%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU129+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 : n008.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 10:42:59 AM UTC 2026
% Result : Theorem 0.40s 0.42s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 19
% Syntax : Number of formulae : 220 ( 113 unt; 0 typ; 0 def)
% Number of atoms : 1455 ( 493 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 2949 ( 630 ~; 450 |; 15 &;1818 @)
% ( 12 <=>; 24 =>; 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 : 554 ( 0 ^; 554 !; 0 ?; 554 :)
% 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_SY36,type,
sK2_SY36: $i ).
thf(tp_sK3_SY38,type,
sK3_SY38: $i ).
thf(tp_sK4_SY65,type,
sK4_SY65: $i > $i > $i ).
thf(tp_sK5_SY68,type,
sK5_SY68: $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_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(7,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(15,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(16,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(17,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(28,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(30,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(32,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(35,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(37,conjecture,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(38,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(43,plain,
$true = $true,
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
$true = $true,
inference(unfold_def,[status(thm)],[16]) ).
thf(45,plain,
$true = $true,
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(50,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)],[27]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(53,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(55,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)],[34]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(58,plain,
( ( ! [SY36: $i,SY37: $i] :
( ( subset @ sK1_A @ SY36 )
=> ( subset @ ( set_intersection2 @ sK1_A @ SY37 ) @ ( set_intersection2 @ SY36 @ SY37 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(59,plain,
( ( ! [SY38: $i] :
( ( subset @ sK1_A @ sK2_SY36 )
=> ( subset @ ( set_intersection2 @ sK1_A @ SY38 ) @ ( set_intersection2 @ sK2_SY36 @ SY38 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(60,plain,
( ( ( subset @ sK1_A @ sK2_SY36 )
=> ( subset @ ( set_intersection2 @ sK1_A @ sK3_SY38 ) @ ( set_intersection2 @ sK2_SY36 @ sK3_SY38 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(61,plain,
( ( subset @ sK1_A @ sK2_SY36 )
= $true ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(62,plain,
( ( subset @ ( set_intersection2 @ sK1_A @ sK3_SY38 ) @ ( set_intersection2 @ sK2_SY36 @ sK3_SY38 ) )
= $false ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(63,plain,
( ( ~ ( subset @ ( set_intersection2 @ sK1_A @ sK3_SY38 ) @ ( set_intersection2 @ sK2_SY36 @ sK3_SY38 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[62]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(66,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(67,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(68,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(70,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(71,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(75,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(76,plain,
$true = $true,
inference(copy,[status(thm)],[45]) ).
thf(77,plain,
$true = $true,
inference(copy,[status(thm)],[44]) ).
thf(78,plain,
$true = $true,
inference(copy,[status(thm)],[43]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(81,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(82,plain,
( ( subset @ sK1_A @ sK2_SY36 )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(83,plain,
( ( ~ ( subset @ ( set_intersection2 @ sK1_A @ sK3_SY38 ) @ ( set_intersection2 @ sK2_SY36 @ sK3_SY38 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(84,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)],[66]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(86,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)],[73]) ).
thf(87,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)],[71]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ 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_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(89,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)],[74]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(91,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(92,plain,
! [SV1: $i] :
( ( ! [SY39: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY39 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(93,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(94,plain,
! [SV3: $i] :
( ( ! [SY40: $i] : ( subset @ SV3 @ ( set_union2 @ SV3 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(95,plain,
! [SV4: $i] :
( ( ! [SY41: $i] :
( ( set_intersection2 @ SV4 @ SY41 )
= ( set_intersection2 @ SY41 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(96,plain,
! [SV5: $i] :
( ( ! [SY42: $i] :
( ( set_intersection2 @ SV5 @ SV5 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(97,plain,
! [SV6: $i] :
( ( ! [SY43: $i] : ( subset @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(98,plain,
! [SV7: $i] :
( ( ( set_intersection2 @ SV7 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(99,plain,
( ( subset @ ( set_intersection2 @ sK1_A @ sK3_SY38 ) @ ( set_intersection2 @ sK2_SY36 @ sK3_SY38 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(100,plain,
! [SV8: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ~ ( ~ ( subset @ SV8 @ SY44 )
| ~ ( subset @ SV8 @ SY45 ) )
| ( subset @ SV8 @ ( set_intersection2 @ SY44 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV9: $i] :
( ( ! [SY46: $i] :
( ~ ( subset @ SV9 @ SY46 )
| ( ( set_union2 @ SV9 @ SY46 )
= SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV10: $i] :
( ( ! [SY47: $i] :
~ ( ~ ( ( SV10 != SY47 )
| ~ ( ~ ( subset @ SV10 @ SY47 )
| ~ ( subset @ SY47 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV10 @ SY47 )
| ~ ( subset @ SY47 @ SV10 ) )
| ( SV10 = SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV11: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ~ ( ~ ( subset @ SV11 @ SY48 )
| ~ ( subset @ SY49 @ SY48 ) )
| ( subset @ ( set_union2 @ SV11 @ SY49 ) @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV12: $i] :
( ( ! [SY50: $i,SY51: $i] :
~ ( ~ ( ( SY51
!= ( set_intersection2 @ SV12 @ SY50 ) )
| ! [SY52: $i] :
~ ( ~ ( ~ ( in @ SY52 @ SY51 )
| ~ ( ~ ( in @ SY52 @ SV12 )
| ~ ( in @ SY52 @ SY50 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY52 @ SV12 )
| ~ ( in @ SY52 @ SY50 ) )
| ( in @ SY52 @ SY51 ) ) ) )
| ~ ( ~ ! [SY53: $i] :
~ ( ~ ( ~ ( in @ SY53 @ SY51 )
| ~ ( ~ ( in @ SY53 @ SV12 )
| ~ ( in @ SY53 @ SY50 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY53 @ SV12 )
| ~ ( in @ SY53 @ SY50 ) )
| ( in @ SY53 @ SY51 ) ) )
| ( SY51
= ( set_intersection2 @ SV12 @ SY50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV13: $i] :
( ( ! [SY54: $i] :
~ ( ~ ( ~ ( subset @ SV13 @ SY54 )
| ! [SY55: $i] :
( ~ ( in @ SY55 @ SV13 )
| ( in @ SY55 @ SY54 ) ) )
| ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ SV13 )
| ( in @ SY56 @ SY54 ) )
| ( subset @ SV13 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV14: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ~ ( ~ ( subset @ SV14 @ SY57 )
| ~ ( subset @ SY57 @ SY58 ) )
| ( subset @ SV14 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(107,plain,
! [SV15: $i] :
( ( ~ ( subset @ SV15 @ empty_set )
| ( SV15 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(108,plain,
! [SV16: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV16 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(109,plain,
! [SV17: $i,SV3: $i] :
( ( subset @ SV3 @ ( set_union2 @ SV3 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV18: $i,SV4: $i] :
( ( ( set_intersection2 @ SV4 @ SV18 )
= ( set_intersection2 @ SV18 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV5: $i] :
( ( ( set_intersection2 @ SV5 @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY59: $i] :
( ~ ~ ( ~ ( subset @ SV8 @ SV21 )
| ~ ( subset @ SV8 @ SY59 ) )
| ( subset @ SV8 @ ( set_intersection2 @ SV21 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV22: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV22 )
| ( ( set_union2 @ SV9 @ SV22 )
= SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV23: $i,SV10: $i] :
( ( ~ ( ~ ( ( SV10 != SV23 )
| ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) )
| ( SV10 = SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(116,plain,
! [SV24: $i,SV11: $i] :
( ( ! [SY60: $i] :
( ~ ~ ( ~ ( subset @ SV11 @ SV24 )
| ~ ( subset @ SY60 @ SV24 ) )
| ( subset @ ( set_union2 @ SV11 @ SY60 ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(117,plain,
! [SV25: $i,SV12: $i] :
( ( ! [SY61: $i] :
~ ( ~ ( ( SY61
!= ( set_intersection2 @ SV12 @ SV25 ) )
| ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ( ~ ( in @ SY62 @ SV12 )
| ~ ( in @ SY62 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY62 @ SV12 )
| ~ ( in @ SY62 @ SV25 ) )
| ( in @ SY62 @ SY61 ) ) ) )
| ~ ( ~ ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SY61 )
| ~ ( ~ ( in @ SY63 @ SV12 )
| ~ ( in @ SY63 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV12 )
| ~ ( in @ SY63 @ SV25 ) )
| ( in @ SY63 @ SY61 ) ) )
| ( SY61
= ( set_intersection2 @ SV12 @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(118,plain,
! [SV26: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV13 @ SV26 )
| ! [SY64: $i] :
( ~ ( in @ SY64 @ SV13 )
| ( in @ SY64 @ SV26 ) ) )
| ~ ( ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ SV13 )
| ( in @ SY65 @ SV26 ) )
| ( subset @ SV13 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(119,plain,
! [SV27: $i,SV14: $i] :
( ( ! [SY66: $i] :
( ~ ~ ( ~ ( subset @ SV14 @ SV27 )
| ~ ( subset @ SV27 @ SY66 ) )
| ( subset @ SV14 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(120,plain,
! [SV15: $i] :
( ( ( ~ ( subset @ SV15 @ empty_set ) )
= $true )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV28: $i,SV21: $i,SV8: $i] :
( ( ~ ~ ( ~ ( subset @ SV8 @ SV21 )
| ~ ( subset @ SV8 @ SV28 ) )
| ( subset @ SV8 @ ( set_intersection2 @ SV21 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV22: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV22 ) )
= $true )
| ( ( ( set_union2 @ SV9 @ SV22 )
= SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(123,plain,
! [SV23: $i,SV10: $i] :
( ( ~ ( ( SV10 != SV23 )
| ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) )
| ( SV10 = SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV29: $i,SV24: $i,SV11: $i] :
( ( ~ ~ ( ~ ( subset @ SV11 @ SV24 )
| ~ ( subset @ SV29 @ SV24 ) )
| ( subset @ ( set_union2 @ SV11 @ SV29 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(125,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ~ ( ~ ( ( SV30
!= ( set_intersection2 @ SV12 @ SV25 ) )
| ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV30 )
| ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) )
| ( in @ SY67 @ SV30 ) ) ) )
| ~ ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV30 )
| ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) )
| ( in @ SY68 @ SV30 ) ) )
| ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV26: $i,SV13: $i] :
( ( ~ ( ~ ( subset @ SV13 @ SV26 )
| ! [SY64: $i] :
( ~ ( in @ SY64 @ SV13 )
| ( in @ SY64 @ SV26 ) ) )
| ~ ( ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ SV13 )
| ( in @ SY65 @ SV26 ) )
| ( subset @ SV13 @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV31: $i,SV27: $i,SV14: $i] :
( ( ~ ~ ( ~ ( subset @ SV14 @ SV27 )
| ~ ( subset @ SV27 @ SV31 ) )
| ( subset @ SV14 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV15: $i] :
( ( ( subset @ SV15 @ empty_set )
= $false )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV28: $i,SV21: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV8 @ SV21 )
| ~ ( subset @ SV8 @ SV28 ) ) )
= $true )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV21 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(130,plain,
! [SV22: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV22 )
= $false )
| ( ( ( set_union2 @ SV9 @ SV22 )
= SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(131,plain,
! [SV23: $i,SV10: $i] :
( ( ~ ( ( SV10 != SV23 )
| ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(132,plain,
! [SV23: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) )
| ( SV10 = SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(133,plain,
! [SV29: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV11 @ SV24 )
| ~ ( subset @ SV29 @ SV24 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV11 @ SV29 ) @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(134,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ~ ( ( SV30
!= ( set_intersection2 @ SV12 @ SV25 ) )
| ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV30 )
| ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) )
| ( in @ SY67 @ SV30 ) ) ) )
| ~ ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV30 )
| ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) )
| ( in @ SY68 @ SV30 ) ) )
| ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(135,plain,
! [SV26: $i,SV13: $i] :
( ( ~ ( ~ ( subset @ SV13 @ SV26 )
| ! [SY64: $i] :
( ~ ( in @ SY64 @ SV13 )
| ( in @ SY64 @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(136,plain,
! [SV26: $i,SV13: $i] :
( ( ~ ( ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ SV13 )
| ( in @ SY65 @ SV26 ) )
| ( subset @ SV13 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(137,plain,
! [SV31: $i,SV27: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV14 @ SV27 )
| ~ ( subset @ SV27 @ SV31 ) ) )
= $true )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV28: $i,SV21: $i,SV8: $i] :
( ( ( ~ ( ~ ( subset @ SV8 @ SV21 )
| ~ ( subset @ SV8 @ SV28 ) ) )
= $false )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV21 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV23: $i,SV10: $i] :
( ( ( SV10 != SV23 )
| ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(140,plain,
! [SV23: $i,SV10: $i] :
( ( ~ ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) )
| ( SV10 = SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(141,plain,
! [SV29: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( ~ ( subset @ SV11 @ SV24 )
| ~ ( subset @ SV29 @ SV24 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV11 @ SV29 ) @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ~ ( ( SV30
!= ( set_intersection2 @ SV12 @ SV25 ) )
| ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV30 )
| ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) )
| ( in @ SY67 @ SV30 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(143,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ~ ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV30 )
| ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) )
| ( in @ SY68 @ SV30 ) ) )
| ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(144,plain,
! [SV26: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV26 )
| ! [SY64: $i] :
( ~ ( in @ SY64 @ SV13 )
| ( in @ SY64 @ SV26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(145,plain,
! [SV26: $i,SV13: $i] :
( ( ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ SV13 )
| ( in @ SY65 @ SV26 ) )
| ( subset @ SV13 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(146,plain,
! [SV31: $i,SV27: $i,SV14: $i] :
( ( ( ~ ( ~ ( subset @ SV14 @ SV27 )
| ~ ( subset @ SV27 @ SV31 ) ) )
= $false )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(147,plain,
! [SV28: $i,SV21: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV21 )
| ~ ( subset @ SV8 @ SV28 ) )
= $true )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV21 @ SV28 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(148,plain,
! [SV23: $i,SV10: $i] :
( ( ( SV10 != SV23 )
= $true )
| ( ( ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(149,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) ) )
= $true )
| ( ( SV10 = SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(150,plain,
! [SV29: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV24 )
| ~ ( subset @ SV29 @ SV24 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV11 @ SV29 ) @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(151,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ( SV30
!= ( set_intersection2 @ SV12 @ SV25 ) )
| ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV30 )
| ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) )
| ( in @ SY67 @ SV30 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(152,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV30 )
| ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) )
| ( in @ SY68 @ SV30 ) ) )
| ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(153,plain,
! [SV26: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV26 ) )
= $true )
| ( ( ! [SY64: $i] :
( ~ ( in @ SY64 @ SV13 )
| ( in @ SY64 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(154,plain,
! [SV26: $i,SV13: $i] :
( ( ( ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ SV13 )
| ( in @ SY65 @ SV26 ) ) )
= $true )
| ( ( subset @ SV13 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(155,plain,
! [SV31: $i,SV27: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV27 )
| ~ ( subset @ SV27 @ SV31 ) )
= $true )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(156,plain,
! [SV28: $i,SV21: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV21 ) )
= $true )
| ( ( ~ ( subset @ SV8 @ SV28 ) )
= $true )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV21 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(157,plain,
! [SV23: $i,SV10: $i] :
( ( ( SV10 = SV23 )
= $false )
| ( ( ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(158,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) ) )
= $false )
| ( ( SV10 = SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(159,plain,
! [SV29: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV24 ) )
= $true )
| ( ( ~ ( subset @ SV29 @ SV24 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV11 @ SV29 ) @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(160,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ( SV30
!= ( set_intersection2 @ SV12 @ SV25 ) )
= $true )
| ( ( ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV30 )
| ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) )
| ( in @ SY67 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(161,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV30 )
| ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) )
| ( in @ SY68 @ SV30 ) ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV26: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV26 )
= $false )
| ( ( ! [SY64: $i] :
( ~ ( in @ SY64 @ SV13 )
| ( in @ SY64 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV26: $i,SV13: $i] :
( ( ( ! [SY65: $i] :
( ~ ( in @ SY65 @ SV13 )
| ( in @ SY65 @ SV26 ) ) )
= $false )
| ( ( subset @ SV13 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV31: $i,SV27: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV27 ) )
= $true )
| ( ( ~ ( subset @ SV27 @ SV31 ) )
= $true )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV28: $i,SV21: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV21 )
= $false )
| ( ( ~ ( subset @ SV8 @ SV28 ) )
= $true )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV21 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) )
= $false )
| ( ( SV10 = SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV23 )
| ~ ( subset @ SV23 @ SV10 ) )
= $true )
| ( ( SV10 = SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(168,plain,
! [SV29: $i,SV24: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV24 )
= $false )
| ( ( ~ ( subset @ SV29 @ SV24 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV11 @ SV29 ) @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false )
| ( ( ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV30 )
| ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY67 @ SV12 )
| ~ ( in @ SY67 @ SV25 ) )
| ( in @ SY67 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV25: $i,SV12: $i,SV30: $i] :
( ( ( ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV30 )
| ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY68 @ SV12 )
| ~ ( in @ SY68 @ SV25 ) )
| ( in @ SY68 @ SV30 ) ) ) )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(171,plain,
! [SV26: $i,SV13: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV13 )
| ( in @ SV32 @ SV26 ) )
= $true )
| ( ( subset @ SV13 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV13: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK4_SY65 @ SV26 @ SV13 ) @ SV13 )
| ( in @ ( sK4_SY65 @ SV26 @ SV13 ) @ SV26 ) )
= $false )
| ( ( subset @ SV13 @ SV26 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[163]) ).
thf(173,plain,
! [SV31: $i,SV27: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV27 )
= $false )
| ( ( ~ ( subset @ SV27 @ SV31 ) )
= $true )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV21: $i,SV28: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV28 )
= $false )
| ( ( subset @ SV8 @ SV21 )
= $false )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV21 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV23 ) )
= $false )
| ( ( SV10 = SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(176,plain,
! [SV10: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV10 ) )
= $false )
| ( ( SV10 = SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(177,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV23 ) )
= $true )
| ( ( ~ ( subset @ SV23 @ SV10 ) )
= $true )
| ( ( SV10 = SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV11: $i,SV24: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV24 )
= $false )
| ( ( subset @ SV11 @ SV24 )
= $false )
| ( ( subset @ ( set_union2 @ SV11 @ SV29 ) @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV25: $i,SV12: $i,SV30: $i,SV33: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV33 @ SV30 )
| ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) )
| ( in @ SV33 @ SV30 ) ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
| ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) ) )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[170]) ).
thf(181,plain,
! [SV26: $i,SV13: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV13 ) )
= $true )
| ( ( in @ SV32 @ SV26 )
= $true )
| ( ( subset @ SV13 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV13: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK4_SY65 @ SV26 @ SV13 ) @ SV13 ) )
= $false )
| ( ( subset @ SV13 @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(183,plain,
! [SV13: $i,SV26: $i] :
( ( ( in @ ( sK4_SY65 @ SV26 @ SV13 ) @ SV26 )
= $false )
| ( ( subset @ SV13 @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(184,plain,
! [SV14: $i,SV31: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV31 )
= $false )
| ( ( subset @ SV14 @ SV27 )
= $false )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV23: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV23 )
= $true )
| ( ( SV10 = SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(186,plain,
! [SV10: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV10 )
= $true )
| ( ( SV10 = SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(187,plain,
! [SV23: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV23 )
= $false )
| ( ( ~ ( subset @ SV23 @ SV10 ) )
= $true )
| ( ( SV10 = SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(188,plain,
! [SV25: $i,SV12: $i,SV30: $i,SV33: $i] :
( ( ( ~ ( ~ ( in @ SV33 @ SV30 )
| ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) )
| ( in @ SV33 @ SV30 ) ) )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(189,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
| ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(190,plain,
! [SV26: $i,SV13: $i,SV32: $i] :
( ( ( in @ SV32 @ SV13 )
= $false )
| ( ( in @ SV32 @ SV26 )
= $true )
| ( ( subset @ SV13 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(191,plain,
! [SV13: $i,SV26: $i] :
( ( ( in @ ( sK4_SY65 @ SV26 @ SV13 ) @ SV13 )
= $true )
| ( ( subset @ SV13 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(192,plain,
! [SV10: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV10 )
= $false )
| ( ( subset @ SV10 @ SV23 )
= $false )
| ( ( SV10 = SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(193,plain,
! [SV25: $i,SV12: $i,SV30: $i,SV33: $i] :
( ( ( ~ ( ~ ( in @ SV33 @ SV30 )
| ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) ) ) )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(194,plain,
! [SV30: $i,SV25: $i,SV12: $i,SV33: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) )
| ( in @ SV33 @ SV30 ) ) )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(195,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
| ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(196,plain,
! [SV25: $i,SV12: $i,SV30: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV30 )
| ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(197,plain,
! [SV30: $i,SV25: $i,SV12: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) )
| ( in @ SV33 @ SV30 ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(198,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
| ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(199,plain,
! [SV25: $i,SV12: $i,SV30: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV30 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(200,plain,
! [SV30: $i,SV25: $i,SV12: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) ) )
= $true )
| ( ( in @ SV33 @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(201,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(202,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(203,plain,
! [SV25: $i,SV12: $i,SV30: $i,SV33: $i] :
( ( ( in @ SV33 @ SV30 )
= $false )
| ( ( ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(204,plain,
! [SV30: $i,SV25: $i,SV12: $i,SV33: $i] :
( ( ( ~ ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) ) )
= $false )
| ( ( in @ SV33 @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(205,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(206,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(207,plain,
! [SV30: $i,SV25: $i,SV12: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) )
= $false )
| ( ( in @ SV33 @ SV30 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(208,plain,
! [SV30: $i,SV25: $i,SV12: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV12 )
| ~ ( in @ SV33 @ SV25 ) )
= $true )
| ( ( in @ SV33 @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(209,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(210,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 ) )
= $true )
| ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(211,plain,
! [SV25: $i,SV30: $i,SV12: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV12 ) )
= $false )
| ( ( in @ SV33 @ SV30 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(212,plain,
! [SV12: $i,SV30: $i,SV25: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV25 ) )
= $false )
| ( ( in @ SV33 @ SV30 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(213,plain,
! [SV30: $i,SV25: $i,SV12: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV33 @ SV25 ) )
= $true )
| ( ( in @ SV33 @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(214,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(215,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(216,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(217,plain,
! [SV25: $i,SV30: $i,SV12: $i,SV33: $i] :
( ( ( in @ SV33 @ SV12 )
= $true )
| ( ( in @ SV33 @ SV30 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(218,plain,
! [SV12: $i,SV30: $i,SV25: $i,SV33: $i] :
( ( ( in @ SV33 @ SV25 )
= $true )
| ( ( in @ SV33 @ SV30 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(219,plain,
! [SV30: $i,SV25: $i,SV12: $i,SV33: $i] :
( ( ( in @ SV33 @ SV12 )
= $false )
| ( ( ~ ( in @ SV33 @ SV25 ) )
= $true )
| ( ( in @ SV33 @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(220,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) ) )
= $true )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(221,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(222,plain,
! [SV30: $i,SV12: $i,SV25: $i,SV33: $i] :
( ( ( in @ SV33 @ SV25 )
= $false )
| ( ( in @ SV33 @ SV12 )
= $false )
| ( ( in @ SV33 @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(223,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(224,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
| ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(225,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(226,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(227,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(228,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(229,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $true )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(230,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $true )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(231,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) ) )
= $true )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(232,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
| ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(233,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(234,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 ) )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(235,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $true )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(236,plain,
! [SV30: $i,SV12: $i,SV25: $i] :
( ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $true )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV12 )
= $false )
| ( ( in @ ( sK5_SY68 @ SV25 @ SV12 @ SV30 ) @ SV25 )
= $false )
| ( ( SV30
= ( set_intersection2 @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(237,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[76,236,235,230,229,228,222,218,217,215,192,191,190,186,185,184,183,178,174,130,128,112,111,110,109,108,99,98,93,82,78,77]) ).
thf(238,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU129+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
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:01:54 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.42
% 0.40/0.42 No.of.Axioms: 18
% 0.40/0.42
% 0.40/0.42 Length.of.Defs: 0
% 0.40/0.42
% 0.40/0.42 Contains.Choice.Funs: false
% 0.40/0.42 ......
% 0.40/0.42
% 0.40/0.42 ********************************
% 0.40/0.42 * All subproblems solved! *
% 0.40/0.42 ********************************
% 0.40/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:19,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:237,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.40/0.42
% 0.40/0.42 %**** Beginning of derivation protocol ****
% 0.40/0.42 % SZS output start CNFRefutation
% See solution above
% 0.40/0.43
% 0.40/0.43 %**** End of derivation protocol ****
% 0.40/0.43 %**** no. of clauses in derivation: 220 ****
% 0.40/0.43 %**** clause counter: 237 ****
% 0.40/0.43
% 0.40/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:19,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:237,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------