TSTP Solution File: SET890+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET890+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 : n005.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 03:06:01 EDT 2022
% Result : Theorem 4.57s 4.76s
% Output : CNFRefutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 23
% Syntax : Number of formulae : 198 ( 92 unt; 13 typ; 0 def)
% Number of atoms : 1294 ( 512 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 2573 ( 533 ~; 453 |; 28 &;1541 @)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 514 ( 0 ^ 508 !; 6 ?; 514 :)
% Comments :
%------------------------------------------------------------------------------
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_A,type,
sK2_A: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_D,type,
sK4_D: $i > $i > $i > $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_sK6_SY22,type,
sK6_SY22: $i > $i > $i ).
thf(tp_sK7_C,type,
sK7_C: $i > $i > $i ).
thf(tp_sK8_C,type,
sK8_C: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
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] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(10,conjecture,
! [A: $i] :
( ( union @ ( singleton @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(11,negated_conjecture,
( ( ! [A: $i] :
( ( union @ ( singleton @ A ) )
= A ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [A: $i] :
( ( union @ ( singleton @ A ) )
= A ) )
= $false ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ? [A: $i] :
~ ( empty @ 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,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,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)],[5]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ 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,
( ( ( union @ ( singleton @ sK1_A ) )
= sK1_A )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ( ( union @ ( singleton @ sK1_A ) )
!= sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(25,plain,
( ( ~ ( empty @ sK2_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(26,plain,
( ( empty @ sK3_A )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY21: $i] :
( ~ ( in @ ( sK5_C @ B @ A ) @ SY21 )
| ~ ( in @ SY21 @ A ) )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK5_C @ B @ A ) @ ( sK6_SY22 @ B @ A ) )
& ( in @ ( sK6_SY22 @ B @ A ) @ A ) )
| ( in @ ( sK5_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 @ ( sK4_D @ C @ B @ A ) )
& ( in @ ( sK4_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK7_C @ B @ A ) @ A )
& ~ ( in @ ( sK7_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK8_C @ B @ A )
!= A )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( sK8_C @ B @ A )
= A )
| ( in @ ( sK8_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK8_C @ B @ A )
!= A )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( sK8_C @ B @ A )
= A )
| ( in @ ( sK8_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK7_C @ B @ A ) @ A )
& ~ ( in @ ( sK7_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY21: $i] :
( ~ ( in @ ( sK5_C @ B @ A ) @ SY21 )
| ~ ( in @ SY21 @ A ) )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK5_C @ B @ A ) @ ( sK6_SY22 @ B @ A ) )
& ( in @ ( sK6_SY22 @ B @ A ) @ A ) )
| ( in @ ( sK5_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 @ ( sK4_D @ C @ B @ A ) )
& ( in @ ( sK4_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( empty @ sK3_A )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( ~ ( empty @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(41,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( ( ( union @ ( singleton @ sK1_A ) )
!= sK1_A ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(43,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(44,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(45,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ ( sK6_SY22 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_SY22 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK5_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 @ ( sK4_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(46,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(47,plain,
! [SV1: $i] :
( ( ! [SY23: $i] :
( ~ ( in @ SV1 @ SY23 )
| ~ ( in @ SY23 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(48,plain,
! [SV2: $i] :
( ( ! [SY24: $i] :
( ~ ( in @ SV2 @ SY24 )
| ( subset @ SV2 @ ( union @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(49,plain,
( ( empty @ sK2_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV3: $i] :
( ( subset @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
( ( ( union @ ( singleton @ sK1_A ) )
= sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(52,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(53,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(54,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ ( sK6_SY22 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_SY22 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK5_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 @ ( sK4_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(55,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV4 )
| ~ ( in @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV5 )
| ( subset @ SV2 @ ( union @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(59,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(60,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(61,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(62,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ ( sK6_SY22 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_SY22 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(63,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 @ ( sK4_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(64,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(65,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(66,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ( in @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV5 ) )
= $true )
| ( ( subset @ SV2 @ ( union @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ ( sK6_SY22 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_SY22 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
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 @ ( sK4_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK4_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(75,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(76,plain,
! [SV4: $i,SV1: $i] :
( ( ( in @ SV1 @ SV4 )
= $false )
| ( ( ~ ( in @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV5: $i,SV2: $i] :
( ( ( in @ SV2 @ SV5 )
= $false )
| ( ( subset @ SV2 @ ( union @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV6: $i] :
( ( ! [SY25: $i] :
( ~ ( ~ ( ( ( sK8_C @ SY25 @ SV6 )
!= SV6 )
| ~ ( in @ ( sK8_C @ SY25 @ SV6 ) @ SY25 ) )
| ~ ( ( ( sK8_C @ SY25 @ SV6 )
= SV6 )
| ( in @ ( sK8_C @ SY25 @ SV6 ) @ SY25 ) ) )
| ( SY25
= ( singleton @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV7: $i] :
( ( ! [SY26: $i] :
( ( SY26
!= ( singleton @ SV7 ) )
| ~ ( ~ ! [SY27: $i] :
( ( SY27 != SV7 )
| ( in @ SY27 @ SY26 ) )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SY26 )
| ( SY28 = SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV8: $i] :
( ( ! [SY29: $i] :
( ~ ( ~ ( in @ ( sK7_C @ SY29 @ SV8 ) @ SV8 )
| ~ ~ ( in @ ( sK7_C @ SY29 @ SV8 ) @ SY29 ) )
| ( subset @ SV8 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV9: $i] :
( ( ! [SY30: $i] :
( ~ ( subset @ SV9 @ SY30 )
| ! [SY31: $i] :
( ~ ( in @ SY31 @ SV9 )
| ( in @ SY31 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV10: $i] :
( ( ! [SY32: $i] :
( ~ ( ~ ( ! [SY33: $i] :
( ~ ( in @ ( sK5_C @ SY32 @ SV10 ) @ SY33 )
| ~ ( in @ SY33 @ SV10 ) )
| ~ ( in @ ( sK5_C @ SY32 @ SV10 ) @ SY32 ) )
| ~ ( ~ ( ~ ( in @ ( sK5_C @ SY32 @ SV10 ) @ ( sK6_SY22 @ SY32 @ SV10 ) )
| ~ ( in @ ( sK6_SY22 @ SY32 @ SV10 ) @ SV10 ) )
| ( in @ ( sK5_C @ SY32 @ SV10 ) @ SY32 ) ) )
| ( SY32
= ( union @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV11: $i] :
( ( ! [SY34: $i] :
( ( SY34
!= ( union @ SV11 ) )
| ~ ( ~ ! [SY35: $i] :
( ! [SY36: $i] :
( ~ ( in @ SY35 @ SY36 )
| ~ ( in @ SY36 @ SV11 ) )
| ( in @ SY35 @ SY34 ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SY34 )
| ~ ( ~ ( in @ SY37 @ ( sK4_D @ SY37 @ SY34 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SY37 @ SY34 @ SV11 ) @ SV11 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV12: $i] :
( ( ! [SY38: $i] :
( ~ ( subset @ SV12 @ SY38 )
| ~ ( subset @ SY38 @ SV12 )
| ( SV12 = SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(85,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV6: $i,SV13: $i] :
( ( ~ ( ~ ( ( ( sK8_C @ SV13 @ SV6 )
!= SV6 )
| ~ ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) )
| ~ ( ( ( sK8_C @ SV13 @ SV6 )
= SV6 )
| ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) ) )
| ( SV13
= ( singleton @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV7: $i,SV14: $i] :
( ( ( SV14
!= ( singleton @ SV7 ) )
| ~ ( ~ ! [SY39: $i] :
( ( SY39 != SV7 )
| ( in @ SY39 @ SV14 ) )
| ~ ! [SY40: $i] :
( ~ ( in @ SY40 @ SV14 )
| ( SY40 = SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV8: $i,SV15: $i] :
( ( ~ ( ~ ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV8 )
| ~ ~ ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV15 ) )
| ( subset @ SV8 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV16: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV16 )
| ! [SY41: $i] :
( ~ ( in @ SY41 @ SV9 )
| ( in @ SY41 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV10: $i,SV17: $i] :
( ( ~ ( ~ ( ! [SY42: $i] :
( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SY42 )
| ~ ( in @ SY42 @ SV10 ) )
| ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
| ~ ( ~ ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ ( sK6_SY22 @ SV17 @ SV10 ) )
| ~ ( in @ ( sK6_SY22 @ SV17 @ SV10 ) @ SV10 ) )
| ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) ) )
| ( SV17
= ( union @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV11: $i,SV18: $i] :
( ( ( SV18
!= ( union @ SV11 ) )
| ~ ( ~ ! [SY43: $i] :
( ! [SY36: $i] :
( ~ ( in @ SY43 @ SY36 )
| ~ ( in @ SY36 @ SV11 ) )
| ( in @ SY43 @ SV18 ) )
| ~ ! [SY45: $i] :
( ~ ( in @ SY45 @ SV18 )
| ~ ( ~ ( in @ SY45 @ ( sK4_D @ SY45 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SY45 @ SV18 @ SV11 ) @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV19: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV19 )
| ~ ( subset @ SV19 @ SV12 )
| ( SV12 = SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(95,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(96,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( ~ ( ( ( sK8_C @ SV13 @ SV6 )
!= SV6 )
| ~ ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) )
| ~ ( ( ( sK8_C @ SV13 @ SV6 )
= SV6 )
| ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) ) ) )
= $true )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV7: $i,SV14: $i] :
( ( ( ( SV14
!= ( singleton @ SV7 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY39: $i] :
( ( SY39 != SV7 )
| ( in @ SY39 @ SV14 ) )
| ~ ! [SY40: $i] :
( ~ ( in @ SY40 @ SV14 )
| ( SY40 = SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV8 )
| ~ ~ ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV15 ) ) )
= $true )
| ( ( subset @ SV8 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV16 ) )
= $true )
| ( ( ! [SY41: $i] :
( ~ ( in @ SY41 @ SV9 )
| ( in @ SY41 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( ~ ( ! [SY42: $i] :
( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SY42 )
| ~ ( in @ SY42 @ SV10 ) )
| ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
| ~ ( ~ ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ ( sK6_SY22 @ SV17 @ SV10 ) )
| ~ ( in @ ( sK6_SY22 @ SV17 @ SV10 ) @ SV10 ) )
| ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) ) ) )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV11: $i,SV18: $i] :
( ( ( ( SV18
!= ( union @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY43: $i] :
( ! [SY36: $i] :
( ~ ( in @ SY43 @ SY36 )
| ~ ( in @ SY36 @ SV11 ) )
| ( in @ SY43 @ SV18 ) )
| ~ ! [SY45: $i] :
( ~ ( in @ SY45 @ SV18 )
| ~ ( ~ ( in @ SY45 @ ( sK4_D @ SY45 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SY45 @ SV18 @ SV11 ) @ SV11 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV19: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV19 )
| ~ ( subset @ SV19 @ SV12 ) )
= $true )
| ( ( SV12 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(105,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( ( ( sK8_C @ SV13 @ SV6 )
!= SV6 )
| ~ ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) )
| ~ ( ( ( sK8_C @ SV13 @ SV6 )
= SV6 )
| ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) ) )
= $false )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV7: $i,SV14: $i] :
( ( ( SV14
= ( singleton @ SV7 ) )
= $false )
| ( ( ~ ( ~ ! [SY39: $i] :
( ( SY39 != SV7 )
| ( in @ SY39 @ SV14 ) )
| ~ ! [SY40: $i] :
( ~ ( in @ SY40 @ SV14 )
| ( SY40 = SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV8 )
| ~ ~ ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV15 ) )
= $false )
| ( ( subset @ SV8 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV16: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV16 )
= $false )
| ( ( ! [SY41: $i] :
( ~ ( in @ SY41 @ SV9 )
| ( in @ SY41 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( ! [SY42: $i] :
( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SY42 )
| ~ ( in @ SY42 @ SV10 ) )
| ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
| ~ ( ~ ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ ( sK6_SY22 @ SV17 @ SV10 ) )
| ~ ( in @ ( sK6_SY22 @ SV17 @ SV10 ) @ SV10 ) )
| ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) ) )
= $false )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV11: $i,SV18: $i] :
( ( ( SV18
= ( union @ SV11 ) )
= $false )
| ( ( ~ ( ~ ! [SY43: $i] :
( ! [SY36: $i] :
( ~ ( in @ SY43 @ SY36 )
| ~ ( in @ SY36 @ SV11 ) )
| ( in @ SY43 @ SV18 ) )
| ~ ! [SY45: $i] :
( ~ ( in @ SY45 @ SV18 )
| ~ ( ~ ( in @ SY45 @ ( sK4_D @ SY45 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SY45 @ SV18 @ SV11 ) @ SV11 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV19: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV19 ) )
= $true )
| ( ( ~ ( subset @ SV19 @ SV12 ) )
= $true )
| ( ( SV12 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV20: $i] :
( ( ! [SY46: $i] :
( ( SV20 != SY46 )
| ( subset @ SV20 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV21: $i] :
( ( ! [SY47: $i] :
( ( SV21 != SY47 )
| ( subset @ SY47 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( ( ( sK8_C @ SV13 @ SV6 )
!= SV6 )
| ~ ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) ) )
= $false )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(115,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( ( ( sK8_C @ SV13 @ SV6 )
= SV6 )
| ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) ) )
= $false )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(116,plain,
! [SV14: $i,SV7: $i] :
( ( ( ~ ! [SY39: $i] :
( ( SY39 != SV7 )
| ( in @ SY39 @ SV14 ) )
| ~ ! [SY40: $i] :
( ~ ( in @ SY40 @ SV14 )
| ( SY40 = SV7 ) ) )
= $false )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV8 ) )
= $false )
| ( ( subset @ SV8 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(118,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ~ ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV15 ) )
= $false )
| ( ( subset @ SV8 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(119,plain,
! [SV16: $i,SV9: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV9 )
| ( in @ SV22 @ SV16 ) )
= $true )
| ( ( subset @ SV9 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( ! [SY42: $i] :
( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SY42 )
| ~ ( in @ SY42 @ SV10 ) )
| ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) ) )
= $false )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(121,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ ( sK6_SY22 @ SV17 @ SV10 ) )
| ~ ( in @ ( sK6_SY22 @ SV17 @ SV10 ) @ SV10 ) )
| ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) ) )
= $false )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(122,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ! [SY43: $i] :
( ! [SY36: $i] :
( ~ ( in @ SY43 @ SY36 )
| ~ ( in @ SY36 @ SV11 ) )
| ( in @ SY43 @ SV18 ) )
| ~ ! [SY45: $i] :
( ~ ( in @ SY45 @ SV18 )
| ~ ( ~ ( in @ SY45 @ ( sK4_D @ SY45 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SY45 @ SV18 @ SV11 ) @ SV11 ) ) ) )
= $false )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV19: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV19 )
= $false )
| ( ( ~ ( subset @ SV19 @ SV12 ) )
= $true )
| ( ( SV12 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV23: $i,SV20: $i] :
( ( ( SV20 != SV23 )
| ( subset @ SV20 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV24: $i,SV21: $i] :
( ( ( SV21 != SV24 )
| ( subset @ SV24 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV6: $i,SV13: $i] :
( ( ( ( ( sK8_C @ SV13 @ SV6 )
!= SV6 )
| ~ ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) )
= $true )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(127,plain,
! [SV6: $i,SV13: $i] :
( ( ( ( ( sK8_C @ SV13 @ SV6 )
= SV6 )
| ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) )
= $true )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(128,plain,
! [SV14: $i,SV7: $i] :
( ( ( ~ ! [SY39: $i] :
( ( SY39 != SV7 )
| ( in @ SY39 @ SV14 ) ) )
= $false )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(129,plain,
! [SV7: $i,SV14: $i] :
( ( ( ~ ! [SY40: $i] :
( ~ ( in @ SY40 @ SV14 )
| ( SY40 = SV7 ) ) )
= $false )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(130,plain,
! [SV8: $i,SV15: $i] :
( ( ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV8 )
= $true )
| ( ( subset @ SV8 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(131,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV15 ) )
= $true )
| ( ( subset @ SV8 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(132,plain,
! [SV16: $i,SV9: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV9 ) )
= $true )
| ( ( in @ SV22 @ SV16 )
= $true )
| ( ( subset @ SV9 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(133,plain,
! [SV10: $i,SV17: $i] :
( ( ( ! [SY42: $i] :
( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SY42 )
| ~ ( in @ SY42 @ SV10 ) )
| ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(134,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ ( sK6_SY22 @ SV17 @ SV10 ) )
| ~ ( in @ ( sK6_SY22 @ SV17 @ SV10 ) @ SV10 ) )
| ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(135,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ! [SY43: $i] :
( ! [SY36: $i] :
( ~ ( in @ SY43 @ SY36 )
| ~ ( in @ SY36 @ SV11 ) )
| ( in @ SY43 @ SV18 ) ) )
= $false )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(136,plain,
! [SV11: $i,SV18: $i] :
( ( ( ~ ! [SY45: $i] :
( ~ ( in @ SY45 @ SV18 )
| ~ ( ~ ( in @ SY45 @ ( sK4_D @ SY45 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SY45 @ SV18 @ SV11 ) @ SV11 ) ) ) )
= $false )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(137,plain,
! [SV12: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV12 )
= $false )
| ( ( subset @ SV12 @ SV19 )
= $false )
| ( ( SV12 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV23: $i,SV20: $i] :
( ( ( ( SV20 != SV23 ) )
= $true )
| ( ( subset @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV24: $i,SV21: $i] :
( ( ( ( SV21 != SV24 ) )
= $true )
| ( ( subset @ SV24 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV6: $i,SV13: $i] :
( ( ( ( ( sK8_C @ SV13 @ SV6 )
!= SV6 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) )
= $true )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV6: $i,SV13: $i] :
( ( ( ( sK8_C @ SV13 @ SV6 )
= SV6 )
= $true )
| ( ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 )
= $true )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV14: $i,SV7: $i] :
( ( ( ! [SY39: $i] :
( ( SY39 != SV7 )
| ( in @ SY39 @ SV14 ) ) )
= $true )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(143,plain,
! [SV7: $i,SV14: $i] :
( ( ( ! [SY40: $i] :
( ~ ( in @ SY40 @ SV14 )
| ( SY40 = SV7 ) ) )
= $true )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(144,plain,
! [SV8: $i,SV15: $i] :
( ( ( in @ ( sK7_C @ SV15 @ SV8 ) @ SV15 )
= $false )
| ( ( subset @ SV8 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(145,plain,
! [SV16: $i,SV9: $i,SV22: $i] :
( ( ( in @ SV22 @ SV9 )
= $false )
| ( ( in @ SV22 @ SV16 )
= $true )
| ( ( subset @ SV9 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(146,plain,
! [SV10: $i,SV17: $i] :
( ( ( ! [SY42: $i] :
( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SY42 )
| ~ ( in @ SY42 @ SV10 ) ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(147,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ ( sK6_SY22 @ SV17 @ SV10 ) )
| ~ ( in @ ( sK6_SY22 @ SV17 @ SV10 ) @ SV10 ) ) )
= $true )
| ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(148,plain,
! [SV18: $i,SV11: $i] :
( ( ( ! [SY43: $i] :
( ! [SY36: $i] :
( ~ ( in @ SY43 @ SY36 )
| ~ ( in @ SY36 @ SV11 ) )
| ( in @ SY43 @ SV18 ) ) )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(149,plain,
! [SV11: $i,SV18: $i] :
( ( ( ! [SY45: $i] :
( ~ ( in @ SY45 @ SV18 )
| ~ ( ~ ( in @ SY45 @ ( sK4_D @ SY45 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SY45 @ SV18 @ SV11 ) @ SV11 ) ) ) )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(150,plain,
! [SV23: $i,SV20: $i] :
( ( ( SV20 = SV23 )
= $false )
| ( ( subset @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(151,plain,
! [SV24: $i,SV21: $i] :
( ( ( SV21 = SV24 )
= $false )
| ( ( subset @ SV24 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV6: $i,SV13: $i] :
( ( ( ( sK8_C @ SV13 @ SV6 )
= SV6 )
= $false )
| ( ( ~ ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 ) )
= $true )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV14: $i,SV7: $i,SV25: $i] :
( ( ( ( SV25 != SV7 )
| ( in @ SV25 @ SV14 ) )
= $true )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV7: $i,SV14: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV14 )
| ( SV26 = SV7 ) )
= $true )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV27: $i,SV10: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV27 )
| ~ ( in @ SV27 @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(156,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ ( sK6_SY22 @ SV17 @ SV10 ) )
| ~ ( in @ ( sK6_SY22 @ SV17 @ SV10 ) @ SV10 ) )
= $false )
| ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(157,plain,
! [SV18: $i,SV11: $i,SV28: $i] :
( ( ( ! [SY48: $i] :
( ~ ( in @ SV28 @ SY48 )
| ~ ( in @ SY48 @ SV11 ) )
| ( in @ SV28 @ SV18 ) )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(158,plain,
! [SV11: $i,SV18: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV18 )
| ~ ( ~ ( in @ SV29 @ ( sK4_D @ SV29 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SV29 @ SV18 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(159,plain,
! [SV6: $i,SV13: $i] :
( ( ( in @ ( sK8_C @ SV13 @ SV6 ) @ SV13 )
= $false )
| ( ( ( sK8_C @ SV13 @ SV6 )
= SV6 )
= $false )
| ( ( SV13
= ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(160,plain,
! [SV14: $i,SV7: $i,SV25: $i] :
( ( ( ( SV25 != SV7 ) )
= $true )
| ( ( in @ SV25 @ SV14 )
= $true )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV7: $i,SV14: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV14 ) )
= $true )
| ( ( SV26 = SV7 )
= $true )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(162,plain,
! [SV27: $i,SV10: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV27 ) )
= $true )
| ( ( ~ ( in @ SV27 @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(163,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ ( sK6_SY22 @ SV17 @ SV10 ) ) )
= $false )
| ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(164,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK6_SY22 @ SV17 @ SV10 ) @ SV10 ) )
= $false )
| ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(165,plain,
! [SV18: $i,SV11: $i,SV28: $i] :
( ( ( ! [SY48: $i] :
( ~ ( in @ SV28 @ SY48 )
| ~ ( in @ SY48 @ SV11 ) ) )
= $true )
| ( ( in @ SV28 @ SV18 )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(166,plain,
! [SV11: $i,SV18: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV29 @ ( sK4_D @ SV29 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SV29 @ SV18 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV14: $i,SV7: $i,SV25: $i] :
( ( ( SV25 = SV7 )
= $false )
| ( ( in @ SV25 @ SV14 )
= $true )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(168,plain,
! [SV7: $i,SV14: $i,SV26: $i] :
( ( ( in @ SV26 @ SV14 )
= $false )
| ( ( SV26 = SV7 )
= $true )
| ( ( SV14
= ( singleton @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(169,plain,
! [SV27: $i,SV10: $i,SV17: $i] :
( ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV27 )
= $false )
| ( ( ~ ( in @ SV27 @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(170,plain,
! [SV10: $i,SV17: $i] :
( ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ ( sK6_SY22 @ SV17 @ SV10 ) )
= $true )
| ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(171,plain,
! [SV10: $i,SV17: $i] :
( ( ( in @ ( sK6_SY22 @ SV17 @ SV10 ) @ SV10 )
= $true )
| ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(172,plain,
! [SV18: $i,SV11: $i,SV30: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV30 )
| ~ ( in @ SV30 @ SV11 ) )
= $true )
| ( ( in @ SV28 @ SV18 )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(173,plain,
! [SV11: $i,SV18: $i,SV29: $i] :
( ( ( in @ SV29 @ SV18 )
= $false )
| ( ( ~ ( ~ ( in @ SV29 @ ( sK4_D @ SV29 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SV29 @ SV18 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(174,plain,
! [SV17: $i,SV10: $i,SV27: $i] :
( ( ( in @ SV27 @ SV10 )
= $false )
| ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV27 )
= $false )
| ( ( ~ ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(175,plain,
! [SV18: $i,SV11: $i,SV30: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV30 @ SV11 ) )
= $true )
| ( ( in @ SV28 @ SV18 )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(176,plain,
! [SV11: $i,SV18: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ ( sK4_D @ SV29 @ SV18 @ SV11 ) )
| ~ ( in @ ( sK4_D @ SV29 @ SV18 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV29 @ SV18 )
= $false )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(177,plain,
! [SV27: $i,SV10: $i,SV17: $i] :
( ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV17 )
= $false )
| ( ( in @ ( sK5_C @ SV17 @ SV10 ) @ SV27 )
= $false )
| ( ( in @ SV27 @ SV10 )
= $false )
| ( ( SV17
= ( union @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(178,plain,
! [SV18: $i,SV11: $i,SV30: $i,SV28: $i] :
( ( ( in @ SV28 @ SV30 )
= $false )
| ( ( ~ ( in @ SV30 @ SV11 ) )
= $true )
| ( ( in @ SV28 @ SV18 )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(179,plain,
! [SV11: $i,SV18: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ ( sK4_D @ SV29 @ SV18 @ SV11 ) ) )
= $false )
| ( ( in @ SV29 @ SV18 )
= $false )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(180,plain,
! [SV11: $i,SV18: $i,SV29: $i] :
( ( ( ~ ( in @ ( sK4_D @ SV29 @ SV18 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV29 @ SV18 )
= $false )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(181,plain,
! [SV18: $i,SV28: $i,SV11: $i,SV30: $i] :
( ( ( in @ SV30 @ SV11 )
= $false )
| ( ( in @ SV28 @ SV30 )
= $false )
| ( ( in @ SV28 @ SV18 )
= $true )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(182,plain,
! [SV11: $i,SV18: $i,SV29: $i] :
( ( ( in @ SV29 @ ( sK4_D @ SV29 @ SV18 @ SV11 ) )
= $true )
| ( ( in @ SV29 @ SV18 )
= $false )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(183,plain,
! [SV11: $i,SV18: $i,SV29: $i] :
( ( ( in @ ( sK4_D @ SV29 @ SV18 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ SV29 @ SV18 )
= $false )
| ( ( SV18
= ( union @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(184,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,183,182,181,177,171,170,168,167,159,151,150,145,144,141,137,130,86,77,51,50,49]) ).
thf(185,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET890+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 09:32:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 9
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.36 (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).............
% 4.57/4.76
% 4.57/4.76 ********************************
% 4.57/4.76 * All subproblems solved! *
% 4.57/4.76 ********************************
% 4.57/4.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:184,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.57/4.77
% 4.57/4.77 %**** Beginning of derivation protocol ****
% 4.57/4.77 % SZS output start CNFRefutation
% See solution above
% 4.57/4.77
% 4.57/4.77 %**** End of derivation protocol ****
% 4.57/4.77 %**** no. of clauses in derivation: 185 ****
% 4.57/4.77 %**** clause counter: 184 ****
% 4.57/4.77
% 4.57/4.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:184,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------