%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU230+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:35 AM UTC 2026
% Result : Theorem 0.38s 0.39s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 163 ( 76 unt; 0 typ; 0 def)
% Number of atoms : 1165 ( 455 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 2159 ( 372 ~; 418 |; 3 &;1345 @)
% ( 12 <=>; 9 =>; 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 : 17 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 388 ( 0 ^; 388 !; 0 ?; 388 :)
% 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_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY30,type,
sK2_SY30: $i > $i > $i ).
thf(tp_sK3_SY35,type,
sK3_SY35: $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(22,axiom,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(30,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(31,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(32,axiom,
! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(38,conjecture,
! [A: $i] : ( in @ A @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(39,negated_conjecture,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[38]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(44,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(45,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(46,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(48,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(49,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(50,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)],[30]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(54,plain,
( ( in @ sK1_A @ ( succ @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(55,plain,
( ( ~ ( in @ sK1_A @ ( succ @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[54]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(59,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)],[50]) ).
thf(60,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(61,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(62,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(63,plain,
$true = $true,
inference(copy,[status(thm)],[46]) ).
thf(64,plain,
$true = $true,
inference(copy,[status(thm)],[45]) ).
thf(65,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(69,plain,
( ( ~ ( in @ sK1_A @ ( succ @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(71,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)],[58]) ).
thf(72,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)],[59]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(76,plain,
! [SV1: $i] :
( ( ( succ @ SV1 )
= ( set_union2 @ SV1 @ ( singleton @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(77,plain,
! [SV2: $i] :
( ( ~ ( empty @ ( succ @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(78,plain,
( ( in @ sK1_A @ ( succ @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV3: $i] :
( ( ! [SY18: $i] :
( ~ ( in @ SV3 @ SY18 )
| ( element @ SV3 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV4: $i] :
( ( ! [SY19: $i] :
~ ( ~ ( ( SY19
!= ( singleton @ SV4 ) )
| ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SY19 )
| ( SY20 = SV4 ) )
| ~ ( ( SY20 != SV4 )
| ( in @ SY20 @ SY19 ) ) ) )
| ~ ( ~ ! [SY21: $i] :
~ ( ~ ( ~ ( in @ SY21 @ SY19 )
| ( SY21 = SV4 ) )
| ~ ( ( SY21 != SV4 )
| ( in @ SY21 @ SY19 ) ) )
| ( SY19
= ( singleton @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV5: $i] :
( ( ! [SY22: $i,SY23: $i] :
~ ( ~ ( ( SY23
!= ( set_union2 @ SV5 @ SY22 ) )
| ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SY23 )
| ( in @ SY24 @ SV5 )
| ( in @ SY24 @ SY22 ) )
| ~ ( ~ ( ( in @ SY24 @ SV5 )
| ( in @ SY24 @ SY22 ) )
| ( in @ SY24 @ SY23 ) ) ) )
| ~ ( ~ ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SY23 )
| ( in @ SY25 @ SV5 )
| ( in @ SY25 @ SY22 ) )
| ~ ( ~ ( ( in @ SY25 @ SV5 )
| ( in @ SY25 @ SY22 ) )
| ( in @ SY25 @ SY23 ) ) )
| ( SY23
= ( set_union2 @ SV5 @ SY22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV6: $i] :
( ( ! [SY26: $i] :
( ~ ( element @ SV6 @ SY26 )
| ( empty @ SY26 )
| ( in @ SV6 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV7: $i] :
( ( ! [SY27: $i] :
~ ~ ( ~ ( in @ SV7 @ SY27 )
| ~ ( empty @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV8: $i] :
( ( ! [SY28: $i] :
( ~ ( in @ SV8 @ SY28 )
| ~ ( in @ SY28 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV2: $i] :
( ( empty @ ( succ @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV9 )
| ( element @ SV3 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV4: $i,SV10: $i] :
( ( ~ ( ~ ( ( SV10
!= ( singleton @ SV4 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV10 )
| ( SY29 = SV4 ) )
| ~ ( ( SY29 != SV4 )
| ( in @ SY29 @ SV10 ) ) ) )
| ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV10 )
| ( SY30 = SV4 ) )
| ~ ( ( SY30 != SV4 )
| ( in @ SY30 @ SV10 ) ) )
| ( SV10
= ( singleton @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY31: $i] :
~ ( ~ ( ( SY31
!= ( set_union2 @ SV5 @ SV11 ) )
| ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY31 )
| ( in @ SY32 @ SV5 )
| ( in @ SY32 @ SV11 ) )
| ~ ( ~ ( ( in @ SY32 @ SV5 )
| ( in @ SY32 @ SV11 ) )
| ( in @ SY32 @ SY31 ) ) ) )
| ~ ( ~ ! [SY33: $i] :
~ ( ~ ( ~ ( in @ SY33 @ SY31 )
| ( in @ SY33 @ SV5 )
| ( in @ SY33 @ SV11 ) )
| ~ ( ~ ( ( in @ SY33 @ SV5 )
| ( in @ SY33 @ SV11 ) )
| ( in @ SY33 @ SY31 ) ) )
| ( SY31
= ( set_union2 @ SV5 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( element @ SV6 @ SV12 )
| ( empty @ SV12 )
| ( in @ SV6 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ~ ( ~ ( in @ SV7 @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV14: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV14 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV9 ) )
= $true )
| ( ( element @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV4: $i,SV10: $i] :
( ( ~ ( ( SV10
!= ( singleton @ SV4 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV10 )
| ( SY29 = SV4 ) )
| ~ ( ( SY29 != SV4 )
| ( in @ SY29 @ SV10 ) ) ) )
| ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV10 )
| ( SY30 = SV4 ) )
| ~ ( ( SY30 != SV4 )
| ( in @ SY30 @ SV10 ) ) )
| ( SV10
= ( singleton @ SV4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ~ ( ~ ( ( SV15
!= ( set_union2 @ SV5 @ SV11 ) )
| ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SV15 )
| ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ~ ( ~ ( ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ( in @ SY34 @ SV15 ) ) ) )
| ~ ( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV15 )
| ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ~ ( ~ ( ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ( in @ SY35 @ SV15 ) ) )
| ( SV15
= ( set_union2 @ SV5 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( element @ SV6 @ SV12 ) )
= $true )
| ( ( ( empty @ SV12 )
| ( in @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( in @ SV7 @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV14 ) )
= $true )
| ( ( ~ ( in @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV9: $i,SV3: $i] :
( ( ( in @ SV3 @ SV9 )
= $false )
| ( ( element @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV4: $i,SV10: $i] :
( ( ~ ( ( SV10
!= ( singleton @ SV4 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV10 )
| ( SY29 = SV4 ) )
| ~ ( ( SY29 != SV4 )
| ( in @ SY29 @ SV10 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(100,plain,
! [SV4: $i,SV10: $i] :
( ( ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV10 )
| ( SY30 = SV4 ) )
| ~ ( ( SY30 != SV4 )
| ( in @ SY30 @ SV10 ) ) )
| ( SV10
= ( singleton @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(101,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ~ ( ( SV15
!= ( set_union2 @ SV5 @ SV11 ) )
| ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SV15 )
| ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ~ ( ~ ( ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ( in @ SY34 @ SV15 ) ) ) )
| ~ ( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV15 )
| ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ~ ( ~ ( ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ( in @ SY35 @ SV15 ) ) )
| ( SV15
= ( set_union2 @ SV5 @ SV11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV12: $i,SV6: $i] :
( ( ( element @ SV6 @ SV12 )
= $false )
| ( ( ( empty @ SV12 )
| ( in @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV13 )
| ~ ( empty @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(104,plain,
! [SV14: $i,SV8: $i] :
( ( ( in @ SV8 @ SV14 )
= $false )
| ( ( ~ ( in @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV4: $i,SV10: $i] :
( ( ( SV10
!= ( singleton @ SV4 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV10 )
| ( SY29 = SV4 ) )
| ~ ( ( SY29 != SV4 )
| ( in @ SY29 @ SV10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(106,plain,
! [SV4: $i,SV10: $i] :
( ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV10 )
| ( SY30 = SV4 ) )
| ~ ( ( SY30 != SV4 )
| ( in @ SY30 @ SV10 ) ) )
| ( SV10
= ( singleton @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(107,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ~ ( ( SV15
!= ( set_union2 @ SV5 @ SV11 ) )
| ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SV15 )
| ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ~ ( ~ ( ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ( in @ SY34 @ SV15 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(108,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ~ ( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV15 )
| ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ~ ( ~ ( ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ( in @ SY35 @ SV15 ) ) )
| ( SV15
= ( set_union2 @ SV5 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(109,plain,
! [SV6: $i,SV12: $i] :
( ( ( empty @ SV12 )
= $true )
| ( ( in @ SV6 @ SV12 )
= $true )
| ( ( element @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( empty @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV8: $i,SV14: $i] :
( ( ( in @ SV14 @ SV8 )
= $false )
| ( ( in @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV4: $i,SV10: $i] :
( ( ( SV10
!= ( singleton @ SV4 ) )
= $true )
| ( ( ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV10 )
| ( SY29 = SV4 ) )
| ~ ( ( SY29 != SV4 )
| ( in @ SY29 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV4: $i,SV10: $i] :
( ( ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV10 )
| ( SY30 = SV4 ) )
| ~ ( ( SY30 != SV4 )
| ( in @ SY30 @ SV10 ) ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ( SV15
!= ( set_union2 @ SV5 @ SV11 ) )
| ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SV15 )
| ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ~ ( ~ ( ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ( in @ SY34 @ SV15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(115,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV15 )
| ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ~ ( ~ ( ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ( in @ SY35 @ SV15 ) ) )
| ( SV15
= ( set_union2 @ SV5 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(116,plain,
! [SV13: $i,SV7: $i] :
( ( ( in @ SV7 @ SV13 )
= $false )
| ( ( ~ ( empty @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(117,plain,
! [SV4: $i,SV10: $i] :
( ( ( SV10
= ( singleton @ SV4 ) )
= $false )
| ( ( ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV10 )
| ( SY29 = SV4 ) )
| ~ ( ( SY29 != SV4 )
| ( in @ SY29 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV4: $i,SV10: $i] :
( ( ( ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV10 )
| ( SY30 = SV4 ) )
| ~ ( ( SY30 != SV4 )
| ( in @ SY30 @ SV10 ) ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ( SV15
!= ( set_union2 @ SV5 @ SV11 ) )
= $true )
| ( ( ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SV15 )
| ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ~ ( ~ ( ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ( in @ SY34 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(120,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV15 )
| ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ~ ( ~ ( ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ( in @ SY35 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV7: $i,SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( in @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(122,plain,
! [SV4: $i,SV10: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV16 @ SV10 )
| ( SV16 = SV4 ) )
| ~ ( ( SV16 != SV4 )
| ( in @ SV16 @ SV10 ) ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
| ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 ) )
| ~ ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
| ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(124,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false )
| ( ( ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SV15 )
| ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ~ ( ~ ( ( in @ SY34 @ SV5 )
| ( in @ SY34 @ SV11 ) )
| ( in @ SY34 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV11: $i,SV5: $i,SV15: $i] :
( ( ( ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV15 )
| ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ~ ( ~ ( ( in @ SY35 @ SV5 )
| ( in @ SY35 @ SV11 ) )
| ( in @ SY35 @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(126,plain,
! [SV4: $i,SV10: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV10 )
| ( SV16 = SV4 ) )
| ~ ( ( SV16 != SV4 )
| ( in @ SV16 @ SV10 ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(127,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
| ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 ) )
| ~ ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
| ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(128,plain,
! [SV11: $i,SV5: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV17 @ SV15 )
| ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
| ~ ( ~ ( ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
| ( in @ SV17 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ~ ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[125]) ).
thf(130,plain,
! [SV4: $i,SV10: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV10 )
| ( SV16 = SV4 ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(131,plain,
! [SV10: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( ( SV16 != SV4 )
| ( in @ SV16 @ SV10 ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(132,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
| ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 ) ) )
= $true )
| ( ( ~ ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
| ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(133,plain,
! [SV11: $i,SV5: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ SV15 )
| ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
| ~ ( ~ ( ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
| ( in @ SV17 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ~ ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(135,plain,
! [SV4: $i,SV10: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV10 )
| ( SV16 = SV4 ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(136,plain,
! [SV10: $i,SV4: $i,SV16: $i] :
( ( ( ( SV16 != SV4 )
| ( in @ SV16 @ SV10 ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(137,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
| ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 ) )
= $false )
| ( ( ~ ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
| ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(138,plain,
! [SV11: $i,SV5: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ SV15 )
| ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(139,plain,
! [SV15: $i,SV11: $i,SV5: $i,SV17: $i] :
( ( ( ~ ( ~ ( ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
| ( in @ SV17 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(140,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV4: $i,SV10: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV10 ) )
= $true )
| ( ( SV16 = SV4 )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(142,plain,
! [SV10: $i,SV4: $i,SV16: $i] :
( ( ( SV16 != SV4 )
= $true )
| ( ( in @ SV16 @ SV10 )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(143,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) )
= $false )
| ( ( ~ ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
| ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(144,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 )
= $false )
| ( ( ~ ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
| ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(145,plain,
! [SV11: $i,SV5: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV15 )
| ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(146,plain,
! [SV15: $i,SV11: $i,SV5: $i,SV17: $i] :
( ( ( ~ ( ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
| ( in @ SV17 @ SV15 ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(147,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(148,plain,
! [SV4: $i,SV10: $i,SV16: $i] :
( ( ( in @ SV16 @ SV10 )
= $false )
| ( ( SV16 = SV4 )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV10: $i,SV4: $i,SV16: $i] :
( ( ( SV16 = SV4 )
= $false )
| ( ( in @ SV16 @ SV10 )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(150,plain,
! [SV10: $i,SV4: $i] :
( ( ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
= $true )
| ( ( ~ ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
| ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(151,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
| ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) )
= $false )
| ( ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 )
= $false )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(152,plain,
! [SV11: $i,SV5: $i,SV15: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV15 ) )
= $true )
| ( ( ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV15: $i,SV11: $i,SV5: $i,SV17: $i] :
( ( ( ~ ( ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(154,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(155,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(156,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
| ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 ) )
= $false )
| ( ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
= $false )
| ( ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 )
= $false )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(158,plain,
! [SV10: $i,SV4: $i] :
( ( ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
= $false )
| ( ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 )
= $false )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(159,plain,
! [SV11: $i,SV5: $i,SV15: $i,SV17: $i] :
( ( ( in @ SV17 @ SV15 )
= $false )
| ( ( ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(160,plain,
! [SV15: $i,SV11: $i,SV5: $i,SV17: $i] :
( ( ( ( in @ SV17 @ SV5 )
| ( in @ SV17 @ SV11 ) )
= $false )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(162,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(163,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(164,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( sK2_SY30 @ SV4 @ SV10 )
!= SV4 )
= $false )
| ( ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(165,plain,
! [SV10: $i,SV4: $i] :
( ( ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
= $false )
| ( ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(166,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 )
= $true )
| ( ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 )
= $false )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(167,plain,
! [SV15: $i,SV11: $i,SV5: $i,SV17: $i] :
( ( ( in @ SV17 @ SV5 )
= $true )
| ( ( in @ SV17 @ SV11 )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV11: $i,SV15: $i,SV5: $i,SV17: $i] :
( ( ( in @ SV17 @ SV5 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(169,plain,
! [SV5: $i,SV15: $i,SV11: $i,SV17: $i] :
( ( ( in @ SV17 @ SV11 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(170,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(171,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(173,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( sK2_SY30 @ SV4 @ SV10 )
= SV4 )
= $true )
| ( ( in @ ( sK2_SY30 @ SV4 @ SV10 ) @ SV10 )
= $true )
| ( ( SV10
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(174,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) ) )
= $false )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(175,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(176,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) ) )
= $false )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(177,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(178,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) ) )
= $false )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(179,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(180,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
= $true )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(181,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
= $true )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(182,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
| ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 ) )
= $true )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(183,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
= $true )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 )
= $true )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(184,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
= $true )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 )
= $true )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(185,plain,
! [SV15: $i,SV5: $i,SV11: $i] :
( ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV5 )
= $true )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 )
= $true )
| ( ( in @ ( sK3_SY35 @ SV11 @ SV5 @ SV15 ) @ SV11 )
= $false )
| ( ( SV15
= ( set_union2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(186,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,185,184,183,179,177,175,173,169,168,167,166,165,158,149,148,121,111,109,98,85,78,76,64,63,62,61]) ).
thf(187,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU230+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.19 % Computer : n003.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Oct 6 15:09:54 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.39
% 0.38/0.39 No.of.Axioms: 13
% 0.38/0.39
% 0.38/0.39 Length.of.Defs: 0
% 0.38/0.39
% 0.38/0.39 Contains.Choice.Funs: false
% 0.38/0.39 ....
% 0.38/0.39
% 0.38/0.39 ********************************
% 0.38/0.39 * All subproblems solved! *
% 0.38/0.39 ********************************
% 0.38/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:13,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:186,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.38/0.39
% 0.38/0.39 %**** Beginning of derivation protocol ****
% 0.38/0.39 % SZS output start CNFRefutation
% See solution above
% 0.38/0.39
% 0.38/0.39 %**** End of derivation protocol ****
% 0.38/0.39 %**** no. of clauses in derivation: 163 ****
% 0.38/0.39 %**** clause counter: 186 ****
% 0.38/0.39
% 0.38/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:13,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:186,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------