( ( ! [X: $i] :
( ( X != null_class )
=> ? [U: $i] :
( ( member @ U @ universal_class )
& ( member @ U @ X )
& ( disjoint @ U @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(79,plain,
( ( ~ ( member @ sK1_X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(80,plain,
( ( ( singleton @ sK1_X )
!= null_class )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ( ~ ( ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(82,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ~ ( member @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ~ ( member @ SX1 @ SX0 ) )
| ( member @ SX1 @ ( complement @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(84,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( member @ ( sum_class @ SX0 ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( ( SX0 = SX1 )
| ( SX0 = SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( ( SX0 = SX1 )
| ( SX0 = SX2 ) ) )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(87,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( member @ ( power_class @ SX0 ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(90,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != null_class ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX1 @ SX0 ) )
| ~ ( disjoint @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(91,plain,
! [SV1: $i] :
( ( subclass @ SV1 @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(92,plain,
! [SV2: $i] :
( ( ! [SY30: $i] : ( member @ ( unordered_pair @ SV2 @ SY30 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(93,plain,
! [SV3: $i] :
( ( ( singleton @ SV3 )
= ( unordered_pair @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(94,plain,
! [SV4: $i] :
( ( ~ ( member @ SV4 @ null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(95,plain,
( ( member @ sK1_X @ universal_class )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(96,plain,
( ( ( singleton @ sK1_X )
= null_class )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(97,plain,
! [SV5: $i] :
( ( ! [SY31: $i,SY32: $i] :
~ ( ~ ( ~ ( member @ SY32 @ ( union @ SV5 @ SY31 ) )
| ( member @ SY32 @ SV5 )
| ( member @ SY32 @ SY31 ) )
| ~ ( ~ ( ( member @ SY32 @ SV5 )
| ( member @ SY32 @ SY31 ) )
| ( member @ SY32 @ ( union @ SV5 @ SY31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(98,plain,
! [SV6: $i] :
( ( ! [SY33: $i] :
~ ( ~ ( ~ ( subclass @ SV6 @ SY33 )
| ! [SY34: $i] :
( ~ ( member @ SY34 @ SV6 )
| ( member @ SY34 @ SY33 ) ) )
| ~ ( ~ ! [SY35: $i] :
( ~ ( member @ SY35 @ SV6 )
| ( member @ SY35 @ SY33 ) )
| ( subclass @ SV6 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(99,plain,
! [SV7: $i] :
( ( ! [SY36: $i] :
~ ( ~ ( ~ ( member @ SY36 @ ( complement @ SV7 ) )
| ~ ( ~ ( member @ SY36 @ universal_class )
| ~ ~ ( member @ SY36 @ SV7 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY36 @ universal_class )
| ~ ~ ( member @ SY36 @ SV7 ) )
| ( member @ SY36 @ ( complement @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(100,plain,
! [SV8: $i] :
( ( ~ ( member @ SV8 @ universal_class )
| ( member @ ( sum_class @ SV8 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV9: $i] :
( ( ! [SY37: $i] :
~ ( ~ ( ~ ( member @ SV9 @ ( sum_class @ SY37 ) )
| ~ ! [SY38: $i] :
~ ~ ( ~ ( member @ SV9 @ SY38 )
| ~ ( member @ SY38 @ SY37 ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ( ~ ( member @ SV9 @ SY39 )
| ~ ( member @ SY39 @ SY37 ) )
| ( member @ SV9 @ ( sum_class @ SY37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV10: $i] :
( ( ! [SY40: $i,SY41: $i] :
~ ( ~ ( ~ ( member @ SV10 @ ( unordered_pair @ SY40 @ SY41 ) )
| ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SY40 )
| ( SV10 = SY41 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SY40 )
| ( SV10 = SY41 ) ) )
| ( member @ SV10 @ ( unordered_pair @ SY40 @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV11: $i] :
( ( ~ ( member @ SV11 @ universal_class )
| ( member @ ( power_class @ SV11 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV12: $i] :
( ( ! [SY42: $i,SY43: $i] :
~ ( ~ ( ~ ( member @ SY43 @ ( intersection @ SV12 @ SY42 ) )
| ~ ( ~ ( member @ SY43 @ SV12 )
| ~ ( member @ SY43 @ SY42 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY43 @ SV12 )
| ~ ( member @ SY43 @ SY42 ) )
| ( member @ SY43 @ ( intersection @ SV12 @ SY42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV13: $i] :
( ( ! [SY44: $i] :
~ ( ~ ( ~ ( disjoint @ SV13 @ SY44 )
| ! [SY45: $i] :
~ ~ ( ~ ( member @ SY45 @ SV13 )
| ~ ( member @ SY45 @ SY44 ) ) )
| ~ ( ~ ! [SY46: $i] :
~ ~ ( ~ ( member @ SY46 @ SV13 )
| ~ ( member @ SY46 @ SY44 ) )
| ( disjoint @ SV13 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV14: $i] :
( ( ~ ( ( SV14 != null_class ) )
| ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY47 @ universal_class )
| ~ ( member @ SY47 @ SV14 ) )
| ~ ( disjoint @ SY47 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(107,plain,
! [SV15: $i,SV2: $i] :
( ( member @ ( unordered_pair @ SV2 @ SV15 ) @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV4: $i] :
( ( member @ SV4 @ null_class )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV16: $i,SV5: $i] :
( ( ! [SY48: $i] :
~ ( ~ ( ~ ( member @ SY48 @ ( union @ SV5 @ SV16 ) )
| ( member @ SY48 @ SV5 )
| ( member @ SY48 @ SV16 ) )
| ~ ( ~ ( ( member @ SY48 @ SV5 )
| ( member @ SY48 @ SV16 ) )
| ( member @ SY48 @ ( union @ SV5 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( subclass @ SV6 @ SV17 )
| ! [SY49: $i] :
( ~ ( member @ SY49 @ SV6 )
| ( member @ SY49 @ SV17 ) ) )
| ~ ( ~ ! [SY50: $i] :
( ~ ( member @ SY50 @ SV6 )
| ( member @ SY50 @ SV17 ) )
| ( subclass @ SV6 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV7: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( member @ SV18 @ ( complement @ SV7 ) )
| ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) )
| ( member @ SV18 @ ( complement @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV8: $i] :
( ( ( ~ ( member @ SV8 @ universal_class ) )
= $true )
| ( ( member @ ( sum_class @ SV8 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( member @ SV9 @ ( sum_class @ SV19 ) )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( member @ SV9 @ SY51 )
| ~ ( member @ SY51 @ SV19 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( member @ SV9 @ SY52 )
| ~ ( member @ SY52 @ SV19 ) )
| ( member @ SV9 @ ( sum_class @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV20: $i,SV10: $i] :
( ( ! [SY53: $i] :
~ ( ~ ( ~ ( member @ SV10 @ ( unordered_pair @ SV20 @ SY53 ) )
| ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SY53 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SY53 ) ) )
| ( member @ SV10 @ ( unordered_pair @ SV20 @ SY53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV11: $i] :
( ( ( ~ ( member @ SV11 @ universal_class ) )
= $true )
| ( ( member @ ( power_class @ SV11 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV21: $i,SV12: $i] :
( ( ! [SY54: $i] :
~ ( ~ ( ~ ( member @ SY54 @ ( intersection @ SV12 @ SV21 ) )
| ~ ( ~ ( member @ SY54 @ SV12 )
| ~ ( member @ SY54 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY54 @ SV12 )
| ~ ( member @ SY54 @ SV21 ) )
| ( member @ SY54 @ ( intersection @ SV12 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV13 @ SV22 )
| ! [SY55: $i] :
~ ~ ( ~ ( member @ SY55 @ SV13 )
| ~ ( member @ SY55 @ SV22 ) ) )
| ~ ( ~ ! [SY56: $i] :
~ ~ ( ~ ( member @ SY56 @ SV13 )
| ~ ( member @ SY56 @ SV22 ) )
| ( disjoint @ SV13 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV14: $i] :
( ( ( ~ ( ( SV14 != null_class ) ) )
= $true )
| ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY47 @ universal_class )
| ~ ( member @ SY47 @ SV14 ) )
| ~ ( disjoint @ SY47 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
| ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
| ~ ( ~ ( ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
| ( member @ SV23 @ ( union @ SV5 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( ~ ( subclass @ SV6 @ SV17 )
| ! [SY49: $i] :
( ~ ( member @ SY49 @ SV6 )
| ( member @ SY49 @ SV17 ) ) )
| ~ ( ~ ! [SY50: $i] :
( ~ ( member @ SY50 @ SV6 )
| ( member @ SY50 @ SV17 ) )
| ( subclass @ SV6 @ SV17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV7: $i,SV18: $i] :
( ( ~ ( ~ ( member @ SV18 @ ( complement @ SV7 ) )
| ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) )
| ( member @ SV18 @ ( complement @ SV7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV8: $i] :
( ( ( member @ SV8 @ universal_class )
= $false )
| ( ( member @ ( sum_class @ SV8 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( ~ ( member @ SV9 @ ( sum_class @ SV19 ) )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( member @ SV9 @ SY51 )
| ~ ( member @ SY51 @ SV19 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( member @ SV9 @ SY52 )
| ~ ( member @ SY52 @ SV19 ) )
| ( member @ SV9 @ ( sum_class @ SV19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
| ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) )
| ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV11: $i] :
( ( ( member @ SV11 @ universal_class )
= $false )
| ( ( member @ ( power_class @ SV11 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ~ ( ~ ( ~ ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
| ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) )
| ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ( ~ ( disjoint @ SV13 @ SV22 )
| ! [SY55: $i] :
~ ~ ( ~ ( member @ SY55 @ SV13 )
| ~ ( member @ SY55 @ SV22 ) ) )
| ~ ( ~ ! [SY56: $i] :
~ ~ ( ~ ( member @ SY56 @ SV13 )
| ~ ( member @ SY56 @ SV22 ) )
| ( disjoint @ SV13 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV14: $i] :
( ( ( SV14 != null_class )
= $false )
| ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY47 @ universal_class )
| ~ ( member @ SY47 @ SV14 ) )
| ~ ( disjoint @ SY47 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ~ ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
| ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
| ~ ( ~ ( ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
| ( member @ SV23 @ ( union @ SV5 @ SV16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( ~ ( subclass @ SV6 @ SV17 )
| ! [SY49: $i] :
( ~ ( member @ SY49 @ SV6 )
| ( member @ SY49 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(131,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( ~ ! [SY50: $i] :
( ~ ( member @ SY50 @ SV6 )
| ( member @ SY50 @ SV17 ) )
| ( subclass @ SV6 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(132,plain,
! [SV7: $i,SV18: $i] :
( ( ~ ( ~ ( member @ SV18 @ ( complement @ SV7 ) )
| ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(133,plain,
! [SV7: $i,SV18: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) )
| ( member @ SV18 @ ( complement @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(134,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( ~ ( member @ SV9 @ ( sum_class @ SV19 ) )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( member @ SV9 @ SY51 )
| ~ ( member @ SY51 @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(135,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( member @ SV9 @ SY52 )
| ~ ( member @ SY52 @ SV19 ) )
| ( member @ SV9 @ ( sum_class @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(136,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
| ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) )
| ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ~ ( ~ ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
| ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) )
| ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(138,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ( ~ ( disjoint @ SV13 @ SV22 )
| ! [SY55: $i] :
~ ~ ( ~ ( member @ SY55 @ SV13 )
| ~ ( member @ SY55 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(139,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ( ~ ! [SY56: $i] :
~ ~ ( ~ ( member @ SY56 @ SV13 )
| ~ ( member @ SY56 @ SV22 ) )
| ( disjoint @ SV13 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(140,plain,
! [SV14: $i] :
( ( ( SV14 = null_class )
= $true )
| ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY47 @ universal_class )
| ~ ( member @ SY47 @ SV14 ) )
| ~ ( disjoint @ SY47 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(141,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ~ ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
| ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(142,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ~ ( ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
| ( member @ SV23 @ ( union @ SV5 @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(143,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( subclass @ SV6 @ SV17 )
| ! [SY49: $i] :
( ~ ( member @ SY49 @ SV6 )
| ( member @ SY49 @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(144,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ! [SY50: $i] :
( ~ ( member @ SY50 @ SV6 )
| ( member @ SY50 @ SV17 ) )
| ( subclass @ SV6 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(145,plain,
! [SV7: $i,SV18: $i] :
( ( ~ ( member @ SV18 @ ( complement @ SV7 ) )
| ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(146,plain,
! [SV7: $i,SV18: $i] :
( ( ~ ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) )
| ( member @ SV18 @ ( complement @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(147,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( member @ SV9 @ ( sum_class @ SV19 ) )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( member @ SV9 @ SY51 )
| ~ ( member @ SY51 @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(148,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( member @ SV9 @ SY52 )
| ~ ( member @ SY52 @ SV19 ) )
| ( member @ SV9 @ ( sum_class @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(149,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
| ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(150,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) )
| ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(151,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ~ ( ~ ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
| ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(152,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) )
| ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(153,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ( disjoint @ SV13 @ SV22 )
| ! [SY55: $i] :
~ ~ ( ~ ( member @ SY55 @ SV13 )
| ~ ( member @ SY55 @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(154,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ! [SY56: $i] :
~ ~ ( ~ ( member @ SY56 @ SV13 )
| ~ ( member @ SY56 @ SV22 ) )
| ( disjoint @ SV13 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(155,plain,
! [SV14: $i] :
( ( ( ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY47 @ universal_class )
| ~ ( member @ SY47 @ SV14 ) )
| ~ ( disjoint @ SY47 @ SV14 ) ) )
= $false )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(156,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
| ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(157,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ~ ( ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
| ( member @ SV23 @ ( union @ SV5 @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(158,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( subclass @ SV6 @ SV17 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( member @ SY49 @ SV6 )
| ( member @ SY49 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ! [SY50: $i] :
( ~ ( member @ SY50 @ SV6 )
| ( member @ SY50 @ SV17 ) ) )
= $true )
| ( ( subclass @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(160,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ ( complement @ SV7 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) ) )
= $true )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ ( sum_class @ SV19 ) ) )
= $true )
| ( ( ~ ! [SY51: $i] :
~ ~ ( ~ ( member @ SV9 @ SY51 )
| ~ ( member @ SY51 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( member @ SV9 @ SY52 )
| ~ ( member @ SY52 @ SV19 ) ) )
= $true )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ~ ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
| ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(165,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ~ ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) )
| ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(166,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ~ ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
| ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(167,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ~ ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) )
| ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(168,plain,
! [SV22: $i,SV13: $i] :
( ( ( ~ ( disjoint @ SV13 @ SV22 ) )
= $true )
| ( ( ! [SY55: $i] :
~ ~ ( ~ ( member @ SY55 @ SV13 )
| ~ ( member @ SY55 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV22: $i,SV13: $i] :
( ( ( ~ ! [SY56: $i] :
~ ~ ( ~ ( member @ SY56 @ SV13 )
| ~ ( member @ SY56 @ SV22 ) ) )
= $true )
| ( ( disjoint @ SV13 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_SY47 @ SV14 ) @ universal_class )
| ~ ( member @ ( sK2_SY47 @ SV14 ) @ SV14 ) )
| ~ ( disjoint @ ( sK2_SY47 @ SV14 ) @ SV14 ) ) )
= $false )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[155]) ).
thf(171,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ ( union @ SV5 @ SV16 ) ) )
= $true )
| ( ( ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) ) )
= $true )
| ( ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(173,plain,
! [SV17: $i,SV6: $i] :
( ( ( subclass @ SV6 @ SV17 )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( member @ SY49 @ SV6 )
| ( member @ SY49 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV17: $i,SV6: $i] :
( ( ( ! [SY50: $i] :
( ~ ( member @ SY50 @ SV6 )
| ( member @ SY50 @ SV17 ) ) )
= $false )
| ( ( subclass @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(175,plain,
! [SV7: $i,SV18: $i] :
( ( ( member @ SV18 @ ( complement @ SV7 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(176,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) ) )
= $false )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV19: $i,SV9: $i] :
( ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $false )
| ( ( ~ ! [SY51: $i] :
~ ~ ( ~ ( member @ SV9 @ SY51 )
| ~ ( member @ SY51 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(178,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ! [SY52: $i] :
~ ~ ( ~ ( member @ SV9 @ SY52 )
| ~ ( member @ SY52 @ SV19 ) ) )
= $false )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(179,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(180,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) ) )
= $true )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(181,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(182,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) ) )
= $true )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(183,plain,
! [SV22: $i,SV13: $i] :
( ( ( disjoint @ SV13 @ SV22 )
= $false )
| ( ( ! [SY55: $i] :
~ ~ ( ~ ( member @ SY55 @ SV13 )
| ~ ( member @ SY55 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(184,plain,
! [SV22: $i,SV13: $i] :
( ( ( ! [SY56: $i] :
~ ~ ( ~ ( member @ SY56 @ SV13 )
| ~ ( member @ SY56 @ SV22 ) ) )
= $false )
| ( ( disjoint @ SV13 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(185,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK2_SY47 @ SV14 ) @ universal_class )
| ~ ( member @ ( sK2_SY47 @ SV14 ) @ SV14 ) )
| ~ ( disjoint @ ( sK2_SY47 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(186,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
= $false )
| ( ( ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(187,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV16 ) )
= $false )
| ( ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(188,plain,
! [SV17: $i,SV6: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV6 )
| ( member @ SV26 @ SV17 ) )
= $true )
| ( ( subclass @ SV6 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(189,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK3_SY50 @ SV17 @ SV6 ) @ SV6 )
| ( member @ ( sK3_SY50 @ SV17 @ SV6 ) @ SV17 ) )
= $false )
| ( ( subclass @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[174]) ).
thf(190,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) )
= $false )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(191,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ universal_class )
| ~ ~ ( member @ SV18 @ SV7 ) )
= $true )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(192,plain,
! [SV19: $i,SV9: $i] :
( ( ( ! [SY51: $i] :
~ ~ ( ~ ( member @ SV9 @ SY51 )
| ~ ( member @ SY51 @ SV19 ) ) )
= $false )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(193,plain,
! [SV19: $i,SV9: $i] :
( ( ( ! [SY52: $i] :
~ ~ ( ~ ( member @ SV9 @ SY52 )
| ~ ( member @ SY52 @ SV19 ) ) )
= $true )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(194,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(195,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) ) )
= $false )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(196,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(197,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) ) )
= $false )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(198,plain,
! [SV22: $i,SV13: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( member @ SV27 @ SV13 )
| ~ ( member @ SV27 @ SV22 ) ) )
= $true )
| ( ( disjoint @ SV13 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(199,plain,
! [SV13: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV13 )
| ~ ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV22 ) ) )
= $false )
| ( ( disjoint @ SV13 @ SV22 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[184]) ).
thf(200,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_SY47 @ SV14 ) @ universal_class )
| ~ ( member @ ( sK2_SY47 @ SV14 ) @ SV14 ) )
| ~ ( disjoint @ ( sK2_SY47 @ SV14 ) @ SV14 ) )
= $false )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(201,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( member @ SV23 @ SV5 )
= $true )
| ( ( member @ SV23 @ SV16 )
= $true )
| ( ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(202,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( member @ SV23 @ SV5 )
= $false )
| ( ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(203,plain,
! [SV5: $i,SV16: $i,SV23: $i] :
( ( ( member @ SV23 @ SV16 )
= $false )
| ( ( member @ SV23 @ ( union @ SV5 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(204,plain,
! [SV17: $i,SV6: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV6 ) )
= $true )
| ( ( member @ SV26 @ SV17 )
= $true )
| ( ( subclass @ SV6 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(205,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK3_SY50 @ SV17 @ SV6 ) @ SV6 ) )
= $false )
| ( ( subclass @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(206,plain,
! [SV6: $i,SV17: $i] :
( ( ( member @ ( sK3_SY50 @ SV17 @ SV6 ) @ SV17 )
= $false )
| ( ( subclass @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(207,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ universal_class ) )
= $false )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(208,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ~ ( member @ SV18 @ SV7 ) )
= $false )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(209,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ universal_class ) )
= $true )
| ( ( ~ ~ ( member @ SV18 @ SV7 ) )
= $true )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(210,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( member @ SV9 @ ( sK5_SY51 @ SV19 @ SV9 ) )
| ~ ( member @ ( sK5_SY51 @ SV19 @ SV9 ) @ SV19 ) ) )
= $false )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[192]) ).
thf(211,plain,
! [SV19: $i,SV28: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( member @ SV9 @ SV28 )
| ~ ( member @ SV28 @ SV19 ) ) )
= $true )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(212,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) )
= $false )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(213,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ universal_class )
| ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) )
= $true )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(214,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) )
= $false )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(215,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV12 )
| ~ ( member @ SV25 @ SV21 ) )
= $true )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(216,plain,
! [SV22: $i,SV13: $i,SV27: $i] :
( ( ( ~ ( ~ ( member @ SV27 @ SV13 )
| ~ ( member @ SV27 @ SV22 ) ) )
= $false )
| ( ( disjoint @ SV13 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(217,plain,
! [SV13: $i,SV22: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV13 )
| ~ ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV22 ) ) )
= $true )
| ( ( disjoint @ SV13 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(218,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_SY47 @ SV14 ) @ universal_class )
| ~ ( member @ ( sK2_SY47 @ SV14 ) @ SV14 ) ) )
= $false )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(219,plain,
! [SV14: $i] :
( ( ( ~ ( disjoint @ ( sK2_SY47 @ SV14 ) @ SV14 ) )
= $false )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(220,plain,
! [SV17: $i,SV6: $i,SV26: $i] :
( ( ( member @ SV26 @ SV6 )
= $false )
| ( ( member @ SV26 @ SV17 )
= $true )
| ( ( subclass @ SV6 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV6: $i,SV17: $i] :
( ( ( member @ ( sK3_SY50 @ SV17 @ SV6 ) @ SV6 )
= $true )
| ( ( subclass @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(222,plain,
! [SV7: $i,SV18: $i] :
( ( ( member @ SV18 @ universal_class )
= $true )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(223,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ SV7 ) )
= $true )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(224,plain,
! [SV7: $i,SV18: $i] :
( ( ( member @ SV18 @ universal_class )
= $false )
| ( ( ~ ~ ( member @ SV18 @ SV7 ) )
= $true )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(225,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( ~ ( member @ SV9 @ ( sK5_SY51 @ SV19 @ SV9 ) )
| ~ ( member @ ( sK5_SY51 @ SV19 @ SV9 ) @ SV19 ) ) )
= $true )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(226,plain,
! [SV19: $i,SV28: $i,SV9: $i] :
( ( ( ~ ( ~ ( member @ SV9 @ SV28 )
| ~ ( member @ SV28 @ SV19 ) ) )
= $false )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(227,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ universal_class ) )
= $false )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(228,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) )
= $false )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(229,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ universal_class ) )
= $true )
| ( ( ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) )
= $true )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(230,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV12 ) )
= $false )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(231,plain,
! [SV12: $i,SV21: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV21 ) )
= $false )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(232,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV21 ) )
= $true )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV22: $i,SV13: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV13 )
| ~ ( member @ SV27 @ SV22 ) )
= $true )
| ( ( disjoint @ SV13 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(234,plain,
! [SV13: $i,SV22: $i] :
( ( ( ~ ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV13 )
| ~ ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV22 ) )
= $false )
| ( ( disjoint @ SV13 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(235,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ( member @ ( sK2_SY47 @ SV14 ) @ universal_class )
| ~ ( member @ ( sK2_SY47 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(236,plain,
! [SV14: $i] :
( ( ( disjoint @ ( sK2_SY47 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(237,plain,
! [SV7: $i,SV18: $i] :
( ( ( member @ SV18 @ SV7 )
= $false )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(238,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ SV7 ) )
= $false )
| ( ( member @ SV18 @ universal_class )
= $false )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(239,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ ( sK5_SY51 @ SV19 @ SV9 ) )
| ~ ( member @ ( sK5_SY51 @ SV19 @ SV9 ) @ SV19 ) )
= $false )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(240,plain,
! [SV19: $i,SV28: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV28 )
| ~ ( member @ SV28 @ SV19 ) )
= $true )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(241,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( member @ SV10 @ universal_class )
= $true )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(242,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ( SV10 = SV20 )
| ( SV10 = SV24 ) )
= $true )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(243,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( member @ SV10 @ universal_class )
= $false )
| ( ( ~ ( ( SV10 = SV20 )
| ( SV10 = SV24 ) ) )
= $true )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(244,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( member @ SV25 @ SV12 )
= $true )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(245,plain,
! [SV12: $i,SV21: $i,SV25: $i] :
( ( ( member @ SV25 @ SV21 )
= $true )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(246,plain,
! [SV21: $i,SV12: $i,SV25: $i] :
( ( ( member @ SV25 @ SV12 )
= $false )
| ( ( ~ ( member @ SV25 @ SV21 ) )
= $true )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(247,plain,
! [SV22: $i,SV13: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV13 ) )
= $true )
| ( ( ~ ( member @ SV27 @ SV22 ) )
= $true )
| ( ( disjoint @ SV13 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(248,plain,
! [SV13: $i,SV22: $i] :
( ( ( ~ ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV13 ) )
= $false )
| ( ( disjoint @ SV13 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(249,plain,
! [SV13: $i,SV22: $i] :
( ( ( ~ ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV22 ) )
= $false )
| ( ( disjoint @ SV13 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(250,plain,
! [SV14: $i] :
( ( ( ~ ( member @ ( sK2_SY47 @ SV14 ) @ universal_class )
| ~ ( member @ ( sK2_SY47 @ SV14 ) @ SV14 ) )
= $false )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(251,plain,
! [SV7: $i,SV18: $i] :
( ( ( member @ SV18 @ SV7 )
= $true )
| ( ( member @ SV18 @ universal_class )
= $false )
| ( ( member @ SV18 @ ( complement @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(252,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ ( sK5_SY51 @ SV19 @ SV9 ) ) )
= $false )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(253,plain,
! [SV9: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK5_SY51 @ SV19 @ SV9 ) @ SV19 ) )
= $false )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(254,plain,
! [SV19: $i,SV28: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV28 ) )
= $true )
| ( ( ~ ( member @ SV28 @ SV19 ) )
= $true )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(255,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( SV10 = SV20 )
= $true )
| ( ( SV10 = SV24 )
= $true )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(256,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( ( SV10 = SV20 )
| ( SV10 = SV24 ) )
= $false )
| ( ( member @ SV10 @ universal_class )
= $false )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(257,plain,
! [SV12: $i,SV21: $i,SV25: $i] :
( ( ( member @ SV25 @ SV21 )
= $false )
| ( ( member @ SV25 @ SV12 )
= $false )
| ( ( member @ SV25 @ ( intersection @ SV12 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(258,plain,
! [SV22: $i,SV13: $i,SV27: $i] :
( ( ( member @ SV27 @ SV13 )
= $false )
| ( ( ~ ( member @ SV27 @ SV22 ) )
= $true )
| ( ( disjoint @ SV13 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(259,plain,
! [SV13: $i,SV22: $i] :
( ( ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV13 )
= $true )
| ( ( disjoint @ SV13 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(260,plain,
! [SV13: $i,SV22: $i] :
( ( ( member @ ( sK4_SY56 @ SV22 @ SV13 ) @ SV22 )
= $true )
| ( ( disjoint @ SV13 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(261,plain,
! [SV14: $i] :
( ( ( ~ ( member @ ( sK2_SY47 @ SV14 ) @ universal_class ) )
= $false )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(262,plain,
! [SV14: $i] :
( ( ( ~ ( member @ ( sK2_SY47 @ SV14 ) @ SV14 ) )
= $false )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(263,plain,
! [SV19: $i,SV9: $i] :
( ( ( member @ SV9 @ ( sK5_SY51 @ SV19 @ SV9 ) )
= $true )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(264,plain,
! [SV9: $i,SV19: $i] :
( ( ( member @ ( sK5_SY51 @ SV19 @ SV9 ) @ SV19 )
= $true )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(265,plain,
! [SV19: $i,SV28: $i,SV9: $i] :
( ( ( member @ SV9 @ SV28 )
= $false )
| ( ( ~ ( member @ SV28 @ SV19 ) )
= $true )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV24: $i,SV20: $i,SV10: $i] :
( ( ( SV10 = SV20 )
= $false )
| ( ( member @ SV10 @ universal_class )
= $false )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(267,plain,
! [SV20: $i,SV24: $i,SV10: $i] :
( ( ( SV10 = SV24 )
= $false )
| ( ( member @ SV10 @ universal_class )
= $false )
| ( ( member @ SV10 @ ( unordered_pair @ SV20 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(268,plain,
! [SV13: $i,SV22: $i,SV27: $i] :
( ( ( member @ SV27 @ SV22 )
= $false )
| ( ( member @ SV27 @ SV13 )
= $false )
| ( ( disjoint @ SV13 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(269,plain,
! [SV14: $i] :
( ( ( member @ ( sK2_SY47 @ SV14 ) @ universal_class )
= $true )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(270,plain,
! [SV14: $i] :
( ( ( member @ ( sK2_SY47 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(271,plain,
! [SV9: $i,SV19: $i,SV28: $i] :
( ( ( member @ SV28 @ SV19 )
= $false )
| ( ( member @ SV9 @ SV28 )
= $false )
| ( ( member @ SV9 @ ( sum_class @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(272,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[91,271,270,269,268,267,266,264,263,260,259,257,255,251,245,244,241,237,236,222,221,220,206,203,202,201,125,122,108,107,96,95,93]) ).
thf(273,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n005.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 14:29:44 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 14
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 0
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 ......
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,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:272,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26
% 0.08/0.26 %**** End of derivation protocol ****
% 0.08/0.26 %**** no. of clauses in derivation: 244 ****
% 0.08/0.26 %**** clause counter: 272 ****
% 0.08/0.26
% 0.08/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,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:272,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------