%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU143+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 10:43:02 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 173 ( 113 unt; 0 typ; 0 def)
% Number of atoms : 863 ( 455 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1161 ( 290 ~; 224 |; 0 &; 623 @)
% ( 18 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 277 ( 0 ^; 277 !; 0 ?; 277 :)
% 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_SY21,type,
sK2_SY21: $i > $i ).
thf(tp_sK3_SY29,type,
sK3_SY29: $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_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(5,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(7,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(8,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(18,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(19,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(32,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(43,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(50,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(56,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(64,conjecture,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(65,negated_conjecture,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $false ),
inference(negate_conjecture,[status(cth)],[64]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $false ),
inference(unfold_def,[status(thm)],[65]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(71,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(72,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(73,plain,
$true = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(74,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(75,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(76,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(77,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(78,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(80,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(85,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(87,plain,
( ( ( singleton @ sK1_A )
!= empty_set )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(88,plain,
( ( ~ ( ( ( singleton @ sK1_A )
!= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[87]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(90,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(92,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(93,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(97,plain,
$true = $true,
inference(copy,[status(thm)],[78]) ).
thf(98,plain,
$true = $true,
inference(copy,[status(thm)],[77]) ).
thf(99,plain,
$true = $true,
inference(copy,[status(thm)],[76]) ).
thf(100,plain,
$true = $true,
inference(copy,[status(thm)],[75]) ).
thf(101,plain,
$true = $true,
inference(copy,[status(thm)],[74]) ).
thf(102,plain,
$true = $true,
inference(copy,[status(thm)],[73]) ).
thf(103,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(104,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(105,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(106,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(107,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(108,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(109,plain,
( ( ~ ( ( ( singleton @ sK1_A )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(110,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(111,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(113,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)],[94]) ).
thf(114,plain,
( ( ~ ( ( ( singleton @ sK1_A )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(118,plain,
! [SV1: $i] :
( ( subset @ empty_set @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(119,plain,
! [SV2: $i] :
( ( ( unordered_pair @ SV2 @ SV2 )
= ( singleton @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(120,plain,
! [SV3: $i] :
( ( ( set_union2 @ SV3 @ empty_set )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV4: $i] :
( ( ( set_intersection2 @ SV4 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(122,plain,
! [SV5: $i] :
( ( ( set_difference @ SV5 @ empty_set )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV6: $i] :
( ( ( set_difference @ empty_set @ SV6 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(124,plain,
! [SV7: $i] :
( ( ~ ( subset @ SV7 @ empty_set )
| ( SV7 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV8: $i] :
( ( ~ ( ~ ( ( SV8 != empty_set )
| ! [SY20: $i] :
~ ( in @ SY20 @ SV8 ) )
| ~ ( ~ ! [SY21: $i] :
~ ( in @ SY21 @ SV8 )
| ( SV8 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV9: $i] :
( ( ! [SY22: $i] :
~ ( ~ ( ( ( set_difference @ SV9 @ SY22 )
!= empty_set )
| ( subset @ SV9 @ SY22 ) )
| ~ ( ~ ( subset @ SV9 @ SY22 )
| ( ( set_difference @ SV9 @ SY22 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV10: $i] :
( ( ! [SY23: $i] :
~ ( ~ ( ( SY23
!= ( singleton @ SV10 ) )
| ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SY23 )
| ( SY24 = SV10 ) )
| ~ ( ( SY24 != SV10 )
| ( in @ SY24 @ SY23 ) ) ) )
| ~ ( ~ ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SY23 )
| ( SY25 = SV10 ) )
| ~ ( ( SY25 != SV10 )
| ( in @ SY25 @ SY23 ) ) )
| ( SY23
= ( singleton @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(128,plain,
( ( ( singleton @ sK1_A )
!= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV11: $i] :
( ( ! [SY26: $i] :
~ ( ~ ( ~ ( disjoint @ SV11 @ SY26 )
| ( ( set_intersection2 @ SV11 @ SY26 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV11 @ SY26 )
!= empty_set )
| ( disjoint @ SV11 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV12: $i] :
( ( ! [SY27: $i] :
~ ( ~ ( ( ( set_difference @ SV12 @ SY27 )
!= empty_set )
| ( subset @ SV12 @ SY27 ) )
| ~ ( ~ ( subset @ SV12 @ SY27 )
| ( ( set_difference @ SV12 @ SY27 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV13: $i] :
( ( ~ ( empty @ SV13 )
| ( SV13 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV7: $i] :
( ( ( ~ ( subset @ SV7 @ empty_set ) )
= $true )
| ( ( SV7 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV8: $i] :
( ( ~ ( ( SV8 != empty_set )
| ! [SY20: $i] :
~ ( in @ SY20 @ SV8 ) )
| ~ ( ~ ! [SY21: $i] :
~ ( in @ SY21 @ SV8 )
| ( SV8 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(134,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV9 @ SV14 )
!= empty_set )
| ( subset @ SV9 @ SV14 ) )
| ~ ( ~ ( subset @ SV9 @ SV14 )
| ( ( set_difference @ SV9 @ SV14 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV10: $i,SV15: $i] :
( ( ~ ( ~ ( ( SV15
!= ( singleton @ SV10 ) )
| ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SV15 )
| ( SY28 = SV10 ) )
| ~ ( ( SY28 != SV10 )
| ( in @ SY28 @ SV15 ) ) ) )
| ~ ( ~ ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV15 )
| ( SY29 = SV10 ) )
| ~ ( ( SY29 != SV10 )
| ( in @ SY29 @ SV15 ) ) )
| ( SV15
= ( singleton @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(136,plain,
( ( ( singleton @ sK1_A )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(137,plain,
! [SV16: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV11 @ SV16 )
| ( ( set_intersection2 @ SV11 @ SV16 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV11 @ SV16 )
!= empty_set )
| ( disjoint @ SV11 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV17: $i,SV12: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV12 @ SV17 )
!= empty_set )
| ( subset @ SV12 @ SV17 ) )
| ~ ( ~ ( subset @ SV12 @ SV17 )
| ( ( set_difference @ SV12 @ SV17 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(139,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $true )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(140,plain,
! [SV7: $i] :
( ( ( subset @ SV7 @ empty_set )
= $false )
| ( ( SV7 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV8: $i] :
( ( ~ ( ( SV8 != empty_set )
| ! [SY20: $i] :
~ ( in @ SY20 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(142,plain,
! [SV8: $i] :
( ( ~ ( ~ ! [SY21: $i] :
~ ( in @ SY21 @ SV8 )
| ( SV8 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(143,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( ( ( set_difference @ SV9 @ SV14 )
!= empty_set )
| ( subset @ SV9 @ SV14 ) )
| ~ ( ~ ( subset @ SV9 @ SV14 )
| ( ( set_difference @ SV9 @ SV14 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(144,plain,
! [SV10: $i,SV15: $i] :
( ( ~ ( ( SV15
!= ( singleton @ SV10 ) )
| ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SV15 )
| ( SY28 = SV10 ) )
| ~ ( ( SY28 != SV10 )
| ( in @ SY28 @ SV15 ) ) ) )
| ~ ( ~ ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV15 )
| ( SY29 = SV10 ) )
| ~ ( ( SY29 != SV10 )
| ( in @ SY29 @ SV15 ) ) )
| ( SV15
= ( singleton @ SV10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV16: $i,SV11: $i] :
( ( ~ ( ~ ( disjoint @ SV11 @ SV16 )
| ( ( set_intersection2 @ SV11 @ SV16 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV11 @ SV16 )
!= empty_set )
| ( disjoint @ SV11 @ SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(146,plain,
! [SV17: $i,SV12: $i] :
( ( ~ ( ( ( set_difference @ SV12 @ SV17 )
!= empty_set )
| ( subset @ SV12 @ SV17 ) )
| ~ ( ~ ( subset @ SV12 @ SV17 )
| ( ( set_difference @ SV12 @ SV17 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(147,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV8: $i] :
( ( ( SV8 != empty_set )
| ! [SY20: $i] :
~ ( in @ SY20 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(149,plain,
! [SV8: $i] :
( ( ~ ! [SY21: $i] :
~ ( in @ SY21 @ SV8 )
| ( SV8 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(150,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( ( ( set_difference @ SV9 @ SV14 )
!= empty_set )
| ( subset @ SV9 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(151,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( ~ ( subset @ SV9 @ SV14 )
| ( ( set_difference @ SV9 @ SV14 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(152,plain,
! [SV10: $i,SV15: $i] :
( ( ~ ( ( SV15
!= ( singleton @ SV10 ) )
| ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SV15 )
| ( SY28 = SV10 ) )
| ~ ( ( SY28 != SV10 )
| ( in @ SY28 @ SV15 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(153,plain,
! [SV10: $i,SV15: $i] :
( ( ~ ( ~ ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV15 )
| ( SY29 = SV10 ) )
| ~ ( ( SY29 != SV10 )
| ( in @ SY29 @ SV15 ) ) )
| ( SV15
= ( singleton @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(154,plain,
! [SV16: $i,SV11: $i] :
( ( ~ ( ~ ( disjoint @ SV11 @ SV16 )
| ( ( set_intersection2 @ SV11 @ SV16 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(155,plain,
! [SV16: $i,SV11: $i] :
( ( ~ ( ( ( set_intersection2 @ SV11 @ SV16 )
!= empty_set )
| ( disjoint @ SV11 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(156,plain,
! [SV17: $i,SV12: $i] :
( ( ~ ( ( ( set_difference @ SV12 @ SV17 )
!= empty_set )
| ( subset @ SV12 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(157,plain,
! [SV17: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV17 )
| ( ( set_difference @ SV12 @ SV17 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(158,plain,
! [SV8: $i] :
( ( ( SV8 != empty_set )
= $true )
| ( ( ! [SY20: $i] :
~ ( in @ SY20 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV8: $i] :
( ( ( ~ ! [SY21: $i] :
~ ( in @ SY21 @ SV8 ) )
= $true )
| ( ( SV8 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV14: $i,SV9: $i] :
( ( ( ( set_difference @ SV9 @ SV14 )
!= empty_set )
| ( subset @ SV9 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(161,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV14 )
| ( ( set_difference @ SV9 @ SV14 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(162,plain,
! [SV10: $i,SV15: $i] :
( ( ( SV15
!= ( singleton @ SV10 ) )
| ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SV15 )
| ( SY28 = SV10 ) )
| ~ ( ( SY28 != SV10 )
| ( in @ SY28 @ SV15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(163,plain,
! [SV10: $i,SV15: $i] :
( ( ~ ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV15 )
| ( SY29 = SV10 ) )
| ~ ( ( SY29 != SV10 )
| ( in @ SY29 @ SV15 ) ) )
| ( SV15
= ( singleton @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(164,plain,
! [SV16: $i,SV11: $i] :
( ( ~ ( disjoint @ SV11 @ SV16 )
| ( ( set_intersection2 @ SV11 @ SV16 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(165,plain,
! [SV16: $i,SV11: $i] :
( ( ( ( set_intersection2 @ SV11 @ SV16 )
!= empty_set )
| ( disjoint @ SV11 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(166,plain,
! [SV17: $i,SV12: $i] :
( ( ( ( set_difference @ SV12 @ SV17 )
!= empty_set )
| ( subset @ SV12 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(167,plain,
! [SV17: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV17 )
| ( ( set_difference @ SV12 @ SV17 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(168,plain,
! [SV8: $i] :
( ( ( SV8 = empty_set )
= $false )
| ( ( ! [SY20: $i] :
~ ( in @ SY20 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV8: $i] :
( ( ( ! [SY21: $i] :
~ ( in @ SY21 @ SV8 ) )
= $false )
| ( ( SV8 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV14: $i,SV9: $i] :
( ( ( ( set_difference @ SV9 @ SV14 )
!= empty_set )
= $true )
| ( ( subset @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV14 ) )
= $true )
| ( ( ( set_difference @ SV9 @ SV14 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV10: $i,SV15: $i] :
( ( ( SV15
!= ( singleton @ SV10 ) )
= $true )
| ( ( ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SV15 )
| ( SY28 = SV10 ) )
| ~ ( ( SY28 != SV10 )
| ( in @ SY28 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV10: $i,SV15: $i] :
( ( ( ~ ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV15 )
| ( SY29 = SV10 ) )
| ~ ( ( SY29 != SV10 )
| ( in @ SY29 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV16: $i,SV11: $i] :
( ( ( ~ ( disjoint @ SV11 @ SV16 ) )
= $true )
| ( ( ( set_intersection2 @ SV11 @ SV16 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV16: $i,SV11: $i] :
( ( ( ( set_intersection2 @ SV11 @ SV16 )
!= empty_set )
= $true )
| ( ( disjoint @ SV11 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV17: $i,SV12: $i] :
( ( ( ( set_difference @ SV12 @ SV17 )
!= empty_set )
= $true )
| ( ( subset @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV17: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV17 ) )
= $true )
| ( ( ( set_difference @ SV12 @ SV17 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV8 ) )
= $true )
| ( ( SV8 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK2_SY21 @ SV8 ) @ SV8 ) )
= $false )
| ( ( SV8 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[169]) ).
thf(180,plain,
! [SV14: $i,SV9: $i] :
( ( ( ( set_difference @ SV9 @ SV14 )
= empty_set )
= $false )
| ( ( subset @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV14: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV14 )
= $false )
| ( ( ( set_difference @ SV9 @ SV14 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV10: $i,SV15: $i] :
( ( ( SV15
= ( singleton @ SV10 ) )
= $false )
| ( ( ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SV15 )
| ( SY28 = SV10 ) )
| ~ ( ( SY28 != SV10 )
| ( in @ SY28 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV10: $i,SV15: $i] :
( ( ( ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SV15 )
| ( SY29 = SV10 ) )
| ~ ( ( SY29 != SV10 )
| ( in @ SY29 @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV16: $i,SV11: $i] :
( ( ( disjoint @ SV11 @ SV16 )
= $false )
| ( ( ( set_intersection2 @ SV11 @ SV16 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV16: $i,SV11: $i] :
( ( ( ( set_intersection2 @ SV11 @ SV16 )
= empty_set )
= $false )
| ( ( disjoint @ SV11 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV17: $i,SV12: $i] :
( ( ( ( set_difference @ SV12 @ SV17 )
= empty_set )
= $false )
| ( ( subset @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV17: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV17 )
= $false )
| ( ( ( set_difference @ SV12 @ SV17 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(188,plain,
! [SV8: $i,SV18: $i] :
( ( ( in @ SV18 @ SV8 )
= $false )
| ( ( SV8 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(189,plain,
! [SV8: $i] :
( ( ( in @ ( sK2_SY21 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(190,plain,
! [SV10: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV19 @ SV15 )
| ( SV19 = SV10 ) )
| ~ ( ( SV19 != SV10 )
| ( in @ SV19 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV15: $i,SV10: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
| ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 ) )
| ~ ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
| ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[183]) ).
thf(192,plain,
! [SV10: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ SV15 )
| ( SV19 = SV10 ) )
| ~ ( ( SV19 != SV10 )
| ( in @ SV19 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(193,plain,
! [SV15: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
| ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 ) )
| ~ ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
| ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(194,plain,
! [SV10: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ SV15 )
| ( SV19 = SV10 ) ) )
= $false )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(195,plain,
! [SV15: $i,SV10: $i,SV19: $i] :
( ( ( ~ ( ( SV19 != SV10 )
| ( in @ SV19 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(196,plain,
! [SV15: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
| ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 ) ) )
= $true )
| ( ( ~ ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
| ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(197,plain,
! [SV10: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV15 )
| ( SV19 = SV10 ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(198,plain,
! [SV15: $i,SV10: $i,SV19: $i] :
( ( ( ( SV19 != SV10 )
| ( in @ SV19 @ SV15 ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(199,plain,
! [SV15: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
| ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 ) )
= $false )
| ( ( ~ ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
| ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(200,plain,
! [SV10: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV15 ) )
= $true )
| ( ( SV19 = SV10 )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(201,plain,
! [SV15: $i,SV10: $i,SV19: $i] :
( ( ( SV19 != SV10 )
= $true )
| ( ( in @ SV19 @ SV15 )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(202,plain,
! [SV15: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ~ ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
| ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(203,plain,
! [SV15: $i,SV10: $i] :
( ( ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 )
= $false )
| ( ( ~ ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
| ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(204,plain,
! [SV10: $i,SV15: $i,SV19: $i] :
( ( ( in @ SV19 @ SV15 )
= $false )
| ( ( SV19 = SV10 )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(205,plain,
! [SV15: $i,SV10: $i,SV19: $i] :
( ( ( SV19 = SV10 )
= $false )
| ( ( in @ SV19 @ SV15 )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(206,plain,
! [SV15: $i,SV10: $i] :
( ( ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
| ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(207,plain,
! [SV15: $i,SV10: $i] :
( ( ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
| ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 )
= $false )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(208,plain,
! [SV15: $i,SV10: $i] :
( ( ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
| ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(209,plain,
! [SV15: $i,SV10: $i] :
( ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
= $false )
| ( ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 )
= $false )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(210,plain,
! [SV15: $i,SV10: $i] :
( ( ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
= $false )
| ( ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 )
= $false )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(211,plain,
! [SV15: $i,SV10: $i] :
( ( ( ( sK3_SY29 @ SV10 @ SV15 )
!= SV10 )
= $false )
| ( ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(212,plain,
! [SV15: $i,SV10: $i] :
( ( ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(213,plain,
! [SV15: $i,SV10: $i] :
( ( ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 )
= $true )
| ( ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 )
= $false )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(214,plain,
! [SV15: $i,SV10: $i] :
( ( ( ( sK3_SY29 @ SV10 @ SV15 )
= SV10 )
= $true )
| ( ( in @ ( sK3_SY29 @ SV10 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(215,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[97,214,213,212,210,205,204,189,188,187,186,185,184,181,180,147,140,136,123,122,121,120,119,118,103,102,101,100,99,98]) ).
thf(216,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU143+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:04:12 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 20
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 0
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 ....
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:20,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:215,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 173 ****
% 0.07/0.25 %**** clause counter: 215 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:20,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:215,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------