%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:42:30 AM UTC 2026
% Result : Theorem 0.12s 0.24s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of formulae : 186 ( 87 unt; 0 typ; 0 def)
% Number of atoms : 1441 ( 923 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2984 (1358 ~; 451 |; 48 &;1111 @)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 354 ( 0 ^; 354 !; 0 ?; 354 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY10,type,
sK2_SY10: $i ).
thf(tp_sK3_SY12,type,
sK3_SY12: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
thf(4,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(7,conjecture,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(8,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [SY10: $i,SY11: $i] :
( ( subset @ sK1_A @ ( unordered_pair @ SY10 @ SY11 ) )
<=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ SY10 ) )
& ( sK1_A
!= ( singleton @ SY11 ) )
& ( sK1_A
!= ( unordered_pair @ SY10 @ SY11 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(15,plain,
( ( ! [SY12: $i] :
( ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ SY12 ) )
<=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A
!= ( singleton @ SY12 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ SY12 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
<=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A
!= ( singleton @ sK3_SY12 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A
!= ( singleton @ sK3_SY12 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(18,plain,
( ( ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A
!= ( singleton @ sK3_SY12 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) )
=> ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(19,plain,
( ( ~ ( ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A
!= ( singleton @ sK3_SY12 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A
!= ( singleton @ sK3_SY12 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) )
=> ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(23,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(24,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(25,plain,
( ( ~ ( ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A
!= ( singleton @ sK3_SY12 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(26,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ( SX0
!= ( singleton @ SX1 ) ) ) )
| ~ ( ( SX0
!= ( singleton @ SX2 ) ) ) )
| ~ ( ( SX0
!= ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ( SX0
!= ( singleton @ SX1 ) ) ) )
| ~ ( ( SX0
!= ( singleton @ SX2 ) ) ) )
| ~ ( ( SX0
!= ( unordered_pair @ SX1 @ SX2 ) ) ) )
| ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( ~ ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ( unordered_pair @ SV1 @ SY13 )
= ( unordered_pair @ SY13 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV2: $i] :
( ( ! [SY14: $i] : ( subset @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV3: $i] :
( ( ! [SY15: $i,SY16: $i] :
~ ( ~ ( ~ ( subset @ SV3 @ ( unordered_pair @ SY15 @ SY16 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SY15 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SY16 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SY15 @ SY16 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SY15 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SY16 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SY15 @ SY16 ) ) ) )
| ( subset @ SV3 @ ( unordered_pair @ SY15 @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV4: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV4 )
= ( unordered_pair @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY17: $i] :
~ ( ~ ( ~ ( subset @ SV3 @ ( unordered_pair @ SV6 @ SY17 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SY17 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SY17 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SY17 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SY17 ) ) ) )
| ( subset @ SV3 @ ( unordered_pair @ SV6 @ SY17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(37,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
| ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ~ ( ~ ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
| ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ~ ( ~ ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
| ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
| ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
( ( ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(52,plain,
( ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
( ( sK1_A
= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
( ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(57,plain,
( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(58,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
( ( ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
( ( sK1_A
!= ( singleton @ sK3_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
| ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
( ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
( ( sK1_A
= ( singleton @ sK3_SY12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
( ( ~ ( ( sK1_A != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(70,plain,
( ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(73,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(74,plain,
( ( sK1_A != empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(75,plain,
( ( sK1_A
!= ( singleton @ sK2_SY10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(76,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(77,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
| ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3
= ( unordered_pair @ SV6 @ SV7 ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(79,plain,
( ( sK1_A = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
( ( sK1_A
= ( singleton @ sK2_SY10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(83,plain,
! [SV6: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(84,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(86,plain,
! [SV6: $i,SV7: $i,SV3: $i] :
( ( ( SV3
!= ( singleton @ SV7 ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(87,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(88,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != empty_set ) )
| ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV6: $i,SV7: $i,SV3: $i] :
( ( ( SV3
= ( singleton @ SV7 ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != empty_set ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != empty_set ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(92,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(93,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3 != empty_set )
= $false )
| ( ( ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3 != empty_set )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(95,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3
!= ( singleton @ SV6 ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(96,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3 = empty_set )
= $true )
| ( ( ~ ( ( SV3
!= ( singleton @ SV6 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(97,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3 = empty_set )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(98,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3
= ( singleton @ SV6 ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(99,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3
!= ( singleton @ SV6 ) )
= $false )
| ( ( SV3 = empty_set )
= $true )
| ( ( ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(100,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3
= ( singleton @ SV6 ) )
= $true )
| ( ( SV3 = empty_set )
= $true )
| ( ( ~ ( ( SV3
!= ( singleton @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(101,plain,
! [SV6: $i,SV7: $i,SV3: $i] :
( ( ( SV3
!= ( singleton @ SV7 ) )
= $false )
| ( ( SV3 = empty_set )
= $true )
| ( ( SV3
= ( singleton @ SV6 ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(102,plain,
! [SV6: $i,SV7: $i,SV3: $i] :
( ( ( SV3
= ( singleton @ SV7 ) )
= $true )
| ( ( SV3 = empty_set )
= $true )
| ( ( SV3
= ( singleton @ SV6 ) )
= $true )
| ( ( ~ ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(103,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3
!= ( unordered_pair @ SV6 @ SV7 ) )
= $false )
| ( ( SV3
= ( singleton @ SV6 ) )
= $true )
| ( ( SV3 = empty_set )
= $true )
| ( ( SV3
= ( singleton @ SV7 ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(104,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( SV3
= ( unordered_pair @ SV6 @ SV7 ) )
= $true )
| ( ( SV3
= ( singleton @ SV6 ) )
= $true )
| ( ( SV3 = empty_set )
= $true )
| ( ( SV3
= ( singleton @ SV7 ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV6 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(105,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,104,98,97,89,80,79,78,65,53,38,33,32]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(108,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(110,plain,
( ( ~ ( ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A
!= ( singleton @ sK3_SY12 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) )
=> ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(111,plain,
( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
| ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ( SX0
!= ( singleton @ SX1 ) ) ) )
| ~ ( ( SX0
!= ( singleton @ SX2 ) ) ) )
| ~ ( ( SX0
!= ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ( SX0
!= ( singleton @ SX1 ) ) ) )
| ~ ( ( SX0
!= ( singleton @ SX2 ) ) ) )
| ~ ( ( SX0
!= ( unordered_pair @ SX1 @ SX2 ) ) ) )
| ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(113,plain,
! [SV8: $i] :
( ( ! [SY18: $i] :
( ( unordered_pair @ SV8 @ SY18 )
= ( unordered_pair @ SY18 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV9: $i] :
( ( ! [SY19: $i] : ( subset @ SV9 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(115,plain,
( ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
| ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV10: $i] :
( ( ! [SY20: $i,SY21: $i] :
~ ( ~ ( ~ ( subset @ SV10 @ ( unordered_pair @ SY20 @ SY21 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SY20 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SY21 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SY20 @ SY21 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SY20 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SY21 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SY20 @ SY21 ) ) ) )
| ( subset @ SV10 @ ( unordered_pair @ SY20 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(117,plain,
! [SV11: $i,SV8: $i] :
( ( ( unordered_pair @ SV8 @ SV11 )
= ( unordered_pair @ SV11 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV9: $i] :
( ( subset @ SV9 @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(119,plain,
( ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(120,plain,
( ( subset @ sK1_A @ ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(121,plain,
! [SV13: $i,SV10: $i] :
( ( ! [SY22: $i] :
~ ( ~ ( ~ ( subset @ SV10 @ ( unordered_pair @ SV13 @ SY22 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SY22 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SY22 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SY22 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SY22 ) ) ) )
| ( subset @ SV10 @ ( unordered_pair @ SV13 @ SY22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(122,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(123,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
| ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(124,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(125,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
| ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(126,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
| ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(127,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(128,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
| ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(129,plain,
( ( ( ~ ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(130,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(131,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
| ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(132,plain,
( ( ( ~ ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) ) )
= $false )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(133,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(134,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(135,plain,
( ( ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
| ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(136,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(137,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(138,plain,
( ( ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(140,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(141,plain,
( ( ( ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) ) )
= $false )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(142,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(143,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
| ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(144,plain,
( ( ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(145,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(146,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(147,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(148,plain,
( ( ( ~ ( ( sK1_A != empty_set ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(149,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(150,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(151,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(152,plain,
( ( ( sK1_A != empty_set )
= $false )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(153,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(154,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
| ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(155,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10
= ( unordered_pair @ SV13 @ SV14 ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(156,plain,
( ( ( sK1_A = empty_set )
= $true )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(157,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(158,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(159,plain,
! [SV13: $i,SV14: $i,SV10: $i] :
( ( ( ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(160,plain,
( ( ( sK1_A
!= ( singleton @ sK2_SY10 ) )
= $false )
| ( ( sK1_A = empty_set )
= $true )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(161,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(162,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(163,plain,
! [SV13: $i,SV14: $i,SV10: $i] :
( ( ( SV10
!= ( singleton @ SV14 ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(164,plain,
( ( ( sK1_A
= ( singleton @ sK2_SY10 ) )
= $true )
| ( ( sK1_A = empty_set )
= $true )
| ( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY12 ) ) ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(165,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(166,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ( SV10 != empty_set ) )
| ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV13: $i,SV14: $i,SV10: $i] :
( ( ( SV10
= ( singleton @ SV14 ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(168,plain,
( ( ( sK1_A
!= ( singleton @ sK3_SY12 ) )
= $false )
| ( ( sK1_A = empty_set )
= $true )
| ( ( sK1_A
= ( singleton @ sK2_SY10 ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(169,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ( SV10 != empty_set ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(170,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ( SV10 != empty_set ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(171,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(172,plain,
( ( ( sK1_A
= ( singleton @ sK3_SY12 ) )
= $true )
| ( ( sK1_A = empty_set )
= $true )
| ( ( sK1_A
= ( singleton @ sK2_SY10 ) )
= $true )
| ( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(173,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10 != empty_set )
= $false )
| ( ( ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(174,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10 != empty_set )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(175,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10
!= ( singleton @ SV13 ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(176,plain,
( ( ( sK1_A
!= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
= $false )
| ( ( sK1_A
= ( singleton @ sK2_SY10 ) )
= $true )
| ( ( sK1_A = empty_set )
= $true )
| ( ( sK1_A
= ( singleton @ sK3_SY12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(177,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10 = empty_set )
= $true )
| ( ( ~ ( ( SV10
!= ( singleton @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(178,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10 = empty_set )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(179,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10
= ( singleton @ SV13 ) )
= $false )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(180,plain,
( ( ( sK1_A
= ( unordered_pair @ sK2_SY10 @ sK3_SY12 ) )
= $true )
| ( ( sK1_A
= ( singleton @ sK2_SY10 ) )
= $true )
| ( ( sK1_A = empty_set )
= $true )
| ( ( sK1_A
= ( singleton @ sK3_SY12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(181,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10
!= ( singleton @ SV13 ) )
= $false )
| ( ( SV10 = empty_set )
= $true )
| ( ( ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(182,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10
= ( singleton @ SV13 ) )
= $true )
| ( ( SV10 = empty_set )
= $true )
| ( ( ~ ( ( SV10
!= ( singleton @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(183,plain,
! [SV13: $i,SV14: $i,SV10: $i] :
( ( ( SV10
!= ( singleton @ SV14 ) )
= $false )
| ( ( SV10 = empty_set )
= $true )
| ( ( SV10
= ( singleton @ SV13 ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(184,plain,
! [SV13: $i,SV14: $i,SV10: $i] :
( ( ( SV10
= ( singleton @ SV14 ) )
= $true )
| ( ( SV10 = empty_set )
= $true )
| ( ( SV10
= ( singleton @ SV13 ) )
= $true )
| ( ( ~ ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) ) ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(185,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10
!= ( unordered_pair @ SV13 @ SV14 ) )
= $false )
| ( ( SV10
= ( singleton @ SV13 ) )
= $true )
| ( ( SV10 = empty_set )
= $true )
| ( ( SV10
= ( singleton @ SV14 ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(186,plain,
! [SV14: $i,SV13: $i,SV10: $i] :
( ( ( SV10
= ( unordered_pair @ SV13 @ SV14 ) )
= $true )
| ( ( SV10
= ( singleton @ SV13 ) )
= $true )
| ( ( SV10 = empty_set )
= $true )
| ( ( SV10
= ( singleton @ SV14 ) )
= $true )
| ( ( subset @ SV10 @ ( unordered_pair @ SV13 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(187,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[108,186,180,179,178,167,155,120,118,117]) ).
thf(188,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[187,105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.16 % Computer : n001.cluster.edu
% 0.12/0.16 % Model : x86_64 x86_64
% 0.12/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.16 % Memory : 8046.5625MB
% 0.12/0.16 % OS : Linux 6.8.0-71-generic
% 0.12/0.16 % CPULimit : 300
% 0.12/0.16 % WCLimit : 300
% 0.12/0.16 % DateTime : Tue Oct 6 15:01:54 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.24
% 0.12/0.24 No.of.Axioms: 4
% 0.12/0.24
% 0.12/0.24 Length.of.Defs: 0
% 0.12/0.24
% 0.12/0.24 Contains.Choice.Funs: false
% 0.12/0.24 ....
% 0.12/0.24
% 0.12/0.24 ********************************
% 0.12/0.24 * All subproblems solved! *
% 0.12/0.24 ********************************
% 0.12/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:187,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.24
% 0.12/0.24 %**** Beginning of derivation protocol ****
% 0.12/0.24 % SZS output start CNFRefutation
% See solution above
% 0.12/0.24
% 0.12/0.24 %**** End of derivation protocol ****
% 0.12/0.24 %**** no. of clauses in derivation: 186 ****
% 0.12/0.24 %**** clause counter: 187 ****
% 0.12/0.24
% 0.12/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:187,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------