%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET697+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:40:53 AM UTC 2026
% Result : Theorem 0.48s 0.44s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 228 ( 119 unt; 0 typ; 0 def)
% Number of atoms : 1407 ( 349 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 2947 ( 714 ~; 424 |; 18 &;1752 @)
% ( 23 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 538 ( 0 ^; 538 !; 0 ?; 538 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_equal_set,type,
equal_set: $i > $i > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_product,type,
product: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_SY28,type,
sK4_SY28: $i > $i > $i ).
thf(tp_sK5_SY39,type,
sK5_SY39: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(5,axiom,
! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(6,axiom,
! [X: $i] :
~ ( member @ X @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(8,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(12,conjecture,
! [A: $i,B: $i,E: $i] :
( ( ( subset @ A @ E )
& ( subset @ B @ E ) )
=> ( ( subset @ A @ B )
<=> ( equal_set @ ( intersection @ A @ ( difference @ E @ B ) ) @ empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI31) ).
thf(13,negated_conjecture,
( ( ! [A: $i,B: $i,E: $i] :
( ( ( subset @ A @ E )
& ( subset @ B @ E ) )
=> ( ( subset @ A @ B )
<=> ( equal_set @ ( intersection @ A @ ( difference @ E @ B ) ) @ empty_set ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,E: $i] :
( ( ( subset @ A @ E )
& ( subset @ B @ E ) )
=> ( ( subset @ A @ B )
<=> ( equal_set @ ( intersection @ A @ ( difference @ E @ B ) ) @ empty_set ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(20,plain,
( ( ! [SY15: $i,SY16: $i] :
( ( ( subset @ sK1_A @ SY16 )
& ( subset @ SY15 @ SY16 ) )
=> ( ( subset @ sK1_A @ SY15 )
<=> ( equal_set @ ( intersection @ sK1_A @ ( difference @ SY16 @ SY15 ) ) @ empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(21,plain,
( ( ! [SY17: $i] :
( ( ( subset @ sK1_A @ SY17 )
& ( subset @ sK2_SY15 @ SY17 ) )
=> ( ( subset @ sK1_A @ sK2_SY15 )
<=> ( equal_set @ ( intersection @ sK1_A @ ( difference @ SY17 @ sK2_SY15 ) ) @ empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
( ( ( ( subset @ sK1_A @ sK3_SY17 )
& ( subset @ sK2_SY15 @ sK3_SY17 ) )
=> ( ( subset @ sK1_A @ sK2_SY15 )
<=> ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(23,plain,
( ( subset @ sK1_A @ sK3_SY17 )
= $true ),
inference(standard_cnf,[status(thm)],[22]) ).
thf(24,plain,
( ( subset @ sK2_SY15 @ sK3_SY17 )
= $true ),
inference(standard_cnf,[status(thm)],[22]) ).
thf(25,plain,
( ( ( subset @ sK1_A @ sK2_SY15 )
<=> ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set ) )
= $false ),
inference(standard_cnf,[status(thm)],[22]) ).
thf(26,plain,
( ( ( subset @ sK1_A @ sK2_SY15 )
=> ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[25]) ).
thf(27,plain,
( ( ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set )
=> ( subset @ sK1_A @ sK2_SY15 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[25]) ).
thf(28,plain,
( ( ~ ( ( subset @ sK1_A @ sK2_SY15 )
=> ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ( ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set )
=> ( subset @ sK1_A @ sK2_SY15 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(32,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(34,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(35,plain,
( ( subset @ sK2_SY15 @ sK3_SY17 )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( subset @ sK1_A @ sK3_SY17 )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(37,plain,
( ( ~ ( ( subset @ sK1_A @ sK2_SY15 )
=> ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ~ ( ~ ( subset @ sK1_A @ sK2_SY15 )
| ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(40,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_set @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( equal_set @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(41,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(42,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ~ ( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(43,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(44,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY15 )
| ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV2: $i] :
( ( ! [SY18: $i,SY19: $i] :
~ ( ~ ( ~ ( member @ SV2 @ ( difference @ SY19 @ SY18 ) )
| ~ ( ~ ( member @ SV2 @ SY19 )
| ~ ~ ( member @ SV2 @ SY18 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV2 @ SY19 )
| ~ ~ ( member @ SV2 @ SY18 ) )
| ( member @ SV2 @ ( difference @ SY19 @ SY18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV3: $i] :
( ( ! [SY20: $i] :
~ ( ~ ( ~ ( equal_set @ SV3 @ SY20 )
| ~ ( ~ ( subset @ SV3 @ SY20 )
| ~ ( subset @ SY20 @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV3 @ SY20 )
| ~ ( subset @ SY20 @ SV3 ) )
| ( equal_set @ SV3 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV4: $i] :
( ( ! [SY21: $i] :
~ ( ~ ( ~ ( subset @ SV4 @ SY21 )
| ! [SY22: $i] :
( ~ ( member @ SY22 @ SV4 )
| ( member @ SY22 @ SY21 ) ) )
| ~ ( ~ ! [SY23: $i] :
( ~ ( member @ SY23 @ SV4 )
| ( member @ SY23 @ SY21 ) )
| ( subset @ SV4 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV5: $i] :
( ( ! [SY24: $i,SY25: $i] :
~ ( ~ ( ~ ( member @ SV5 @ ( intersection @ SY24 @ SY25 ) )
| ~ ( ~ ( member @ SV5 @ SY24 )
| ~ ( member @ SV5 @ SY25 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV5 @ SY24 )
| ~ ( member @ SV5 @ SY25 ) )
| ( member @ SV5 @ ( intersection @ SY24 @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY15 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(51,plain,
( ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(52,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY26: $i] :
~ ( ~ ( ~ ( member @ SV2 @ ( difference @ SY26 @ SV6 ) )
| ~ ( ~ ( member @ SV2 @ SY26 )
| ~ ~ ( member @ SV2 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV2 @ SY26 )
| ~ ~ ( member @ SV2 @ SV6 ) )
| ( member @ SV2 @ ( difference @ SY26 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV3 @ SV7 )
| ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) )
| ( equal_set @ SV3 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV4 @ SV8 )
| ! [SY27: $i] :
( ~ ( member @ SY27 @ SV4 )
| ( member @ SY27 @ SV8 ) ) )
| ~ ( ~ ! [SY28: $i] :
( ~ ( member @ SY28 @ SV4 )
| ( member @ SY28 @ SV8 ) )
| ( subset @ SV4 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY29: $i] :
~ ( ~ ( ~ ( member @ SV5 @ ( intersection @ SV9 @ SY29 ) )
| ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SY29 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SY29 ) )
| ( member @ SV5 @ ( intersection @ SV9 @ SY29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(56,plain,
( ( subset @ sK1_A @ sK2_SY15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(57,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
| ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) )
| ( member @ SV2 @ ( difference @ SV10 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( ~ ( equal_set @ SV3 @ SV7 )
| ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) )
| ( equal_set @ SV3 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( ~ ( subset @ SV4 @ SV8 )
| ! [SY27: $i] :
( ~ ( member @ SY27 @ SV4 )
| ( member @ SY27 @ SV8 ) ) )
| ~ ( ~ ! [SY28: $i] :
( ~ ( member @ SY28 @ SV4 )
| ( member @ SY28 @ SV8 ) )
| ( subset @ SV4 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
| ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) )
| ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ~ ( ~ ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
| ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) )
| ( member @ SV2 @ ( difference @ SV10 @ SV6 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( ~ ( equal_set @ SV3 @ SV7 )
| ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) )
| ( equal_set @ SV3 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( ~ ( subset @ SV4 @ SV8 )
| ! [SY27: $i] :
( ~ ( member @ SY27 @ SV4 )
| ( member @ SY27 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(65,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( ~ ! [SY28: $i] :
( ~ ( member @ SY28 @ SV4 )
| ( member @ SY28 @ SV8 ) )
| ( subset @ SV4 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ~ ( ~ ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
| ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) )
| ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ~ ( ~ ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
| ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) )
| ( member @ SV2 @ ( difference @ SV10 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( equal_set @ SV3 @ SV7 )
| ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(70,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) )
| ( equal_set @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(71,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( subset @ SV4 @ SV8 )
| ! [SY27: $i] :
( ~ ( member @ SY27 @ SV4 )
| ( member @ SY27 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(72,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ! [SY28: $i] :
( ~ ( member @ SY28 @ SV4 )
| ( member @ SY28 @ SV8 ) )
| ( subset @ SV4 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(73,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ~ ( ~ ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
| ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) )
| ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(75,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ~ ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
| ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(76,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ~ ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) )
| ( member @ SV2 @ ( difference @ SV10 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( equal_set @ SV3 @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) ) )
= $true )
| ( ( equal_set @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV8 ) )
= $true )
| ( ( ! [SY27: $i] :
( ~ ( member @ SY27 @ SV4 )
| ( member @ SY27 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ! [SY28: $i] :
( ~ ( member @ SY28 @ SV4 )
| ( member @ SY28 @ SV8 ) ) )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
| ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(82,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ~ ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) )
| ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(83,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ ( difference @ SV10 @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV7: $i,SV3: $i] :
( ( ( equal_set @ SV3 @ SV7 )
= $false )
| ( ( ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) ) )
= $false )
| ( ( equal_set @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV8: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV8 )
= $false )
| ( ( ! [SY27: $i] :
( ~ ( member @ SY27 @ SV4 )
| ( member @ SY27 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV8: $i,SV4: $i] :
( ( ( ! [SY28: $i] :
( ~ ( member @ SY28 @ SV4 )
| ( member @ SY28 @ SV8 ) ) )
= $false )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) ) )
= $true )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( ~ ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) ) )
= $false )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) )
= $false )
| ( ( equal_set @ SV3 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV7 )
| ~ ( subset @ SV7 @ SV3 ) )
= $true )
| ( ( equal_set @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(95,plain,
! [SV8: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ SV4 )
| ( member @ SV12 @ SV8 ) )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( member @ ( sK4_SY28 @ SV8 @ SV4 ) @ SV4 )
| ( member @ ( sK4_SY28 @ SV8 @ SV4 ) @ SV8 ) )
= $false )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(97,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) ) )
= $false )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) )
= $false )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV10 )
| ~ ~ ( member @ SV2 @ SV6 ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(101,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV7 ) )
= $false )
| ( ( equal_set @ SV3 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(102,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV3 ) )
= $false )
| ( ( equal_set @ SV3 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(103,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV7 ) )
= $true )
| ( ( ~ ( subset @ SV7 @ SV3 ) )
= $true )
| ( ( equal_set @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV8: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ SV4 ) )
= $true )
| ( ( member @ SV12 @ SV8 )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( member @ ( sK4_SY28 @ SV8 @ SV4 ) @ SV4 ) )
= $false )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(106,plain,
! [SV4: $i,SV8: $i] :
( ( ( member @ ( sK4_SY28 @ SV8 @ SV4 ) @ SV8 )
= $false )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(107,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) )
= $false )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV9 )
| ~ ( member @ SV5 @ SV11 ) )
= $true )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(109,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV10 ) )
= $false )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(110,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( member @ SV2 @ SV6 ) )
= $false )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(111,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV10 ) )
= $true )
| ( ( ~ ~ ( member @ SV2 @ SV6 ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV7: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV7 )
= $true )
| ( ( equal_set @ SV3 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(113,plain,
! [SV3: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV3 )
= $true )
| ( ( equal_set @ SV3 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(114,plain,
! [SV7: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV7 )
= $false )
| ( ( ~ ( subset @ SV7 @ SV3 ) )
= $true )
| ( ( equal_set @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV8: $i,SV4: $i,SV12: $i] :
( ( ( member @ SV12 @ SV4 )
= $false )
| ( ( member @ SV12 @ SV8 )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV4: $i,SV8: $i] :
( ( ( member @ ( sK4_SY28 @ SV8 @ SV4 ) @ SV4 )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(117,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV9 ) )
= $false )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(118,plain,
! [SV9: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV11 ) )
= $false )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(119,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV9 ) )
= $true )
| ( ( ~ ( member @ SV5 @ SV11 ) )
= $true )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( member @ SV2 @ SV10 )
= $true )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(121,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV6 ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(122,plain,
! [SV6: $i,SV10: $i,SV2: $i] :
( ( ( member @ SV2 @ SV10 )
= $false )
| ( ( ~ ~ ( member @ SV2 @ SV6 ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV3: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV3 )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $false )
| ( ( equal_set @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(124,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( member @ SV5 @ SV9 )
= $true )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(125,plain,
! [SV9: $i,SV11: $i,SV5: $i] :
( ( ( member @ SV5 @ SV11 )
= $true )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(126,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( member @ SV5 @ SV9 )
= $false )
| ( ( ~ ( member @ SV5 @ SV11 ) )
= $true )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(127,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( member @ SV2 @ SV6 )
= $false )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV6 ) )
= $false )
| ( ( member @ SV2 @ SV10 )
= $false )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV9: $i,SV11: $i,SV5: $i] :
( ( ( member @ SV5 @ SV11 )
= $false )
| ( ( member @ SV5 @ SV9 )
= $false )
| ( ( member @ SV5 @ ( intersection @ SV9 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(130,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( member @ SV2 @ SV6 )
= $true )
| ( ( member @ SV2 @ SV10 )
= $false )
| ( ( member @ SV2 @ ( difference @ SV10 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(131,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,130,129,127,125,124,123,120,116,115,113,112,106,56,51,49,36]) ).
thf(132,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(133,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(134,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(135,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(136,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(137,plain,
( ( subset @ sK2_SY15 @ sK3_SY17 )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(138,plain,
( ( subset @ sK1_A @ sK3_SY17 )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(139,plain,
( ( ~ ( ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set )
=> ( subset @ sK1_A @ sK2_SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(140,plain,
( ( ~ ( ~ ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set )
| ( subset @ sK1_A @ sK2_SY15 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(142,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ~ ( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_set @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( equal_set @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(144,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(145,plain,
! [SV13: $i] :
( ( ~ ( member @ SV13 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(146,plain,
( ( ~ ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set )
| ( subset @ sK1_A @ sK2_SY15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(147,plain,
! [SV14: $i] :
( ( ! [SY30: $i] :
~ ( ~ ( ~ ( subset @ SV14 @ SY30 )
| ! [SY31: $i] :
( ~ ( member @ SY31 @ SV14 )
| ( member @ SY31 @ SY30 ) ) )
| ~ ( ~ ! [SY32: $i] :
( ~ ( member @ SY32 @ SV14 )
| ( member @ SY32 @ SY30 ) )
| ( subset @ SV14 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(148,plain,
! [SV15: $i] :
( ( ! [SY33: $i,SY34: $i] :
~ ( ~ ( ~ ( member @ SV15 @ ( intersection @ SY33 @ SY34 ) )
| ~ ( ~ ( member @ SV15 @ SY33 )
| ~ ( member @ SV15 @ SY34 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV15 @ SY33 )
| ~ ( member @ SV15 @ SY34 ) )
| ( member @ SV15 @ ( intersection @ SY33 @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(149,plain,
! [SV16: $i] :
( ( ! [SY35: $i] :
~ ( ~ ( ~ ( equal_set @ SV16 @ SY35 )
| ~ ( ~ ( subset @ SV16 @ SY35 )
| ~ ( subset @ SY35 @ SV16 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV16 @ SY35 )
| ~ ( subset @ SY35 @ SV16 ) )
| ( equal_set @ SV16 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(150,plain,
! [SV17: $i] :
( ( ! [SY36: $i,SY37: $i] :
~ ( ~ ( ~ ( member @ SV17 @ ( difference @ SY37 @ SY36 ) )
| ~ ( ~ ( member @ SV17 @ SY37 )
| ~ ~ ( member @ SV17 @ SY36 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV17 @ SY37 )
| ~ ~ ( member @ SV17 @ SY36 ) )
| ( member @ SV17 @ ( difference @ SY37 @ SY36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(151,plain,
! [SV13: $i] :
( ( member @ SV13 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(152,plain,
( ( ~ ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(153,plain,
( ( subset @ sK1_A @ sK2_SY15 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(154,plain,
! [SV18: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV14 @ SV18 )
| ! [SY38: $i] :
( ~ ( member @ SY38 @ SV14 )
| ( member @ SY38 @ SV18 ) ) )
| ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV14 )
| ( member @ SY39 @ SV18 ) )
| ( subset @ SV14 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(155,plain,
! [SV19: $i,SV15: $i] :
( ( ! [SY40: $i] :
~ ( ~ ( ~ ( member @ SV15 @ ( intersection @ SV19 @ SY40 ) )
| ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SY40 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SY40 ) )
| ( member @ SV15 @ ( intersection @ SV19 @ SY40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(156,plain,
! [SV20: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV16 @ SV20 )
| ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) )
| ( equal_set @ SV16 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV21: $i,SV17: $i] :
( ( ! [SY41: $i] :
~ ( ~ ( ~ ( member @ SV17 @ ( difference @ SY41 @ SV21 ) )
| ~ ( ~ ( member @ SV17 @ SY41 )
| ~ ~ ( member @ SV17 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV17 @ SY41 )
| ~ ~ ( member @ SV17 @ SV21 ) )
| ( member @ SV17 @ ( difference @ SY41 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(158,plain,
( ( equal_set @ ( intersection @ sK1_A @ ( difference @ sK3_SY17 @ sK2_SY15 ) ) @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(159,plain,
! [SV18: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV18 )
| ! [SY38: $i] :
( ~ ( member @ SY38 @ SV14 )
| ( member @ SY38 @ SV18 ) ) )
| ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV14 )
| ( member @ SY39 @ SV18 ) )
| ( subset @ SV14 @ SV18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(160,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
| ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) )
| ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(161,plain,
! [SV20: $i,SV16: $i] :
( ( ~ ( ~ ( equal_set @ SV16 @ SV20 )
| ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) )
| ( equal_set @ SV16 @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(162,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ~ ( ~ ( ~ ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
| ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) )
| ( member @ SV17 @ ( difference @ SV23 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(163,plain,
! [SV18: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV18 )
| ! [SY38: $i] :
( ~ ( member @ SY38 @ SV14 )
| ( member @ SY38 @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(164,plain,
! [SV18: $i,SV14: $i] :
( ( ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV14 )
| ( member @ SY39 @ SV18 ) )
| ( subset @ SV14 @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(165,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ~ ( ~ ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
| ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) )
| ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(166,plain,
! [SV20: $i,SV16: $i] :
( ( ~ ( ~ ( equal_set @ SV16 @ SV20 )
| ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(167,plain,
! [SV20: $i,SV16: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) )
| ( equal_set @ SV16 @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(168,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ~ ( ~ ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
| ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) )
| ( member @ SV17 @ ( difference @ SV23 @ SV21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(169,plain,
! [SV18: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV18 )
| ! [SY38: $i] :
( ~ ( member @ SY38 @ SV14 )
| ( member @ SY38 @ SV18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(170,plain,
! [SV18: $i,SV14: $i] :
( ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV14 )
| ( member @ SY39 @ SV18 ) )
| ( subset @ SV14 @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(171,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ~ ( ~ ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
| ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(172,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) )
| ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(173,plain,
! [SV20: $i,SV16: $i] :
( ( ~ ( equal_set @ SV16 @ SV20 )
| ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(174,plain,
! [SV20: $i,SV16: $i] :
( ( ~ ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) )
| ( equal_set @ SV16 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(175,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ~ ( ~ ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
| ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(176,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) )
| ( member @ SV17 @ ( difference @ SV23 @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(177,plain,
! [SV18: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV18 ) )
= $true )
| ( ( ! [SY38: $i] :
( ~ ( member @ SY38 @ SV14 )
| ( member @ SY38 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV18: $i,SV14: $i] :
( ( ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV14 )
| ( member @ SY39 @ SV18 ) ) )
= $true )
| ( ( subset @ SV14 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
| ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(180,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ~ ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) )
| ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(181,plain,
! [SV20: $i,SV16: $i] :
( ( ( ~ ( equal_set @ SV16 @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV20: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) ) )
= $true )
| ( ( equal_set @ SV16 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(183,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ~ ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
| ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(184,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ~ ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) )
| ( member @ SV17 @ ( difference @ SV23 @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(185,plain,
! [SV18: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV18 )
= $false )
| ( ( ! [SY38: $i] :
( ~ ( member @ SY38 @ SV14 )
| ( member @ SY38 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV18: $i,SV14: $i] :
( ( ( ! [SY39: $i] :
( ~ ( member @ SY39 @ SV14 )
| ( member @ SY39 @ SV18 ) ) )
= $false )
| ( ( subset @ SV14 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(187,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) ) )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(189,plain,
! [SV20: $i,SV16: $i] :
( ( ( equal_set @ SV16 @ SV20 )
= $false )
| ( ( ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV20: $i,SV16: $i] :
( ( ( ~ ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) ) )
= $false )
| ( ( equal_set @ SV16 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ ( difference @ SV23 @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) ) )
= $true )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV18: $i,SV14: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV14 )
| ( member @ SV24 @ SV18 ) )
= $true )
| ( ( subset @ SV14 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV14: $i,SV18: $i] :
( ( ( ~ ( member @ ( sK5_SY39 @ SV18 @ SV14 ) @ SV14 )
| ( member @ ( sK5_SY39 @ SV18 @ SV14 ) @ SV18 ) )
= $false )
| ( ( subset @ SV14 @ SV18 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[186]) ).
thf(195,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( ~ ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) ) )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(197,plain,
! [SV20: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) )
= $false )
| ( ( equal_set @ SV16 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(198,plain,
! [SV20: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV20 )
| ~ ( subset @ SV20 @ SV16 ) )
= $true )
| ( ( equal_set @ SV16 @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(199,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(200,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) ) )
= $false )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV18: $i,SV14: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV14 ) )
= $true )
| ( ( member @ SV24 @ SV18 )
= $true )
| ( ( subset @ SV14 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV14: $i,SV18: $i] :
( ( ( ~ ( member @ ( sK5_SY39 @ SV18 @ SV14 ) @ SV14 ) )
= $false )
| ( ( subset @ SV14 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(203,plain,
! [SV14: $i,SV18: $i] :
( ( ( member @ ( sK5_SY39 @ SV18 @ SV14 ) @ SV18 )
= $false )
| ( ( subset @ SV14 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(204,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(205,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV19 )
| ~ ( member @ SV15 @ SV22 ) )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(206,plain,
! [SV20: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV20 ) )
= $false )
| ( ( equal_set @ SV16 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(207,plain,
! [SV16: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV16 ) )
= $false )
| ( ( equal_set @ SV16 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(208,plain,
! [SV20: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV20 ) )
= $true )
| ( ( ~ ( subset @ SV20 @ SV16 ) )
= $true )
| ( ( equal_set @ SV16 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(209,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) )
= $false )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(210,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV23 )
| ~ ~ ( member @ SV17 @ SV21 ) )
= $true )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(211,plain,
! [SV18: $i,SV14: $i,SV24: $i] :
( ( ( member @ SV24 @ SV14 )
= $false )
| ( ( member @ SV24 @ SV18 )
= $true )
| ( ( subset @ SV14 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(212,plain,
! [SV14: $i,SV18: $i] :
( ( ( member @ ( sK5_SY39 @ SV18 @ SV14 ) @ SV14 )
= $true )
| ( ( subset @ SV14 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(213,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV19 ) )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(214,plain,
! [SV19: $i,SV22: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV22 ) )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(215,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV19 ) )
= $true )
| ( ( ~ ( member @ SV15 @ SV22 ) )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(216,plain,
! [SV20: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV20 )
= $true )
| ( ( equal_set @ SV16 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(217,plain,
! [SV16: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV16 )
= $true )
| ( ( equal_set @ SV16 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(218,plain,
! [SV20: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV20 )
= $false )
| ( ( ~ ( subset @ SV20 @ SV16 ) )
= $true )
| ( ( equal_set @ SV16 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(219,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV23 ) )
= $false )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(220,plain,
! [SV23: $i,SV21: $i,SV17: $i] :
( ( ( ~ ~ ( member @ SV17 @ SV21 ) )
= $false )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(221,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV23 ) )
= $true )
| ( ( ~ ~ ( member @ SV17 @ SV21 ) )
= $true )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(222,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( member @ SV15 @ SV19 )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(223,plain,
! [SV19: $i,SV22: $i,SV15: $i] :
( ( ( member @ SV15 @ SV22 )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(224,plain,
! [SV22: $i,SV19: $i,SV15: $i] :
( ( ( member @ SV15 @ SV19 )
= $false )
| ( ( ~ ( member @ SV15 @ SV22 ) )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(225,plain,
! [SV16: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV16 )
= $false )
| ( ( subset @ SV16 @ SV20 )
= $false )
| ( ( equal_set @ SV16 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(226,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( member @ SV17 @ SV23 )
= $true )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(227,plain,
! [SV23: $i,SV21: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV21 ) )
= $true )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(228,plain,
! [SV21: $i,SV23: $i,SV17: $i] :
( ( ( member @ SV17 @ SV23 )
= $false )
| ( ( ~ ~ ( member @ SV17 @ SV21 ) )
= $true )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(229,plain,
! [SV19: $i,SV22: $i,SV15: $i] :
( ( ( member @ SV15 @ SV22 )
= $false )
| ( ( member @ SV15 @ SV19 )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV19 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(230,plain,
! [SV23: $i,SV21: $i,SV17: $i] :
( ( ( member @ SV17 @ SV21 )
= $false )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(231,plain,
! [SV23: $i,SV21: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV21 ) )
= $false )
| ( ( member @ SV17 @ SV23 )
= $false )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(232,plain,
! [SV23: $i,SV21: $i,SV17: $i] :
( ( ( member @ SV17 @ SV21 )
= $true )
| ( ( member @ SV17 @ SV23 )
= $false )
| ( ( member @ SV17 @ ( difference @ SV23 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(233,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[137,232,230,229,226,225,223,222,217,216,212,211,203,158,153,151,138]) ).
thf(234,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[233,131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET697+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 14:50:54 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.44
% 0.48/0.44 No.of.Axioms: 5
% 0.48/0.44
% 0.48/0.44 Length.of.Defs: 0
% 0.48/0.44
% 0.48/0.44 Contains.Choice.Funs: false
% 0.48/0.44 ......
% 0.48/0.44
% 0.48/0.44 ********************************
% 0.48/0.44 * All subproblems solved! *
% 0.48/0.44 ********************************
% 0.48/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:233,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.48/0.44
% 0.48/0.44 %**** Beginning of derivation protocol ****
% 0.48/0.44 % SZS output start CNFRefutation
% See solution above
% 0.48/0.45
% 0.48/0.45 %**** End of derivation protocol ****
% 0.48/0.45 %**** no. of clauses in derivation: 228 ****
% 0.48/0.45 %**** clause counter: 233 ****
% 0.48/0.45
% 0.48/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:233,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------