%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET062+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 : n014.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 10:39:14 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 148 ( 88 unt; 0 typ; 0 def)
% Number of atoms : 787 ( 246 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1396 ( 362 ~; 209 |; 18 &; 789 @)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 9 con; 0-3 aty)
% Number of variables : 240 ( 0 ^; 234 !; 6 ?; 240 :)
% 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_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY19,type,
sK3_SY19: $i > $i ).
thf(tp_sK4_SY26,type,
sK4_SY26: $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(9,axiom,
! [XR: $i,YR: $i] : ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn1) ).
thf(11,axiom,
! [U: $i,X: $i] :
( ( member @ U @ ( power_class @ X ) )
<=> ( ( member @ U @ universal_class )
& ( subclass @ U @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_defn) ).
thf(14,axiom,
? [X: $i] :
( ( member @ X @ universal_class )
& ( inductive @ X )
& ! [Y: $i] :
( ( inductive @ Y )
=> ( subclass @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity) ).
thf(20,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn1) ).
thf(23,axiom,
! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip) ).
thf(25,axiom,
! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate) ).
thf(28,axiom,
! [X: $i] :
~ ( member @ X @ null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
thf(32,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation) ).
thf(41,axiom,
! [X: $i,Y: $i] :
( ( X = Y )
<=> ( ( subclass @ X @ Y )
& ( subclass @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
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] : ( subclass @ null_class @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).
thf(45,negated_conjecture,
( ( ! [X: $i] : ( subclass @ null_class @ X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,plain,
( ( ! [X: $i] : ( subclass @ null_class @ X ) )
= $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,
( ( ! [XR: $i,YR: $i] : ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(49,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( power_class @ X ) )
<=> ( ( member @ U @ universal_class )
& ( subclass @ U @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(50,plain,
( ( ? [X: $i] :
( ( member @ X @ universal_class )
& ( inductive @ X )
& ! [Y: $i] :
( ( inductive @ Y )
=> ( subclass @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(51,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(52,plain,
( ( ! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(53,plain,
( ( ! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(54,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(55,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
<=> ( ( subclass @ X @ Y )
& ( subclass @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(57,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(59,plain,
( ( subclass @ null_class @ sK1_X )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(60,plain,
( ( ~ ( subclass @ null_class @ sK1_X ) )
= $true ),
inference(polarity_switch,[status(thm)],[59]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(62,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
<=> ( ( subclass @ X @ Y )
& ( subclass @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(64,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(65,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(66,plain,
( ( ! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(67,plain,
( ( ! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(68,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(69,plain,
( ( ? [X: $i] :
( ( member @ X @ universal_class )
& ( inductive @ X )
& ! [Y: $i] :
( ( inductive @ Y )
=> ( subclass @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(70,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( power_class @ X ) )
<=> ( ( member @ U @ universal_class )
& ( subclass @ U @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(71,plain,
( ( ! [XR: $i,YR: $i] : ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(72,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(73,plain,
( ( ~ ( subclass @ null_class @ sK1_X ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(74,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != null_class ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX1 @ SX0 ) )
| ~ ( disjoint @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(75,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)],[61]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 ) )
| ( member @ SX0 @ ( power_class @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(78,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( inductive @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( inductive @ SX1 )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(79,plain,
! [SV1: $i] :
( ( subclass @ SV1 @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(80,plain,
! [SV2: $i] :
( ( ~ ( member @ SV2 @ null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
! [SV3: $i] :
( ( subclass @ ( rotate @ SV3 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(82,plain,
! [SV4: $i] :
( ( subclass @ ( flip @ SV4 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(83,plain,
! [SV5: $i] :
( ( ! [SY18: $i] : ( subclass @ ( compose @ SY18 @ SV5 ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(84,plain,
( ( subclass @ null_class @ sK1_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(85,plain,
! [SV6: $i] :
( ( ~ ( ( SV6 != null_class ) )
| ~ ! [SY19: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY19 @ universal_class )
| ~ ( member @ SY19 @ SV6 ) )
| ~ ( disjoint @ SY19 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(86,plain,
! [SV7: $i] :
( ( ! [SY20: $i] :
~ ( ~ ( ~ ( subclass @ SV7 @ SY20 )
| ! [SY21: $i] :
( ~ ( member @ SY21 @ SV7 )
| ( member @ SY21 @ SY20 ) ) )
| ~ ( ~ ! [SY22: $i] :
( ~ ( member @ SY22 @ SV7 )
| ( member @ SY22 @ SY20 ) )
| ( subclass @ SV7 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(87,plain,
! [SV8: $i] :
( ( ! [SY23: $i] :
~ ( ~ ( ( SV8 != SY23 )
| ~ ( ~ ( subclass @ SV8 @ SY23 )
| ~ ( subclass @ SY23 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SV8 @ SY23 )
| ~ ( subclass @ SY23 @ SV8 ) )
| ( SV8 = SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV9: $i] :
( ( ! [SY24: $i] :
~ ( ~ ( ~ ( member @ SV9 @ ( power_class @ SY24 ) )
| ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SY24 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SY24 ) )
| ( member @ SV9 @ ( power_class @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(89,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( inductive @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( inductive @ SX1 )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(90,plain,
! [SV2: $i] :
( ( member @ SV2 @ null_class )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV5: $i,SV10: $i] :
( ( subclass @ ( compose @ SV10 @ SV5 ) @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV6: $i] :
( ( ( ~ ( ( SV6 != null_class ) ) )
= $true )
| ( ( ~ ! [SY19: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY19 @ universal_class )
| ~ ( member @ SY19 @ SV6 ) )
| ~ ( disjoint @ SY19 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV11: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( subclass @ SV7 @ SV11 )
| ! [SY25: $i] :
( ~ ( member @ SY25 @ SV7 )
| ( member @ SY25 @ SV11 ) ) )
| ~ ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV7 )
| ( member @ SY26 @ SV11 ) )
| ( subclass @ SV7 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( ~ ( ( SV8 != SV12 )
| ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) )
| ( SV8 = SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( member @ SV9 @ ( power_class @ SV13 ) )
| ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) )
| ( member @ SV9 @ ( power_class @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(96,plain,
( ( ~ ~ ( ~ ~ ( ~ ( member @ sK2_SX0 @ universal_class )
| ~ ( inductive @ sK2_SX0 ) )
| ~ ! [SY27: $i] :
( ~ ( inductive @ SY27 )
| ( subclass @ sK2_SX0 @ SY27 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(97,plain,
! [SV6: $i] :
( ( ( SV6 != null_class )
= $false )
| ( ( ~ ! [SY19: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY19 @ universal_class )
| ~ ( member @ SY19 @ SV6 ) )
| ~ ( disjoint @ SY19 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV11: $i,SV7: $i] :
( ( ~ ( ~ ( subclass @ SV7 @ SV11 )
| ! [SY25: $i] :
( ~ ( member @ SY25 @ SV7 )
| ( member @ SY25 @ SV11 ) ) )
| ~ ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV7 )
| ( member @ SY26 @ SV11 ) )
| ( subclass @ SV7 @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( ( SV8 != SV12 )
| ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) )
| ( SV8 = SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ( ~ ( member @ SV9 @ ( power_class @ SV13 ) )
| ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) )
| ( member @ SV9 @ ( power_class @ SV13 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(101,plain,
( ( ~ ( ~ ~ ( ~ ( member @ sK2_SX0 @ universal_class )
| ~ ( inductive @ sK2_SX0 ) )
| ~ ! [SY27: $i] :
( ~ ( inductive @ SY27 )
| ( subclass @ sK2_SX0 @ SY27 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(102,plain,
! [SV6: $i] :
( ( ( SV6 = null_class )
= $true )
| ( ( ~ ! [SY19: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY19 @ universal_class )
| ~ ( member @ SY19 @ SV6 ) )
| ~ ( disjoint @ SY19 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(103,plain,
! [SV11: $i,SV7: $i] :
( ( ~ ( ~ ( subclass @ SV7 @ SV11 )
| ! [SY25: $i] :
( ~ ( member @ SY25 @ SV7 )
| ( member @ SY25 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(104,plain,
! [SV11: $i,SV7: $i] :
( ( ~ ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV7 )
| ( member @ SY26 @ SV11 ) )
| ( subclass @ SV7 @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(105,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( ( SV8 != SV12 )
| ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(106,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( ~ ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) )
| ( SV8 = SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(107,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ( ~ ( member @ SV9 @ ( power_class @ SV13 ) )
| ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(108,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) )
| ( member @ SV9 @ ( power_class @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(109,plain,
( ( ~ ~ ( ~ ( member @ sK2_SX0 @ universal_class )
| ~ ( inductive @ sK2_SX0 ) )
| ~ ! [SY27: $i] :
( ~ ( inductive @ SY27 )
| ( subclass @ sK2_SX0 @ SY27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV6: $i] :
( ( ( ! [SY19: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY19 @ universal_class )
| ~ ( member @ SY19 @ SV6 ) )
| ~ ( disjoint @ SY19 @ SV6 ) ) )
= $false )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV11: $i,SV7: $i] :
( ( ~ ( subclass @ SV7 @ SV11 )
| ! [SY25: $i] :
( ~ ( member @ SY25 @ SV7 )
| ( member @ SY25 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(112,plain,
! [SV11: $i,SV7: $i] :
( ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV7 )
| ( member @ SY26 @ SV11 ) )
| ( subclass @ SV7 @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(113,plain,
! [SV12: $i,SV8: $i] :
( ( ( SV8 != SV12 )
| ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(114,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) )
| ( SV8 = SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(115,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ( member @ SV9 @ ( power_class @ SV13 ) )
| ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(116,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) )
| ( member @ SV9 @ ( power_class @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(117,plain,
( ( ~ ~ ( ~ ( member @ sK2_SX0 @ universal_class )
| ~ ( inductive @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(118,plain,
( ( ~ ! [SY27: $i] :
( ~ ( inductive @ SY27 )
| ( subclass @ sK2_SX0 @ SY27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(119,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK3_SY19 @ SV6 ) @ universal_class )
| ~ ( member @ ( sK3_SY19 @ SV6 ) @ SV6 ) )
| ~ ( disjoint @ ( sK3_SY19 @ SV6 ) @ SV6 ) ) )
= $false )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[110]) ).
thf(120,plain,
! [SV11: $i,SV7: $i] :
( ( ( ~ ( subclass @ SV7 @ SV11 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( member @ SY25 @ SV7 )
| ( member @ SY25 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(121,plain,
! [SV11: $i,SV7: $i] :
( ( ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV7 )
| ( member @ SY26 @ SV11 ) ) )
= $true )
| ( ( subclass @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(122,plain,
! [SV12: $i,SV8: $i] :
( ( ( SV8 != SV12 )
= $true )
| ( ( ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(123,plain,
! [SV12: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) ) )
= $true )
| ( ( SV8 = SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(124,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ ( power_class @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(125,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) ) )
= $true )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(126,plain,
( ( ~ ( ~ ( member @ sK2_SX0 @ universal_class )
| ~ ( inductive @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(127,plain,
( ( ! [SY27: $i] :
( ~ ( inductive @ SY27 )
| ( subclass @ sK2_SX0 @ SY27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(128,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK3_SY19 @ SV6 ) @ universal_class )
| ~ ( member @ ( sK3_SY19 @ SV6 ) @ SV6 ) )
| ~ ( disjoint @ ( sK3_SY19 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(129,plain,
! [SV11: $i,SV7: $i] :
( ( ( subclass @ SV7 @ SV11 )
= $false )
| ( ( ! [SY25: $i] :
( ~ ( member @ SY25 @ SV7 )
| ( member @ SY25 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(130,plain,
! [SV11: $i,SV7: $i] :
( ( ( ! [SY26: $i] :
( ~ ( member @ SY26 @ SV7 )
| ( member @ SY26 @ SV11 ) ) )
= $false )
| ( ( subclass @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(131,plain,
! [SV12: $i,SV8: $i] :
( ( ( SV8 = SV12 )
= $false )
| ( ( ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(132,plain,
! [SV12: $i,SV8: $i] :
( ( ( ~ ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) ) )
= $false )
| ( ( SV8 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV13: $i,SV9: $i] :
( ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(134,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) ) )
= $false )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(135,plain,
( ( ~ ( member @ sK2_SX0 @ universal_class )
| ~ ( inductive @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV14: $i] :
( ( ~ ( inductive @ SV14 )
| ( subclass @ sK2_SX0 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK3_SY19 @ SV6 ) @ universal_class )
| ~ ( member @ ( sK3_SY19 @ SV6 ) @ SV6 ) )
| ~ ( disjoint @ ( sK3_SY19 @ SV6 ) @ SV6 ) )
= $false )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(138,plain,
! [SV11: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV7 )
| ( member @ SV15 @ SV11 ) )
= $true )
| ( ( subclass @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV7: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK4_SY26 @ SV11 @ SV7 ) @ SV7 )
| ( member @ ( sK4_SY26 @ SV11 @ SV7 ) @ SV11 ) )
= $false )
| ( ( subclass @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[130]) ).
thf(140,plain,
! [SV12: $i,SV8: $i] :
( ( ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) )
= $false )
| ( ( SV8 = SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV12: $i,SV8: $i] :
( ( ( ~ ( subclass @ SV8 @ SV12 )
| ~ ( subclass @ SV12 @ SV8 ) )
= $true )
| ( ( SV8 = SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(142,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) )
= $false )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(143,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ universal_class )
| ~ ( subclass @ SV9 @ SV13 ) )
= $true )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(144,plain,
( ( ~ ( member @ sK2_SX0 @ universal_class ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(145,plain,
( ( ~ ( inductive @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(146,plain,
! [SV14: $i] :
( ( ( ~ ( inductive @ SV14 ) )
= $true )
| ( ( subclass @ sK2_SX0 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(147,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK3_SY19 @ SV6 ) @ universal_class )
| ~ ( member @ ( sK3_SY19 @ SV6 ) @ SV6 ) ) )
= $false )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(148,plain,
! [SV6: $i] :
( ( ( ~ ( disjoint @ ( sK3_SY19 @ SV6 ) @ SV6 ) )
= $false )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(149,plain,
! [SV11: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV7 ) )
= $true )
| ( ( member @ SV15 @ SV11 )
= $true )
| ( ( subclass @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV7: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK4_SY26 @ SV11 @ SV7 ) @ SV7 ) )
= $false )
| ( ( subclass @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(151,plain,
! [SV7: $i,SV11: $i] :
( ( ( member @ ( sK4_SY26 @ SV11 @ SV7 ) @ SV11 )
= $false )
| ( ( subclass @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(152,plain,
! [SV12: $i,SV8: $i] :
( ( ( ~ ( subclass @ SV8 @ SV12 ) )
= $false )
| ( ( SV8 = SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(153,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ( subclass @ SV12 @ SV8 ) )
= $false )
| ( ( SV8 = SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(154,plain,
! [SV12: $i,SV8: $i] :
( ( ( ~ ( subclass @ SV8 @ SV12 ) )
= $true )
| ( ( ~ ( subclass @ SV12 @ SV8 ) )
= $true )
| ( ( SV8 = SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(155,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ universal_class ) )
= $false )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(156,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( subclass @ SV9 @ SV13 ) )
= $false )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(157,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ universal_class ) )
= $true )
| ( ( ~ ( subclass @ SV9 @ SV13 ) )
= $true )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(158,plain,
( ( member @ sK2_SX0 @ universal_class )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(159,plain,
( ( inductive @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(160,plain,
! [SV14: $i] :
( ( ( inductive @ SV14 )
= $false )
| ( ( subclass @ sK2_SX0 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(161,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( member @ ( sK3_SY19 @ SV6 ) @ universal_class )
| ~ ( member @ ( sK3_SY19 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(162,plain,
! [SV6: $i] :
( ( ( disjoint @ ( sK3_SY19 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(163,plain,
! [SV11: $i,SV7: $i,SV15: $i] :
( ( ( member @ SV15 @ SV7 )
= $false )
| ( ( member @ SV15 @ SV11 )
= $true )
| ( ( subclass @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(164,plain,
! [SV7: $i,SV11: $i] :
( ( ( member @ ( sK4_SY26 @ SV11 @ SV7 ) @ SV7 )
= $true )
| ( ( subclass @ SV7 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(165,plain,
! [SV12: $i,SV8: $i] :
( ( ( subclass @ SV8 @ SV12 )
= $true )
| ( ( SV8 = SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(166,plain,
! [SV8: $i,SV12: $i] :
( ( ( subclass @ SV12 @ SV8 )
= $true )
| ( ( SV8 = SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(167,plain,
! [SV12: $i,SV8: $i] :
( ( ( subclass @ SV8 @ SV12 )
= $false )
| ( ( ~ ( subclass @ SV12 @ SV8 ) )
= $true )
| ( ( SV8 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV13: $i,SV9: $i] :
( ( ( member @ SV9 @ universal_class )
= $true )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(169,plain,
! [SV13: $i,SV9: $i] :
( ( ( subclass @ SV9 @ SV13 )
= $true )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(170,plain,
! [SV13: $i,SV9: $i] :
( ( ( member @ SV9 @ universal_class )
= $false )
| ( ( ~ ( subclass @ SV9 @ SV13 ) )
= $true )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV6: $i] :
( ( ( ~ ( member @ ( sK3_SY19 @ SV6 ) @ universal_class )
| ~ ( member @ ( sK3_SY19 @ SV6 ) @ SV6 ) )
= $false )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV8: $i,SV12: $i] :
( ( ( subclass @ SV12 @ SV8 )
= $false )
| ( ( subclass @ SV8 @ SV12 )
= $false )
| ( ( SV8 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(173,plain,
! [SV13: $i,SV9: $i] :
( ( ( subclass @ SV9 @ SV13 )
= $false )
| ( ( member @ SV9 @ universal_class )
= $false )
| ( ( member @ SV9 @ ( power_class @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(174,plain,
! [SV6: $i] :
( ( ( ~ ( member @ ( sK3_SY19 @ SV6 ) @ universal_class ) )
= $false )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(175,plain,
! [SV6: $i] :
( ( ( ~ ( member @ ( sK3_SY19 @ SV6 ) @ SV6 ) )
= $false )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(176,plain,
! [SV6: $i] :
( ( ( member @ ( sK3_SY19 @ SV6 ) @ universal_class )
= $true )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(177,plain,
! [SV6: $i] :
( ( ( member @ ( sK3_SY19 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(178,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[64,177,176,173,172,169,168,166,165,164,163,162,160,159,158,151,91,90,84,82,81,79,68]) ).
thf(179,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET062+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
% 0.07/0.19 % Computer : n014.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:29:11 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 12
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 0
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 ...
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:12,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:178,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26
% 0.07/0.26 %**** End of derivation protocol ****
% 0.07/0.26 %**** no. of clauses in derivation: 148 ****
% 0.07/0.26 %**** clause counter: 178 ****
% 0.07/0.26
% 0.07/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:12,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:178,loop_count:0,foatp_calls:1,translation:fof_full)
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