%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU820^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 10:49:02 AM UTC 2026
% Result : Theorem 0.51s 0.30s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 265 ( 162 unt; 0 typ; 8 def)
% Number of atoms : 1373 ( 487 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 2150 ( 557 ~; 296 |; 52 &;1172 @)
% ( 0 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 14 con; 0-2 aty)
% Number of variables : 321 ( 5 ^; 311 !; 5 ?; 321 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetE1,type,
powersetE1: $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY1,type,
sK2_SY1: $i ).
thf(tp_sK3_SY25,type,
sK3_SY25: $i ).
thf(tp_sK4_SY27,type,
sK4_SY27: $i ).
thf(tp_sK5_SY4,type,
sK5_SY4: $i ).
thf(tp_sK6_SY28,type,
sK6_SY28: $i ).
thf(tp_sK7_SY6,type,
sK7_SY6: $i ).
thf(tp_sK8_SY7,type,
sK8_SY7: $i ).
thf(tp_sK9_SY30,type,
sK9_SY30: $i > $i ).
thf(tp_stricttotalorderedByIn,type,
stricttotalorderedByIn: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetemptysetimpeq,type,
subsetemptysetimpeq: $o ).
thf(tp_transitiveset,type,
transitiveset: $i > $o ).
thf(tp_vacuousDall,type,
vacuousDall: $o ).
thf(tp_wellorderedByIn,type,
wellorderedByIn: $i > $o ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(ordinal,definition,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(stricttotalorderedByIn,definition,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( ( in @ Xx @ X )
& ( in @ X @ Y ) )
=> ( in @ Xx @ Y ) ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( X = Y )
| ( in @ X @ Y )
| ( in @ Y @ X ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ~ ( in @ X @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(transitiveset,definition,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderedByIn,definition,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( ( nonempty @ X )
=> ? [Xx: $i] :
( ( in @ Xx @ X )
& ! [Y: $i] :
( ( in @ Y @ X )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(1,conjecture,
( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetOrdinal) ).
thf(2,negated_conjecture,
( ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [SY0: $i] :
( ( in @ SY0 @ emptyset )
=> ( subset @ SY0 @ emptyset ) )
& ! [SY1: $i] :
( ( in @ SY1 @ emptyset )
=> ! [SY2: $i] :
( ( in @ SY2 @ emptyset )
=> ! [SY3: $i] :
( ( in @ SY3 @ emptyset )
=> ( ( ( in @ SY1 @ SY2 )
& ( in @ SY2 @ SY3 ) )
=> ( in @ SY1 @ SY3 ) ) ) ) )
& ! [SY4: $i] :
( ( in @ SY4 @ emptyset )
=> ! [SY5: $i] :
( ( in @ SY5 @ emptyset )
=> ( ( SY4 = SY5 )
| ( in @ SY4 @ SY5 )
| ( in @ SY5 @ SY4 ) ) ) )
& ! [SY6: $i] :
( ( in @ SY6 @ emptyset )
=> ~ ( in @ SY6 @ SY6 ) )
& ! [SY7: $i] :
( ( in @ SY7 @ ( powerset @ emptyset ) )
=> ( ( SY7 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY7 )
& ! [Y: $i] :
( ( in @ Y @ SY7 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,nonempty,ordinal,powersetE1,stricttotalorderedByIn,subsetemptysetimpeq,transitiveset,vacuousDall,wellorderedByIn]) ).
thf(4,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [SY0: $i] :
( ( in @ SY0 @ emptyset )
=> ( subset @ SY0 @ emptyset ) )
& ! [SY1: $i] :
( ( in @ SY1 @ emptyset )
=> ! [SY2: $i] :
( ( in @ SY2 @ emptyset )
=> ! [SY3: $i] :
( ( in @ SY3 @ emptyset )
=> ( ( ( in @ SY1 @ SY2 )
& ( in @ SY2 @ SY3 ) )
=> ( in @ SY1 @ SY3 ) ) ) ) )
& ! [SY4: $i] :
( ( in @ SY4 @ emptyset )
=> ! [SY5: $i] :
( ( in @ SY5 @ emptyset )
=> ( ( SY4 = SY5 )
| ( in @ SY4 @ SY5 )
| ( in @ SY5 @ SY4 ) ) ) )
& ! [SY6: $i] :
( ( in @ SY6 @ emptyset )
=> ~ ( in @ SY6 @ SY6 ) )
& ! [SY7: $i] :
( ( in @ SY7 @ ( powerset @ emptyset ) )
=> ( ( SY7 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY7 )
& ! [Y: $i] :
( ( in @ Y @ SY7 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [SY0: $i] :
( ( in @ SY0 @ emptyset )
=> ( subset @ SY0 @ emptyset ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ! [SY1: $i] :
( ( in @ SY1 @ emptyset )
=> ! [SY2: $i] :
( ( in @ SY2 @ emptyset )
=> ! [SY3: $i] :
( ( in @ SY3 @ emptyset )
=> ( ( ( in @ SY1 @ SY2 )
& ( in @ SY2 @ SY3 ) )
=> ( in @ SY1 @ SY3 ) ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ! [SY4: $i] :
( ( in @ SY4 @ emptyset )
=> ! [SY5: $i] :
( ( in @ SY5 @ emptyset )
=> ( ( SY4 = SY5 )
| ( in @ SY4 @ SY5 )
| ( in @ SY5 @ SY4 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(11,plain,
( ( ! [SY6: $i] :
( ( in @ SY6 @ emptyset )
=> ~ ( in @ SY6 @ SY6 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(12,plain,
( ( ! [SY7: $i] :
( ( in @ SY7 @ ( powerset @ emptyset ) )
=> ( ( SY7 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY7 )
& ! [Y: $i] :
( ( in @ Y @ SY7 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(13,plain,
( ( ~ ! [SY0: $i] :
( ( in @ SY0 @ emptyset )
=> ( subset @ SY0 @ emptyset ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ! [SY1: $i] :
( ( in @ SY1 @ emptyset )
=> ! [SY2: $i] :
( ( in @ SY2 @ emptyset )
=> ! [SY3: $i] :
( ( in @ SY3 @ emptyset )
=> ( ( ( in @ SY1 @ SY2 )
& ( in @ SY2 @ SY3 ) )
=> ( in @ SY1 @ SY3 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(15,plain,
( ( ~ ! [SY4: $i] :
( ( in @ SY4 @ emptyset )
=> ! [SY5: $i] :
( ( in @ SY5 @ emptyset )
=> ( ( SY4 = SY5 )
| ( in @ SY4 @ SY5 )
| ( in @ SY5 @ SY4 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(16,plain,
( ( ~ ! [SY6: $i] :
( ( in @ SY6 @ emptyset )
=> ~ ( in @ SY6 @ SY6 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(17,plain,
( ( ~ ! [SY7: $i] :
( ( in @ SY7 @ ( powerset @ emptyset ) )
=> ( ( SY7 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY7 )
& ! [Y: $i] :
( ( in @ Y @ SY7 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(18,plain,
( ( ( in @ sK1_SY0 @ emptyset )
& ~ ( subset @ sK1_SY0 @ emptyset ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(19,plain,
( ( ( in @ sK2_SY1 @ emptyset )
& ( in @ sK3_SY25 @ emptyset )
& ( in @ sK4_SY27 @ emptyset )
& ( in @ sK2_SY1 @ sK3_SY25 )
& ( in @ sK3_SY25 @ sK4_SY27 )
& ~ ( in @ sK2_SY1 @ sK4_SY27 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(20,plain,
( ( ( in @ sK5_SY4 @ emptyset )
& ( in @ sK6_SY28 @ emptyset )
& ~ ( in @ sK6_SY28 @ sK5_SY4 )
& ( sK5_SY4 != sK6_SY28 )
& ~ ( in @ sK5_SY4 @ sK6_SY28 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(21,plain,
( ( ( in @ sK7_SY6 @ emptyset )
& ( in @ sK7_SY6 @ sK7_SY6 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(22,plain,
( ( ( in @ sK8_SY7 @ ( powerset @ emptyset ) )
& ( sK8_SY7 != emptyset )
& ! [SY29: $i] :
( ( ( in @ ( sK9_SY30 @ SY29 ) @ sK8_SY7 )
& ( SY29
!= ( sK9_SY30 @ SY29 ) )
& ~ ( in @ SY29 @ ( sK9_SY30 @ SY29 ) ) )
| ~ ( in @ SY29 @ sK8_SY7 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(23,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(24,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(28,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(29,plain,
( ( ( in @ sK1_SY0 @ emptyset )
& ~ ( subset @ sK1_SY0 @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(30,plain,
( ( ~ ( ~ ( in @ sK1_SY0 @ emptyset )
| ~ ~ ( subset @ sK1_SY0 @ emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,nonempty,ordinal,powersetE1,stricttotalorderedByIn,subsetemptysetimpeq,transitiveset,vacuousDall,wellorderedByIn]) ).
thf(31,plain,
! [SV1: $i] :
( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ ( powerset @ SV1 ) )
| ( subset @ SY31 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV2: $i] :
( ( ~ ( subset @ SV2 @ emptyset )
| ( SV2 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV3: $i > $o] :
( ( ! [SY32: $i] :
( ~ ( in @ SY32 @ emptyset )
| ( SV3 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ( in @ sK1_SY0 @ emptyset )
| ~ ~ ( subset @ sK1_SY0 @ emptyset ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) )
| ( subset @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: $i] :
( ( ( ~ ( subset @ SV2 @ emptyset ) )
= $true )
| ( ( SV2 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV3: $i > $o,SV5: $i] :
( ( ~ ( in @ SV5 @ emptyset )
| ( SV3 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ( in @ sK1_SY0 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( ~ ~ ( subset @ sK1_SY0 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( subset @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( subset @ SV2 @ emptyset )
= $false )
| ( ( SV2 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV3: $i > $o,SV5: $i] :
( ( ( ~ ( in @ SV5 @ emptyset ) )
= $true )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
( ( in @ sK1_SY0 @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(44,plain,
( ( ~ ( subset @ sK1_SY0 @ emptyset ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(45,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false )
| ( ( subset @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV3: $i > $o,SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( subset @ sK1_SY0 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV17: $i] : $false ))]]) ).
thf(50,plain,
! [SV16: $i > $o,SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( ~ ( SV16 @ SV5 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV15: $i] : ~ ( SV16 @ SV15 ) ))]]) ).
thf(51,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV5 = emptyset )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV6: $i] : ( SV6 = emptyset ) ))]]) ).
thf(52,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV5 = sK4_SY27 )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV7: $i] : ( SV7 = sK4_SY27 ) ))]]) ).
thf(53,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV5 = sK1_SY0 )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV8: $i] : ( SV8 = sK1_SY0 ) ))]]) ).
thf(54,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV5 = sK5_SY4 )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV9: $i] : ( SV9 = sK5_SY4 ) ))]]) ).
thf(55,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV5 = sK2_SY1 )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV10: $i] : ( SV10 = sK2_SY1 ) ))]]) ).
thf(56,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV5 = sK3_SY25 )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV11: $i] : ( SV11 = sK3_SY25 ) ))]]) ).
thf(57,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV5 = sK7_SY6 )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV12: $i] : ( SV12 = sK7_SY6 ) ))]]) ).
thf(58,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV5 = sK8_SY7 )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV13: $i] : ( SV13 = sK8_SY7 ) ))]]) ).
thf(59,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV5 = sK6_SY28 )
= $true ) ),
inference(prim_subst,[status(thm)],[46:[bind(SV3,$thf( ^ [SV14: $i] : ( SV14 = sK6_SY28 ) ))]]) ).
thf(60,plain,
! [SV3: $i > $o,SV5: $i] :
( ( ( SV3 @ SV5 )
= $true )
| ( ( ( SV3 @ SV5 )
= ( ~ ( in @ SV5 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[46]) ).
thf(61,plain,
! [SV5: $i,SV3: $i > $o] :
( ( ( ~ ( ( SV3 @ SV5 )
| ~ ( in @ SV5 @ emptyset ) )
| ~ ( ~ ( SV3 @ SV5 )
| ~ ~ ( in @ SV5 @ emptyset ) ) )
= $false )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[60]) ).
thf(62,plain,
! [SV5: $i,SV3: $i > $o] :
( ( ( ( SV3 @ SV5 )
= ( ~ ( in @ SV5 @ emptyset ) ) )
= $false )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[60]) ).
thf(63,plain,
! [SV5: $i,SV3: $i > $o] :
( ( ( ~ ( ( SV3 @ SV5 )
| ~ ( in @ SV5 @ emptyset ) ) )
= $false )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(65,plain,
! [SV5: $i,SV3: $i > $o] :
( ( ( ( SV3 @ SV5 )
| ~ ( in @ SV5 @ emptyset ) )
= $true )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(67,plain,
! [SV5: $i,SV3: $i > $o] :
( ( ( SV3 @ SV5 )
= $true )
| ( ( ~ ( in @ SV5 @ emptyset ) )
= $true )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV3: $i > $o,SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV3 @ SV5 )
= $true )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV25: $i > $i,SV5: $i,SV24: $i > $i] :
( ( ( ~ ( in @ ( SV24 @ SV5 ) @ ( SV25 @ SV5 ) ) )
= $true )
| ( ( in @ ( SV24 @ SV5 ) @ ( SV25 @ SV5 ) )
= $false )
| ( ( in @ SV5 @ emptyset )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV3,$thf( ^ [SX0: $i] : ~ ( in @ ( SV24 @ SX0 ) @ ( SV25 @ SX0 ) ) ))]]) ).
thf(75,plain,
! [SV5: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV5 ) )
= $true )
| ( ( ~ ( SV21 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV5 @ emptyset ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV3,$thf( ^ [SX0: $i] : ~ ( SV21 @ SX0 ) ))]]) ).
thf(78,plain,
! [SV5: $i,SV21: $i > $o] :
( ( ( SV21 @ SV5 )
= $false )
| ( ( ~ ( SV21 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV5 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
! [SV25: $i > $i,SV5: $i,SV24: $i > $i] :
( ( ( in @ ( SV24 @ SV5 ) @ ( SV25 @ SV5 ) )
= $false )
| ( ( in @ ( SV24 @ SV5 ) @ ( SV25 @ SV5 ) )
= $false )
| ( ( in @ SV5 @ emptyset )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV5: $i,SV21: $i > $o] :
( ( ( SV21 @ SV5 )
= $false )
| ( ( SV21 @ SV5 )
= $false )
| ( ( ~ ( in @ SV5 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV21: $i > $o,SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV21 @ SV5 )
= $false )
| ( ( SV21 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(85,plain,
! [SV5: $i,SV16: $i > $o] :
( ( ( SV16 @ SV5 )
= $false )
| ( ( in @ SV5 @ emptyset )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(86,plain,
! [SV3: $i > $o,SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(sim,[status(thm)],[69]) ).
thf(87,plain,
! [SV21: $i > $o,SV5: $i] :
( ( ( in @ SV5 @ emptyset )
= $false )
| ( ( SV21 @ SV5 )
= $false ) ),
inference(sim,[status(thm)],[84]) ).
thf(88,plain,
! [SV25: $i > $i,SV5: $i,SV24: $i > $i] :
( ( ( in @ ( SV24 @ SV5 ) @ ( SV25 @ SV5 ) )
= $false )
| ( ( in @ SV5 @ emptyset )
= $false ) ),
inference(sim,[status(thm)],[79]) ).
thf(89,plain,
! [SV5: $i] :
( ( in @ SV5 @ emptyset )
= $false ),
inference(sim,[status(thm)],[49]) ).
thf(90,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,89,88,87,86,85,59,58,57,56,55,54,53,52,51,47,46,45,43]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(92,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(93,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(94,plain,
( ( ( in @ sK2_SY1 @ emptyset )
& ( in @ sK3_SY25 @ emptyset )
& ( in @ sK4_SY27 @ emptyset )
& ( in @ sK2_SY1 @ sK3_SY25 )
& ( in @ sK3_SY25 @ sK4_SY27 )
& ~ ( in @ sK2_SY1 @ sK4_SY27 ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(95,plain,
( ( ~ ( ~ ( in @ sK2_SY1 @ emptyset )
| ~ ~ ( ~ ( in @ sK3_SY25 @ emptyset )
| ~ ~ ( ~ ( in @ sK4_SY27 @ emptyset )
| ~ ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94,nonempty,ordinal,powersetE1,stricttotalorderedByIn,subsetemptysetimpeq,transitiveset,vacuousDall,wellorderedByIn]) ).
thf(96,plain,
! [SV26: $i] :
( ( ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ SV26 ) )
| ( subset @ SY38 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV27: $i] :
( ( ~ ( subset @ SV27 @ emptyset )
| ( SV27 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV28: $i > $o] :
( ( ! [SY39: $i] :
( ~ ( in @ SY39 @ emptyset )
| ( SV28 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(99,plain,
( ( ~ ( in @ sK2_SY1 @ emptyset )
| ~ ~ ( ~ ( in @ sK3_SY25 @ emptyset )
| ~ ~ ( ~ ( in @ sK4_SY27 @ emptyset )
| ~ ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV26: $i,SV29: $i] :
( ( ~ ( in @ SV29 @ ( powerset @ SV26 ) )
| ( subset @ SV29 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(101,plain,
! [SV27: $i] :
( ( ( ~ ( subset @ SV27 @ emptyset ) )
= $true )
| ( ( SV27 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV28: $i > $o,SV30: $i] :
( ( ~ ( in @ SV30 @ emptyset )
| ( SV28 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(103,plain,
( ( ~ ( in @ sK2_SY1 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(104,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY25 @ emptyset )
| ~ ~ ( ~ ( in @ sK4_SY27 @ emptyset )
| ~ ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(105,plain,
! [SV26: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( subset @ SV29 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV27: $i] :
( ( ( subset @ SV27 @ emptyset )
= $false )
| ( ( SV27 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV28: $i > $o,SV30: $i] :
( ( ( ~ ( in @ SV30 @ emptyset ) )
= $true )
| ( ( SV28 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(108,plain,
( ( in @ sK2_SY1 @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(109,plain,
( ( ~ ( ~ ( in @ sK3_SY25 @ emptyset )
| ~ ~ ( ~ ( in @ sK4_SY27 @ emptyset )
| ~ ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(110,plain,
! [SV26: $i,SV29: $i] :
( ( ( in @ SV29 @ ( powerset @ SV26 ) )
= $false )
| ( ( subset @ SV29 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV28: $i > $o,SV30: $i] :
( ( ( in @ SV30 @ emptyset )
= $false )
| ( ( SV28 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
( ( ~ ( in @ sK3_SY25 @ emptyset )
| ~ ~ ( ~ ( in @ sK4_SY27 @ emptyset )
| ~ ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(113,plain,
( ( ~ ( in @ sK3_SY25 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(114,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY27 @ emptyset )
| ~ ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(115,plain,
( ( in @ sK3_SY25 @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(116,plain,
( ( ~ ( ~ ( in @ sK4_SY27 @ emptyset )
| ~ ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(117,plain,
( ( ~ ( in @ sK4_SY27 @ emptyset )
| ~ ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(118,plain,
( ( ~ ( in @ sK4_SY27 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(119,plain,
( ( ~ ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(120,plain,
( ( in @ sK4_SY27 @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(121,plain,
( ( ~ ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(122,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
| ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(123,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(124,plain,
( ( ~ ~ ( in @ sK2_SY1 @ sK4_SY27 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(125,plain,
( ( ~ ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(126,plain,
( ( ~ ( in @ sK2_SY1 @ sK4_SY27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(127,plain,
( ( ~ ( in @ sK2_SY1 @ sK3_SY25 )
| ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(128,plain,
( ( in @ sK2_SY1 @ sK4_SY27 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(129,plain,
( ( ~ ( in @ sK2_SY1 @ sK3_SY25 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(130,plain,
( ( ~ ( in @ sK3_SY25 @ sK4_SY27 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(131,plain,
( ( in @ sK2_SY1 @ sK3_SY25 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(132,plain,
( ( in @ sK3_SY25 @ sK4_SY27 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(133,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[106,132,131,128,120,115,111,110,108]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(135,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(136,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(137,plain,
( ( ( in @ sK5_SY4 @ emptyset )
& ( in @ sK6_SY28 @ emptyset )
& ~ ( in @ sK6_SY28 @ sK5_SY4 )
& ( sK5_SY4 != sK6_SY28 )
& ~ ( in @ sK5_SY4 @ sK6_SY28 ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(138,plain,
( ( ~ ( ~ ( in @ sK5_SY4 @ emptyset )
| ~ ~ ( ~ ( in @ sK6_SY28 @ emptyset )
| ~ ~ ( ~ ~ ( in @ sK6_SY28 @ sK5_SY4 )
| ~ ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137,nonempty,ordinal,powersetE1,stricttotalorderedByIn,subsetemptysetimpeq,transitiveset,vacuousDall,wellorderedByIn]) ).
thf(139,plain,
! [SV31: $i] :
( ( ! [SY40: $i] :
( ~ ( in @ SY40 @ ( powerset @ SV31 ) )
| ( subset @ SY40 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(140,plain,
! [SV32: $i] :
( ( ~ ( subset @ SV32 @ emptyset )
| ( SV32 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(141,plain,
! [SV33: $i > $o] :
( ( ! [SY41: $i] :
( ~ ( in @ SY41 @ emptyset )
| ( SV33 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(142,plain,
( ( ~ ( in @ sK5_SY4 @ emptyset )
| ~ ~ ( ~ ( in @ sK6_SY28 @ emptyset )
| ~ ~ ( ~ ~ ( in @ sK6_SY28 @ sK5_SY4 )
| ~ ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV31: $i,SV34: $i] :
( ( ~ ( in @ SV34 @ ( powerset @ SV31 ) )
| ( subset @ SV34 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV32: $i] :
( ( ( ~ ( subset @ SV32 @ emptyset ) )
= $true )
| ( ( SV32 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(145,plain,
! [SV33: $i > $o,SV35: $i] :
( ( ~ ( in @ SV35 @ emptyset )
| ( SV33 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(146,plain,
( ( ~ ( in @ sK5_SY4 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(147,plain,
( ( ~ ~ ( ~ ( in @ sK6_SY28 @ emptyset )
| ~ ~ ( ~ ~ ( in @ sK6_SY28 @ sK5_SY4 )
| ~ ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(148,plain,
! [SV31: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( subset @ SV34 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(149,plain,
! [SV32: $i] :
( ( ( subset @ SV32 @ emptyset )
= $false )
| ( ( SV32 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(150,plain,
! [SV33: $i > $o,SV35: $i] :
( ( ( ~ ( in @ SV35 @ emptyset ) )
= $true )
| ( ( SV33 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(151,plain,
( ( in @ sK5_SY4 @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(152,plain,
( ( ~ ( ~ ( in @ sK6_SY28 @ emptyset )
| ~ ~ ( ~ ~ ( in @ sK6_SY28 @ sK5_SY4 )
| ~ ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(153,plain,
! [SV31: $i,SV34: $i] :
( ( ( in @ SV34 @ ( powerset @ SV31 ) )
= $false )
| ( ( subset @ SV34 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(154,plain,
! [SV33: $i > $o,SV35: $i] :
( ( ( in @ SV35 @ emptyset )
= $false )
| ( ( SV33 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(155,plain,
( ( ~ ( in @ sK6_SY28 @ emptyset )
| ~ ~ ( ~ ~ ( in @ sK6_SY28 @ sK5_SY4 )
| ~ ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(156,plain,
( ( ~ ( in @ sK6_SY28 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(157,plain,
( ( ~ ~ ( ~ ~ ( in @ sK6_SY28 @ sK5_SY4 )
| ~ ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(158,plain,
( ( in @ sK6_SY28 @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(159,plain,
( ( ~ ( ~ ~ ( in @ sK6_SY28 @ sK5_SY4 )
| ~ ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(160,plain,
( ( ~ ~ ( in @ sK6_SY28 @ sK5_SY4 )
| ~ ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(161,plain,
( ( ~ ~ ( in @ sK6_SY28 @ sK5_SY4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(162,plain,
( ( ~ ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(163,plain,
( ( ~ ( in @ sK6_SY28 @ sK5_SY4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(164,plain,
( ( ~ ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(165,plain,
( ( in @ sK6_SY28 @ sK5_SY4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(166,plain,
( ( ~ ( ( sK5_SY4 != sK6_SY28 ) )
| ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(167,plain,
( ( ~ ( ( sK5_SY4 != sK6_SY28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(168,plain,
( ( ~ ~ ( in @ sK5_SY4 @ sK6_SY28 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(169,plain,
( ( sK5_SY4 != sK6_SY28 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(170,plain,
( ( ~ ( in @ sK5_SY4 @ sK6_SY28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(171,plain,
( ( sK5_SY4 = sK6_SY28 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(172,plain,
( ( in @ sK5_SY4 @ sK6_SY28 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(173,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[149,172,171,165,158,154,153,151]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(175,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(176,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(177,plain,
( ( ( in @ sK7_SY6 @ emptyset )
& ( in @ sK7_SY6 @ sK7_SY6 ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(178,plain,
( ( ~ ( ~ ( in @ sK7_SY6 @ emptyset )
| ~ ( in @ sK7_SY6 @ sK7_SY6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177,nonempty,ordinal,powersetE1,stricttotalorderedByIn,subsetemptysetimpeq,transitiveset,vacuousDall,wellorderedByIn]) ).
thf(179,plain,
! [SV36: $i] :
( ( ! [SY42: $i] :
( ~ ( in @ SY42 @ ( powerset @ SV36 ) )
| ( subset @ SY42 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(180,plain,
! [SV37: $i] :
( ( ~ ( subset @ SV37 @ emptyset )
| ( SV37 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(181,plain,
! [SV38: $i > $o] :
( ( ! [SY43: $i] :
( ~ ( in @ SY43 @ emptyset )
| ( SV38 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(182,plain,
( ( ~ ( in @ sK7_SY6 @ emptyset )
| ~ ( in @ sK7_SY6 @ sK7_SY6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(183,plain,
! [SV36: $i,SV39: $i] :
( ( ~ ( in @ SV39 @ ( powerset @ SV36 ) )
| ( subset @ SV39 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(184,plain,
! [SV37: $i] :
( ( ( ~ ( subset @ SV37 @ emptyset ) )
= $true )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV38: $i > $o,SV40: $i] :
( ( ~ ( in @ SV40 @ emptyset )
| ( SV38 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(186,plain,
( ( ~ ( in @ sK7_SY6 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(187,plain,
( ( ~ ( in @ sK7_SY6 @ sK7_SY6 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(188,plain,
! [SV36: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( powerset @ SV36 ) ) )
= $true )
| ( ( subset @ SV39 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(189,plain,
! [SV37: $i] :
( ( ( subset @ SV37 @ emptyset )
= $false )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(190,plain,
! [SV38: $i > $o,SV40: $i] :
( ( ( ~ ( in @ SV40 @ emptyset ) )
= $true )
| ( ( SV38 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(191,plain,
( ( in @ sK7_SY6 @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(192,plain,
( ( in @ sK7_SY6 @ sK7_SY6 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(193,plain,
! [SV36: $i,SV39: $i] :
( ( ( in @ SV39 @ ( powerset @ SV36 ) )
= $false )
| ( ( subset @ SV39 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(194,plain,
! [SV38: $i > $o,SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV38 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(196,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV52: $i] : $false ))]]) ).
thf(197,plain,
! [SV51: $i > $o,SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( ~ ( SV51 @ SV40 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV50: $i] : ~ ( SV51 @ SV50 ) ))]]) ).
thf(198,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV40 = sK4_SY27 )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV41: $i] : ( SV41 = sK4_SY27 ) ))]]) ).
thf(199,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV40 = sK5_SY4 )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV42: $i] : ( SV42 = sK5_SY4 ) ))]]) ).
thf(200,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV40 = sK3_SY25 )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV43: $i] : ( SV43 = sK3_SY25 ) ))]]) ).
thf(201,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV40 = sK7_SY6 )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV44: $i] : ( SV44 = sK7_SY6 ) ))]]) ).
thf(202,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV40 = emptyset )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV45: $i] : ( SV45 = emptyset ) ))]]) ).
thf(203,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV40 = sK1_SY0 )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV46: $i] : ( SV46 = sK1_SY0 ) ))]]) ).
thf(204,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV40 = sK2_SY1 )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV47: $i] : ( SV47 = sK2_SY1 ) ))]]) ).
thf(205,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV40 = sK8_SY7 )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV48: $i] : ( SV48 = sK8_SY7 ) ))]]) ).
thf(206,plain,
! [SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV40 = sK6_SY28 )
= $true ) ),
inference(prim_subst,[status(thm)],[194:[bind(SV38,$thf( ^ [SV49: $i] : ( SV49 = sK6_SY28 ) ))]]) ).
thf(207,plain,
! [SV38: $i > $o,SV40: $i] :
( ( ( SV38 @ SV40 )
= $true )
| ( ( ( SV38 @ SV40 )
= ( ~ ( in @ SV40 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[194]) ).
thf(208,plain,
! [SV40: $i,SV38: $i > $o] :
( ( ( ~ ( ( SV38 @ SV40 )
| ~ ( in @ SV40 @ emptyset ) )
| ~ ( ~ ( SV38 @ SV40 )
| ~ ~ ( in @ SV40 @ emptyset ) ) )
= $false )
| ( ( SV38 @ SV40 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[207]) ).
thf(209,plain,
! [SV40: $i,SV38: $i > $o] :
( ( ( ( SV38 @ SV40 )
= ( ~ ( in @ SV40 @ emptyset ) ) )
= $false )
| ( ( SV38 @ SV40 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[207]) ).
thf(210,plain,
! [SV40: $i,SV38: $i > $o] :
( ( ( ~ ( ( SV38 @ SV40 )
| ~ ( in @ SV40 @ emptyset ) ) )
= $false )
| ( ( SV38 @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(212,plain,
! [SV40: $i,SV38: $i > $o] :
( ( ( ( SV38 @ SV40 )
| ~ ( in @ SV40 @ emptyset ) )
= $true )
| ( ( SV38 @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(214,plain,
! [SV40: $i,SV38: $i > $o] :
( ( ( SV38 @ SV40 )
= $true )
| ( ( ~ ( in @ SV40 @ emptyset ) )
= $true )
| ( ( SV38 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(216,plain,
! [SV38: $i > $o,SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV38 @ SV40 )
= $true )
| ( ( SV38 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(221,plain,
! [SV60: $i > $i,SV40: $i,SV59: $i > $i] :
( ( ( ~ ( in @ ( SV59 @ SV40 ) @ ( SV60 @ SV40 ) ) )
= $true )
| ( ( in @ ( SV59 @ SV40 ) @ ( SV60 @ SV40 ) )
= $false )
| ( ( in @ SV40 @ emptyset )
= $false ) ),
inference(extuni,[status(esa)],[209:[bind(SV38,$thf( ^ [SX0: $i] : ~ ( in @ ( SV59 @ SX0 ) @ ( SV60 @ SX0 ) ) ))]]) ).
thf(222,plain,
! [SV40: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV40 ) )
= $true )
| ( ( ~ ( SV56 @ SV40 ) )
= $true )
| ( ( ~ ( in @ SV40 @ emptyset ) )
= $true ) ),
inference(extuni,[status(esa)],[209:[bind(SV38,$thf( ^ [SX0: $i] : ~ ( SV56 @ SX0 ) ))]]) ).
thf(225,plain,
! [SV40: $i,SV56: $i > $o] :
( ( ( SV56 @ SV40 )
= $false )
| ( ( ~ ( SV56 @ SV40 ) )
= $true )
| ( ( ~ ( in @ SV40 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(226,plain,
! [SV60: $i > $i,SV40: $i,SV59: $i > $i] :
( ( ( in @ ( SV59 @ SV40 ) @ ( SV60 @ SV40 ) )
= $false )
| ( ( in @ ( SV59 @ SV40 ) @ ( SV60 @ SV40 ) )
= $false )
| ( ( in @ SV40 @ emptyset )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(229,plain,
! [SV40: $i,SV56: $i > $o] :
( ( ( SV56 @ SV40 )
= $false )
| ( ( SV56 @ SV40 )
= $false )
| ( ( ~ ( in @ SV40 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(231,plain,
! [SV56: $i > $o,SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV56 @ SV40 )
= $false )
| ( ( SV56 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(232,plain,
! [SV40: $i,SV51: $i > $o] :
( ( ( SV51 @ SV40 )
= $false )
| ( ( in @ SV40 @ emptyset )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(233,plain,
! [SV38: $i > $o,SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV38 @ SV40 )
= $true ) ),
inference(sim,[status(thm)],[216]) ).
thf(234,plain,
! [SV56: $i > $o,SV40: $i] :
( ( ( in @ SV40 @ emptyset )
= $false )
| ( ( SV56 @ SV40 )
= $false ) ),
inference(sim,[status(thm)],[231]) ).
thf(235,plain,
! [SV60: $i > $i,SV40: $i,SV59: $i > $i] :
( ( ( in @ ( SV59 @ SV40 ) @ ( SV60 @ SV40 ) )
= $false )
| ( ( in @ SV40 @ emptyset )
= $false ) ),
inference(sim,[status(thm)],[226]) ).
thf(236,plain,
! [SV40: $i] :
( ( in @ SV40 @ emptyset )
= $false ),
inference(sim,[status(thm)],[196]) ).
thf(237,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[189,236,235,234,233,232,206,205,204,203,202,201,200,199,198,194,193,192,191]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(239,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(240,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(241,plain,
( ( ( in @ sK8_SY7 @ ( powerset @ emptyset ) )
& ( sK8_SY7 != emptyset )
& ! [SY29: $i] :
( ( ( in @ ( sK9_SY30 @ SY29 ) @ sK8_SY7 )
& ( SY29
!= ( sK9_SY30 @ SY29 ) )
& ~ ( in @ SY29 @ ( sK9_SY30 @ SY29 ) ) )
| ~ ( in @ SY29 @ sK8_SY7 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(242,plain,
( ( ~ ( ~ ( in @ sK8_SY7 @ ( powerset @ emptyset ) )
| ~ ~ ( ~ ( ( sK8_SY7 != emptyset ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK9_SY30 @ SX0 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SX0
!= ( sK9_SY30 @ SX0 ) ) )
| ~ ~ ( in @ SX0 @ ( sK9_SY30 @ SX0 ) ) ) )
| ~ ( in @ SX0 @ sK8_SY7 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241,nonempty,ordinal,powersetE1,stricttotalorderedByIn,subsetemptysetimpeq,transitiveset,vacuousDall,wellorderedByIn]) ).
thf(243,plain,
! [SV61: $i] :
( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( powerset @ SV61 ) )
| ( subset @ SY49 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(244,plain,
! [SV62: $i] :
( ( ~ ( subset @ SV62 @ emptyset )
| ( SV62 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(245,plain,
! [SV63: $i > $o] :
( ( ! [SY50: $i] :
( ~ ( in @ SY50 @ emptyset )
| ( SV63 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(246,plain,
( ( ~ ( in @ sK8_SY7 @ ( powerset @ emptyset ) )
| ~ ~ ( ~ ( ( sK8_SY7 != emptyset ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK9_SY30 @ SX0 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SX0
!= ( sK9_SY30 @ SX0 ) ) )
| ~ ~ ( in @ SX0 @ ( sK9_SY30 @ SX0 ) ) ) )
| ~ ( in @ SX0 @ sK8_SY7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(247,plain,
! [SV61: $i,SV64: $i] :
( ( ~ ( in @ SV64 @ ( powerset @ SV61 ) )
| ( subset @ SV64 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(248,plain,
! [SV62: $i] :
( ( ( ~ ( subset @ SV62 @ emptyset ) )
= $true )
| ( ( SV62 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(249,plain,
! [SV63: $i > $o,SV65: $i] :
( ( ~ ( in @ SV65 @ emptyset )
| ( SV63 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(250,plain,
( ( ~ ( in @ sK8_SY7 @ ( powerset @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(251,plain,
( ( ~ ~ ( ~ ( ( sK8_SY7 != emptyset ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK9_SY30 @ SX0 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SX0
!= ( sK9_SY30 @ SX0 ) ) )
| ~ ~ ( in @ SX0 @ ( sK9_SY30 @ SX0 ) ) ) )
| ~ ( in @ SX0 @ sK8_SY7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(252,plain,
! [SV61: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ ( powerset @ SV61 ) ) )
= $true )
| ( ( subset @ SV64 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(253,plain,
! [SV62: $i] :
( ( ( subset @ SV62 @ emptyset )
= $false )
| ( ( SV62 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(254,plain,
! [SV63: $i > $o,SV65: $i] :
( ( ( ~ ( in @ SV65 @ emptyset ) )
= $true )
| ( ( SV63 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(255,plain,
( ( in @ sK8_SY7 @ ( powerset @ emptyset ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(256,plain,
( ( ~ ( ~ ( ( sK8_SY7 != emptyset ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK9_SY30 @ SX0 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SX0
!= ( sK9_SY30 @ SX0 ) ) )
| ~ ~ ( in @ SX0 @ ( sK9_SY30 @ SX0 ) ) ) )
| ~ ( in @ SX0 @ sK8_SY7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(257,plain,
! [SV61: $i,SV64: $i] :
( ( ( in @ SV64 @ ( powerset @ SV61 ) )
= $false )
| ( ( subset @ SV64 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(258,plain,
! [SV63: $i > $o,SV65: $i] :
( ( ( in @ SV65 @ emptyset )
= $false )
| ( ( SV63 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(259,plain,
( ( ~ ( ( sK8_SY7 != emptyset ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK9_SY30 @ SX0 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SX0
!= ( sK9_SY30 @ SX0 ) ) )
| ~ ~ ( in @ SX0 @ ( sK9_SY30 @ SX0 ) ) ) )
| ~ ( in @ SX0 @ sK8_SY7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(260,plain,
( ( ~ ( ( sK8_SY7 != emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(261,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK9_SY30 @ SX0 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SX0
!= ( sK9_SY30 @ SX0 ) ) )
| ~ ~ ( in @ SX0 @ ( sK9_SY30 @ SX0 ) ) ) )
| ~ ( in @ SX0 @ sK8_SY7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(262,plain,
( ( sK8_SY7 != emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(263,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK9_SY30 @ SX0 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SX0
!= ( sK9_SY30 @ SX0 ) ) )
| ~ ~ ( in @ SX0 @ ( sK9_SY30 @ SX0 ) ) ) )
| ~ ( in @ SX0 @ sK8_SY7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(264,plain,
( ( sK8_SY7 = emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(265,plain,
! [SV66: $i] :
( ( ~ ( ~ ( in @ ( sK9_SY30 @ SV66 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SV66
!= ( sK9_SY30 @ SV66 ) ) )
| ~ ~ ( in @ SV66 @ ( sK9_SY30 @ SV66 ) ) ) )
| ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(266,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY30 @ SV66 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SV66
!= ( sK9_SY30 @ SV66 ) ) )
| ~ ~ ( in @ SV66 @ ( sK9_SY30 @ SV66 ) ) ) ) )
= $true )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(267,plain,
! [SV66: $i] :
( ( ( ~ ( in @ ( sK9_SY30 @ SV66 ) @ sK8_SY7 )
| ~ ~ ( ~ ( ( SV66
!= ( sK9_SY30 @ SV66 ) ) )
| ~ ~ ( in @ SV66 @ ( sK9_SY30 @ SV66 ) ) ) )
= $false )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(268,plain,
! [SV66: $i] :
( ( ( ~ ( in @ ( sK9_SY30 @ SV66 ) @ sK8_SY7 ) )
= $false )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(269,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ( ( SV66
!= ( sK9_SY30 @ SV66 ) ) )
| ~ ~ ( in @ SV66 @ ( sK9_SY30 @ SV66 ) ) ) )
= $false )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(270,plain,
! [SV66: $i] :
( ( ( in @ ( sK9_SY30 @ SV66 ) @ sK8_SY7 )
= $true )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(271,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ( ( SV66
!= ( sK9_SY30 @ SV66 ) ) )
| ~ ~ ( in @ SV66 @ ( sK9_SY30 @ SV66 ) ) ) )
= $true )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(272,plain,
! [SV66: $i] :
( ( ( in @ SV66 @ sK8_SY7 )
= $false )
| ( ( in @ ( sK9_SY30 @ SV66 ) @ sK8_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(273,plain,
! [SV66: $i] :
( ( ( ~ ( ( SV66
!= ( sK9_SY30 @ SV66 ) ) )
| ~ ~ ( in @ SV66 @ ( sK9_SY30 @ SV66 ) ) )
= $false )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(274,plain,
! [SV66: $i] :
( ( ( ~ ( ( SV66
!= ( sK9_SY30 @ SV66 ) ) ) )
= $false )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(275,plain,
! [SV66: $i] :
( ( ( ~ ~ ( in @ SV66 @ ( sK9_SY30 @ SV66 ) ) )
= $false )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(276,plain,
! [SV66: $i] :
( ( ( SV66
!= ( sK9_SY30 @ SV66 ) )
= $true )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(277,plain,
! [SV66: $i] :
( ( ( ~ ( in @ SV66 @ ( sK9_SY30 @ SV66 ) ) )
= $true )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(278,plain,
! [SV66: $i] :
( ( ( SV66
= ( sK9_SY30 @ SV66 ) )
= $false )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(279,plain,
! [SV66: $i] :
( ( ( in @ SV66 @ ( sK9_SY30 @ SV66 ) )
= $false )
| ( ( ~ ( in @ SV66 @ sK8_SY7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(280,plain,
! [SV66: $i] :
( ( ( in @ SV66 @ sK8_SY7 )
= $false )
| ( ( SV66
= ( sK9_SY30 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(281,plain,
! [SV66: $i] :
( ( ( in @ SV66 @ sK8_SY7 )
= $false )
| ( ( in @ SV66 @ ( sK9_SY30 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(282,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[253,281,280,272,264,258,257,255]) ).
thf(283,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[282,90,133,173,237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU820^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n019.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 15:36:46 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.30
% 0.51/0.30 No.of.Axioms: 0
% 0.51/0.30
% 0.51/0.30 Length.of.Defs: 1745
% 0.51/0.30
% 0.51/0.30 Contains.Choice.Funs: false
% 0.51/0.30 .....
% 0.51/0.30
% 0.51/0.30 ********************************
% 0.51/0.30 * All subproblems solved! *
% 0.51/0.30 ********************************
% 0.51/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:282,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.51/0.30
% 0.51/0.30 %**** Beginning of derivation protocol ****
% 0.51/0.30 % SZS output start CNFRefutation
% See solution above
% 0.51/0.30
% 0.51/0.30 %**** End of derivation protocol ****
% 0.51/0.30 %**** no. of clauses in derivation: 257 ****
% 0.51/0.30 %**** clause counter: 282 ****
% 0.51/0.30
% 0.51/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:282,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------