%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU125+2 : 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 : n004.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 10:42:58 AM UTC 2026
% Result : Theorem 57.77s 9.86s
% Output : CNFRefutation 57.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of formulae : 192 ( 103 unt; 0 typ; 0 def)
% Number of atoms : 1213 ( 403 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 2277 ( 378 ~; 384 |; 12 &;1470 @)
% ( 12 <=>; 21 =>; 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 : 15 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 451 ( 0 ^; 451 !; 0 ?; 451 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY30,type,
sK2_SY30: $i ).
thf(tp_sK3_SY32,type,
sK3_SY32: $i ).
thf(tp_sK4_SY53,type,
sK4_SY53: $i > $i > $i ).
thf(tp_sK5_SY56,type,
sK5_SY56: $i > $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(4,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(6,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(14,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(15,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(16,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(20,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(22,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(26,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(28,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(30,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(32,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(33,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[32]) ).
thf(34,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(40,plain,
$true = $true,
inference(unfold_def,[status(thm)],[14]) ).
thf(41,plain,
$true = $true,
inference(unfold_def,[status(thm)],[15]) ).
thf(42,plain,
$true = $true,
inference(unfold_def,[status(thm)],[16]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,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)],[20]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(49,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(50,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(51,plain,
( ( ! [SY30: $i,SY31: $i] :
( ( ( subset @ sK1_A @ SY30 )
& ( subset @ SY31 @ SY30 ) )
=> ( subset @ ( set_union2 @ sK1_A @ SY31 ) @ SY30 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(52,plain,
( ( ! [SY32: $i] :
( ( ( subset @ sK1_A @ sK2_SY30 )
& ( subset @ SY32 @ sK2_SY30 ) )
=> ( subset @ ( set_union2 @ sK1_A @ SY32 ) @ sK2_SY30 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(53,plain,
( ( ( ( subset @ sK1_A @ sK2_SY30 )
& ( subset @ sK3_SY32 @ sK2_SY30 ) )
=> ( subset @ ( set_union2 @ sK1_A @ sK3_SY32 ) @ sK2_SY30 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[52]) ).
thf(54,plain,
( ( subset @ sK1_A @ sK2_SY30 )
= $true ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(55,plain,
( ( subset @ sK3_SY32 @ sK2_SY30 )
= $true ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(56,plain,
( ( subset @ ( set_union2 @ sK1_A @ sK3_SY32 ) @ sK2_SY30 )
= $false ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(57,plain,
( ( ~ ( subset @ ( set_union2 @ sK1_A @ sK3_SY32 ) @ sK2_SY30 ) )
= $true ),
inference(polarity_switch,[status(thm)],[56]) ).
thf(58,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(59,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(64,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)],[44]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(66,plain,
$true = $true,
inference(copy,[status(thm)],[42]) ).
thf(67,plain,
$true = $true,
inference(copy,[status(thm)],[41]) ).
thf(68,plain,
$true = $true,
inference(copy,[status(thm)],[40]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(70,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(73,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(74,plain,
( ( subset @ sK3_SY32 @ sK2_SY30 )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(75,plain,
( ( subset @ sK1_A @ sK2_SY30 )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(76,plain,
( ( ~ ( subset @ ( set_union2 @ sK1_A @ sK3_SY32 ) @ sK2_SY30 ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(77,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)],[64]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(82,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ( empty @ ( set_union2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ( empty @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(84,plain,
! [SV1: $i] :
( ( subset @ empty_set @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(85,plain,
! [SV2: $i] :
( ( ! [SY33: $i] : ( subset @ SV2 @ ( set_union2 @ SV2 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(86,plain,
! [SV3: $i] :
( ( ! [SY34: $i] :
( ( set_union2 @ SV3 @ SY34 )
= ( set_union2 @ SY34 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(87,plain,
! [SV4: $i] :
( ( ! [SY35: $i] :
( ( set_union2 @ SV4 @ SV4 )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(88,plain,
! [SV5: $i] :
( ( ! [SY36: $i] : ( subset @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(89,plain,
! [SV6: $i] :
( ( ( set_union2 @ SV6 @ empty_set )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(90,plain,
( ( subset @ ( set_union2 @ sK1_A @ sK3_SY32 ) @ sK2_SY30 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(91,plain,
! [SV7: $i] :
( ( ! [SY37: $i,SY38: $i] :
~ ( ~ ( ( SY38
!= ( set_union2 @ SV7 @ SY37 ) )
| ! [SY39: $i] :
~ ( ~ ( ~ ( in @ SY39 @ SY38 )
| ( in @ SY39 @ SV7 )
| ( in @ SY39 @ SY37 ) )
| ~ ( ~ ( ( in @ SY39 @ SV7 )
| ( in @ SY39 @ SY37 ) )
| ( in @ SY39 @ SY38 ) ) ) )
| ~ ( ~ ! [SY40: $i] :
~ ( ~ ( ~ ( in @ SY40 @ SY38 )
| ( in @ SY40 @ SV7 )
| ( in @ SY40 @ SY37 ) )
| ~ ( ~ ( ( in @ SY40 @ SV7 )
| ( in @ SY40 @ SY37 ) )
| ( in @ SY40 @ SY38 ) ) )
| ( SY38
= ( set_union2 @ SV7 @ SY37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(92,plain,
! [SV8: $i] :
( ( ! [SY41: $i] :
~ ( ~ ( ~ ( subset @ SV8 @ SY41 )
| ! [SY42: $i] :
( ~ ( in @ SY42 @ SV8 )
| ( in @ SY42 @ SY41 ) ) )
| ~ ( ~ ! [SY43: $i] :
( ~ ( in @ SY43 @ SV8 )
| ( in @ SY43 @ SY41 ) )
| ( subset @ SV8 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(93,plain,
! [SV9: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ~ ( ~ ( subset @ SV9 @ SY44 )
| ~ ( subset @ SY44 @ SY45 ) )
| ( subset @ SV9 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(94,plain,
! [SV10: $i] :
( ( ~ ( subset @ SV10 @ empty_set )
| ( SV10 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(95,plain,
! [SV11: $i] :
( ( ! [SY46: $i] :
~ ( ~ ( ( SV11 != SY46 )
| ~ ( ~ ( subset @ SV11 @ SY46 )
| ~ ( subset @ SY46 @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV11 @ SY46 )
| ~ ( subset @ SY46 @ SV11 ) )
| ( SV11 = SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(96,plain,
! [SV12: $i] :
( ( ! [SY47: $i] :
( ~ ~ ( empty @ SV12 )
| ~ ( empty @ ( set_union2 @ SY47 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(97,plain,
! [SV13: $i] :
( ( ! [SY48: $i] :
( ~ ~ ( empty @ SV13 )
| ~ ( empty @ ( set_union2 @ SV13 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(98,plain,
! [SV14: $i,SV2: $i] :
( ( subset @ SV2 @ ( set_union2 @ SV2 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV15: $i,SV3: $i] :
( ( ( set_union2 @ SV3 @ SV15 )
= ( set_union2 @ SV15 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV4: $i] :
( ( ( set_union2 @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV5: $i] :
( ( subset @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(102,plain,
! [SV18: $i,SV7: $i] :
( ( ! [SY49: $i] :
~ ( ~ ( ( SY49
!= ( set_union2 @ SV7 @ SV18 ) )
| ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SY49 )
| ( in @ SY50 @ SV7 )
| ( in @ SY50 @ SV18 ) )
| ~ ( ~ ( ( in @ SY50 @ SV7 )
| ( in @ SY50 @ SV18 ) )
| ( in @ SY50 @ SY49 ) ) ) )
| ~ ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY49 )
| ( in @ SY51 @ SV7 )
| ( in @ SY51 @ SV18 ) )
| ~ ( ~ ( ( in @ SY51 @ SV7 )
| ( in @ SY51 @ SV18 ) )
| ( in @ SY51 @ SY49 ) ) )
| ( SY49
= ( set_union2 @ SV7 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(103,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV8 @ SV19 )
| ! [SY52: $i] :
( ~ ( in @ SY52 @ SV8 )
| ( in @ SY52 @ SV19 ) ) )
| ~ ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV8 )
| ( in @ SY53 @ SV19 ) )
| ( subset @ SV8 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV20: $i,SV9: $i] :
( ( ! [SY54: $i] :
( ~ ~ ( ~ ( subset @ SV9 @ SV20 )
| ~ ( subset @ SV20 @ SY54 ) )
| ( subset @ SV9 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV10: $i] :
( ( ( ~ ( subset @ SV10 @ empty_set ) )
= $true )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( ~ ( ( SV11 != SV21 )
| ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) )
| ( SV11 = SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ~ ( empty @ SV12 )
| ~ ( empty @ ( set_union2 @ SV22 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ~ ( empty @ SV13 )
| ~ ( empty @ ( set_union2 @ SV13 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(109,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ~ ( ~ ( ( SV24
!= ( set_union2 @ SV7 @ SV18 ) )
| ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV24 )
| ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ~ ( ~ ( ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ( in @ SY55 @ SV24 ) ) ) )
| ~ ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV24 )
| ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ~ ( ~ ( ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ( in @ SY56 @ SV24 ) ) )
| ( SV24
= ( set_union2 @ SV7 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ( ~ ( subset @ SV8 @ SV19 )
| ! [SY52: $i] :
( ~ ( in @ SY52 @ SV8 )
| ( in @ SY52 @ SV19 ) ) )
| ~ ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV8 )
| ( in @ SY53 @ SV19 ) )
| ( subset @ SV8 @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV25: $i,SV20: $i,SV9: $i] :
( ( ~ ~ ( ~ ( subset @ SV9 @ SV20 )
| ~ ( subset @ SV20 @ SV25 ) )
| ( subset @ SV9 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV10: $i] :
( ( ( subset @ SV10 @ empty_set )
= $false )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( ( SV11 != SV21 )
| ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) )
| ( SV11 = SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV22: $i,SV12: $i] :
( ( ( ~ ~ ( empty @ SV12 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV22 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV13 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ~ ( ( SV24
!= ( set_union2 @ SV7 @ SV18 ) )
| ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV24 )
| ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ~ ( ~ ( ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ( in @ SY55 @ SV24 ) ) ) )
| ~ ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV24 )
| ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ~ ( ~ ( ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ( in @ SY56 @ SV24 ) ) )
| ( SV24
= ( set_union2 @ SV7 @ SV18 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ( ~ ( subset @ SV8 @ SV19 )
| ! [SY52: $i] :
( ~ ( in @ SY52 @ SV8 )
| ( in @ SY52 @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(118,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV8 )
| ( in @ SY53 @ SV19 ) )
| ( subset @ SV8 @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(119,plain,
! [SV25: $i,SV20: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV9 @ SV20 )
| ~ ( subset @ SV20 @ SV25 ) ) )
= $true )
| ( ( subset @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( ( SV11 != SV21 )
| ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(121,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) )
| ( SV11 = SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(122,plain,
! [SV22: $i,SV12: $i] :
( ( ( ~ ( empty @ SV12 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV22 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(123,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV13 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ~ ( ( SV24
!= ( set_union2 @ SV7 @ SV18 ) )
| ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV24 )
| ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ~ ( ~ ( ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ( in @ SY55 @ SV24 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(125,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ~ ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV24 )
| ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ~ ( ~ ( ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ( in @ SY56 @ SV24 ) ) )
| ( SV24
= ( set_union2 @ SV7 @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(126,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV19 )
| ! [SY52: $i] :
( ~ ( in @ SY52 @ SV8 )
| ( in @ SY52 @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(127,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV8 )
| ( in @ SY53 @ SV19 ) )
| ( subset @ SV8 @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(128,plain,
! [SV25: $i,SV20: $i,SV9: $i] :
( ( ( ~ ( ~ ( subset @ SV9 @ SV20 )
| ~ ( subset @ SV20 @ SV25 ) ) )
= $false )
| ( ( subset @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV21: $i,SV11: $i] :
( ( ( SV11 != SV21 )
| ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(130,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) )
| ( SV11 = SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(131,plain,
! [SV22: $i,SV12: $i] :
( ( ( empty @ SV12 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV22 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(132,plain,
! [SV23: $i,SV13: $i] :
( ( ( empty @ SV13 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV13 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(133,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ( SV24
!= ( set_union2 @ SV7 @ SV18 ) )
| ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV24 )
| ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ~ ( ~ ( ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ( in @ SY55 @ SV24 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(134,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV24 )
| ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ~ ( ~ ( ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ( in @ SY56 @ SV24 ) ) )
| ( SV24
= ( set_union2 @ SV7 @ SV18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(135,plain,
! [SV19: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV19 ) )
= $true )
| ( ( ! [SY52: $i] :
( ~ ( in @ SY52 @ SV8 )
| ( in @ SY52 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV19: $i,SV8: $i] :
( ( ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV8 )
| ( in @ SY53 @ SV19 ) ) )
= $true )
| ( ( subset @ SV8 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV25: $i,SV20: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV20 )
| ~ ( subset @ SV20 @ SV25 ) )
= $true )
| ( ( subset @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(138,plain,
! [SV21: $i,SV11: $i] :
( ( ( SV11 != SV21 )
= $true )
| ( ( ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) ) )
= $true )
| ( ( SV11 = SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(140,plain,
! [SV12: $i,SV22: $i] :
( ( ( empty @ ( set_union2 @ SV22 @ SV12 ) )
= $false )
| ( ( empty @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV23: $i,SV13: $i] :
( ( ( empty @ ( set_union2 @ SV13 @ SV23 ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(142,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ( SV24
!= ( set_union2 @ SV7 @ SV18 ) )
= $true )
| ( ( ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV24 )
| ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ~ ( ~ ( ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ( in @ SY55 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(143,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV24 )
| ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ~ ( ~ ( ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ( in @ SY56 @ SV24 ) ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(144,plain,
! [SV19: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV19 )
= $false )
| ( ( ! [SY52: $i] :
( ~ ( in @ SY52 @ SV8 )
| ( in @ SY52 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV19: $i,SV8: $i] :
( ( ( ! [SY53: $i] :
( ~ ( in @ SY53 @ SV8 )
| ( in @ SY53 @ SV19 ) ) )
= $false )
| ( ( subset @ SV8 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(146,plain,
! [SV25: $i,SV20: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV20 ) )
= $true )
| ( ( ~ ( subset @ SV20 @ SV25 ) )
= $true )
| ( ( subset @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(147,plain,
! [SV21: $i,SV11: $i] :
( ( ( SV11 = SV21 )
= $false )
| ( ( ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(148,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) ) )
= $false )
| ( ( SV11 = SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(149,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false )
| ( ( ! [SY55: $i] :
~ ( ~ ( ~ ( in @ SY55 @ SV24 )
| ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ~ ( ~ ( ( in @ SY55 @ SV7 )
| ( in @ SY55 @ SV18 ) )
| ( in @ SY55 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(150,plain,
! [SV18: $i,SV7: $i,SV24: $i] :
( ( ( ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV24 )
| ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ~ ( ~ ( ( in @ SY56 @ SV7 )
| ( in @ SY56 @ SV18 ) )
| ( in @ SY56 @ SV24 ) ) ) )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(151,plain,
! [SV19: $i,SV8: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV8 )
| ( in @ SV26 @ SV19 ) )
= $true )
| ( ( subset @ SV8 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(152,plain,
! [SV8: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK4_SY53 @ SV19 @ SV8 ) @ SV8 )
| ( in @ ( sK4_SY53 @ SV19 @ SV8 ) @ SV19 ) )
= $false )
| ( ( subset @ SV8 @ SV19 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[145]) ).
thf(153,plain,
! [SV25: $i,SV20: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV20 )
= $false )
| ( ( ~ ( subset @ SV20 @ SV25 ) )
= $true )
| ( ( subset @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(154,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) )
= $false )
| ( ( SV11 = SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(155,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV21 )
| ~ ( subset @ SV21 @ SV11 ) )
= $true )
| ( ( SV11 = SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(156,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV27: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV27 @ SV24 )
| ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
| ~ ( ~ ( ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
| ( in @ SV27 @ SV24 ) ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ~ ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) ) ) )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(158,plain,
! [SV19: $i,SV8: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV8 ) )
= $true )
| ( ( in @ SV26 @ SV19 )
= $true )
| ( ( subset @ SV8 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(159,plain,
! [SV8: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK4_SY53 @ SV19 @ SV8 ) @ SV8 ) )
= $false )
| ( ( subset @ SV8 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(160,plain,
! [SV8: $i,SV19: $i] :
( ( ( in @ ( sK4_SY53 @ SV19 @ SV8 ) @ SV19 )
= $false )
| ( ( subset @ SV8 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(161,plain,
! [SV9: $i,SV25: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV25 )
= $false )
| ( ( subset @ SV9 @ SV20 )
= $false )
| ( ( subset @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV21 ) )
= $false )
| ( ( SV11 = SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(163,plain,
! [SV11: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV11 ) )
= $false )
| ( ( SV11 = SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(164,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV21 ) )
= $true )
| ( ( ~ ( subset @ SV21 @ SV11 ) )
= $true )
| ( ( SV11 = SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ SV27 @ SV24 )
| ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
| ~ ( ~ ( ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
| ( in @ SV27 @ SV24 ) ) )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ~ ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(167,plain,
! [SV19: $i,SV8: $i,SV26: $i] :
( ( ( in @ SV26 @ SV8 )
= $false )
| ( ( in @ SV26 @ SV19 )
= $true )
| ( ( subset @ SV8 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV8: $i,SV19: $i] :
( ( ( in @ ( sK4_SY53 @ SV19 @ SV8 ) @ SV8 )
= $true )
| ( ( subset @ SV8 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(169,plain,
! [SV21: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV21 )
= $true )
| ( ( SV11 = SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(170,plain,
! [SV11: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV11 )
= $true )
| ( ( SV11 = SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(171,plain,
! [SV21: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV21 )
= $false )
| ( ( ~ ( subset @ SV21 @ SV11 ) )
= $true )
| ( ( SV11 = SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(172,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ SV27 @ SV24 )
| ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) ) )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(173,plain,
! [SV24: $i,SV18: $i,SV7: $i,SV27: $i] :
( ( ( ~ ( ~ ( ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
| ( in @ SV27 @ SV24 ) ) )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(174,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV11: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV11 )
= $false )
| ( ( subset @ SV11 @ SV21 )
= $false )
| ( ( SV11 = SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(176,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV24 )
| ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(177,plain,
! [SV24: $i,SV18: $i,SV7: $i,SV27: $i] :
( ( ( ~ ( ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
| ( in @ SV27 @ SV24 ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(178,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(179,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV24 ) )
= $true )
| ( ( ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(180,plain,
! [SV24: $i,SV18: $i,SV7: $i,SV27: $i] :
( ( ( ~ ( ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) ) )
= $true )
| ( ( in @ SV27 @ SV24 )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(182,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(183,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV27: $i] :
( ( ( in @ SV27 @ SV24 )
= $false )
| ( ( ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(184,plain,
! [SV24: $i,SV18: $i,SV7: $i,SV27: $i] :
( ( ( ( in @ SV27 @ SV7 )
| ( in @ SV27 @ SV18 ) )
= $false )
| ( ( in @ SV27 @ SV24 )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(186,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(187,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(188,plain,
! [SV24: $i,SV18: $i,SV7: $i,SV27: $i] :
( ( ( in @ SV27 @ SV7 )
= $true )
| ( ( in @ SV27 @ SV18 )
= $true )
| ( ( in @ SV27 @ SV24 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(189,plain,
! [SV18: $i,SV24: $i,SV7: $i,SV27: $i] :
( ( ( in @ SV27 @ SV7 )
= $false )
| ( ( in @ SV27 @ SV24 )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(190,plain,
! [SV7: $i,SV24: $i,SV18: $i,SV27: $i] :
( ( ( in @ SV27 @ SV18 )
= $false )
| ( ( in @ SV27 @ SV24 )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(191,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) )
= $false )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(192,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) )
= $false )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(193,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 ) )
= $false )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(194,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) ) )
= $false )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(195,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
= $false )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(196,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) ) )
= $false )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(197,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
= $false )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(198,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) ) )
= $false )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(199,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
= $false )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(200,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
= $true )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(201,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
= $true )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(202,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
| ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 ) )
= $true )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(203,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
= $true )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 )
= $true )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(204,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
= $true )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 )
= $true )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(205,plain,
! [SV24: $i,SV7: $i,SV18: $i] :
( ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV7 )
= $true )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 )
= $true )
| ( ( in @ ( sK5_SY56 @ SV18 @ SV7 @ SV24 ) @ SV18 )
= $false )
| ( ( SV24
= ( set_union2 @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(206,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[66,205,204,203,199,197,195,190,189,188,175,170,169,168,167,161,160,141,140,112,101,100,99,98,90,89,84,75,74,68,67]) ).
thf(207,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU125+2 : 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
% 0.09/0.16 % Computer : n004.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 15:01:18 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.77/9.86
% 57.77/9.86 No.of.Axioms: 16
% 57.77/9.86
% 57.77/9.86 Length.of.Defs: 0
% 57.77/9.86
% 57.77/9.86 Contains.Choice.Funs: false
% 57.77/9.86 .....
% 57.77/9.86
% 57.77/9.86 ********************************
% 57.77/9.86 * All subproblems solved! *
% 57.77/9.86 ********************************
% 57.77/9.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:18,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:206,loop_count:0,foatp_calls:1,translation:fof_full)
% 57.77/9.86
% 57.77/9.86 %**** Beginning of derivation protocol ****
% 57.77/9.86 % SZS output start CNFRefutation
% See solution above
% 57.77/9.86
% 57.77/9.86 %**** End of derivation protocol ****
% 57.77/9.86 %**** no. of clauses in derivation: 192 ****
% 57.77/9.86 %**** clause counter: 206 ****
% 57.77/9.86
% 57.77/9.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:18,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:206,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------