TSTP Solution File: SET945+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n013.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 03:06:28 EDT 2022
% Result : Theorem 76.60s 76.81s
% Output : CNFRefutation 76.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of formulae : 225 ( 84 unt; 14 typ; 0 def)
% Number of atoms : 1602 ( 515 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 3699 ( 620 ~; 562 |; 32 &;2462 @)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 640 ( 0 ^ 632 !; 8 ?; 640 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY25,type,
sK2_SY25: $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $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_C,type,
sK7_C: $i > $i > $i ).
thf(tp_sK8_SY29,type,
sK8_SY29: $i > $i > $i ).
thf(tp_sK9_D,type,
sK9_D: $i > $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_union,type,
union: $i > $i ).
thf(1,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(3,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(10,conjecture,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( disjoint @ C @ B ) )
=> ( disjoint @ ( union @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(11,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( disjoint @ C @ B ) )
=> ( disjoint @ ( union @ A ) @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( disjoint @ C @ B ) )
=> ( disjoint @ ( union @ A ) @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,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)],[7]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(22,plain,
( ( ! [SY25: $i] :
( ! [SY26: $i] :
( ( in @ SY26 @ sK1_A )
=> ( disjoint @ SY26 @ SY25 ) )
=> ( disjoint @ ( union @ sK1_A ) @ SY25 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ! [SY27: $i] :
( ( in @ SY27 @ sK1_A )
=> ( disjoint @ SY27 @ sK2_SY25 ) )
=> ( disjoint @ ( union @ sK1_A ) @ sK2_SY25 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( ! [SY27: $i] :
( ( in @ SY27 @ sK1_A )
=> ( disjoint @ SY27 @ sK2_SY25 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(25,plain,
( ( disjoint @ ( union @ sK1_A ) @ sK2_SY25 )
= $false ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ( disjoint @ ( union @ sK1_A ) @ sK2_SY25 ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [SY27: $i] :
( ~ ( in @ SY27 @ sK1_A )
| ( disjoint @ SY27 @ sK2_SY25 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK3_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(30,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(31,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY28: $i] :
( ~ ( in @ ( sK7_C @ B @ A ) @ SY28 )
| ~ ( in @ SY28 @ A ) )
| ~ ( in @ ( sK7_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK7_C @ B @ A ) @ ( sK8_SY29 @ B @ A ) )
& ( in @ ( sK8_SY29 @ B @ A ) @ A ) )
| ( in @ ( sK7_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK6_D @ C @ B @ A ) )
& ( in @ ( sK6_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(34,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK9_D @ C @ B @ A ) @ A )
| ( in @ ( sK9_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK9_D @ C @ B @ A ) @ B )
| ( in @ ( sK9_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)],[19]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(38,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK9_D @ C @ B @ A ) @ A )
| ( in @ ( sK9_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK9_D @ C @ B @ A ) @ B )
| ( in @ ( sK9_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)],[34]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY28: $i] :
( ~ ( in @ ( sK7_C @ B @ A ) @ SY28 )
| ~ ( in @ SY28 @ A ) )
| ~ ( in @ ( sK7_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK7_C @ B @ A ) @ ( sK8_SY29 @ B @ A ) )
& ( in @ ( sK8_SY29 @ B @ A ) @ A ) )
| ( in @ ( sK7_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK6_D @ C @ B @ A ) )
& ( in @ ( sK6_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(41,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(42,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK3_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(45,plain,
( ( ! [SY27: $i] :
( ~ ( in @ SY27 @ sK1_A )
| ( disjoint @ SY27 @ sK2_SY25 ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(46,plain,
( ( ~ ( disjoint @ ( union @ sK1_A ) @ sK2_SY25 ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(47,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ ( sK8_SY29 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK8_SY29 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK6_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(48,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(49,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK9_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)],[38]) ).
thf(50,plain,
! [SV1: $i] :
( ( ! [SY30: $i] :
( ~ ( in @ SV1 @ SY30 )
| ~ ( in @ SY30 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV2: $i] :
( ( ! [SY31: $i] :
( ( set_intersection2 @ SV2 @ SY31 )
= ( set_intersection2 @ SY31 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV3: $i] :
( ( ( set_intersection2 @ SV3 @ SV3 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(53,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(54,plain,
! [SV4: $i] :
( ( ! [SY32: $i] :
( ~ ( disjoint @ SV4 @ SY32 )
| ( disjoint @ SY32 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(55,plain,
! [SV5: $i] :
( ( ~ ( in @ SV5 @ sK1_A )
| ( disjoint @ SV5 @ sK2_SY25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
( ( disjoint @ ( union @ sK1_A ) @ sK2_SY25 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(57,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ ( sK8_SY29 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK8_SY29 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK6_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(58,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(59,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY33: $i,SY34: $i] :
( ~ ( ~ ( ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY33 )
| ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) )
| ~ ~ ( ~ ( ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) )
| ~ ( ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY33 )
| ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) ) ) )
| ( SY34
= ( set_intersection2 @ SV6 @ SY33 ) ) )
| ~ ! [SY35: $i,SY36: $i] :
( ( SY36
!= ( set_intersection2 @ SV6 @ SY35 ) )
| ~ ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SV6 )
| ~ ( in @ SY37 @ SY35 )
| ( in @ SY37 @ SY36 ) )
| ~ ~ ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ SY36 )
| ( in @ SY38 @ SV6 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY36 )
| ( in @ SX3 @ SY35 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV7 )
| ~ ( in @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV8: $i,SV2: $i] :
( ( ( set_intersection2 @ SV2 @ SV8 )
= ( set_intersection2 @ SV8 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( disjoint @ SV4 @ SV9 )
| ( disjoint @ SV9 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV5: $i] :
( ( ( ~ ( in @ SV5 @ sK1_A ) )
= $true )
| ( ( disjoint @ SV5 @ sK2_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(64,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ ( sK8_SY29 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK8_SY29 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(65,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK6_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(66,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(67,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(68,plain,
! [SV6: $i] :
( ( ~ ! [SY33: $i,SY34: $i] :
( ~ ( ~ ( ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY33 )
| ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) )
| ~ ~ ( ~ ( ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) )
| ~ ( ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY33 )
| ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) ) ) )
| ( SY34
= ( set_intersection2 @ SV6 @ SY33 ) ) )
| ~ ! [SY35: $i,SY36: $i] :
( ( SY36
!= ( set_intersection2 @ SV6 @ SY35 ) )
| ~ ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SV6 )
| ~ ( in @ SY37 @ SY35 )
| ( in @ SY37 @ SY36 ) )
| ~ ~ ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ SY36 )
| ( in @ SY38 @ SV6 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY36 )
| ( in @ SX3 @ SY35 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( disjoint @ SV4 @ SV9 ) )
= $true )
| ( ( disjoint @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ sK1_A )
= $false )
| ( ( disjoint @ SV5 @ sK2_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ ( sK8_SY29 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK8_SY29 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK6_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(76,plain,
! [SV6: $i] :
( ( ~ ! [SY33: $i,SY34: $i] :
( ~ ( ~ ( ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY33 )
| ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) )
| ~ ~ ( ~ ( ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) )
| ~ ( ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY33 )
| ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) ) ) )
| ( SY34
= ( set_intersection2 @ SV6 @ SY33 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV6: $i] :
( ( ~ ! [SY35: $i,SY36: $i] :
( ( SY36
!= ( set_intersection2 @ SV6 @ SY35 ) )
| ~ ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SV6 )
| ~ ( in @ SY37 @ SY35 )
| ( in @ SY37 @ SY36 ) )
| ~ ~ ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ SY36 )
| ( in @ SY38 @ SV6 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY36 )
| ( in @ SX3 @ SY35 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(78,plain,
! [SV7: $i,SV1: $i] :
( ( ( in @ SV1 @ SV7 )
= $false )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV9: $i,SV4: $i] :
( ( ( disjoint @ SV4 @ SV9 )
= $false )
| ( ( disjoint @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV10: $i] :
( ( ! [SY40: $i] :
( ~ ( ~ ( ! [SY41: $i] :
( ~ ( in @ ( sK7_C @ SY40 @ SV10 ) @ SY41 )
| ~ ( in @ SY41 @ SV10 ) )
| ~ ( in @ ( sK7_C @ SY40 @ SV10 ) @ SY40 ) )
| ~ ( ~ ( ~ ( in @ ( sK7_C @ SY40 @ SV10 ) @ ( sK8_SY29 @ SY40 @ SV10 ) )
| ~ ( in @ ( sK8_SY29 @ SY40 @ SV10 ) @ SV10 ) )
| ( in @ ( sK7_C @ SY40 @ SV10 ) @ SY40 ) ) )
| ( SY40
= ( union @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV11: $i] :
( ( ! [SY42: $i] :
( ( SY42
!= ( union @ SV11 ) )
| ~ ( ~ ! [SY43: $i] :
( ! [SY44: $i] :
( ~ ( in @ SY43 @ SY44 )
| ~ ( in @ SY44 @ SV11 ) )
| ( in @ SY43 @ SY42 ) )
| ~ ! [SY45: $i] :
( ~ ( in @ SY45 @ SY42 )
| ~ ( ~ ( in @ SY45 @ ( sK6_D @ SY45 @ SY42 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SY45 @ SY42 @ SV11 ) @ SV11 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV12: $i] :
( ( ! [SY46: $i] :
( ( disjoint @ SV12 @ SY46 )
| ( in @ ( sK3_C @ SY46 @ SV12 ) @ ( set_intersection2 @ SV12 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV13: $i] :
( ( ! [SY47: $i] :
( ! [SY48: $i] :
~ ( in @ SY48 @ ( set_intersection2 @ SV13 @ SY47 ) )
| ~ ( disjoint @ SV13 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV6: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( ~ ( ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY33 )
| ~ ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) )
| ~ ~ ( ~ ( ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) )
| ~ ( ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY33 )
| ( in @ ( sK9_D @ SY34 @ SY33 @ SV6 ) @ SY34 ) ) ) )
| ( SY34
= ( set_intersection2 @ SV6 @ SY33 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(85,plain,
! [SV6: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ( SY36
!= ( set_intersection2 @ SV6 @ SY35 ) )
| ~ ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SV6 )
| ~ ( in @ SY37 @ SY35 )
| ( in @ SY37 @ SY36 ) )
| ~ ~ ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ SY36 )
| ( in @ SY38 @ SV6 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY36 )
| ( in @ SX3 @ SY35 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(86,plain,
! [SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV10: $i,SV14: $i] :
( ( ~ ( ~ ( ! [SY49: $i] :
( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SY49 )
| ~ ( in @ SY49 @ SV10 ) )
| ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
| ~ ( ~ ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ ( sK8_SY29 @ SV14 @ SV10 ) )
| ~ ( in @ ( sK8_SY29 @ SV14 @ SV10 ) @ SV10 ) )
| ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) ) )
| ( SV14
= ( union @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV11: $i,SV15: $i] :
( ( ( SV15
!= ( union @ SV11 ) )
| ~ ( ~ ! [SY50: $i] :
( ! [SY44: $i] :
( ~ ( in @ SY50 @ SY44 )
| ~ ( in @ SY44 @ SV11 ) )
| ( in @ SY50 @ SV15 ) )
| ~ ! [SY52: $i] :
( ~ ( in @ SY52 @ SV15 )
| ~ ( ~ ( in @ SY52 @ ( sK6_D @ SY52 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SY52 @ SV15 @ SV11 ) @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV16: $i,SV12: $i] :
( ( ( disjoint @ SV12 @ SV16 )
| ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV17: $i,SV13: $i] :
( ( ! [SY53: $i] :
~ ( in @ SY53 @ ( set_intersection2 @ SV13 @ SV17 ) )
| ~ ( disjoint @ SV13 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV6: $i,SV18: $i] :
( ( ! [SY54: $i] :
( ~ ( ~ ( ~ ( in @ ( sK9_D @ SY54 @ SV18 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SY54 @ SV18 @ SV6 ) @ SV18 )
| ~ ( in @ ( sK9_D @ SY54 @ SV18 @ SV6 ) @ SY54 ) )
| ~ ~ ( ~ ( ( in @ ( sK9_D @ SY54 @ SV18 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SY54 @ SV18 @ SV6 ) @ SY54 ) )
| ~ ( ( in @ ( sK9_D @ SY54 @ SV18 @ SV6 ) @ SV18 )
| ( in @ ( sK9_D @ SY54 @ SV18 @ SV6 ) @ SY54 ) ) ) )
| ( SY54
= ( set_intersection2 @ SV6 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV19: $i,SV6: $i] :
( ( ! [SY55: $i] :
( ( SY55
!= ( set_intersection2 @ SV6 @ SV19 ) )
| ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ SV6 )
| ~ ( in @ SY56 @ SV19 )
| ( in @ SY56 @ SY55 ) )
| ~ ~ ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ SY55 )
| ( in @ SY38 @ SV6 ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ SY55 )
| ( in @ SY58 @ SV19 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ~ ( ! [SY49: $i] :
( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SY49 )
| ~ ( in @ SY49 @ SV10 ) )
| ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
| ~ ( ~ ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ ( sK8_SY29 @ SV14 @ SV10 ) )
| ~ ( in @ ( sK8_SY29 @ SV14 @ SV10 ) @ SV10 ) )
| ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) ) ) )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV11: $i,SV15: $i] :
( ( ( ( SV15
!= ( union @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY50: $i] :
( ! [SY44: $i] :
( ~ ( in @ SY50 @ SY44 )
| ~ ( in @ SY44 @ SV11 ) )
| ( in @ SY50 @ SV15 ) )
| ~ ! [SY52: $i] :
( ~ ( in @ SY52 @ SV15 )
| ~ ( ~ ( in @ SY52 @ ( sK6_D @ SY52 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SY52 @ SV15 @ SV11 ) @ SV11 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV16: $i,SV12: $i] :
( ( ( disjoint @ SV12 @ SV16 )
= $true )
| ( ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV17: $i,SV13: $i] :
( ( ( ! [SY53: $i] :
~ ( in @ SY53 @ ( set_intersection2 @ SV13 @ SV17 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV13 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
| ~ ~ ( ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
| ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) ) ) )
| ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV19: $i,SV6: $i,SV21: $i] :
( ( ( SV21
!= ( set_intersection2 @ SV6 @ SV19 ) )
| ~ ( ~ ! [SY59: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY59 @ SV19 )
| ( in @ SY59 @ SV21 ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV21 )
| ( in @ SY60 @ SV6 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV21 )
| ( in @ SY61 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ! [SY49: $i] :
( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SY49 )
| ~ ( in @ SY49 @ SV10 ) )
| ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
| ~ ( ~ ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ ( sK8_SY29 @ SV14 @ SV10 ) )
| ~ ( in @ ( sK8_SY29 @ SV14 @ SV10 ) @ SV10 ) )
| ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) ) )
= $false )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV11: $i,SV15: $i] :
( ( ( SV15
= ( union @ SV11 ) )
= $false )
| ( ( ~ ( ~ ! [SY50: $i] :
( ! [SY44: $i] :
( ~ ( in @ SY50 @ SY44 )
| ~ ( in @ SY44 @ SV11 ) )
| ( in @ SY50 @ SV15 ) )
| ~ ! [SY52: $i] :
( ~ ( in @ SY52 @ SV15 )
| ~ ( ~ ( in @ SY52 @ ( sK6_D @ SY52 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SY52 @ SV15 @ SV11 ) @ SV11 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV17: $i,SV13: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV13 @ SV17 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
| ~ ~ ( ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
| ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) ) ) ) )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV19: $i,SV6: $i,SV21: $i] :
( ( ( ( SV21
!= ( set_intersection2 @ SV6 @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY59: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY59 @ SV19 )
| ( in @ SY59 @ SV21 ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV21 )
| ( in @ SY60 @ SV6 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV21 )
| ( in @ SY61 @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ! [SY49: $i] :
( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SY49 )
| ~ ( in @ SY49 @ SV10 ) )
| ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) ) )
= $false )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(105,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ ( sK8_SY29 @ SV14 @ SV10 ) )
| ~ ( in @ ( sK8_SY29 @ SV14 @ SV10 ) @ SV10 ) )
| ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) ) )
= $false )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(106,plain,
! [SV15: $i,SV11: $i] :
( ( ( ~ ! [SY50: $i] :
( ! [SY44: $i] :
( ~ ( in @ SY50 @ SY44 )
| ~ ( in @ SY44 @ SV11 ) )
| ( in @ SY50 @ SV15 ) )
| ~ ! [SY52: $i] :
( ~ ( in @ SY52 @ SV15 )
| ~ ( ~ ( in @ SY52 @ ( sK6_D @ SY52 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SY52 @ SV15 @ SV11 ) @ SV11 ) ) ) )
= $false )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV17: $i,SV13: $i,SV22: $i] :
( ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false )
| ( ( ~ ( disjoint @ SV13 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
| ~ ~ ( ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
| ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) ) ) )
= $false )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV19: $i,SV6: $i,SV21: $i] :
( ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false )
| ( ( ~ ( ~ ! [SY59: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY59 @ SV19 )
| ( in @ SY59 @ SV21 ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV21 )
| ( in @ SY60 @ SV6 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV21 )
| ( in @ SY61 @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV10: $i,SV14: $i] :
( ( ( ! [SY49: $i] :
( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SY49 )
| ~ ( in @ SY49 @ SV10 ) )
| ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(111,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ ( sK8_SY29 @ SV14 @ SV10 ) )
| ~ ( in @ ( sK8_SY29 @ SV14 @ SV10 ) @ SV10 ) )
| ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV15: $i,SV11: $i] :
( ( ( ~ ! [SY50: $i] :
( ! [SY44: $i] :
( ~ ( in @ SY50 @ SY44 )
| ~ ( in @ SY44 @ SV11 ) )
| ( in @ SY50 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(113,plain,
! [SV11: $i,SV15: $i] :
( ( ( ~ ! [SY52: $i] :
( ~ ( in @ SY52 @ SV15 )
| ~ ( ~ ( in @ SY52 @ ( sK6_D @ SY52 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SY52 @ SV15 @ SV11 ) @ SV11 ) ) ) )
= $false )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(114,plain,
! [SV22: $i,SV17: $i,SV13: $i] :
( ( ( disjoint @ SV13 @ SV17 )
= $false )
| ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) ) )
= $false )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(116,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
| ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) ) ) )
= $false )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(117,plain,
! [SV21: $i,SV19: $i,SV6: $i] :
( ( ( ~ ! [SY59: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY59 @ SV19 )
| ( in @ SY59 @ SV21 ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV21 )
| ( in @ SY60 @ SV6 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV21 )
| ( in @ SY61 @ SV19 ) ) ) )
= $false )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(118,plain,
! [SV10: $i,SV14: $i] :
( ( ( ! [SY49: $i] :
( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SY49 )
| ~ ( in @ SY49 @ SV10 ) ) )
= $true )
| ( ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(119,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ ( sK8_SY29 @ SV14 @ SV10 ) )
| ~ ( in @ ( sK8_SY29 @ SV14 @ SV10 ) @ SV10 ) ) )
= $true )
| ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV15: $i,SV11: $i] :
( ( ( ! [SY50: $i] :
( ! [SY44: $i] :
( ~ ( in @ SY50 @ SY44 )
| ~ ( in @ SY44 @ SV11 ) )
| ( in @ SY50 @ SV15 ) ) )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(121,plain,
! [SV11: $i,SV15: $i] :
( ( ( ! [SY52: $i] :
( ~ ( in @ SY52 @ SV15 )
| ~ ( ~ ( in @ SY52 @ ( sK6_D @ SY52 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SY52 @ SV15 @ SV11 ) @ SV11 ) ) ) )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(122,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(123,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
| ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) ) ) )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(124,plain,
! [SV21: $i,SV19: $i,SV6: $i] :
( ( ( ~ ! [SY59: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY59 @ SV19 )
| ( in @ SY59 @ SV21 ) ) )
= $false )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(125,plain,
! [SV19: $i,SV6: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV21 )
| ( in @ SY60 @ SV6 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV21 )
| ( in @ SY61 @ SV19 ) ) ) )
= $false )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(126,plain,
! [SV23: $i,SV10: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV23 )
| ~ ( in @ SV23 @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ ( sK8_SY29 @ SV14 @ SV10 ) )
| ~ ( in @ ( sK8_SY29 @ SV14 @ SV10 ) @ SV10 ) )
= $false )
| ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV15: $i,SV11: $i,SV24: $i] :
( ( ( ! [SY62: $i] :
( ~ ( in @ SV24 @ SY62 )
| ~ ( in @ SY62 @ SV11 ) )
| ( in @ SV24 @ SV15 ) )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV11: $i,SV15: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV15 )
| ~ ( ~ ( in @ SV25 @ ( sK6_D @ SV25 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SV25 @ SV15 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(130,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(131,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
| ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) ) )
= $false )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(132,plain,
! [SV21: $i,SV19: $i,SV6: $i] :
( ( ( ! [SY59: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY59 @ SV19 )
| ( in @ SY59 @ SV21 ) ) )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(133,plain,
! [SV19: $i,SV6: $i,SV21: $i] :
( ( ( ~ ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV21 )
| ( in @ SY60 @ SV6 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV21 )
| ( in @ SY61 @ SV19 ) ) ) )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(134,plain,
! [SV23: $i,SV10: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV23 @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ ( sK8_SY29 @ SV14 @ SV10 ) ) )
= $false )
| ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(136,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK8_SY29 @ SV14 @ SV10 ) @ SV10 ) )
= $false )
| ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(137,plain,
! [SV15: $i,SV11: $i,SV24: $i] :
( ( ( ! [SY62: $i] :
( ~ ( in @ SV24 @ SY62 )
| ~ ( in @ SY62 @ SV11 ) ) )
= $true )
| ( ( in @ SV24 @ SV15 )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(138,plain,
! [SV11: $i,SV15: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV25 @ ( sK6_D @ SV25 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SV25 @ SV15 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(140,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) ) )
= $false )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(141,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) ) )
= $false )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(142,plain,
! [SV21: $i,SV19: $i,SV6: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV6 )
| ~ ( in @ SV26 @ SV19 )
| ( in @ SV26 @ SV21 ) )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(143,plain,
! [SV19: $i,SV6: $i,SV21: $i] :
( ( ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV21 )
| ( in @ SY60 @ SV6 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV21 )
| ( in @ SY61 @ SV19 ) ) )
= $false )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(144,plain,
! [SV23: $i,SV10: $i,SV14: $i] :
( ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV23 )
= $false )
| ( ( ~ ( in @ SV23 @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV10: $i,SV14: $i] :
( ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ ( sK8_SY29 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(146,plain,
! [SV10: $i,SV14: $i] :
( ( ( in @ ( sK8_SY29 @ SV14 @ SV10 ) @ SV10 )
= $true )
| ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(147,plain,
! [SV15: $i,SV11: $i,SV27: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV27 )
| ~ ( in @ SV27 @ SV11 ) )
= $true )
| ( ( in @ SV24 @ SV15 )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV11: $i,SV15: $i,SV25: $i] :
( ( ( in @ SV25 @ SV15 )
= $false )
| ( ( ~ ( ~ ( in @ SV25 @ ( sK6_D @ SV25 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SV25 @ SV15 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(149,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
= $false )
| ( ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(150,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(151,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
| ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(152,plain,
! [SV21: $i,SV19: $i,SV6: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV6 )
| ~ ( in @ SV26 @ SV19 ) )
= $true )
| ( ( in @ SV26 @ SV21 )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV19: $i,SV6: $i,SV21: $i] :
( ( ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV21 )
| ( in @ SY60 @ SV6 ) ) )
= $false )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(154,plain,
! [SV6: $i,SV19: $i,SV21: $i] :
( ( ( ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV21 )
| ( in @ SY61 @ SV19 ) ) )
= $false )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(155,plain,
! [SV14: $i,SV10: $i,SV23: $i] :
( ( ( in @ SV23 @ SV10 )
= $false )
| ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV23 )
= $false )
| ( ( ~ ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV15: $i,SV11: $i,SV27: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV27 ) )
= $true )
| ( ( ~ ( in @ SV27 @ SV11 ) )
= $true )
| ( ( in @ SV24 @ SV15 )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(157,plain,
! [SV11: $i,SV15: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ ( sK6_D @ SV25 @ SV15 @ SV11 ) )
| ~ ( in @ ( sK6_D @ SV25 @ SV15 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV25 @ SV15 )
= $false )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(158,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
= $false )
| ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
= $false )
| ( ( ~ ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 ) )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(159,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
= $true )
| ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(160,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
= $true )
| ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 )
= $true )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(161,plain,
! [SV21: $i,SV19: $i,SV6: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV26 @ SV19 ) )
= $true )
| ( ( in @ SV26 @ SV21 )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV19: $i,SV6: $i,SV21: $i] :
( ( ( ! [SY60: $i] :
( ~ ( in @ SY60 @ SV21 )
| ( in @ SY60 @ SV6 ) ) )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(163,plain,
! [SV6: $i,SV19: $i,SV21: $i] :
( ( ( ! [SY61: $i] :
( ~ ( in @ SY61 @ SV21 )
| ( in @ SY61 @ SV19 ) ) )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(164,plain,
! [SV23: $i,SV10: $i,SV14: $i] :
( ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV14 )
= $false )
| ( ( in @ ( sK7_C @ SV14 @ SV10 ) @ SV23 )
= $false )
| ( ( in @ SV23 @ SV10 )
= $false )
| ( ( SV14
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV15: $i,SV11: $i,SV27: $i,SV24: $i] :
( ( ( in @ SV24 @ SV27 )
= $false )
| ( ( ~ ( in @ SV27 @ SV11 ) )
= $true )
| ( ( in @ SV24 @ SV15 )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV11: $i,SV15: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ ( sK6_D @ SV25 @ SV15 @ SV11 ) ) )
= $false )
| ( ( in @ SV25 @ SV15 )
= $false )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(167,plain,
! [SV11: $i,SV15: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV25 @ SV15 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV25 @ SV15 )
= $false )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(168,plain,
! [SV6: $i,SV18: $i,SV20: $i] :
( ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV20 )
= $false )
| ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV6 )
= $false )
| ( ( in @ ( sK9_D @ SV20 @ SV18 @ SV6 ) @ SV18 )
= $false )
| ( ( SV20
= ( set_intersection2 @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV21: $i,SV19: $i,SV6: $i,SV26: $i] :
( ( ( in @ SV26 @ SV6 )
= $false )
| ( ( ~ ( in @ SV26 @ SV19 ) )
= $true )
| ( ( in @ SV26 @ SV21 )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV19: $i,SV6: $i,SV21: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV21 )
| ( in @ SV28 @ SV6 ) )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV6: $i,SV19: $i,SV21: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV21 )
| ( in @ SV29 @ SV19 ) )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV15: $i,SV24: $i,SV11: $i,SV27: $i] :
( ( ( in @ SV27 @ SV11 )
= $false )
| ( ( in @ SV24 @ SV27 )
= $false )
| ( ( in @ SV24 @ SV15 )
= $true )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(173,plain,
! [SV11: $i,SV15: $i,SV25: $i] :
( ( ( in @ SV25 @ ( sK6_D @ SV25 @ SV15 @ SV11 ) )
= $true )
| ( ( in @ SV25 @ SV15 )
= $false )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(174,plain,
! [SV11: $i,SV15: $i,SV25: $i] :
( ( ( in @ ( sK6_D @ SV25 @ SV15 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ SV25 @ SV15 )
= $false )
| ( ( SV15
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(175,plain,
! [SV21: $i,SV6: $i,SV19: $i,SV26: $i] :
( ( ( in @ SV26 @ SV19 )
= $false )
| ( ( in @ SV26 @ SV6 )
= $false )
| ( ( in @ SV26 @ SV21 )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(176,plain,
! [SV19: $i,SV6: $i,SV21: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV21 ) )
= $true )
| ( ( in @ SV28 @ SV6 )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(177,plain,
! [SV6: $i,SV19: $i,SV21: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV21 ) )
= $true )
| ( ( in @ SV29 @ SV19 )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(178,plain,
! [SV19: $i,SV6: $i,SV21: $i,SV28: $i] :
( ( ( in @ SV28 @ SV21 )
= $false )
| ( ( in @ SV28 @ SV6 )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(179,plain,
! [SV6: $i,SV19: $i,SV21: $i,SV29: $i] :
( ( ( in @ SV29 @ SV21 )
= $false )
| ( ( in @ SV29 @ SV19 )
= $true )
| ( ( SV21
= ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(180,plain,
! [SV1: $i,SV7: $i] :
( ( ( in @ SV1 @ SV7 )
= $false )
| ( ( ( in @ SV7 @ SV1 )
= ( in @ SV1 @ SV7 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[86]) ).
thf(181,plain,
! [SV16: $i,SV12: $i] :
( ( ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) )
= $true )
| ( ( ( disjoint @ SV12 @ SV16 )
= ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[95]) ).
thf(182,plain,
! [SV22: $i,SV17: $i,SV13: $i] :
( ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false )
| ( ( ( disjoint @ SV13 @ SV17 )
= ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[114]) ).
thf(183,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( ( in @ SV7 @ SV1 )
| ( in @ SV1 @ SV7 ) )
| ~ ( ~ ( in @ SV7 @ SV1 )
| ~ ( in @ SV1 @ SV7 ) ) )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[180]) ).
thf(184,plain,
! [SV1: $i,SV7: $i] :
( ( ( ( in @ SV7 @ SV1 )
= ( in @ SV1 @ SV7 ) )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[180]) ).
thf(185,plain,
! [SV16: $i,SV12: $i] :
( ( ( ~ ( ( disjoint @ SV12 @ SV16 )
| ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) ) )
| ~ ( ~ ( disjoint @ SV12 @ SV16 )
| ~ ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[181]) ).
thf(187,plain,
! [SV22: $i,SV17: $i,SV13: $i] :
( ( ( ~ ( ( disjoint @ SV13 @ SV17 )
| ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) ) )
| ~ ( ~ ( disjoint @ SV13 @ SV17 )
| ~ ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[182]) ).
thf(190,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| ~ ( in @ SV1 @ SV7 ) ) )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(191,plain,
! [SV16: $i,SV12: $i] :
( ( ( ~ ( ( disjoint @ SV12 @ SV16 )
| ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(194,plain,
! [SV22: $i,SV17: $i,SV13: $i] :
( ( ( ~ ( ~ ( disjoint @ SV13 @ SV17 )
| ~ ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(196,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 )
| ~ ( in @ SV1 @ SV7 ) )
= $true )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(197,plain,
! [SV16: $i,SV12: $i] :
( ( ( ( disjoint @ SV12 @ SV16 )
| ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) ) )
= $true )
| ( ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(200,plain,
! [SV22: $i,SV17: $i,SV13: $i] :
( ( ( ~ ( disjoint @ SV13 @ SV17 )
| ~ ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) ) )
= $true )
| ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(202,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 ) )
= $true )
| ( ( ~ ( in @ SV1 @ SV7 ) )
= $true )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(203,plain,
! [SV16: $i,SV12: $i] :
( ( ( disjoint @ SV12 @ SV16 )
= $true )
| ( ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(206,plain,
! [SV22: $i,SV17: $i,SV13: $i] :
( ( ( ~ ( disjoint @ SV13 @ SV17 ) )
= $true )
| ( ( ~ ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) ) )
= $true )
| ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(207,plain,
! [SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( ~ ( in @ SV1 @ SV7 ) )
= $true )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(209,plain,
! [SV22: $i,SV17: $i,SV13: $i] :
( ( ( disjoint @ SV13 @ SV17 )
= $false )
| ( ( ~ ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) ) )
= $true )
| ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(210,plain,
! [SV7: $i,SV1: $i] :
( ( ( in @ SV1 @ SV7 )
= $false )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(212,plain,
! [SV17: $i,SV13: $i,SV22: $i] :
( ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false )
| ( ( disjoint @ SV13 @ SV17 )
= $false )
| ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(213,plain,
! [SV1: $i] :
( ( in @ SV1 @ SV1 )
= $false ),
inference(extuni,[status(esa)],[184:[bind(SV7,$thf( SV1 ))]]) ).
thf(214,plain,
! [SV27: $i,SV11: $i,SV24: $i] :
( ( ( in @ SV24 @ ( union @ SV11 ) )
= $true )
| ( ( in @ SV24 @ SV27 )
= $false )
| ( ( in @ SV27 @ SV11 )
= $false ) ),
inference(extuni,[status(esa)],[172:[bind(SV15,$thf( union @ SV11 ))]]) ).
thf(215,plain,
! [SV11: $i,SV25: $i] :
( ( ( in @ SV25 @ ( union @ SV11 ) )
= $false )
| ( ( in @ SV25 @ ( sK6_D @ SV25 @ ( union @ SV11 ) @ SV11 ) )
= $true ) ),
inference(extuni,[status(esa)],[173:[bind(SV15,$thf( union @ SV11 ))]]) ).
thf(216,plain,
! [SV11: $i,SV25: $i] :
( ( ( in @ SV25 @ ( union @ SV11 ) )
= $false )
| ( ( in @ ( sK6_D @ SV25 @ ( union @ SV11 ) @ SV11 ) @ SV11 )
= $true ) ),
inference(extuni,[status(esa)],[174:[bind(SV15,$thf( union @ SV11 ))]]) ).
thf(217,plain,
! [SV19: $i,SV6: $i,SV26: $i] :
( ( ( in @ SV26 @ ( set_intersection2 @ SV6 @ SV19 ) )
= $true )
| ( ( in @ SV26 @ SV6 )
= $false )
| ( ( in @ SV26 @ SV19 )
= $false ) ),
inference(extuni,[status(esa)],[175:[bind(SV21,$thf( set_intersection2 @ SV6 @ SV19 ))]]) ).
thf(218,plain,
! [SV19: $i,SV6: $i,SV28: $i] :
( ( ( in @ SV28 @ SV6 )
= $true )
| ( ( in @ SV28 @ ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extuni,[status(esa)],[178:[bind(SV21,$thf( set_intersection2 @ SV6 @ SV19 ))]]) ).
thf(219,plain,
! [SV6: $i,SV19: $i,SV29: $i] :
( ( ( in @ SV29 @ SV19 )
= $true )
| ( ( in @ SV29 @ ( set_intersection2 @ SV6 @ SV19 ) )
= $false ) ),
inference(extuni,[status(esa)],[179:[bind(SV21,$thf( set_intersection2 @ SV6 @ SV19 ))]]) ).
thf(220,plain,
! [SV7: $i,SV1: $i] :
( ( ( in @ SV1 @ SV7 )
= $false )
| ( ( in @ SV7 @ SV1 )
= $false ) ),
inference(sim,[status(thm)],[210]) ).
thf(221,plain,
! [SV16: $i,SV12: $i] :
( ( ( disjoint @ SV12 @ SV16 )
= $true )
| ( ( in @ ( sK3_C @ SV16 @ SV12 ) @ ( set_intersection2 @ SV12 @ SV16 ) )
= $true ) ),
inference(sim,[status(thm)],[203]) ).
thf(222,plain,
! [SV17: $i,SV13: $i,SV22: $i] :
( ( ( in @ SV22 @ ( set_intersection2 @ SV13 @ SV17 ) )
= $false )
| ( ( disjoint @ SV13 @ SV17 )
= $false ) ),
inference(sim,[status(thm)],[212]) ).
thf(223,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,222,221,220,219,218,217,216,215,214,213,179,178,175,174,173,172,168,164,160,159,146,145,114,95,86,79,71,61,56,53,52]) ).
thf(224,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 01:39:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 9
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.36 (rf:0,axioms:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)..............eprover: CPU time limit exceeded, terminating
% 74.35/74.53 .
% 76.60/76.81
% 76.60/76.81 ********************************
% 76.60/76.81 * All subproblems solved! *
% 76.60/76.81 ********************************
% 76.60/76.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:223,loop_count:0,foatp_calls:2,translation:fof_full)
% 76.60/76.83
% 76.60/76.83 %**** Beginning of derivation protocol ****
% 76.60/76.83 % SZS output start CNFRefutation
% See solution above
% 76.60/76.83
% 76.60/76.83 %**** End of derivation protocol ****
% 76.60/76.83 %**** no. of clauses in derivation: 211 ****
% 76.60/76.83 %**** clause counter: 223 ****
% 76.60/76.83
% 76.60/76.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:223,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------