%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU139+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 : n011.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 10:43:01 AM UTC 2026
% Result : Theorem 0.56s 0.30s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of formulae : 218 ( 135 unt; 0 typ; 0 def)
% Number of atoms : 1087 ( 361 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1736 ( 375 ~; 244 |; 22 &;1056 @)
% ( 9 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 454 ( 0 ^; 454 !; 0 ?; 454 :)
% 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_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY42,type,
sK2_SY42: $i ).
thf(tp_sK3_SY68,type,
sK3_SY68: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $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(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(19,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(27,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(30,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(35,axiom,
! [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(36,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(41,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(45,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(47,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(50,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(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(52,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(55,conjecture,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(56,negated_conjecture,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[55]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[56]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(61,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(62,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(63,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(68,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(72,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(73,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(75,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(76,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(77,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(80,plain,
( ( ! [SY42: $i] :
~ ( ( subset @ sK1_A @ SY42 )
& ( proper_subset @ SY42 @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(81,plain,
( ( ~ ( ( subset @ sK1_A @ sK2_SY42 )
& ( proper_subset @ sK2_SY42 @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[80]) ).
thf(82,plain,
( ( ( subset @ sK1_A @ sK2_SY42 )
& ( proper_subset @ sK2_SY42 @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[81]) ).
thf(83,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(87,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(89,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(92,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(94,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(99,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(100,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(101,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(102,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(105,plain,
( ( ( subset @ sK1_A @ sK2_SY42 )
& ( proper_subset @ sK2_SY42 @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(109,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(111,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)],[97]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(115,plain,
( ( ~ ( ~ ( subset @ sK1_A @ sK2_SY42 )
| ~ ( proper_subset @ sK2_SY42 @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(118,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)],[96]) ).
thf(119,plain,
! [SV1: $i] :
( ( ! [SY43: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY43 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(120,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(121,plain,
! [SV3: $i] :
( ( ! [SY44: $i] : ( subset @ ( set_difference @ SV3 @ SY44 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(122,plain,
! [SV4: $i] :
( ( ! [SY45: $i] : ( subset @ SV4 @ ( set_union2 @ SV4 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(123,plain,
! [SV5: $i] :
( ( ! [SY46: $i] :
~ ( proper_subset @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(124,plain,
! [SV6: $i] :
( ( ! [SY47: $i] : ( subset @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(125,plain,
! [SV7: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ~ ( ~ ( subset @ SV7 @ SY48 )
| ~ ( subset @ SY48 @ SY49 ) )
| ( subset @ SV7 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(126,plain,
! [SV8: $i] :
( ( ! [SY50: $i] :
( ~ ( subset @ SV8 @ SY50 )
| ( ( set_intersection2 @ SV8 @ SY50 )
= SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(127,plain,
! [SV9: $i] :
( ( ! [SY51: $i] :
( ~ ( subset @ SV9 @ SY51 )
| ( ( set_union2 @ SV9 @ SY51 )
= SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(128,plain,
! [SV10: $i] :
( ( ~ ( subset @ SV10 @ empty_set )
| ( SV10 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(129,plain,
! [SV11: $i] :
( ( ! [SY52: $i] :
( ~ ( proper_subset @ SV11 @ SY52 )
| ~ ( proper_subset @ SY52 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(130,plain,
! [SV12: $i] :
( ( ! [SY53: $i] :
~ ( ~ ( ~ ( subset @ SV12 @ SY53 )
| ! [SY54: $i] :
( ~ ( in @ SY54 @ SV12 )
| ( in @ SY54 @ SY53 ) ) )
| ~ ( ~ ! [SY55: $i] :
( ~ ( in @ SY55 @ SV12 )
| ( in @ SY55 @ SY53 ) )
| ( subset @ SV12 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(131,plain,
! [SV13: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( subset @ SV13 @ SY56 )
| ( subset @ ( set_intersection2 @ SV13 @ SY57 ) @ ( set_intersection2 @ SY56 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(132,plain,
! [SV14: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ( subset @ SV14 @ SY58 )
| ( subset @ ( set_difference @ SV14 @ SY59 ) @ ( set_difference @ SY58 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(133,plain,
! [SV15: $i] :
( ( ! [SY60: $i] :
~ ( ~ ( ~ ( proper_subset @ SV15 @ SY60 )
| ~ ( ~ ( subset @ SV15 @ SY60 )
| ~ ( ( SV15 != SY60 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV15 @ SY60 )
| ~ ( ( SV15 != SY60 ) ) )
| ( proper_subset @ SV15 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(134,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY42 )
| ~ ( proper_subset @ sK2_SY42 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(135,plain,
! [SV16: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ~ ~ ( ~ ( subset @ SV16 @ SY61 )
| ~ ( subset @ SV16 @ SY62 ) )
| ( subset @ SV16 @ ( set_intersection2 @ SY61 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(136,plain,
! [SV17: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ~ ( ~ ( subset @ SV17 @ SY63 )
| ~ ( subset @ SY64 @ SY63 ) )
| ( subset @ ( set_union2 @ SV17 @ SY64 ) @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(137,plain,
! [SV18: $i] :
( ( ! [SY65: $i] :
~ ( ~ ( ( SV18 != SY65 )
| ~ ( ~ ( subset @ SV18 @ SY65 )
| ~ ( subset @ SY65 @ SV18 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV18 @ SY65 )
| ~ ( subset @ SY65 @ SV18 ) )
| ( SV18 = SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(138,plain,
! [SV19: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV19 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(139,plain,
! [SV20: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV20 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(140,plain,
! [SV21: $i,SV4: $i] :
( ( subset @ SV4 @ ( set_union2 @ SV4 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(141,plain,
! [SV5: $i] :
( ( ~ ( proper_subset @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(142,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(143,plain,
! [SV24: $i,SV7: $i] :
( ( ! [SY66: $i] :
( ~ ~ ( ~ ( subset @ SV7 @ SV24 )
| ~ ( subset @ SV24 @ SY66 ) )
| ( subset @ SV7 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(144,plain,
! [SV25: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV25 )
| ( ( set_intersection2 @ SV8 @ SV25 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(145,plain,
! [SV26: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV26 )
| ( ( set_union2 @ SV9 @ SV26 )
= SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(146,plain,
! [SV10: $i] :
( ( ( ~ ( subset @ SV10 @ empty_set ) )
= $true )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(147,plain,
! [SV27: $i,SV11: $i] :
( ( ~ ( proper_subset @ SV11 @ SV27 )
| ~ ( proper_subset @ SV27 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(148,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV12 @ SV28 )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SV12 )
| ( in @ SY67 @ SV28 ) ) )
| ~ ( ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SV12 )
| ( in @ SY68 @ SV28 ) )
| ( subset @ SV12 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(149,plain,
! [SV29: $i,SV13: $i] :
( ( ! [SY69: $i] :
( ~ ( subset @ SV13 @ SV29 )
| ( subset @ ( set_intersection2 @ SV13 @ SY69 ) @ ( set_intersection2 @ SV29 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(150,plain,
! [SV30: $i,SV14: $i] :
( ( ! [SY70: $i] :
( ~ ( subset @ SV14 @ SV30 )
| ( subset @ ( set_difference @ SV14 @ SY70 ) @ ( set_difference @ SV30 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(151,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV15 @ SV31 )
| ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) )
| ( proper_subset @ SV15 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(152,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY42 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(153,plain,
( ( ~ ( proper_subset @ sK2_SY42 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(154,plain,
! [SV32: $i,SV16: $i] :
( ( ! [SY71: $i] :
( ~ ~ ( ~ ( subset @ SV16 @ SV32 )
| ~ ( subset @ SV16 @ SY71 ) )
| ( subset @ SV16 @ ( set_intersection2 @ SV32 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV33: $i,SV17: $i] :
( ( ! [SY72: $i] :
( ~ ~ ( ~ ( subset @ SV17 @ SV33 )
| ~ ( subset @ SY72 @ SV33 ) )
| ( subset @ ( set_union2 @ SV17 @ SY72 ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV34: $i,SV18: $i] :
( ( ~ ( ~ ( ( SV18 != SV34 )
| ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) )
| ( SV18 = SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV5: $i] :
( ( proper_subset @ SV5 @ SV5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(158,plain,
! [SV35: $i,SV24: $i,SV7: $i] :
( ( ~ ~ ( ~ ( subset @ SV7 @ SV24 )
| ~ ( subset @ SV24 @ SV35 ) )
| ( subset @ SV7 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV25: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV25 ) )
= $true )
| ( ( ( set_intersection2 @ SV8 @ SV25 )
= SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(160,plain,
! [SV26: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV26 ) )
= $true )
| ( ( ( set_union2 @ SV9 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV10: $i] :
( ( ( subset @ SV10 @ empty_set )
= $false )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV27: $i,SV11: $i] :
( ( ( ~ ( proper_subset @ SV11 @ SV27 ) )
= $true )
| ( ( ~ ( proper_subset @ SV27 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV28 )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SV12 )
| ( in @ SY67 @ SV28 ) ) )
| ~ ( ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SV12 )
| ( in @ SY68 @ SV28 ) )
| ( subset @ SV12 @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV36: $i,SV29: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV29 )
| ( subset @ ( set_intersection2 @ SV13 @ SV36 ) @ ( set_intersection2 @ SV29 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV37: $i,SV30: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV30 )
| ( subset @ ( set_difference @ SV14 @ SV37 ) @ ( set_difference @ SV30 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( ~ ( proper_subset @ SV15 @ SV31 )
| ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) )
| ( proper_subset @ SV15 @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(167,plain,
( ( subset @ sK1_A @ sK2_SY42 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(168,plain,
( ( proper_subset @ sK2_SY42 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(169,plain,
! [SV38: $i,SV32: $i,SV16: $i] :
( ( ~ ~ ( ~ ( subset @ SV16 @ SV32 )
| ~ ( subset @ SV16 @ SV38 ) )
| ( subset @ SV16 @ ( set_intersection2 @ SV32 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV39: $i,SV33: $i,SV17: $i] :
( ( ~ ~ ( ~ ( subset @ SV17 @ SV33 )
| ~ ( subset @ SV39 @ SV33 ) )
| ( subset @ ( set_union2 @ SV17 @ SV39 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(171,plain,
! [SV34: $i,SV18: $i] :
( ( ~ ( ( SV18 != SV34 )
| ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) )
| ( SV18 = SV34 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV35: $i,SV24: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV7 @ SV24 )
| ~ ( subset @ SV24 @ SV35 ) ) )
= $true )
| ( ( subset @ SV7 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV25: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV25 )
= $false )
| ( ( ( set_intersection2 @ SV8 @ SV25 )
= SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(174,plain,
! [SV26: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV26 )
= $false )
| ( ( ( set_union2 @ SV9 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(175,plain,
! [SV27: $i,SV11: $i] :
( ( ( proper_subset @ SV11 @ SV27 )
= $false )
| ( ( ~ ( proper_subset @ SV27 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(176,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV28 )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SV12 )
| ( in @ SY67 @ SV28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(177,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SV12 )
| ( in @ SY68 @ SV28 ) )
| ( subset @ SV12 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(178,plain,
! [SV36: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV29 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV13 @ SV36 ) @ ( set_intersection2 @ SV29 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(179,plain,
! [SV37: $i,SV30: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV30 ) )
= $true )
| ( ( subset @ ( set_difference @ SV14 @ SV37 ) @ ( set_difference @ SV30 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(180,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( ~ ( proper_subset @ SV15 @ SV31 )
| ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(181,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) )
| ( proper_subset @ SV15 @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(182,plain,
! [SV38: $i,SV32: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV16 @ SV32 )
| ~ ( subset @ SV16 @ SV38 ) ) )
= $true )
| ( ( subset @ SV16 @ ( set_intersection2 @ SV32 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(183,plain,
! [SV39: $i,SV33: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV17 @ SV33 )
| ~ ( subset @ SV39 @ SV33 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV17 @ SV39 ) @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(184,plain,
! [SV34: $i,SV18: $i] :
( ( ~ ( ( SV18 != SV34 )
| ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(185,plain,
! [SV34: $i,SV18: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) )
| ( SV18 = SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(186,plain,
! [SV35: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( ~ ( subset @ SV7 @ SV24 )
| ~ ( subset @ SV24 @ SV35 ) ) )
= $false )
| ( ( subset @ SV7 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(187,plain,
! [SV11: $i,SV27: $i] :
( ( ( proper_subset @ SV27 @ SV11 )
= $false )
| ( ( proper_subset @ SV11 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV28 )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SV12 )
| ( in @ SY67 @ SV28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(189,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SV12 )
| ( in @ SY68 @ SV28 ) )
| ( subset @ SV12 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(190,plain,
! [SV36: $i,SV29: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV29 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV13 @ SV36 ) @ ( set_intersection2 @ SV29 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV37: $i,SV30: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV30 )
= $false )
| ( ( subset @ ( set_difference @ SV14 @ SV37 ) @ ( set_difference @ SV30 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(192,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( proper_subset @ SV15 @ SV31 )
| ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(193,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) )
| ( proper_subset @ SV15 @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(194,plain,
! [SV38: $i,SV32: $i,SV16: $i] :
( ( ( ~ ( ~ ( subset @ SV16 @ SV32 )
| ~ ( subset @ SV16 @ SV38 ) ) )
= $false )
| ( ( subset @ SV16 @ ( set_intersection2 @ SV32 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV39: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( ~ ( subset @ SV17 @ SV33 )
| ~ ( subset @ SV39 @ SV33 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV17 @ SV39 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV34: $i,SV18: $i] :
( ( ( SV18 != SV34 )
| ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(197,plain,
! [SV34: $i,SV18: $i] :
( ( ~ ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) )
| ( SV18 = SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(198,plain,
! [SV35: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV24 )
| ~ ( subset @ SV24 @ SV35 ) )
= $true )
| ( ( subset @ SV7 @ SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(199,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV28 ) )
= $true )
| ( ( ! [SY67: $i] :
( ~ ( in @ SY67 @ SV12 )
| ( in @ SY67 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SV12 )
| ( in @ SY68 @ SV28 ) ) )
= $true )
| ( ( subset @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( proper_subset @ SV15 @ SV31 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(202,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) ) )
= $true )
| ( ( proper_subset @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(203,plain,
! [SV38: $i,SV32: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV32 )
| ~ ( subset @ SV16 @ SV38 ) )
= $true )
| ( ( subset @ SV16 @ ( set_intersection2 @ SV32 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(204,plain,
! [SV39: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV33 )
| ~ ( subset @ SV39 @ SV33 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV17 @ SV39 ) @ SV33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(205,plain,
! [SV34: $i,SV18: $i] :
( ( ( SV18 != SV34 )
= $true )
| ( ( ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(206,plain,
! [SV34: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) ) )
= $true )
| ( ( SV18 = SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(207,plain,
! [SV35: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV24 ) )
= $true )
| ( ( ~ ( subset @ SV24 @ SV35 ) )
= $true )
| ( ( subset @ SV7 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(208,plain,
! [SV28: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV28 )
= $false )
| ( ( ! [SY67: $i] :
( ~ ( in @ SY67 @ SV12 )
| ( in @ SY67 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(209,plain,
! [SV28: $i,SV12: $i] :
( ( ( ! [SY68: $i] :
( ~ ( in @ SY68 @ SV12 )
| ( in @ SY68 @ SV28 ) ) )
= $false )
| ( ( subset @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(210,plain,
! [SV31: $i,SV15: $i] :
( ( ( proper_subset @ SV15 @ SV31 )
= $false )
| ( ( ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(211,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) ) )
= $false )
| ( ( proper_subset @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(212,plain,
! [SV38: $i,SV32: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV32 ) )
= $true )
| ( ( ~ ( subset @ SV16 @ SV38 ) )
= $true )
| ( ( subset @ SV16 @ ( set_intersection2 @ SV32 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(213,plain,
! [SV39: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV33 ) )
= $true )
| ( ( ~ ( subset @ SV39 @ SV33 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV17 @ SV39 ) @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(214,plain,
! [SV34: $i,SV18: $i] :
( ( ( SV18 = SV34 )
= $false )
| ( ( ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(215,plain,
! [SV34: $i,SV18: $i] :
( ( ( ~ ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) ) )
= $false )
| ( ( SV18 = SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(216,plain,
! [SV35: $i,SV24: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV24 )
= $false )
| ( ( ~ ( subset @ SV24 @ SV35 ) )
= $true )
| ( ( subset @ SV7 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(217,plain,
! [SV28: $i,SV12: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV12 )
| ( in @ SV40 @ SV28 ) )
= $true )
| ( ( subset @ SV12 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV12: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK3_SY68 @ SV28 @ SV12 ) @ SV12 )
| ( in @ ( sK3_SY68 @ SV28 @ SV12 ) @ SV28 ) )
= $false )
| ( ( subset @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[209]) ).
thf(219,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) )
= $false )
| ( ( proper_subset @ SV15 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(220,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV31 )
| ~ ( ( SV15 != SV31 ) ) )
= $true )
| ( ( proper_subset @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(221,plain,
! [SV38: $i,SV32: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV32 )
= $false )
| ( ( ~ ( subset @ SV16 @ SV38 ) )
= $true )
| ( ( subset @ SV16 @ ( set_intersection2 @ SV32 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(222,plain,
! [SV39: $i,SV33: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV33 )
= $false )
| ( ( ~ ( subset @ SV39 @ SV33 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV17 @ SV39 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(223,plain,
! [SV34: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) )
= $false )
| ( ( SV18 = SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(224,plain,
! [SV34: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV34 )
| ~ ( subset @ SV34 @ SV18 ) )
= $true )
| ( ( SV18 = SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(225,plain,
! [SV7: $i,SV35: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV35 )
= $false )
| ( ( subset @ SV7 @ SV24 )
= $false )
| ( ( subset @ SV7 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(226,plain,
! [SV28: $i,SV12: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV12 ) )
= $true )
| ( ( in @ SV40 @ SV28 )
= $true )
| ( ( subset @ SV12 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(227,plain,
! [SV12: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK3_SY68 @ SV28 @ SV12 ) @ SV12 ) )
= $false )
| ( ( subset @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(228,plain,
! [SV12: $i,SV28: $i] :
( ( ( in @ ( sK3_SY68 @ SV28 @ SV12 ) @ SV28 )
= $false )
| ( ( subset @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(229,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV31 ) )
= $false )
| ( ( proper_subset @ SV15 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(230,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( ( SV15 != SV31 ) ) )
= $false )
| ( ( proper_subset @ SV15 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(231,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV31 ) )
= $true )
| ( ( ~ ( ( SV15 != SV31 ) ) )
= $true )
| ( ( proper_subset @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(232,plain,
! [SV32: $i,SV38: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV38 )
= $false )
| ( ( subset @ SV16 @ SV32 )
= $false )
| ( ( subset @ SV16 @ ( set_intersection2 @ SV32 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(233,plain,
! [SV17: $i,SV33: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV33 )
= $false )
| ( ( subset @ SV17 @ SV33 )
= $false )
| ( ( subset @ ( set_union2 @ SV17 @ SV39 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(234,plain,
! [SV34: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV34 ) )
= $false )
| ( ( SV18 = SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(235,plain,
! [SV18: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV18 ) )
= $false )
| ( ( SV18 = SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(236,plain,
! [SV34: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV34 ) )
= $true )
| ( ( ~ ( subset @ SV34 @ SV18 ) )
= $true )
| ( ( SV18 = SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(237,plain,
! [SV28: $i,SV12: $i,SV40: $i] :
( ( ( in @ SV40 @ SV12 )
= $false )
| ( ( in @ SV40 @ SV28 )
= $true )
| ( ( subset @ SV12 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV12: $i,SV28: $i] :
( ( ( in @ ( sK3_SY68 @ SV28 @ SV12 ) @ SV12 )
= $true )
| ( ( subset @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(239,plain,
! [SV31: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV31 )
= $true )
| ( ( proper_subset @ SV15 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(240,plain,
! [SV31: $i,SV15: $i] :
( ( ( SV15 != SV31 )
= $true )
| ( ( proper_subset @ SV15 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(241,plain,
! [SV31: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV31 )
= $false )
| ( ( ~ ( ( SV15 != SV31 ) ) )
= $true )
| ( ( proper_subset @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(242,plain,
! [SV34: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV34 )
= $true )
| ( ( SV18 = SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(243,plain,
! [SV18: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV18 )
= $true )
| ( ( SV18 = SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(244,plain,
! [SV34: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV34 )
= $false )
| ( ( ~ ( subset @ SV34 @ SV18 ) )
= $true )
| ( ( SV18 = SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(245,plain,
! [SV31: $i,SV15: $i] :
( ( ( SV15 = SV31 )
= $false )
| ( ( proper_subset @ SV15 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(246,plain,
! [SV31: $i,SV15: $i] :
( ( ( SV15 != SV31 )
= $false )
| ( ( subset @ SV15 @ SV31 )
= $false )
| ( ( proper_subset @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(247,plain,
! [SV18: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV18 )
= $false )
| ( ( subset @ SV18 @ SV34 )
= $false )
| ( ( SV18 = SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(248,plain,
! [SV31: $i,SV15: $i] :
( ( ( SV15 = SV31 )
= $true )
| ( ( subset @ SV15 @ SV31 )
= $false )
| ( ( proper_subset @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(249,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[99,248,247,245,243,242,239,238,237,233,232,228,225,191,190,187,174,173,168,167,161,157,142,140,139,138,120,102,101,100]) ).
thf(250,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU139+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
% 0.08/0.20 % Computer : n011.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 15:01:36 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.30
% 0.56/0.30 No.of.Axioms: 22
% 0.56/0.30
% 0.56/0.30 Length.of.Defs: 0
% 0.56/0.30
% 0.56/0.30 Contains.Choice.Funs: false
% 0.56/0.30 ......
% 0.56/0.30
% 0.56/0.30 ********************************
% 0.56/0.30 * All subproblems solved! *
% 0.56/0.30 ********************************
% 0.56/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,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:249,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.56/0.30
% 0.56/0.30 %**** Beginning of derivation protocol ****
% 0.56/0.30 % SZS output start CNFRefutation
% See solution above
% 0.56/0.30
% 0.56/0.30 %**** End of derivation protocol ****
% 0.56/0.30 %**** no. of clauses in derivation: 218 ****
% 0.56/0.30 %**** clause counter: 249 ****
% 0.56/0.30
% 0.56/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,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:249,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------