%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET014+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 10:38:53 AM UTC 2026
% Result : Theorem 2.81s 0.66s
% Output : CNFRefutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 158 ( 89 unt; 0 typ; 0 def)
% Number of atoms : 966 ( 230 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 1872 ( 368 ~; 304 |; 16 &;1156 @)
% ( 18 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 338 ( 0 ^; 338 !; 0 ?; 338 :)
% 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_SY11,type,
sK2_SY11: $i ).
thf(tp_sK3_SY13,type,
sK3_SY13: $i ).
thf(tp_sK4_SY22,type,
sK4_SY22: $i > $i > $i ).
thf(tp_sK5_SY31,type,
sK5_SY31: $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(7,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',subset) ).
thf(12,conjecture,
! [A: $i,X: $i,Y: $i] :
( ( ( subset @ X @ A )
& ( subset @ Y @ A ) )
<=> ( subset @ ( union @ X @ Y ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI45) ).
thf(13,negated_conjecture,
( ( ! [A: $i,X: $i,Y: $i] :
( ( ( subset @ X @ A )
& ( subset @ Y @ A ) )
<=> ( subset @ ( union @ X @ Y ) @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,X: $i,Y: $i] :
( ( ( subset @ X @ A )
& ( subset @ Y @ A ) )
<=> ( subset @ ( union @ X @ Y ) @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [SY11: $i,SY12: $i] :
( ( ( subset @ SY11 @ sK1_A )
& ( subset @ SY12 @ sK1_A ) )
<=> ( subset @ ( union @ SY11 @ SY12 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(19,plain,
( ( ! [SY13: $i] :
( ( ( subset @ sK2_SY11 @ sK1_A )
& ( subset @ SY13 @ sK1_A ) )
<=> ( subset @ ( union @ sK2_SY11 @ SY13 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( ( ( subset @ sK2_SY11 @ sK1_A )
& ( subset @ sK3_SY13 @ sK1_A ) )
<=> ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(21,plain,
( ( ( ( subset @ sK2_SY11 @ sK1_A )
& ( subset @ sK3_SY13 @ sK1_A ) )
=> ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[20]) ).
thf(22,plain,
( ( ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A )
=> ( ( subset @ sK2_SY11 @ sK1_A )
& ( subset @ sK3_SY13 @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[20]) ).
thf(23,plain,
( ( ~ ( ( ( subset @ sK2_SY11 @ sK1_A )
& ( subset @ sK3_SY13 @ sK1_A ) )
=> ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A )
=> ( ( subset @ sK2_SY11 @ sK1_A )
& ( subset @ sK3_SY13 @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(28,plain,
( ( ~ ( ( ( subset @ sK2_SY11 @ sK1_A )
& ( subset @ sK3_SY13 @ sK1_A ) )
=> ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(29,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)],[26]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ~ ( ~ ( ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(31,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)],[25]) ).
thf(32,plain,
( ( ~ ( ~ ~ ( ~ ( subset @ sK2_SY11 @ sK1_A )
| ~ ( subset @ sK3_SY13 @ sK1_A ) )
| ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(33,plain,
! [SV1: $i] :
( ( ! [SY14: $i] :
~ ( ~ ( ~ ( equal_set @ SV1 @ SY14 )
| ~ ( ~ ( subset @ SV1 @ SY14 )
| ~ ( subset @ SY14 @ SV1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV1 @ SY14 )
| ~ ( subset @ SY14 @ SV1 ) )
| ( equal_set @ SV1 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i] :
( ( ! [SY15: $i,SY16: $i] :
~ ( ~ ( ~ ( member @ SV2 @ ( union @ SY15 @ SY16 ) )
| ( member @ SV2 @ SY15 )
| ( member @ SV2 @ SY16 ) )
| ~ ( ~ ( ( member @ SV2 @ SY15 )
| ( member @ SV2 @ SY16 ) )
| ( member @ SV2 @ ( union @ SY15 @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i] :
( ( ! [SY17: $i] :
~ ( ~ ( ~ ( subset @ SV3 @ SY17 )
| ! [SY18: $i] :
( ~ ( member @ SY18 @ SV3 )
| ( member @ SY18 @ SY17 ) ) )
| ~ ( ~ ! [SY19: $i] :
( ~ ( member @ SY19 @ SV3 )
| ( member @ SY19 @ SY17 ) )
| ( subset @ SV3 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ~ ( ~ ( subset @ sK2_SY11 @ sK1_A )
| ~ ( subset @ sK3_SY13 @ sK1_A ) )
| ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV1 @ SV4 )
| ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
| ( equal_set @ SV1 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY20: $i] :
~ ( ~ ( ~ ( member @ SV2 @ ( union @ SV5 @ SY20 ) )
| ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SY20 ) )
| ~ ( ~ ( ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SY20 ) )
| ( member @ SV2 @ ( union @ SV5 @ SY20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV3 @ SV6 )
| ! [SY21: $i] :
( ~ ( member @ SY21 @ SV3 )
| ( member @ SY21 @ SV6 ) ) )
| ~ ( ~ ! [SY22: $i] :
( ~ ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SV6 ) )
| ( subset @ SV3 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ~ ( ~ ( subset @ sK2_SY11 @ sK1_A )
| ~ ( subset @ sK3_SY13 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
( ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ( equal_set @ SV1 @ SV4 )
| ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
| ( equal_set @ SV1 @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
| ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
| ~ ( ~ ( ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
| ( member @ SV2 @ ( union @ SV5 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( subset @ SV3 @ SV6 )
| ! [SY21: $i] :
( ~ ( member @ SY21 @ SV3 )
| ( member @ SY21 @ SV6 ) ) )
| ~ ( ~ ! [SY22: $i] :
( ~ ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SV6 ) )
| ( subset @ SV3 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ( ~ ( subset @ sK2_SY11 @ sK1_A )
| ~ ( subset @ sK3_SY13 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ( equal_set @ SV1 @ SV4 )
| ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
| ( equal_set @ SV1 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
| ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
| ~ ( ~ ( ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
| ( member @ SV2 @ ( union @ SV5 @ SV7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( subset @ SV3 @ SV6 )
| ! [SY21: $i] :
( ~ ( member @ SY21 @ SV3 )
| ( member @ SY21 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ! [SY22: $i] :
( ~ ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SV6 ) )
| ( subset @ SV3 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(51,plain,
( ( ~ ( subset @ sK2_SY11 @ sK1_A )
| ~ ( subset @ sK3_SY13 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( equal_set @ SV1 @ SV4 )
| ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
| ( equal_set @ SV1 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(54,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
| ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(55,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
| ( member @ SV2 @ ( union @ SV5 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(56,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV6 )
| ! [SY21: $i] :
( ~ ( member @ SY21 @ SV3 )
| ( member @ SY21 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(57,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ! [SY22: $i] :
( ~ ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SV6 ) )
| ( subset @ SV3 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(58,plain,
( ( ~ ( subset @ sK2_SY11 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(59,plain,
( ( ~ ( subset @ sK3_SY13 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(60,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( equal_set @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
| ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(63,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
| ( member @ SV2 @ ( union @ SV5 @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(64,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY21: $i] :
( ~ ( member @ SY21 @ SV3 )
| ( member @ SY21 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ! [SY22: $i] :
( ~ ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SV6 ) ) )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(66,plain,
( ( subset @ sK2_SY11 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(67,plain,
( ( subset @ sK3_SY13 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(68,plain,
! [SV4: $i,SV1: $i] :
( ( ( equal_set @ SV1 @ SV4 )
= $false )
| ( ( ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ ( union @ SV5 @ SV7 ) ) )
= $true )
| ( ( ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) ) )
= $true )
| ( ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV6: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV6 )
= $false )
| ( ( ! [SY21: $i] :
( ~ ( member @ SY21 @ SV3 )
| ( member @ SY21 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV6: $i,SV3: $i] :
( ( ( ! [SY22: $i] :
( ~ ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SV6 ) ) )
= $false )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(76,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
= $false )
| ( ( ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ( member @ SV2 @ SV5 )
| ( member @ SV2 @ SV7 ) )
= $false )
| ( ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV3 )
| ( member @ SV8 @ SV6 ) )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK4_SY22 @ SV6 @ SV3 ) @ SV3 )
| ( member @ ( sK4_SY22 @ SV6 @ SV3 ) @ SV6 ) )
= $false )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(80,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV4 ) )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(81,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV1 ) )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(82,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ( subset @ SV4 @ SV1 ) )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( member @ SV2 @ SV5 )
= $true )
| ( ( member @ SV2 @ SV7 )
= $true )
| ( ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( member @ SV2 @ SV5 )
= $false )
| ( ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(85,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( member @ SV2 @ SV7 )
= $false )
| ( ( member @ SV2 @ ( union @ SV5 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(86,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV3 ) )
= $true )
| ( ( member @ SV8 @ SV6 )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK4_SY22 @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(88,plain,
! [SV3: $i,SV6: $i] :
( ( ( member @ ( sK4_SY22 @ SV6 @ SV3 ) @ SV6 )
= $false )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(89,plain,
! [SV4: $i,SV1: $i] :
( ( ( subset @ SV1 @ SV4 )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(90,plain,
! [SV1: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV1 )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(91,plain,
! [SV4: $i,SV1: $i] :
( ( ( subset @ SV1 @ SV4 )
= $false )
| ( ( ~ ( subset @ SV4 @ SV1 ) )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( member @ SV8 @ SV3 )
= $false )
| ( ( member @ SV8 @ SV6 )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV3: $i,SV6: $i] :
( ( ( member @ ( sK4_SY22 @ SV6 @ SV3 ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(94,plain,
! [SV1: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV1 @ SV4 )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,94,93,92,90,89,88,85,84,83,67,66]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(98,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(99,plain,
( ( ~ ( ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A )
=> ( ( subset @ sK2_SY11 @ sK1_A )
& ( subset @ sK3_SY13 @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(100,plain,
( ( ~ ( ~ ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A )
| ~ ( ~ ( subset @ sK2_SY11 @ sK1_A )
| ~ ( subset @ sK3_SY13 @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(101,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)],[97]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ~ ( ~ ( ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(103,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)],[96]) ).
thf(104,plain,
( ( ~ ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A )
| ~ ( ~ ( subset @ sK2_SY11 @ sK1_A )
| ~ ( subset @ sK3_SY13 @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV9: $i] :
( ( ! [SY23: $i] :
~ ( ~ ( ~ ( equal_set @ SV9 @ SY23 )
| ~ ( ~ ( subset @ SV9 @ SY23 )
| ~ ( subset @ SY23 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV9 @ SY23 )
| ~ ( subset @ SY23 @ SV9 ) )
| ( equal_set @ SV9 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV10: $i] :
( ( ! [SY24: $i,SY25: $i] :
~ ( ~ ( ~ ( member @ SV10 @ ( union @ SY24 @ SY25 ) )
| ( member @ SV10 @ SY24 )
| ( member @ SV10 @ SY25 ) )
| ~ ( ~ ( ( member @ SV10 @ SY24 )
| ( member @ SV10 @ SY25 ) )
| ( member @ SV10 @ ( union @ SY24 @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV11: $i] :
( ( ! [SY26: $i] :
~ ( ~ ( ~ ( subset @ SV11 @ SY26 )
| ! [SY27: $i] :
( ~ ( member @ SY27 @ SV11 )
| ( member @ SY27 @ SY26 ) ) )
| ~ ( ~ ! [SY28: $i] :
( ~ ( member @ SY28 @ SV11 )
| ( member @ SY28 @ SY26 ) )
| ( subset @ SV11 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(108,plain,
( ( ~ ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(109,plain,
( ( ~ ( ~ ( subset @ sK2_SY11 @ sK1_A )
| ~ ( subset @ sK3_SY13 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(110,plain,
! [SV12: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV9 @ SV12 )
| ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) )
| ( equal_set @ SV9 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV13: $i,SV10: $i] :
( ( ! [SY29: $i] :
~ ( ~ ( ~ ( member @ SV10 @ ( union @ SV13 @ SY29 ) )
| ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SY29 ) )
| ~ ( ~ ( ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SY29 ) )
| ( member @ SV10 @ ( union @ SV13 @ SY29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV14: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV11 @ SV14 )
| ! [SY30: $i] :
( ~ ( member @ SY30 @ SV11 )
| ( member @ SY30 @ SV14 ) ) )
| ~ ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV11 )
| ( member @ SY31 @ SV14 ) )
| ( subset @ SV11 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(113,plain,
( ( subset @ ( union @ sK2_SY11 @ sK3_SY13 ) @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(114,plain,
( ( ~ ( subset @ sK2_SY11 @ sK1_A )
| ~ ( subset @ sK3_SY13 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(115,plain,
! [SV12: $i,SV9: $i] :
( ( ~ ( ~ ( equal_set @ SV9 @ SV12 )
| ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) )
| ( equal_set @ SV9 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
| ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
| ~ ( ~ ( ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
| ( member @ SV10 @ ( union @ SV13 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV14: $i,SV11: $i] :
( ( ~ ( ~ ( subset @ SV11 @ SV14 )
| ! [SY30: $i] :
( ~ ( member @ SY30 @ SV11 )
| ( member @ SY30 @ SV14 ) ) )
| ~ ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV11 )
| ( member @ SY31 @ SV14 ) )
| ( subset @ SV11 @ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(118,plain,
( ( ( ~ ( subset @ sK2_SY11 @ sK1_A ) )
= $true )
| ( ( ~ ( subset @ sK3_SY13 @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV12: $i,SV9: $i] :
( ( ~ ( ~ ( equal_set @ SV9 @ SV12 )
| ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(120,plain,
! [SV12: $i,SV9: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) )
| ( equal_set @ SV9 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(121,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
| ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
| ~ ( ~ ( ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
| ( member @ SV10 @ ( union @ SV13 @ SV15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(122,plain,
! [SV14: $i,SV11: $i] :
( ( ~ ( ~ ( subset @ SV11 @ SV14 )
| ! [SY30: $i] :
( ~ ( member @ SY30 @ SV11 )
| ( member @ SY30 @ SV14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(123,plain,
! [SV14: $i,SV11: $i] :
( ( ~ ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV11 )
| ( member @ SY31 @ SV14 ) )
| ( subset @ SV11 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(124,plain,
( ( ( subset @ sK2_SY11 @ sK1_A )
= $false )
| ( ( ~ ( subset @ sK3_SY13 @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV12: $i,SV9: $i] :
( ( ~ ( equal_set @ SV9 @ SV12 )
| ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(126,plain,
! [SV12: $i,SV9: $i] :
( ( ~ ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) )
| ( equal_set @ SV9 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(127,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
| ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(128,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ~ ( ~ ( ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
| ( member @ SV10 @ ( union @ SV13 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(129,plain,
! [SV14: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ SV14 )
| ! [SY30: $i] :
( ~ ( member @ SY30 @ SV11 )
| ( member @ SY30 @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(130,plain,
! [SV14: $i,SV11: $i] :
( ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV11 )
| ( member @ SY31 @ SV14 ) )
| ( subset @ SV11 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(131,plain,
( ( ( subset @ sK3_SY13 @ sK1_A )
= $false )
| ( ( subset @ sK2_SY11 @ sK1_A )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV12: $i,SV9: $i] :
( ( ( ~ ( equal_set @ SV9 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV12: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) ) )
= $true )
| ( ( equal_set @ SV9 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ~ ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
| ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(135,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ~ ( ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
| ( member @ SV10 @ ( union @ SV13 @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(136,plain,
! [SV14: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV14 ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( member @ SY30 @ SV11 )
| ( member @ SY30 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV14: $i,SV11: $i] :
( ( ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV11 )
| ( member @ SY31 @ SV14 ) ) )
= $true )
| ( ( subset @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(138,plain,
! [SV12: $i,SV9: $i] :
( ( ( equal_set @ SV9 @ SV12 )
= $false )
| ( ( ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV12: $i,SV9: $i] :
( ( ( ~ ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) ) )
= $false )
| ( ( equal_set @ SV9 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( union @ SV13 @ SV15 ) ) )
= $true )
| ( ( ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) ) )
= $true )
| ( ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(142,plain,
! [SV14: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV14 )
= $false )
| ( ( ! [SY30: $i] :
( ~ ( member @ SY30 @ SV11 )
| ( member @ SY30 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(143,plain,
! [SV14: $i,SV11: $i] :
( ( ( ! [SY31: $i] :
( ~ ( member @ SY31 @ SV11 )
| ( member @ SY31 @ SV14 ) ) )
= $false )
| ( ( subset @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(144,plain,
! [SV12: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) )
= $false )
| ( ( equal_set @ SV9 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(145,plain,
! [SV12: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV12 )
| ~ ( subset @ SV12 @ SV9 ) )
= $true )
| ( ( equal_set @ SV9 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(146,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
= $false )
| ( ( ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(147,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ( ( member @ SV10 @ SV13 )
| ( member @ SV10 @ SV15 ) )
= $false )
| ( ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(148,plain,
! [SV14: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV11 )
| ( member @ SV16 @ SV14 ) )
= $true )
| ( ( subset @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(149,plain,
! [SV11: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK5_SY31 @ SV14 @ SV11 ) @ SV11 )
| ( member @ ( sK5_SY31 @ SV14 @ SV11 ) @ SV14 ) )
= $false )
| ( ( subset @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[143]) ).
thf(150,plain,
! [SV12: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV12 ) )
= $false )
| ( ( equal_set @ SV9 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(151,plain,
! [SV9: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV9 ) )
= $false )
| ( ( equal_set @ SV9 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(152,plain,
! [SV12: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV12 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ SV9 ) )
= $true )
| ( ( equal_set @ SV9 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ( member @ SV10 @ SV13 )
= $true )
| ( ( member @ SV10 @ SV15 )
= $true )
| ( ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(154,plain,
! [SV15: $i,SV13: $i,SV10: $i] :
( ( ( member @ SV10 @ SV13 )
= $false )
| ( ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(155,plain,
! [SV13: $i,SV15: $i,SV10: $i] :
( ( ( member @ SV10 @ SV15 )
= $false )
| ( ( member @ SV10 @ ( union @ SV13 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(156,plain,
! [SV14: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV11 ) )
= $true )
| ( ( member @ SV16 @ SV14 )
= $true )
| ( ( subset @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(157,plain,
! [SV11: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK5_SY31 @ SV14 @ SV11 ) @ SV11 ) )
= $false )
| ( ( subset @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(158,plain,
! [SV11: $i,SV14: $i] :
( ( ( member @ ( sK5_SY31 @ SV14 @ SV11 ) @ SV14 )
= $false )
| ( ( subset @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(159,plain,
! [SV12: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV12 )
= $true )
| ( ( equal_set @ SV9 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(160,plain,
! [SV9: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV9 )
= $true )
| ( ( equal_set @ SV9 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(161,plain,
! [SV12: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV12 )
= $false )
| ( ( ~ ( subset @ SV12 @ SV9 ) )
= $true )
| ( ( equal_set @ SV9 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV14: $i,SV11: $i,SV16: $i] :
( ( ( member @ SV16 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV14 )
= $true )
| ( ( subset @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(163,plain,
! [SV11: $i,SV14: $i] :
( ( ( member @ ( sK5_SY31 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( subset @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(164,plain,
! [SV9: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV9 )
= $false )
| ( ( subset @ SV9 @ SV12 )
= $false )
| ( ( equal_set @ SV9 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(165,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[113,164,163,162,160,159,158,155,154,153,131]) ).
thf(166,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[165,95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET014+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n018.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 14:28:37 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.81/0.66
% 2.81/0.66 No.of.Axioms: 3
% 2.81/0.66
% 2.81/0.66 Length.of.Defs: 0
% 2.81/0.66
% 2.81/0.66 Contains.Choice.Funs: false
% 2.81/0.66 ....
% 2.81/0.66
% 2.81/0.66 ********************************
% 2.81/0.66 * All subproblems solved! *
% 2.81/0.66 ********************************
% 2.81/0.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:165,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.81/0.66
% 2.81/0.66 %**** Beginning of derivation protocol ****
% 2.81/0.66 % SZS output start CNFRefutation
% See solution above
% 2.81/0.67
% 2.81/0.67 %**** End of derivation protocol ****
% 2.81/0.67 %**** no. of clauses in derivation: 158 ****
% 2.81/0.67 %**** clause counter: 165 ****
% 2.81/0.67
% 2.81/0.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:165,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------