TSTP Solution File: SEU120+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:06:48 EDT 2022
% Result : Theorem 0.35s 0.54s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 27
% Syntax : Number of formulae : 332 ( 178 unt; 13 typ; 0 def)
% Number of atoms : 2081 ( 701 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 4630 ( 872 ~; 709 |; 61 &;2976 @)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 859 ( 0 ^ 846 !; 13 ?; 859 :)
% 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_SY26,type,
sK2_SY26: $i ).
thf(tp_sK3_SY30,type,
sK3_SY30: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_D,type,
sK6_D: $i > $i > $i > $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK8_C,type,
sK8_C: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(2,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(3,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(5,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(6,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(8,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(9,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(10,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(11,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(12,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(14,conjecture,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(15,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
$true = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
$true = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,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)],[9]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [SY26: $i] :
( ~ ( ~ ( disjoint @ sK1_A @ SY26 )
& ! [SY27: $i] :
~ ( in @ SY27 @ ( set_intersection2 @ sK1_A @ SY26 ) ) )
& ~ ( ? [SY28: $i] : ( in @ SY28 @ ( set_intersection2 @ sK1_A @ SY26 ) )
& ( disjoint @ sK1_A @ SY26 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(31,plain,
( ( ~ ( ~ ( disjoint @ sK1_A @ sK2_SY26 )
& ! [SY29: $i] :
~ ( in @ SY29 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) )
& ~ ( ? [SY30: $i] : ( in @ SY30 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) )
& ( disjoint @ sK1_A @ sK2_SY26 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(32,plain,
( ( ~ ( ~ ( disjoint @ sK1_A @ sK2_SY26 )
& ! [SY29: $i] :
~ ( in @ SY29 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(33,plain,
( ( ~ ( ? [SY30: $i] : ( in @ SY30 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) )
& ( disjoint @ sK1_A @ sK2_SY26 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(34,plain,
( ( ~ ( disjoint @ sK1_A @ sK2_SY26 )
& ! [SY29: $i] :
~ ( in @ SY29 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(35,plain,
( ( ? [SY30: $i] : ( in @ SY30 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) )
& ( disjoint @ sK1_A @ sK2_SY26 ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(36,plain,
( ( ( in @ sK3_SY30 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) )
& ( disjoint @ sK1_A @ sK2_SY26 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(38,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(39,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(42,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( in @ ( sK7_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK8_C @ B @ A ) @ A )
& ( in @ ( sK8_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK8_C @ B @ A ) @ A )
& ( in @ ( sK8_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( in @ ( sK7_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(52,plain,
$true = $true,
inference(copy,[status(thm)],[23]) ).
thf(53,plain,
$true = $true,
inference(copy,[status(thm)],[22]) ).
thf(54,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(56,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(57,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(59,plain,
( ( ~ ( disjoint @ sK1_A @ sK2_SY26 )
& ! [SY29: $i] :
~ ( in @ SY29 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(60,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(61,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(62,plain,
( ( ~ ( ~ ~ ( disjoint @ sK1_A @ sK2_SY26 )
| ~ ! [SX0: $i] :
~ ( in @ SX0 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(63,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK7_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(64,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(65,plain,
! [SV1: $i] :
( ( ! [SY31: $i] :
( ~ ( in @ SV1 @ SY31 )
| ~ ( in @ SY31 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(66,plain,
! [SV2: $i] :
( ( ! [SY32: $i] :
( ( set_intersection2 @ SV2 @ SY32 )
= ( set_intersection2 @ SY32 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(67,plain,
! [SV3: $i] :
( ( ( set_intersection2 @ SV3 @ SV3 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(68,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV4: $i] :
( ( ! [SY33: $i] :
( ~ ( disjoint @ SV4 @ SY33 )
| ( disjoint @ SY33 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(71,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(72,plain,
( ( ~ ~ ( disjoint @ sK1_A @ sK2_SY26 )
| ~ ! [SX0: $i] :
~ ( in @ SX0 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(73,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK7_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY34 )
| ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) )
| ~ ( ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY34 )
| ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) ) ) )
| ( SY35
= ( set_intersection2 @ SV5 @ SY34 ) ) )
| ~ ! [SY36: $i,SY37: $i] :
( ( SY37
!= ( set_intersection2 @ SV5 @ SY36 ) )
| ~ ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ SV5 )
| ~ ( in @ SY38 @ SY36 )
| ( in @ SY38 @ SY37 ) )
| ~ ~ ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SY37 )
| ( in @ SY39 @ SV5 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY37 )
| ( in @ SX3 @ SY36 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV6: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV6 )
| ~ ( in @ SV6 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV7: $i,SV2: $i] :
( ( ( set_intersection2 @ SV2 @ SV7 )
= ( set_intersection2 @ SV7 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( disjoint @ SV4 @ SV8 )
| ( disjoint @ SV8 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(79,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(80,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(81,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(82,plain,
( ( ~ ~ ( disjoint @ sK1_A @ sK2_SY26 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(83,plain,
( ( ~ ! [SX0: $i] :
~ ( in @ SX0 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(84,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK7_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(85,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(86,plain,
! [SV5: $i] :
( ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY34 )
| ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) )
| ~ ( ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY34 )
| ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) ) ) )
| ( SY35
= ( set_intersection2 @ SV5 @ SY34 ) ) )
| ~ ! [SY36: $i,SY37: $i] :
( ( SY37
!= ( set_intersection2 @ SV5 @ SY36 ) )
| ~ ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ SV5 )
| ~ ( in @ SY38 @ SY36 )
| ( in @ SY38 @ SY37 ) )
| ~ ~ ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SY37 )
| ( in @ SY39 @ SV5 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY37 )
| ( in @ SX3 @ SY36 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( disjoint @ SV4 @ SV8 ) )
= $true )
| ( ( disjoint @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(93,plain,
( ( ~ ( disjoint @ sK1_A @ sK2_SY26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(94,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(95,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK7_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(96,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(97,plain,
! [SV5: $i] :
( ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY34 )
| ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) )
| ~ ( ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY34 )
| ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) ) ) )
| ( SY35
= ( set_intersection2 @ SV5 @ SY34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(98,plain,
! [SV5: $i] :
( ( ~ ! [SY36: $i,SY37: $i] :
( ( SY37
!= ( set_intersection2 @ SV5 @ SY36 ) )
| ~ ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ SV5 )
| ~ ( in @ SY38 @ SY36 )
| ( in @ SY38 @ SY37 ) )
| ~ ~ ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SY37 )
| ( in @ SY39 @ SV5 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY37 )
| ( in @ SX3 @ SY36 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(99,plain,
! [SV6: $i,SV1: $i] :
( ( ( in @ SV1 @ SV6 )
= $false )
| ( ( ~ ( in @ SV6 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(100,plain,
! [SV8: $i,SV4: $i] :
( ( ( disjoint @ SV4 @ SV8 )
= $false )
| ( ( disjoint @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(101,plain,
! [SV9: $i] :
( ( ! [SY41: $i] :
( ( ( set_intersection2 @ SV9 @ SY41 )
!= empty_set )
| ( disjoint @ SV9 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV10: $i] :
( ( ! [SY42: $i] :
( ~ ( disjoint @ SV10 @ SY42 )
| ( ( set_intersection2 @ SV10 @ SY42 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV11: $i] :
( ( ! [SY43: $i] :
( ( disjoint @ SV11 @ SY43 )
| ~ ( ~ ( in @ ( sK8_C @ SY43 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK8_C @ SY43 @ SV11 ) @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV12: $i] :
( ( ! [SY44: $i] :
( ! [SY45: $i] :
( ~ ( in @ SY45 @ SV12 )
| ~ ( in @ SY45 @ SY44 ) )
| ~ ( disjoint @ SV12 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(105,plain,
( ( disjoint @ sK1_A @ sK2_SY26 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV13: $i] :
( ( ~ ( in @ SV13 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV14: $i] :
( ( ( in @ ( sK7_B @ SV14 ) @ SV14 )
| ( SV14 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV15: $i] :
( ( ( SV15 != empty_set )
| ! [SY46: $i] :
~ ( in @ SY46 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV5: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY34 )
| ~ ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) )
| ~ ( ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY34 )
| ( in @ ( sK6_D @ SY35 @ SY34 @ SV5 ) @ SY35 ) ) ) )
| ( SY35
= ( set_intersection2 @ SV5 @ SY34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(110,plain,
! [SV5: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( SY37
!= ( set_intersection2 @ SV5 @ SY36 ) )
| ~ ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ SV5 )
| ~ ( in @ SY38 @ SY36 )
| ( in @ SY38 @ SY37 ) )
| ~ ~ ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SY37 )
| ( in @ SY39 @ SV5 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY37 )
| ( in @ SX3 @ SY36 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(111,plain,
! [SV1: $i,SV6: $i] :
( ( ( in @ SV6 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV16: $i,SV9: $i] :
( ( ( ( set_intersection2 @ SV9 @ SV16 )
!= empty_set )
| ( disjoint @ SV9 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV17: $i,SV10: $i] :
( ( ~ ( disjoint @ SV10 @ SV17 )
| ( ( set_intersection2 @ SV10 @ SV17 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV18: $i,SV11: $i] :
( ( ( disjoint @ SV11 @ SV18 )
| ~ ( ~ ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV19: $i,SV12: $i] :
( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ SV12 )
| ~ ( in @ SY47 @ SV19 ) )
| ~ ( disjoint @ SV12 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV13: $i] :
( ( in @ SV13 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV14: $i] :
( ( ( in @ ( sK7_B @ SV14 ) @ SV14 )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV15: $i] :
( ( ( ( SV15 != empty_set ) )
= $true )
| ( ( ! [SY46: $i] :
~ ( in @ SY46 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV5: $i,SV20: $i] :
( ( ! [SY48: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY48 @ SV20 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY48 @ SV20 @ SV5 ) @ SV20 )
| ~ ( in @ ( sK6_D @ SY48 @ SV20 @ SV5 ) @ SY48 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY48 @ SV20 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY48 @ SV20 @ SV5 ) @ SY48 ) )
| ~ ( ( in @ ( sK6_D @ SY48 @ SV20 @ SV5 ) @ SV20 )
| ( in @ ( sK6_D @ SY48 @ SV20 @ SV5 ) @ SY48 ) ) ) )
| ( SY48
= ( set_intersection2 @ SV5 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV21: $i,SV5: $i] :
( ( ! [SY49: $i] :
( ( SY49
!= ( set_intersection2 @ SV5 @ SV21 ) )
| ~ ( ~ ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ~ ( in @ SY50 @ SV21 )
| ( in @ SY50 @ SY49 ) )
| ~ ~ ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SY49 )
| ( in @ SY39 @ SV5 ) )
| ~ ! [SY52: $i] :
( ~ ( in @ SY52 @ SY49 )
| ( in @ SY52 @ SV21 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV16: $i,SV9: $i] :
( ( ( ( ( set_intersection2 @ SV9 @ SV16 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV9 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(122,plain,
! [SV17: $i,SV10: $i] :
( ( ( ~ ( disjoint @ SV10 @ SV17 ) )
= $true )
| ( ( ( set_intersection2 @ SV10 @ SV17 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(123,plain,
! [SV18: $i,SV11: $i] :
( ( ( disjoint @ SV11 @ SV18 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(124,plain,
! [SV19: $i,SV12: $i] :
( ( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ SV12 )
| ~ ( in @ SY47 @ SV19 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV12 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(125,plain,
! [SV15: $i] :
( ( ( SV15 = empty_set )
= $false )
| ( ( ! [SY46: $i] :
~ ( in @ SY46 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
| ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) ) ) )
| ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(127,plain,
! [SV21: $i,SV5: $i,SV23: $i] :
( ( ( SV23
!= ( set_intersection2 @ SV5 @ SV21 ) )
| ~ ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV5 )
| ~ ( in @ SY53 @ SV21 )
| ( in @ SY53 @ SV23 ) )
| ~ ~ ( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV5 ) )
| ~ ! [SY55: $i] :
( ~ ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(128,plain,
! [SV16: $i,SV9: $i] :
( ( ( ( set_intersection2 @ SV9 @ SV16 )
= empty_set )
= $false )
| ( ( disjoint @ SV9 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV17: $i,SV10: $i] :
( ( ( disjoint @ SV10 @ SV17 )
= $false )
| ( ( ( set_intersection2 @ SV10 @ SV17 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV11: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV18 ) )
= $false )
| ( ( disjoint @ SV11 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV19: $i,SV12: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV12 )
| ~ ( in @ SV24 @ SV19 ) )
= $true )
| ( ( ~ ( disjoint @ SV12 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV15: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV15 ) )
= $true )
| ( ( SV15 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
| ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) ) ) ) )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV21: $i,SV5: $i,SV23: $i] :
( ( ( ( SV23
!= ( set_intersection2 @ SV5 @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV5 )
| ~ ( in @ SY53 @ SV21 )
| ( in @ SY53 @ SV23 ) )
| ~ ~ ( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV5 ) )
| ~ ! [SY55: $i] :
( ~ ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV11: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV11 ) )
= $false )
| ( ( disjoint @ SV11 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(136,plain,
! [SV11: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV18 ) )
= $false )
| ( ( disjoint @ SV11 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(137,plain,
! [SV19: $i,SV12: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV24 @ SV19 ) )
= $true )
| ( ( ~ ( disjoint @ SV12 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV15: $i,SV25: $i] :
( ( ( in @ SV25 @ SV15 )
= $false )
| ( ( SV15 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
| ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) ) ) )
= $false )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV21: $i,SV5: $i,SV23: $i] :
( ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false )
| ( ( ~ ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV5 )
| ~ ( in @ SY53 @ SV21 )
| ( in @ SY53 @ SV23 ) )
| ~ ~ ( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV5 ) )
| ~ ! [SY55: $i] :
( ~ ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV11: $i,SV18: $i] :
( ( ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV11 )
= $true )
| ( ( disjoint @ SV11 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(142,plain,
! [SV11: $i,SV18: $i] :
( ( ( in @ ( sK8_C @ SV18 @ SV11 ) @ SV18 )
= $true )
| ( ( disjoint @ SV11 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(143,plain,
! [SV19: $i,SV12: $i,SV24: $i] :
( ( ( in @ SV24 @ SV12 )
= $false )
| ( ( ~ ( in @ SV24 @ SV19 ) )
= $true )
| ( ( ~ ( disjoint @ SV12 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(144,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) ) )
= $false )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(145,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
| ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) ) ) )
= $false )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(146,plain,
! [SV23: $i,SV21: $i,SV5: $i] :
( ( ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV5 )
| ~ ( in @ SY53 @ SV21 )
| ( in @ SY53 @ SV23 ) )
| ~ ~ ( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV5 ) )
| ~ ! [SY55: $i] :
( ~ ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV21 ) ) ) )
= $false )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(147,plain,
! [SV12: $i,SV19: $i,SV24: $i] :
( ( ( in @ SV24 @ SV19 )
= $false )
| ( ( in @ SV24 @ SV12 )
= $false )
| ( ( ~ ( disjoint @ SV12 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(148,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
| ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) ) ) )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(150,plain,
! [SV23: $i,SV21: $i,SV5: $i] :
( ( ( ~ ! [SY53: $i] :
( ~ ( in @ SY53 @ SV5 )
| ~ ( in @ SY53 @ SV21 )
| ( in @ SY53 @ SV23 ) ) )
= $false )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(151,plain,
! [SV21: $i,SV5: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV5 ) )
| ~ ! [SY55: $i] :
( ~ ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV21 ) ) ) )
= $false )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(152,plain,
! [SV24: $i,SV19: $i,SV12: $i] :
( ( ( disjoint @ SV12 @ SV19 )
= $false )
| ( ( in @ SV24 @ SV12 )
= $false )
| ( ( in @ SV24 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(153,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(154,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
| ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) ) )
= $false )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(155,plain,
! [SV23: $i,SV21: $i,SV5: $i] :
( ( ( ! [SY53: $i] :
( ~ ( in @ SY53 @ SV5 )
| ~ ( in @ SY53 @ SV21 )
| ( in @ SY53 @ SV23 ) ) )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(156,plain,
! [SV21: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV5 ) )
| ~ ! [SY55: $i] :
( ~ ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV21 ) ) ) )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(157,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(158,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) ) )
= $false )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(159,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) ) )
= $false )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(160,plain,
! [SV23: $i,SV21: $i,SV5: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV5 )
| ~ ( in @ SV26 @ SV21 )
| ( in @ SV26 @ SV23 ) )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(161,plain,
! [SV21: $i,SV5: $i,SV23: $i] :
( ( ( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV5 ) )
| ~ ! [SY55: $i] :
( ~ ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV21 ) ) )
= $false )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(162,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
= $false )
| ( ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(163,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(164,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
| ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(165,plain,
! [SV23: $i,SV21: $i,SV5: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV5 )
| ~ ( in @ SV26 @ SV21 ) )
= $true )
| ( ( in @ SV26 @ SV23 )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(166,plain,
! [SV21: $i,SV5: $i,SV23: $i] :
( ( ( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV5 ) ) )
= $false )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(167,plain,
! [SV5: $i,SV21: $i,SV23: $i] :
( ( ( ~ ! [SY55: $i] :
( ~ ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV21 ) ) )
= $false )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(168,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
= $false )
| ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
= $false )
| ( ( ~ ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(169,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(170,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
= $true )
| ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 )
= $true )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(171,plain,
! [SV23: $i,SV21: $i,SV5: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV26 @ SV21 ) )
= $true )
| ( ( in @ SV26 @ SV23 )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(172,plain,
! [SV21: $i,SV5: $i,SV23: $i] :
( ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ SV23 )
| ( in @ SY54 @ SV5 ) ) )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(173,plain,
! [SV5: $i,SV21: $i,SV23: $i] :
( ( ( ! [SY55: $i] :
( ~ ( in @ SY55 @ SV23 )
| ( in @ SY55 @ SV21 ) ) )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(174,plain,
! [SV5: $i,SV20: $i,SV22: $i] :
( ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV22 )
= $false )
| ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV5 )
= $false )
| ( ( in @ ( sK6_D @ SV22 @ SV20 @ SV5 ) @ SV20 )
= $false )
| ( ( SV22
= ( set_intersection2 @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(175,plain,
! [SV23: $i,SV21: $i,SV5: $i,SV26: $i] :
( ( ( in @ SV26 @ SV5 )
= $false )
| ( ( ~ ( in @ SV26 @ SV21 ) )
= $true )
| ( ( in @ SV26 @ SV23 )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(176,plain,
! [SV21: $i,SV5: $i,SV23: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV23 )
| ( in @ SV27 @ SV5 ) )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(177,plain,
! [SV5: $i,SV21: $i,SV23: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV23 )
| ( in @ SV28 @ SV21 ) )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(178,plain,
! [SV23: $i,SV5: $i,SV21: $i,SV26: $i] :
( ( ( in @ SV26 @ SV21 )
= $false )
| ( ( in @ SV26 @ SV5 )
= $false )
| ( ( in @ SV26 @ SV23 )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(179,plain,
! [SV21: $i,SV5: $i,SV23: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV23 ) )
= $true )
| ( ( in @ SV27 @ SV5 )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(180,plain,
! [SV5: $i,SV21: $i,SV23: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV23 ) )
= $true )
| ( ( in @ SV28 @ SV21 )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV21: $i,SV5: $i,SV23: $i,SV27: $i] :
( ( ( in @ SV27 @ SV23 )
= $false )
| ( ( in @ SV27 @ SV5 )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(182,plain,
! [SV5: $i,SV21: $i,SV23: $i,SV28: $i] :
( ( ( in @ SV28 @ SV23 )
= $false )
| ( ( in @ SV28 @ SV21 )
= $true )
| ( ( SV23
= ( set_intersection2 @ SV5 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(183,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[52,182,181,178,174,170,169,152,142,141,138,129,128,117,116,111,105,100,76,68,67,56,54,53]) ).
thf(184,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK8_C @ B @ A ) @ A )
& ( in @ ( sK8_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(186,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(187,plain,
( ( ! [A: $i] :
( ( in @ ( sK7_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(188,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(190,plain,
$true = $true,
inference(copy,[status(thm)],[23]) ).
thf(191,plain,
$true = $true,
inference(copy,[status(thm)],[22]) ).
thf(192,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(193,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(194,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(195,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(196,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(197,plain,
( ( ( in @ sK3_SY30 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) )
& ( disjoint @ sK1_A @ sK2_SY26 ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(198,plain,
( ( ~ ( ~ ( in @ sK3_SY30 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) )
| ~ ( disjoint @ sK1_A @ sK2_SY26 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(199,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(200,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK7_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(201,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(202,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(203,plain,
! [SV29: $i] :
( ( ! [SY56: $i] :
( ~ ( in @ SV29 @ SY56 )
| ~ ( in @ SY56 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(204,plain,
! [SV30: $i] :
( ( ! [SY57: $i] :
( ( set_intersection2 @ SV30 @ SY57 )
= ( set_intersection2 @ SY57 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(205,plain,
! [SV31: $i] :
( ( ( set_intersection2 @ SV31 @ SV31 )
= SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(206,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(207,plain,
! [SV32: $i] :
( ( ! [SY58: $i] :
( ~ ( disjoint @ SV32 @ SY58 )
| ( disjoint @ SY58 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(208,plain,
( ( ~ ( in @ sK3_SY30 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) )
| ~ ( disjoint @ sK1_A @ sK2_SY26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(209,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(210,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK7_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(211,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(212,plain,
! [SV33: $i] :
( ( ~ ( ~ ! [SY59: $i,SY60: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY59 )
| ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) )
| ~ ( ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY59 )
| ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) ) ) )
| ( SY60
= ( set_intersection2 @ SV33 @ SY59 ) ) )
| ~ ! [SY61: $i,SY62: $i] :
( ( SY62
!= ( set_intersection2 @ SV33 @ SY61 ) )
| ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV33 )
| ~ ( in @ SY63 @ SY61 )
| ( in @ SY63 @ SY62 ) )
| ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SY62 )
| ( in @ SY64 @ SV33 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY62 )
| ( in @ SX3 @ SY61 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(213,plain,
! [SV34: $i,SV29: $i] :
( ( ~ ( in @ SV29 @ SV34 )
| ~ ( in @ SV34 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(214,plain,
! [SV35: $i,SV30: $i] :
( ( ( set_intersection2 @ SV30 @ SV35 )
= ( set_intersection2 @ SV35 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(215,plain,
! [SV36: $i,SV32: $i] :
( ( ~ ( disjoint @ SV32 @ SV36 )
| ( disjoint @ SV36 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(216,plain,
( ( ~ ( in @ sK3_SY30 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(217,plain,
( ( ~ ( disjoint @ sK1_A @ sK2_SY26 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(218,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(219,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(220,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK7_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(221,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(222,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(223,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(224,plain,
! [SV33: $i] :
( ( ~ ! [SY59: $i,SY60: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY59 )
| ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) )
| ~ ( ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY59 )
| ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) ) ) )
| ( SY60
= ( set_intersection2 @ SV33 @ SY59 ) ) )
| ~ ! [SY61: $i,SY62: $i] :
( ( SY62
!= ( set_intersection2 @ SV33 @ SY61 ) )
| ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV33 )
| ~ ( in @ SY63 @ SY61 )
| ( in @ SY63 @ SY62 ) )
| ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SY62 )
| ( in @ SY64 @ SV33 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY62 )
| ( in @ SX3 @ SY61 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(225,plain,
! [SV34: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV34 ) )
= $true )
| ( ( ~ ( in @ SV34 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(226,plain,
! [SV36: $i,SV32: $i] :
( ( ( ~ ( disjoint @ SV32 @ SV36 ) )
= $true )
| ( ( disjoint @ SV36 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(227,plain,
( ( in @ sK3_SY30 @ ( set_intersection2 @ sK1_A @ sK2_SY26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(228,plain,
( ( disjoint @ sK1_A @ sK2_SY26 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(229,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(230,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(231,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK7_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(232,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(233,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(234,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(235,plain,
! [SV33: $i] :
( ( ~ ! [SY59: $i,SY60: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY59 )
| ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) )
| ~ ( ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY59 )
| ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) ) ) )
| ( SY60
= ( set_intersection2 @ SV33 @ SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(236,plain,
! [SV33: $i] :
( ( ~ ! [SY61: $i,SY62: $i] :
( ( SY62
!= ( set_intersection2 @ SV33 @ SY61 ) )
| ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV33 )
| ~ ( in @ SY63 @ SY61 )
| ( in @ SY63 @ SY62 ) )
| ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SY62 )
| ( in @ SY64 @ SV33 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY62 )
| ( in @ SX3 @ SY61 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(237,plain,
! [SV34: $i,SV29: $i] :
( ( ( in @ SV29 @ SV34 )
= $false )
| ( ( ~ ( in @ SV34 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(238,plain,
! [SV36: $i,SV32: $i] :
( ( ( disjoint @ SV32 @ SV36 )
= $false )
| ( ( disjoint @ SV36 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(239,plain,
! [SV37: $i] :
( ( ! [SY66: $i] :
( ( disjoint @ SV37 @ SY66 )
| ~ ( ~ ( in @ ( sK8_C @ SY66 @ SV37 ) @ SV37 )
| ~ ( in @ ( sK8_C @ SY66 @ SV37 ) @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(240,plain,
! [SV38: $i] :
( ( ! [SY67: $i] :
( ! [SY68: $i] :
( ~ ( in @ SY68 @ SV38 )
| ~ ( in @ SY68 @ SY67 ) )
| ~ ( disjoint @ SV38 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(241,plain,
! [SV39: $i] :
( ( ( in @ ( sK7_B @ SV39 ) @ SV39 )
| ( SV39 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(242,plain,
! [SV40: $i] :
( ( ( SV40 != empty_set )
| ! [SY69: $i] :
~ ( in @ SY69 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(243,plain,
! [SV41: $i] :
( ( ! [SY70: $i] :
( ( ( set_intersection2 @ SV41 @ SY70 )
!= empty_set )
| ( disjoint @ SV41 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV42: $i] :
( ( ! [SY71: $i] :
( ~ ( disjoint @ SV42 @ SY71 )
| ( ( set_intersection2 @ SV42 @ SY71 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(245,plain,
! [SV33: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY59 )
| ~ ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) )
| ~ ( ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY59 )
| ( in @ ( sK6_D @ SY60 @ SY59 @ SV33 ) @ SY60 ) ) ) )
| ( SY60
= ( set_intersection2 @ SV33 @ SY59 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(246,plain,
! [SV33: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ( SY62
!= ( set_intersection2 @ SV33 @ SY61 ) )
| ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV33 )
| ~ ( in @ SY63 @ SY61 )
| ( in @ SY63 @ SY62 ) )
| ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SY62 )
| ( in @ SY64 @ SV33 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY62 )
| ( in @ SX3 @ SY61 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(247,plain,
! [SV29: $i,SV34: $i] :
( ( ( in @ SV34 @ SV29 )
= $false )
| ( ( in @ SV29 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV43: $i,SV37: $i] :
( ( ( disjoint @ SV37 @ SV43 )
| ~ ( ~ ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV37 )
| ~ ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(249,plain,
! [SV44: $i,SV38: $i] :
( ( ! [SY72: $i] :
( ~ ( in @ SY72 @ SV38 )
| ~ ( in @ SY72 @ SV44 ) )
| ~ ( disjoint @ SV38 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(250,plain,
! [SV39: $i] :
( ( ( in @ ( sK7_B @ SV39 ) @ SV39 )
= $true )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(251,plain,
! [SV40: $i] :
( ( ( ( SV40 != empty_set ) )
= $true )
| ( ( ! [SY69: $i] :
~ ( in @ SY69 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(252,plain,
! [SV45: $i,SV41: $i] :
( ( ( ( set_intersection2 @ SV41 @ SV45 )
!= empty_set )
| ( disjoint @ SV41 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(253,plain,
! [SV46: $i,SV42: $i] :
( ( ~ ( disjoint @ SV42 @ SV46 )
| ( ( set_intersection2 @ SV42 @ SV46 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(254,plain,
! [SV33: $i,SV47: $i] :
( ( ! [SY73: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY73 @ SV47 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SY73 @ SV47 @ SV33 ) @ SV47 )
| ~ ( in @ ( sK6_D @ SY73 @ SV47 @ SV33 ) @ SY73 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY73 @ SV47 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SY73 @ SV47 @ SV33 ) @ SY73 ) )
| ~ ( ( in @ ( sK6_D @ SY73 @ SV47 @ SV33 ) @ SV47 )
| ( in @ ( sK6_D @ SY73 @ SV47 @ SV33 ) @ SY73 ) ) ) )
| ( SY73
= ( set_intersection2 @ SV33 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(255,plain,
! [SV48: $i,SV33: $i] :
( ( ! [SY74: $i] :
( ( SY74
!= ( set_intersection2 @ SV33 @ SV48 ) )
| ~ ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV33 )
| ~ ( in @ SY75 @ SV48 )
| ( in @ SY75 @ SY74 ) )
| ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SY74 )
| ( in @ SY64 @ SV33 ) )
| ~ ! [SY77: $i] :
( ~ ( in @ SY77 @ SY74 )
| ( in @ SY77 @ SV48 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(256,plain,
! [SV43: $i,SV37: $i] :
( ( ( disjoint @ SV37 @ SV43 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV37 )
| ~ ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(257,plain,
! [SV44: $i,SV38: $i] :
( ( ( ! [SY72: $i] :
( ~ ( in @ SY72 @ SV38 )
| ~ ( in @ SY72 @ SV44 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV38 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(258,plain,
! [SV40: $i] :
( ( ( SV40 = empty_set )
= $false )
| ( ( ! [SY69: $i] :
~ ( in @ SY69 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(259,plain,
! [SV45: $i,SV41: $i] :
( ( ( ( ( set_intersection2 @ SV41 @ SV45 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV41 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(260,plain,
! [SV46: $i,SV42: $i] :
( ( ( ~ ( disjoint @ SV42 @ SV46 ) )
= $true )
| ( ( ( set_intersection2 @ SV42 @ SV46 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(261,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
| ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) ) ) )
| ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(262,plain,
! [SV48: $i,SV33: $i,SV50: $i] :
( ( ( SV50
!= ( set_intersection2 @ SV33 @ SV48 ) )
| ~ ( ~ ! [SY78: $i] :
( ~ ( in @ SY78 @ SV33 )
| ~ ( in @ SY78 @ SV48 )
| ( in @ SY78 @ SV50 ) )
| ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV50 )
| ( in @ SY79 @ SV33 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SV50 )
| ( in @ SY80 @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(263,plain,
! [SV37: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV37 )
| ~ ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV43 ) )
= $false )
| ( ( disjoint @ SV37 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(264,plain,
! [SV44: $i,SV38: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ SV38 )
| ~ ( in @ SV51 @ SV44 ) )
= $true )
| ( ( ~ ( disjoint @ SV38 @ SV44 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(265,plain,
! [SV40: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV40 ) )
= $true )
| ( ( SV40 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(266,plain,
! [SV45: $i,SV41: $i] :
( ( ( ( set_intersection2 @ SV41 @ SV45 )
= empty_set )
= $false )
| ( ( disjoint @ SV41 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(267,plain,
! [SV46: $i,SV42: $i] :
( ( ( disjoint @ SV42 @ SV46 )
= $false )
| ( ( ( set_intersection2 @ SV42 @ SV46 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(268,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
| ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) ) ) ) )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(269,plain,
! [SV48: $i,SV33: $i,SV50: $i] :
( ( ( ( SV50
!= ( set_intersection2 @ SV33 @ SV48 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY78: $i] :
( ~ ( in @ SY78 @ SV33 )
| ~ ( in @ SY78 @ SV48 )
| ( in @ SY78 @ SV50 ) )
| ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV50 )
| ( in @ SY79 @ SV33 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SV50 )
| ( in @ SY80 @ SV48 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(270,plain,
! [SV37: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV37 ) )
= $false )
| ( ( disjoint @ SV37 @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(271,plain,
! [SV37: $i,SV43: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV43 ) )
= $false )
| ( ( disjoint @ SV37 @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(272,plain,
! [SV44: $i,SV38: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ SV38 ) )
= $true )
| ( ( ~ ( in @ SV51 @ SV44 ) )
= $true )
| ( ( ~ ( disjoint @ SV38 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(273,plain,
! [SV40: $i,SV52: $i] :
( ( ( in @ SV52 @ SV40 )
= $false )
| ( ( SV40 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(274,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
| ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) ) ) )
= $false )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(275,plain,
! [SV48: $i,SV33: $i,SV50: $i] :
( ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false )
| ( ( ~ ( ~ ! [SY78: $i] :
( ~ ( in @ SY78 @ SV33 )
| ~ ( in @ SY78 @ SV48 )
| ( in @ SY78 @ SV50 ) )
| ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV50 )
| ( in @ SY79 @ SV33 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SV50 )
| ( in @ SY80 @ SV48 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(276,plain,
! [SV37: $i,SV43: $i] :
( ( ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV37 )
= $true )
| ( ( disjoint @ SV37 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(277,plain,
! [SV37: $i,SV43: $i] :
( ( ( in @ ( sK8_C @ SV43 @ SV37 ) @ SV43 )
= $true )
| ( ( disjoint @ SV37 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(278,plain,
! [SV44: $i,SV38: $i,SV51: $i] :
( ( ( in @ SV51 @ SV38 )
= $false )
| ( ( ~ ( in @ SV51 @ SV44 ) )
= $true )
| ( ( ~ ( disjoint @ SV38 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(279,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) ) )
= $false )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(280,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
| ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) ) ) )
= $false )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(281,plain,
! [SV50: $i,SV48: $i,SV33: $i] :
( ( ( ~ ! [SY78: $i] :
( ~ ( in @ SY78 @ SV33 )
| ~ ( in @ SY78 @ SV48 )
| ( in @ SY78 @ SV50 ) )
| ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV50 )
| ( in @ SY79 @ SV33 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SV50 )
| ( in @ SY80 @ SV48 ) ) ) )
= $false )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(282,plain,
! [SV38: $i,SV44: $i,SV51: $i] :
( ( ( in @ SV51 @ SV44 )
= $false )
| ( ( in @ SV51 @ SV38 )
= $false )
| ( ( ~ ( disjoint @ SV38 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(283,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(284,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
| ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) ) ) )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(285,plain,
! [SV50: $i,SV48: $i,SV33: $i] :
( ( ( ~ ! [SY78: $i] :
( ~ ( in @ SY78 @ SV33 )
| ~ ( in @ SY78 @ SV48 )
| ( in @ SY78 @ SV50 ) ) )
= $false )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(286,plain,
! [SV48: $i,SV33: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV50 )
| ( in @ SY79 @ SV33 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SV50 )
| ( in @ SY80 @ SV48 ) ) ) )
= $false )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(287,plain,
! [SV51: $i,SV44: $i,SV38: $i] :
( ( ( disjoint @ SV38 @ SV44 )
= $false )
| ( ( in @ SV51 @ SV38 )
= $false )
| ( ( in @ SV51 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(288,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(289,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
| ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) ) )
= $false )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(290,plain,
! [SV50: $i,SV48: $i,SV33: $i] :
( ( ( ! [SY78: $i] :
( ~ ( in @ SY78 @ SV33 )
| ~ ( in @ SY78 @ SV48 )
| ( in @ SY78 @ SV50 ) ) )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(291,plain,
! [SV48: $i,SV33: $i,SV50: $i] :
( ( ( ~ ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV50 )
| ( in @ SY79 @ SV33 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SV50 )
| ( in @ SY80 @ SV48 ) ) ) )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(292,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(293,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) ) )
= $false )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(294,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) ) )
= $false )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(295,plain,
! [SV50: $i,SV48: $i,SV33: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV33 )
| ~ ( in @ SV53 @ SV48 )
| ( in @ SV53 @ SV50 ) )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(296,plain,
! [SV48: $i,SV33: $i,SV50: $i] :
( ( ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV50 )
| ( in @ SY79 @ SV33 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SV50 )
| ( in @ SY80 @ SV48 ) ) )
= $false )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(297,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
= $false )
| ( ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(298,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(299,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
| ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(300,plain,
! [SV50: $i,SV48: $i,SV33: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV33 )
| ~ ( in @ SV53 @ SV48 ) )
= $true )
| ( ( in @ SV53 @ SV50 )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(301,plain,
! [SV48: $i,SV33: $i,SV50: $i] :
( ( ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV50 )
| ( in @ SY79 @ SV33 ) ) )
= $false )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(302,plain,
! [SV33: $i,SV48: $i,SV50: $i] :
( ( ( ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SV50 )
| ( in @ SY80 @ SV48 ) ) )
= $false )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(303,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
= $false )
| ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
= $false )
| ( ( ~ ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(304,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
= $true )
| ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(305,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
= $true )
| ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 )
= $true )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(306,plain,
! [SV50: $i,SV48: $i,SV33: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV33 ) )
= $true )
| ( ( ~ ( in @ SV53 @ SV48 ) )
= $true )
| ( ( in @ SV53 @ SV50 )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(307,plain,
! [SV48: $i,SV33: $i,SV50: $i] :
( ( ( ! [SY79: $i] :
( ~ ( in @ SY79 @ SV50 )
| ( in @ SY79 @ SV33 ) ) )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(308,plain,
! [SV33: $i,SV48: $i,SV50: $i] :
( ( ( ! [SY80: $i] :
( ~ ( in @ SY80 @ SV50 )
| ( in @ SY80 @ SV48 ) ) )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(309,plain,
! [SV33: $i,SV47: $i,SV49: $i] :
( ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV49 )
= $false )
| ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV33 )
= $false )
| ( ( in @ ( sK6_D @ SV49 @ SV47 @ SV33 ) @ SV47 )
= $false )
| ( ( SV49
= ( set_intersection2 @ SV33 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(310,plain,
! [SV50: $i,SV48: $i,SV33: $i,SV53: $i] :
( ( ( in @ SV53 @ SV33 )
= $false )
| ( ( ~ ( in @ SV53 @ SV48 ) )
= $true )
| ( ( in @ SV53 @ SV50 )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(311,plain,
! [SV48: $i,SV33: $i,SV50: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV50 )
| ( in @ SV54 @ SV33 ) )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(312,plain,
! [SV33: $i,SV48: $i,SV50: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV50 )
| ( in @ SV55 @ SV48 ) )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(313,plain,
! [SV50: $i,SV33: $i,SV48: $i,SV53: $i] :
( ( ( in @ SV53 @ SV48 )
= $false )
| ( ( in @ SV53 @ SV33 )
= $false )
| ( ( in @ SV53 @ SV50 )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(314,plain,
! [SV48: $i,SV33: $i,SV50: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV50 ) )
= $true )
| ( ( in @ SV54 @ SV33 )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(315,plain,
! [SV33: $i,SV48: $i,SV50: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV50 ) )
= $true )
| ( ( in @ SV55 @ SV48 )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(316,plain,
! [SV48: $i,SV33: $i,SV50: $i,SV54: $i] :
( ( ( in @ SV54 @ SV50 )
= $false )
| ( ( in @ SV54 @ SV33 )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(317,plain,
! [SV33: $i,SV48: $i,SV50: $i,SV55: $i] :
( ( ( in @ SV55 @ SV50 )
= $false )
| ( ( in @ SV55 @ SV48 )
= $true )
| ( ( SV50
= ( set_intersection2 @ SV33 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(318,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[190,317,316,313,309,305,304,287,277,276,273,267,266,250,247,238,228,227,214,206,205,194,192,191]) ).
thf(319,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[318,183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 13:29:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 13
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:15,loop_count:0,foatp_calls:0,translation:fof_full)...................
% 0.35/0.54
% 0.35/0.54 ********************************
% 0.35/0.54 * All subproblems solved! *
% 0.35/0.54 ********************************
% 0.35/0.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:318,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.35/0.56
% 0.35/0.56 %**** Beginning of derivation protocol ****
% 0.35/0.56 % SZS output start CNFRefutation
% See solution above
% 0.35/0.57
% 0.35/0.57 %**** End of derivation protocol ****
% 0.35/0.57 %**** no. of clauses in derivation: 319 ****
% 0.35/0.57 %**** clause counter: 318 ****
% 0.35/0.57
% 0.35/0.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:318,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------