%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n020.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 10:33:34 AM UTC 2026
% Result : Theorem 5.15s 1.06s
% Output : CNFRefutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 289 ( 119 unt; 0 typ; 0 def)
% Number of atoms : 2275 ( 906 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 4320 ( 746 ~; 855 |; 4 &;2676 @)
% ( 21 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 743 ( 0 ^; 743 !; 0 ?; 743 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_non_empty,type,
relation_non_empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i ).
thf(tp_sK3_SY32,type,
sK3_SY32: $i > $i > $i ).
thf(tp_sK4_SY37,type,
sK4_SY37: $i > $i > $i > $i ).
thf(tp_sK5_SY50,type,
sK5_SY50: $i > $i > $i ).
thf(tp_sK6_SY55,type,
sK6_SY55: $i > $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(23,axiom,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(28,axiom,
! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(34,conjecture,
! [A: $i,B: $i] :
( ( in @ A @ ( succ @ B ) )
<=> ( ( in @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_ordinal1) ).
thf(35,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( in @ A @ ( succ @ B ) )
<=> ( ( in @ A @ B )
| ( A = B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[34]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ ( succ @ B ) )
<=> ( ( in @ A @ B )
| ( A = B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(40,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(45,plain,
( ( ! [SY19: $i] :
( ( in @ sK1_A @ ( succ @ SY19 ) )
<=> ( ( in @ sK1_A @ SY19 )
| ( sK1_A = SY19 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(46,plain,
( ( ( in @ sK1_A @ ( succ @ sK2_SY19 ) )
<=> ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(47,plain,
( ( ( in @ sK1_A @ ( succ @ sK2_SY19 ) )
=> ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[46]) ).
thf(48,plain,
( ( ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) )
=> ( in @ sK1_A @ ( succ @ sK2_SY19 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[46]) ).
thf(49,plain,
( ( ~ ( ( in @ sK1_A @ ( succ @ sK2_SY19 ) )
=> ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(50,plain,
( ( ~ ( ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) )
=> ( in @ sK1_A @ ( succ @ sK2_SY19 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[48]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(55,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(59,plain,
( ( ~ ( ( in @ sK1_A @ ( succ @ sK2_SY19 ) )
=> ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(60,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(63,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(66,plain,
( ( ~ ( ~ ( in @ sK1_A @ ( succ @ sK2_SY19 ) )
| ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(67,plain,
! [SV1: $i] :
( ( ( succ @ SV1 )
= ( set_union2 @ SV1 @ ( singleton @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(68,plain,
! [SV2: $i] :
( ( ~ ( empty @ ( succ @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(69,plain,
! [SV3: $i] :
( ( ! [SY20: $i] :
( ~ ( in @ SV3 @ SY20 )
| ~ ( in @ SY20 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV4: $i] :
( ( ! [SY21: $i] :
( ~ ( element @ SV4 @ SY21 )
| ( empty @ SY21 )
| ( in @ SV4 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV5: $i] :
( ( ! [SY22: $i] :
~ ( ~ ( ( SY22
!= ( singleton @ SV5 ) )
| ! [SY23: $i] :
~ ( ~ ( ~ ( in @ SY23 @ SY22 )
| ( SY23 = SV5 ) )
| ~ ( ( SY23 != SV5 )
| ( in @ SY23 @ SY22 ) ) ) )
| ~ ( ~ ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SY22 )
| ( SY24 = SV5 ) )
| ~ ( ( SY24 != SV5 )
| ( in @ SY24 @ SY22 ) ) )
| ( SY22
= ( singleton @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV6: $i] :
( ( ! [SY25: $i,SY26: $i] :
~ ( ~ ( ( SY26
!= ( set_union2 @ SV6 @ SY25 ) )
| ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SY26 )
| ( in @ SY27 @ SV6 )
| ( in @ SY27 @ SY25 ) )
| ~ ( ~ ( ( in @ SY27 @ SV6 )
| ( in @ SY27 @ SY25 ) )
| ( in @ SY27 @ SY26 ) ) ) )
| ~ ( ~ ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SY26 )
| ( in @ SY28 @ SV6 )
| ( in @ SY28 @ SY25 ) )
| ~ ( ~ ( ( in @ SY28 @ SV6 )
| ( in @ SY28 @ SY25 ) )
| ( in @ SY28 @ SY26 ) ) )
| ( SY26
= ( set_union2 @ SV6 @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV7: $i] :
( ( ! [SY29: $i] :
~ ~ ( ~ ( in @ SV7 @ SY29 )
| ~ ( empty @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(74,plain,
! [SV8: $i] :
( ( ! [SY30: $i] :
( ~ ( in @ SV8 @ SY30 )
| ( element @ SV8 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(75,plain,
( ( ~ ( in @ sK1_A @ ( succ @ sK2_SY19 ) )
| ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV2: $i] :
( ( empty @ ( succ @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV9 )
| ~ ( in @ SV9 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( element @ SV4 @ SV10 )
| ( empty @ SV10 )
| ( in @ SV4 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ( ~ ( ( SV11
!= ( singleton @ SV5 ) )
| ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV11 )
| ( SY31 = SV5 ) )
| ~ ( ( SY31 != SV5 )
| ( in @ SY31 @ SV11 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SV11 )
| ( SY32 = SV5 ) )
| ~ ( ( SY32 != SV5 )
| ( in @ SY32 @ SV11 ) ) )
| ( SV11
= ( singleton @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY33: $i] :
~ ( ~ ( ( SY33
!= ( set_union2 @ SV6 @ SV12 ) )
| ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SY33 )
| ( in @ SY34 @ SV6 )
| ( in @ SY34 @ SV12 ) )
| ~ ( ~ ( ( in @ SY34 @ SV6 )
| ( in @ SY34 @ SV12 ) )
| ( in @ SY34 @ SY33 ) ) ) )
| ~ ( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SY33 )
| ( in @ SY35 @ SV6 )
| ( in @ SY35 @ SV12 ) )
| ~ ( ~ ( ( in @ SY35 @ SV6 )
| ( in @ SY35 @ SV12 ) )
| ( in @ SY35 @ SY33 ) ) )
| ( SY33
= ( set_union2 @ SV6 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ~ ( ~ ( in @ SV7 @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV14: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV14 )
| ( element @ SV8 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(83,plain,
( ( ~ ( in @ sK1_A @ ( succ @ sK2_SY19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(84,plain,
( ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV9 ) )
= $true )
| ( ( ~ ( in @ SV9 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( element @ SV4 @ SV10 ) )
= $true )
| ( ( ( empty @ SV10 )
| ( in @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ( ( SV11
!= ( singleton @ SV5 ) )
| ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV11 )
| ( SY31 = SV5 ) )
| ~ ( ( SY31 != SV5 )
| ( in @ SY31 @ SV11 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SV11 )
| ( SY32 = SV5 ) )
| ~ ( ( SY32 != SV5 )
| ( in @ SY32 @ SV11 ) ) )
| ( SV11
= ( singleton @ SV5 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ~ ( ~ ( ( SV15
!= ( set_union2 @ SV6 @ SV12 ) )
| ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV15 )
| ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ~ ( ~ ( ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ( in @ SY36 @ SV15 ) ) ) )
| ~ ( ~ ! [SY37: $i] :
~ ( ~ ( ~ ( in @ SY37 @ SV15 )
| ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ~ ( ~ ( ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ( in @ SY37 @ SV15 ) ) )
| ( SV15
= ( set_union2 @ SV6 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( in @ SV7 @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV14 ) )
= $true )
| ( ( element @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(91,plain,
( ( in @ sK1_A @ ( succ @ sK2_SY19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(92,plain,
( ( in @ sK1_A @ sK2_SY19 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(93,plain,
( ( sK1_A = sK2_SY19 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(94,plain,
! [SV9: $i,SV3: $i] :
( ( ( in @ SV3 @ SV9 )
= $false )
| ( ( ~ ( in @ SV9 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV10: $i,SV4: $i] :
( ( ( element @ SV4 @ SV10 )
= $false )
| ( ( ( empty @ SV10 )
| ( in @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ( ( SV11
!= ( singleton @ SV5 ) )
| ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV11 )
| ( SY31 = SV5 ) )
| ~ ( ( SY31 != SV5 )
| ( in @ SY31 @ SV11 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(97,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SV11 )
| ( SY32 = SV5 ) )
| ~ ( ( SY32 != SV5 )
| ( in @ SY32 @ SV11 ) ) )
| ( SV11
= ( singleton @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(98,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ~ ( ( SV15
!= ( set_union2 @ SV6 @ SV12 ) )
| ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV15 )
| ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ~ ( ~ ( ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ( in @ SY36 @ SV15 ) ) ) )
| ~ ( ~ ! [SY37: $i] :
~ ( ~ ( ~ ( in @ SY37 @ SV15 )
| ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ~ ( ~ ( ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ( in @ SY37 @ SV15 ) ) )
| ( SV15
= ( set_union2 @ SV6 @ SV12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV13 )
| ~ ( empty @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(100,plain,
! [SV14: $i,SV8: $i] :
( ( ( in @ SV8 @ SV14 )
= $false )
| ( ( element @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV3: $i,SV9: $i] :
( ( ( in @ SV9 @ SV3 )
= $false )
| ( ( in @ SV3 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV4: $i,SV10: $i] :
( ( ( empty @ SV10 )
= $true )
| ( ( in @ SV4 @ SV10 )
= $true )
| ( ( element @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV5: $i,SV11: $i] :
( ( ( SV11
!= ( singleton @ SV5 ) )
| ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV11 )
| ( SY31 = SV5 ) )
| ~ ( ( SY31 != SV5 )
| ( in @ SY31 @ SV11 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(104,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SV11 )
| ( SY32 = SV5 ) )
| ~ ( ( SY32 != SV5 )
| ( in @ SY32 @ SV11 ) ) )
| ( SV11
= ( singleton @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(105,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ~ ( ( SV15
!= ( set_union2 @ SV6 @ SV12 ) )
| ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV15 )
| ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ~ ( ~ ( ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ( in @ SY36 @ SV15 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(106,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ~ ( ~ ! [SY37: $i] :
~ ( ~ ( ~ ( in @ SY37 @ SV15 )
| ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ~ ( ~ ( ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ( in @ SY37 @ SV15 ) ) )
| ( SV15
= ( set_union2 @ SV6 @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(107,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( empty @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(108,plain,
! [SV5: $i,SV11: $i] :
( ( ( SV11
!= ( singleton @ SV5 ) )
= $true )
| ( ( ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV11 )
| ( SY31 = SV5 ) )
| ~ ( ( SY31 != SV5 )
| ( in @ SY31 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SV11 )
| ( SY32 = SV5 ) )
| ~ ( ( SY32 != SV5 )
| ( in @ SY32 @ SV11 ) ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( SV15
!= ( set_union2 @ SV6 @ SV12 ) )
| ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV15 )
| ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ~ ( ~ ( ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ( in @ SY36 @ SV15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(111,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ~ ! [SY37: $i] :
~ ( ~ ( ~ ( in @ SY37 @ SV15 )
| ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ~ ( ~ ( ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ( in @ SY37 @ SV15 ) ) )
| ( SV15
= ( set_union2 @ SV6 @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(112,plain,
! [SV13: $i,SV7: $i] :
( ( ( in @ SV7 @ SV13 )
= $false )
| ( ( ~ ( empty @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV5: $i,SV11: $i] :
( ( ( SV11
= ( singleton @ SV5 ) )
= $false )
| ( ( ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV11 )
| ( SY31 = SV5 ) )
| ~ ( ( SY31 != SV5 )
| ( in @ SY31 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV5: $i,SV11: $i] :
( ( ( ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SV11 )
| ( SY32 = SV5 ) )
| ~ ( ( SY32 != SV5 )
| ( in @ SY32 @ SV11 ) ) ) )
= $false )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(115,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( SV15
!= ( set_union2 @ SV6 @ SV12 ) )
= $true )
| ( ( ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV15 )
| ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ~ ( ~ ( ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ( in @ SY36 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ! [SY37: $i] :
~ ( ~ ( ~ ( in @ SY37 @ SV15 )
| ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ~ ( ~ ( ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ( in @ SY37 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV7: $i,SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( in @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV16 @ SV11 )
| ( SV16 = SV5 ) )
| ~ ( ( SV16 != SV5 )
| ( in @ SV16 @ SV11 ) ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
| ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 ) )
| ~ ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
| ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) ) ) )
= $false )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(120,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false )
| ( ( ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV15 )
| ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ~ ( ~ ( ( in @ SY36 @ SV6 )
| ( in @ SY36 @ SV12 ) )
| ( in @ SY36 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ! [SY37: $i] :
~ ( ~ ( ~ ( in @ SY37 @ SV15 )
| ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ~ ( ~ ( ( in @ SY37 @ SV6 )
| ( in @ SY37 @ SV12 ) )
| ( in @ SY37 @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(122,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV11 )
| ( SV16 = SV5 ) )
| ~ ( ( SV16 != SV5 )
| ( in @ SV16 @ SV11 ) ) )
= $false )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
| ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 ) )
| ~ ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
| ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(124,plain,
! [SV12: $i,SV6: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV17 @ SV15 )
| ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
| ~ ( ~ ( ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
| ( in @ SV17 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ~ ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(126,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV11 )
| ( SV16 = SV5 ) ) )
= $false )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(127,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( ( SV16 != SV5 )
| ( in @ SV16 @ SV11 ) ) )
= $false )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(128,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
| ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 ) ) )
= $true )
| ( ( ~ ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
| ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(129,plain,
! [SV12: $i,SV6: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ SV15 )
| ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
| ~ ( ~ ( ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
| ( in @ SV17 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(130,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ~ ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(131,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV11 )
| ( SV16 = SV5 ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(132,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( ( SV16 != SV5 )
| ( in @ SV16 @ SV11 ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(133,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
| ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 ) )
= $false )
| ( ( ~ ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
| ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV12: $i,SV6: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ SV15 )
| ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(135,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( ~ ( ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
| ( in @ SV17 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(136,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV11 ) )
= $true )
| ( ( SV16 = SV5 )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( SV16 != SV5 )
= $true )
| ( ( in @ SV16 @ SV11 )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) )
= $false )
| ( ( ~ ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
| ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(140,plain,
! [SV11: $i,SV5: $i] :
( ( ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 )
= $false )
| ( ( ~ ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
| ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(141,plain,
! [SV12: $i,SV6: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV15 )
| ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(142,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
| ( in @ SV17 @ SV15 ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(143,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(144,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( in @ SV16 @ SV11 )
= $false )
| ( ( SV16 = SV5 )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(145,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( SV16 = SV5 )
= $false )
| ( ( in @ SV16 @ SV11 )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(146,plain,
! [SV11: $i,SV5: $i] :
( ( ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
= $true )
| ( ( ~ ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
| ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(147,plain,
! [SV11: $i,SV5: $i] :
( ( ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
| ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) )
= $false )
| ( ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 )
= $false )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(148,plain,
! [SV12: $i,SV6: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV15 ) )
= $true )
| ( ( ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(150,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(151,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(152,plain,
! [SV11: $i,SV5: $i] :
( ( ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
| ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV11: $i,SV5: $i] :
( ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
= $false )
| ( ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 )
= $false )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(154,plain,
! [SV11: $i,SV5: $i] :
( ( ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
= $false )
| ( ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 )
= $false )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(155,plain,
! [SV12: $i,SV6: $i,SV15: $i,SV17: $i] :
( ( ( in @ SV17 @ SV15 )
= $false )
| ( ( ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(156,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV17: $i] :
( ( ( ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
= $false )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(158,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(159,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(160,plain,
! [SV11: $i,SV5: $i] :
( ( ( ( sK3_SY32 @ SV5 @ SV11 )
!= SV5 )
= $false )
| ( ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(161,plain,
! [SV11: $i,SV5: $i] :
( ( ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(162,plain,
! [SV11: $i,SV5: $i] :
( ( ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 )
= $true )
| ( ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 )
= $false )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(163,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV17: $i] :
( ( ( in @ SV17 @ SV6 )
= $true )
| ( ( in @ SV17 @ SV12 )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(164,plain,
! [SV12: $i,SV15: $i,SV6: $i,SV17: $i] :
( ( ( in @ SV17 @ SV6 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(165,plain,
! [SV6: $i,SV15: $i,SV12: $i,SV17: $i] :
( ( ( in @ SV17 @ SV12 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(166,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV11: $i,SV5: $i] :
( ( ( ( sK3_SY32 @ SV5 @ SV11 )
= SV5 )
= $true )
| ( ( in @ ( sK3_SY32 @ SV5 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(170,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) ) )
= $false )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(171,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(172,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) ) )
= $false )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(173,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(174,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) ) )
= $false )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(175,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(176,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
= $true )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(177,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
= $true )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(178,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
| ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 ) )
= $true )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(179,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
= $true )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 )
= $true )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(180,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
= $true )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 )
= $true )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV6 )
= $true )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 )
= $true )
| ( ( in @ ( sK4_SY37 @ SV12 @ SV6 @ SV15 ) @ SV12 )
= $false )
| ( ( SV15
= ( set_union2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(182,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[67,181,180,179,175,173,171,169,165,164,163,162,161,154,145,144,117,102,101,100,93,92,91,76]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(184,plain,
( ( ! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(186,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(187,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(188,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(191,plain,
( ( ~ ( ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) )
=> ( in @ sK1_A @ ( succ @ sK2_SY19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(192,plain,
( ( ~ ( ~ ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) )
| ( in @ sK1_A @ ( succ @ sK2_SY19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(193,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(194,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(195,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(196,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(197,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(198,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(199,plain,
! [SV18: $i] :
( ( ( succ @ SV18 )
= ( set_union2 @ SV18 @ ( singleton @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(200,plain,
! [SV19: $i] :
( ( ~ ( empty @ ( succ @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(201,plain,
( ( ~ ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) )
| ( in @ sK1_A @ ( succ @ sK2_SY19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(202,plain,
! [SV20: $i] :
( ( ! [SY38: $i] :
~ ~ ( ~ ( in @ SV20 @ SY38 )
| ~ ( empty @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(203,plain,
! [SV21: $i] :
( ( ! [SY39: $i] :
~ ( ~ ( ( SY39
!= ( singleton @ SV21 ) )
| ! [SY40: $i] :
~ ( ~ ( ~ ( in @ SY40 @ SY39 )
| ( SY40 = SV21 ) )
| ~ ( ( SY40 != SV21 )
| ( in @ SY40 @ SY39 ) ) ) )
| ~ ( ~ ! [SY41: $i] :
~ ( ~ ( ~ ( in @ SY41 @ SY39 )
| ( SY41 = SV21 ) )
| ~ ( ( SY41 != SV21 )
| ( in @ SY41 @ SY39 ) ) )
| ( SY39
= ( singleton @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(204,plain,
! [SV22: $i] :
( ( ! [SY42: $i] :
( ~ ( in @ SV22 @ SY42 )
| ~ ( in @ SY42 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(205,plain,
! [SV23: $i] :
( ( ! [SY43: $i,SY44: $i] :
~ ( ~ ( ( SY44
!= ( set_union2 @ SV23 @ SY43 ) )
| ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SY44 )
| ( in @ SY45 @ SV23 )
| ( in @ SY45 @ SY43 ) )
| ~ ( ~ ( ( in @ SY45 @ SV23 )
| ( in @ SY45 @ SY43 ) )
| ( in @ SY45 @ SY44 ) ) ) )
| ~ ( ~ ! [SY46: $i] :
~ ( ~ ( ~ ( in @ SY46 @ SY44 )
| ( in @ SY46 @ SV23 )
| ( in @ SY46 @ SY43 ) )
| ~ ( ~ ( ( in @ SY46 @ SV23 )
| ( in @ SY46 @ SY43 ) )
| ( in @ SY46 @ SY44 ) ) )
| ( SY44
= ( set_union2 @ SV23 @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(206,plain,
! [SV24: $i] :
( ( ! [SY47: $i] :
( ~ ( element @ SV24 @ SY47 )
| ( empty @ SY47 )
| ( in @ SV24 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(207,plain,
! [SV25: $i] :
( ( ! [SY48: $i] :
( ~ ( in @ SV25 @ SY48 )
| ( element @ SV25 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(208,plain,
! [SV19: $i] :
( ( empty @ ( succ @ SV19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(209,plain,
( ( ~ ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(210,plain,
( ( in @ sK1_A @ ( succ @ sK2_SY19 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(211,plain,
! [SV26: $i,SV20: $i] :
( ( ~ ~ ( ~ ( in @ SV20 @ SV26 )
| ~ ( empty @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(212,plain,
! [SV21: $i,SV27: $i] :
( ( ~ ( ~ ( ( SV27
!= ( singleton @ SV21 ) )
| ! [SY49: $i] :
~ ( ~ ( ~ ( in @ SY49 @ SV27 )
| ( SY49 = SV21 ) )
| ~ ( ( SY49 != SV21 )
| ( in @ SY49 @ SV27 ) ) ) )
| ~ ( ~ ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SV27 )
| ( SY50 = SV21 ) )
| ~ ( ( SY50 != SV21 )
| ( in @ SY50 @ SV27 ) ) )
| ( SV27
= ( singleton @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(213,plain,
! [SV28: $i,SV22: $i] :
( ( ~ ( in @ SV22 @ SV28 )
| ~ ( in @ SV28 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(214,plain,
! [SV29: $i,SV23: $i] :
( ( ! [SY51: $i] :
~ ( ~ ( ( SY51
!= ( set_union2 @ SV23 @ SV29 ) )
| ! [SY52: $i] :
~ ( ~ ( ~ ( in @ SY52 @ SY51 )
| ( in @ SY52 @ SV23 )
| ( in @ SY52 @ SV29 ) )
| ~ ( ~ ( ( in @ SY52 @ SV23 )
| ( in @ SY52 @ SV29 ) )
| ( in @ SY52 @ SY51 ) ) ) )
| ~ ( ~ ! [SY53: $i] :
~ ( ~ ( ~ ( in @ SY53 @ SY51 )
| ( in @ SY53 @ SV23 )
| ( in @ SY53 @ SV29 ) )
| ~ ( ~ ( ( in @ SY53 @ SV23 )
| ( in @ SY53 @ SV29 ) )
| ( in @ SY53 @ SY51 ) ) )
| ( SY51
= ( set_union2 @ SV23 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(215,plain,
! [SV30: $i,SV24: $i] :
( ( ~ ( element @ SV24 @ SV30 )
| ( empty @ SV30 )
| ( in @ SV24 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(216,plain,
! [SV31: $i,SV25: $i] :
( ( ~ ( in @ SV25 @ SV31 )
| ( element @ SV25 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(217,plain,
( ( ( in @ sK1_A @ sK2_SY19 )
| ( sK1_A = sK2_SY19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(218,plain,
! [SV26: $i,SV20: $i] :
( ( ~ ( ~ ( in @ SV20 @ SV26 )
| ~ ( empty @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(219,plain,
! [SV21: $i,SV27: $i] :
( ( ~ ( ( SV27
!= ( singleton @ SV21 ) )
| ! [SY49: $i] :
~ ( ~ ( ~ ( in @ SY49 @ SV27 )
| ( SY49 = SV21 ) )
| ~ ( ( SY49 != SV21 )
| ( in @ SY49 @ SV27 ) ) ) )
| ~ ( ~ ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SV27 )
| ( SY50 = SV21 ) )
| ~ ( ( SY50 != SV21 )
| ( in @ SY50 @ SV27 ) ) )
| ( SV27
= ( singleton @ SV21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(220,plain,
! [SV28: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV28 ) )
= $true )
| ( ( ~ ( in @ SV28 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(221,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ~ ( ~ ( ( SV32
!= ( set_union2 @ SV23 @ SV29 ) )
| ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV32 )
| ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ~ ( ~ ( ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ( in @ SY54 @ SV32 ) ) ) )
| ~ ( ~ ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV32 )
| ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ~ ( ~ ( ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ( in @ SY55 @ SV32 ) ) )
| ( SV32
= ( set_union2 @ SV23 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(222,plain,
! [SV30: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ SV30 ) )
= $true )
| ( ( ( empty @ SV30 )
| ( in @ SV24 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(223,plain,
! [SV31: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV31 ) )
= $true )
| ( ( element @ SV25 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(224,plain,
( ( ( in @ sK1_A @ sK2_SY19 )
= $true )
| ( ( sK1_A = sK2_SY19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(225,plain,
! [SV26: $i,SV20: $i] :
( ( ~ ( in @ SV20 @ SV26 )
| ~ ( empty @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(226,plain,
! [SV21: $i,SV27: $i] :
( ( ~ ( ( SV27
!= ( singleton @ SV21 ) )
| ! [SY49: $i] :
~ ( ~ ( ~ ( in @ SY49 @ SV27 )
| ( SY49 = SV21 ) )
| ~ ( ( SY49 != SV21 )
| ( in @ SY49 @ SV27 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(227,plain,
! [SV21: $i,SV27: $i] :
( ( ~ ( ~ ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SV27 )
| ( SY50 = SV21 ) )
| ~ ( ( SY50 != SV21 )
| ( in @ SY50 @ SV27 ) ) )
| ( SV27
= ( singleton @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(228,plain,
! [SV28: $i,SV22: $i] :
( ( ( in @ SV22 @ SV28 )
= $false )
| ( ( ~ ( in @ SV28 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(229,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ~ ( ( SV32
!= ( set_union2 @ SV23 @ SV29 ) )
| ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV32 )
| ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ~ ( ~ ( ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ( in @ SY54 @ SV32 ) ) ) )
| ~ ( ~ ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV32 )
| ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ~ ( ~ ( ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ( in @ SY55 @ SV32 ) ) )
| ( SV32
= ( set_union2 @ SV23 @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(230,plain,
! [SV30: $i,SV24: $i] :
( ( ( element @ SV24 @ SV30 )
= $false )
| ( ( ( empty @ SV30 )
| ( in @ SV24 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(231,plain,
! [SV31: $i,SV25: $i] :
( ( ( in @ SV25 @ SV31 )
= $false )
| ( ( element @ SV25 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(232,plain,
! [SV26: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV26 ) )
= $true )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(233,plain,
! [SV21: $i,SV27: $i] :
( ( ( SV27
!= ( singleton @ SV21 ) )
| ! [SY49: $i] :
~ ( ~ ( ~ ( in @ SY49 @ SV27 )
| ( SY49 = SV21 ) )
| ~ ( ( SY49 != SV21 )
| ( in @ SY49 @ SV27 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(234,plain,
! [SV21: $i,SV27: $i] :
( ( ~ ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SV27 )
| ( SY50 = SV21 ) )
| ~ ( ( SY50 != SV21 )
| ( in @ SY50 @ SV27 ) ) )
| ( SV27
= ( singleton @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(235,plain,
! [SV22: $i,SV28: $i] :
( ( ( in @ SV28 @ SV22 )
= $false )
| ( ( in @ SV22 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(236,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ~ ( ( SV32
!= ( set_union2 @ SV23 @ SV29 ) )
| ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV32 )
| ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ~ ( ~ ( ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ( in @ SY54 @ SV32 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(237,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ~ ( ~ ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV32 )
| ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ~ ( ~ ( ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ( in @ SY55 @ SV32 ) ) )
| ( SV32
= ( set_union2 @ SV23 @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(238,plain,
! [SV24: $i,SV30: $i] :
( ( ( empty @ SV30 )
= $true )
| ( ( in @ SV24 @ SV30 )
= $true )
| ( ( element @ SV24 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(239,plain,
! [SV26: $i,SV20: $i] :
( ( ( in @ SV20 @ SV26 )
= $false )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(240,plain,
! [SV21: $i,SV27: $i] :
( ( ( SV27
!= ( singleton @ SV21 ) )
= $true )
| ( ( ! [SY49: $i] :
~ ( ~ ( ~ ( in @ SY49 @ SV27 )
| ( SY49 = SV21 ) )
| ~ ( ( SY49 != SV21 )
| ( in @ SY49 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(241,plain,
! [SV21: $i,SV27: $i] :
( ( ( ~ ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SV27 )
| ( SY50 = SV21 ) )
| ~ ( ( SY50 != SV21 )
| ( in @ SY50 @ SV27 ) ) ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(242,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ( SV32
!= ( set_union2 @ SV23 @ SV29 ) )
| ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV32 )
| ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ~ ( ~ ( ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ( in @ SY54 @ SV32 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(243,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ~ ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV32 )
| ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ~ ( ~ ( ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ( in @ SY55 @ SV32 ) ) )
| ( SV32
= ( set_union2 @ SV23 @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(244,plain,
! [SV20: $i,SV26: $i] :
( ( ( empty @ SV26 )
= $false )
| ( ( in @ SV20 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(245,plain,
! [SV21: $i,SV27: $i] :
( ( ( SV27
= ( singleton @ SV21 ) )
= $false )
| ( ( ! [SY49: $i] :
~ ( ~ ( ~ ( in @ SY49 @ SV27 )
| ( SY49 = SV21 ) )
| ~ ( ( SY49 != SV21 )
| ( in @ SY49 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(246,plain,
! [SV21: $i,SV27: $i] :
( ( ( ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SV27 )
| ( SY50 = SV21 ) )
| ~ ( ( SY50 != SV21 )
| ( in @ SY50 @ SV27 ) ) ) )
= $false )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(247,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ( SV32
!= ( set_union2 @ SV23 @ SV29 ) )
= $true )
| ( ( ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV32 )
| ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ~ ( ~ ( ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ( in @ SY54 @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(248,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ( ~ ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV32 )
| ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ~ ( ~ ( ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ( in @ SY55 @ SV32 ) ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(249,plain,
! [SV21: $i,SV27: $i,SV33: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV33 @ SV27 )
| ( SV33 = SV21 ) )
| ~ ( ( SV33 != SV21 )
| ( in @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(250,plain,
! [SV27: $i,SV21: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
| ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 ) )
| ~ ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
| ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) ) ) )
= $false )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[246]) ).
thf(251,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false )
| ( ( ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV32 )
| ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ~ ( ~ ( ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV29 ) )
| ( in @ SY54 @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(252,plain,
! [SV29: $i,SV23: $i,SV32: $i] :
( ( ( ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV32 )
| ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ~ ( ~ ( ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV29 ) )
| ( in @ SY55 @ SV32 ) ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(253,plain,
! [SV21: $i,SV27: $i,SV33: $i] :
( ( ( ~ ( ~ ( in @ SV33 @ SV27 )
| ( SV33 = SV21 ) )
| ~ ( ( SV33 != SV21 )
| ( in @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(254,plain,
! [SV27: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
| ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 ) )
| ~ ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
| ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(255,plain,
! [SV29: $i,SV23: $i,SV32: $i,SV34: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV34 @ SV32 )
| ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
| ~ ( ~ ( ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
| ( in @ SV34 @ SV32 ) ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(256,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ~ ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[252]) ).
thf(257,plain,
! [SV21: $i,SV27: $i,SV33: $i] :
( ( ( ~ ( ~ ( in @ SV33 @ SV27 )
| ( SV33 = SV21 ) ) )
= $false )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(258,plain,
! [SV27: $i,SV21: $i,SV33: $i] :
( ( ( ~ ( ( SV33 != SV21 )
| ( in @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(259,plain,
! [SV27: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
| ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 ) ) )
= $true )
| ( ( ~ ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
| ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(260,plain,
! [SV29: $i,SV23: $i,SV32: $i,SV34: $i] :
( ( ( ~ ( ~ ( in @ SV34 @ SV32 )
| ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
| ~ ( ~ ( ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
| ( in @ SV34 @ SV32 ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(261,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ~ ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(262,plain,
! [SV21: $i,SV27: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV27 )
| ( SV33 = SV21 ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(263,plain,
! [SV27: $i,SV21: $i,SV33: $i] :
( ( ( ( SV33 != SV21 )
| ( in @ SV33 @ SV27 ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(264,plain,
! [SV27: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
| ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 ) )
= $false )
| ( ( ~ ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
| ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(265,plain,
! [SV29: $i,SV23: $i,SV32: $i,SV34: $i] :
( ( ( ~ ( ~ ( in @ SV34 @ SV32 )
| ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(266,plain,
! [SV32: $i,SV29: $i,SV23: $i,SV34: $i] :
( ( ( ~ ( ~ ( ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
| ( in @ SV34 @ SV32 ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(267,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(268,plain,
! [SV21: $i,SV27: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV27 ) )
= $true )
| ( ( SV33 = SV21 )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(269,plain,
! [SV27: $i,SV21: $i,SV33: $i] :
( ( ( SV33 != SV21 )
= $true )
| ( ( in @ SV33 @ SV27 )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(270,plain,
! [SV27: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) )
= $false )
| ( ( ~ ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
| ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(271,plain,
! [SV27: $i,SV21: $i] :
( ( ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 )
= $false )
| ( ( ~ ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
| ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(272,plain,
! [SV29: $i,SV23: $i,SV32: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ SV32 )
| ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(273,plain,
! [SV32: $i,SV29: $i,SV23: $i,SV34: $i] :
( ( ( ~ ( ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
| ( in @ SV34 @ SV32 ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(274,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(275,plain,
! [SV21: $i,SV27: $i,SV33: $i] :
( ( ( in @ SV33 @ SV27 )
= $false )
| ( ( SV33 = SV21 )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(276,plain,
! [SV27: $i,SV21: $i,SV33: $i] :
( ( ( SV33 = SV21 )
= $false )
| ( ( in @ SV33 @ SV27 )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(277,plain,
! [SV27: $i,SV21: $i] :
( ( ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
= $true )
| ( ( ~ ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
| ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) ) )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(278,plain,
! [SV27: $i,SV21: $i] :
( ( ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
| ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) )
= $false )
| ( ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 )
= $false )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(279,plain,
! [SV29: $i,SV23: $i,SV32: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ SV32 ) )
= $true )
| ( ( ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(280,plain,
! [SV32: $i,SV29: $i,SV23: $i,SV34: $i] :
( ( ( ~ ( ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) ) )
= $true )
| ( ( in @ SV34 @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(281,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(282,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(283,plain,
! [SV27: $i,SV21: $i] :
( ( ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
| ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 ) )
= $false )
| ( ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(284,plain,
! [SV27: $i,SV21: $i] :
( ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
= $false )
| ( ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 )
= $false )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(285,plain,
! [SV27: $i,SV21: $i] :
( ( ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
= $false )
| ( ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 )
= $false )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(286,plain,
! [SV29: $i,SV23: $i,SV32: $i,SV34: $i] :
( ( ( in @ SV34 @ SV32 )
= $false )
| ( ( ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(287,plain,
! [SV32: $i,SV29: $i,SV23: $i,SV34: $i] :
( ( ( ( in @ SV34 @ SV23 )
| ( in @ SV34 @ SV29 ) )
= $false )
| ( ( in @ SV34 @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(288,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(289,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(290,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(291,plain,
! [SV27: $i,SV21: $i] :
( ( ( ( sK5_SY50 @ SV21 @ SV27 )
!= SV21 )
= $false )
| ( ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(292,plain,
! [SV27: $i,SV21: $i] :
( ( ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
= $false )
| ( ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(293,plain,
! [SV27: $i,SV21: $i] :
( ( ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 )
= $true )
| ( ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 )
= $false )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(294,plain,
! [SV32: $i,SV29: $i,SV23: $i,SV34: $i] :
( ( ( in @ SV34 @ SV23 )
= $true )
| ( ( in @ SV34 @ SV29 )
= $true )
| ( ( in @ SV34 @ SV32 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(295,plain,
! [SV29: $i,SV32: $i,SV23: $i,SV34: $i] :
( ( ( in @ SV34 @ SV23 )
= $false )
| ( ( in @ SV34 @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(296,plain,
! [SV23: $i,SV32: $i,SV29: $i,SV34: $i] :
( ( ( in @ SV34 @ SV29 )
= $false )
| ( ( in @ SV34 @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(297,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(298,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(299,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(300,plain,
! [SV27: $i,SV21: $i] :
( ( ( ( sK5_SY50 @ SV21 @ SV27 )
= SV21 )
= $true )
| ( ( in @ ( sK5_SY50 @ SV21 @ SV27 ) @ SV27 )
= $true )
| ( ( SV27
= ( singleton @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(301,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) ) )
= $false )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(302,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
= $false )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(303,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) ) )
= $false )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(304,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
= $false )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(305,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ~ ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) ) )
= $false )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(306,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
= $false )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(307,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
= $true )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(308,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
= $true )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(309,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
| ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 ) )
= $true )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(310,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
= $true )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 )
= $true )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(311,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
= $true )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 )
= $true )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(312,plain,
! [SV32: $i,SV23: $i,SV29: $i] :
( ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV23 )
= $true )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 )
= $true )
| ( ( in @ ( sK6_SY55 @ SV29 @ SV23 @ SV32 ) @ SV29 )
= $false )
| ( ( SV32
= ( set_union2 @ SV23 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(313,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[199,312,311,310,306,304,302,300,296,295,294,293,292,285,276,275,244,238,235,231,224,210,208]) ).
thf(314,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[313,182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n020.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 13:13:51 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.15/1.06
% 5.15/1.06 No.of.Axioms: 8
% 5.15/1.06
% 5.15/1.06 Length.of.Defs: 0
% 5.15/1.06
% 5.15/1.06 Contains.Choice.Funs: false
% 5.15/1.06 ........
% 5.15/1.06
% 5.15/1.06 ********************************
% 5.15/1.06 * All subproblems solved! *
% 5.15/1.06 ********************************
% 5.15/1.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,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:313,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.15/1.06
% 5.15/1.06 %**** Beginning of derivation protocol ****
% 5.15/1.06 % SZS output start CNFRefutation
% See solution above
% 5.15/1.06
% 5.15/1.06 %**** End of derivation protocol ****
% 5.15/1.06 %**** no. of clauses in derivation: 289 ****
% 5.15/1.06 %**** clause counter: 313 ****
% 5.15/1.06
% 5.15/1.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,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:313,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------