%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU683^2 : 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 : n010.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 10:46:15 AM UTC 2026
% Result : Theorem 5.24s 1.28s
% Output : CNFRefutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 240 ( 75 unt; 0 typ; 4 def)
% Number of atoms : 2124 ( 843 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 3413 ( 185 ~; 399 |; 16 &;2773 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 192 ( 192 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 9 con; 0-4 aty)
% Number of variables : 847 ( 409 ^; 434 !; 4 ?; 847 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK10_E,type,
sK10_E: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK11_E,type,
sK11_E: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK12_E,type,
sK12_E: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK13_E,type,
sK13_E: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY24,type,
sK2_SY24: $i > $o ).
thf(tp_sK3_SY33,type,
sK3_SY33: $i ).
thf(tp_sK4_SY35,type,
sK4_SY35: $i ).
thf(tp_sK5_SY30,type,
sK5_SY30: $i ).
thf(tp_sK6_E,type,
sK6_E: $i > ( $i > $i ) > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
thf(tp_sK8_E,type,
sK8_E: $i > ( $i > $i ) > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK9_E,type,
sK9_E: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(1,conjecture,
( dsetconstrI
=> ( uniqinunit
=> ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(2,negated_conjecture,
( ( dsetconstrI
=> ( uniqinunit
=> ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ! [SY0: $i,SY1: $i > $o] :
( ? [SY6: $i] :
( ( in @ SY6
@ ( dsetconstr @ SY0
@ ^ [SY7: $i] : ( SY1 @ SY7 ) ) )
& ( ( dsetconstr @ SY0
@ ^ [SY8: $i] : ( SY1 @ SY8 ) )
= ( setadjoin @ SY6 @ emptyset ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY0 )
=> ( ( SY1 @ Xx )
=> ( ( SY1 @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,dsetconstrI,ex1,singleton,uniqinunit]) ).
thf(4,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY0: $i,SY1: $i > $o] :
( ? [SY6: $i] :
( ( in @ SY6
@ ( dsetconstr @ SY0
@ ^ [SY7: $i] : ( SY1 @ SY7 ) ) )
& ( ( dsetconstr @ SY0
@ ^ [SY8: $i] : ( SY1 @ SY8 ) )
= ( setadjoin @ SY6 @ emptyset ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY0 )
=> ( ( SY1 @ Xx )
=> ( ( SY1 @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [SY0: $i,SY1: $i > $o] :
( ? [SY6: $i] :
( ( in @ SY6
@ ( dsetconstr @ SY0
@ ^ [SY7: $i] : ( SY1 @ SY7 ) ) )
& ( ( dsetconstr @ SY0
@ ^ [SY8: $i] : ( SY1 @ SY8 ) )
= ( setadjoin @ SY6 @ emptyset ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY0 )
=> ( ( SY1 @ Xx )
=> ( ( SY1 @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( ( dsetconstr @ sK1_SY0
@ ^ [SY31: $i] : ( sK2_SY24 @ SY31 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
& ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SY32: $i] : ( sK2_SY24 @ SY32 ) ) )
& ( in @ sK3_SY33 @ sK1_SY0 )
& ( in @ sK4_SY35 @ sK1_SY0 )
& ( sK2_SY24 @ sK3_SY33 )
& ( sK2_SY24 @ sK4_SY35 )
& ( sK3_SY33 != sK4_SY35 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( ( dsetconstr @ sK1_SY0
@ ^ [SY31: $i] : ( sK2_SY24 @ SY31 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
& ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SY32: $i] : ( sK2_SY24 @ SY32 ) ) )
& ( in @ sK3_SY33 @ sK1_SY0 )
& ( in @ sK4_SY35 @ sK1_SY0 )
& ( sK2_SY24 @ sK3_SY33 )
& ( sK2_SY24 @ sK4_SY35 )
& ( sK3_SY33 != sK4_SY35 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ~ ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
!= ( setadjoin @ sK5_SY30 @ emptyset ) )
| ~ ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
| ~ ~ ( ~ ( in @ sK3_SY33 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,dsetconstrI,ex1,singleton,uniqinunit]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY38: $i] :
( ~ ( in @ SV1 @ ( setadjoin @ SY38 @ emptyset ) )
| ( SV1 = SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: $i] :
( ( ! [SY39: $i > $o,SY40: $i] :
( ~ ( in @ SY40 @ SV2 )
| ~ ( SY39 @ SY40 )
| ( in @ SY40
@ ( dsetconstr @ SV2
@ ^ [Xy: $i] : ( SY39 @ Xy ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ~ ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
!= ( setadjoin @ sK5_SY30 @ emptyset ) )
| ~ ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
| ~ ~ ( ~ ( in @ sK3_SY33 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ ( setadjoin @ SV3 @ emptyset ) )
| ( SV1 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV4: $i > $o,SV2: $i] :
( ( ! [SY42: $i] :
( ~ ( in @ SY42 @ SV2 )
| ~ ( SV4 @ SY42 )
| ( in @ SY42
@ ( dsetconstr @ SV2
@ ^ [SY43: $i] : ( SV4 @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ~ ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
!= ( setadjoin @ sK5_SY30 @ emptyset ) )
| ~ ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY33 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) )
= $true )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i > $o,SV2: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV2 )
| ~ ( SV4 @ SV5 )
| ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SY43: $i] : ( SV4 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
!= ( setadjoin @ sK5_SY30 @ emptyset ) )
| ~ ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( in @ sK3_SY33 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: $i,SV1: $i] :
( ( ( in @ SV1 @ ( setadjoin @ SV3 @ emptyset ) )
= $false )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV4: $i > $o,SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV2 ) )
= $true )
| ( ( ~ ( SV4 @ SV5 )
| ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SY43: $i] : ( SV4 @ SY43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
!= ( setadjoin @ sK5_SY30 @ emptyset ) )
| ~ ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( in @ sK3_SY33 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV4: $i > $o,SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ SV2 )
= $false )
| ( ( ~ ( SV4 @ SV5 )
| ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SY43: $i] : ( SV4 @ SY43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
!= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ( in @ sK3_SY33 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV2: $i,SV5: $i,SV4: $i > $o] :
( ( ( ~ ( SV4 @ SV5 ) )
= $true )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SY43: $i] : ( SV4 @ SY43 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(36,plain,
( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(37,plain,
( ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(38,plain,
( ( in @ sK3_SY33 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV2: $i,SV5: $i,SV4: $i > $o] :
( ( ( SV4 @ SV5 )
= $false )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SY43: $i] : ( SV4 @ SY43 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
( ( ~ ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(43,plain,
( ( ~ ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
( ( in @ sK4_SY35 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
( ( ~ ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
( ( ~ ( sK2_SY24 @ sK3_SY33 )
| ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(47,plain,
( ( ~ ( sK2_SY24 @ sK3_SY33 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(48,plain,
( ( ~ ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(49,plain,
( ( sK2_SY24 @ sK3_SY33 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(50,plain,
( ( ~ ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(51,plain,
( ( ~ ( sK2_SY24 @ sK4_SY35 )
| ~ ( ( sK3_SY33 != sK4_SY35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(52,plain,
( ( ~ ( sK2_SY24 @ sK4_SY35 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(53,plain,
( ( ~ ( ( sK3_SY33 != sK4_SY35 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(54,plain,
( ( sK2_SY24 @ sK4_SY35 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(55,plain,
( ( sK3_SY33 != sK4_SY35 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
( ( sK3_SY33 = sK4_SY35 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(57,plain,
! [SV2: $i,SV5: $i] :
( ( $true = $false )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV4,$thf( ^ [SV14: $i] : $true ))]]) ).
thf(59,plain,
! [SV2: $i,SV5: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV5 ) )
= $false )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV4,$thf( ^ [SV11: $i] : ~ ( SV12 @ SV11 ) ))]]) ).
thf(60,plain,
! [SV2: $i,SV5: $i] :
( ( ( SV5 = emptyset )
= $false )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV4,$thf( ^ [SV6: $i] : ( SV6 = emptyset ) ))]]) ).
thf(61,plain,
! [SV2: $i,SV5: $i] :
( ( ( SV5 = sK1_SY0 )
= $false )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = sK1_SY0 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV4,$thf( ^ [SV7: $i] : ( SV7 = sK1_SY0 ) ))]]) ).
thf(62,plain,
! [SV2: $i,SV5: $i] :
( ( ( SV5 = sK5_SY30 )
= $false )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = sK5_SY30 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV4,$thf( ^ [SV8: $i] : ( SV8 = sK5_SY30 ) ))]]) ).
thf(63,plain,
! [SV2: $i,SV5: $i] :
( ( ( SV5 = sK4_SY35 )
= $false )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = sK4_SY35 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV4,$thf( ^ [SV9: $i] : ( SV9 = sK4_SY35 ) ))]]) ).
thf(64,plain,
! [SV2: $i,SV5: $i] :
( ( ( SV5 = sK3_SY33 )
= $false )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = sK3_SY33 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV4,$thf( ^ [SV10: $i] : ( SV10 = sK3_SY33 ) ))]]) ).
thf(65,plain,
! [SV2: $i,SV5: $i,SV12: $i > $o] :
( ( ( SV12 @ SV5 )
= $true )
| ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV2: $i] :
( ( ( in @ emptyset @ SV2 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(extuni,[status(esa)],[60:[bind(SV5,$thf( emptyset ))]]) ).
thf(67,plain,
! [SV2: $i] :
( ( ( in @ sK1_SY0 @ SV2 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[61:[bind(SV5,$thf( sK1_SY0 ))]]) ).
thf(68,plain,
! [SV2: $i] :
( ( ( in @ sK5_SY30 @ SV2 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = sK5_SY30 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV5,$thf( sK5_SY30 ))]]) ).
thf(69,plain,
! [SV2: $i] :
( ( ( in @ sK4_SY35 @ SV2 )
= $false )
| ( ( in @ sK4_SY35
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = sK4_SY35 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[63:[bind(SV5,$thf( sK4_SY35 ))]]) ).
thf(70,plain,
! [SV2: $i] :
( ( ( in @ sK3_SY33 @ SV2 )
= $false )
| ( ( in @ sK3_SY33
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : ( SX0 = sK3_SY33 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[64:[bind(SV5,$thf( sK3_SY33 ))]]) ).
thf(71,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ SV5
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(sim,[status(thm)],[57]) ).
thf(72,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= $false )
| ( ( SV16 = SV15 )
= $true ) ),
inference(rename,[status(thm)],[26]) ).
thf(75,plain,
! [SV15: $i,SV16: $i] :
( ( ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false )
| ( ( SV16 = SV15 )
= $true ) ),
inference(res,[status(thm)],[72,44]) ).
thf(76,plain,
! [SV15: $i,SV16: $i] :
( ( ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= ( in @ sK3_SY33 @ sK1_SY0 ) )
= $false )
| ( ( SV16 = SV15 )
= $true ) ),
inference(res,[status(thm)],[72,38]) ).
thf(77,plain,
! [SV15: $i,SV16: $i] :
( ( ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= $false )
| ( ( SV16 = SV15 )
= $true ) ),
inference(res,[status(thm)],[72,37]) ).
thf(79,plain,
! [SV15: $i] :
( ( ( sK5_SY30 = SV15 )
= $true )
| ( ( ( setadjoin @ SV15 @ emptyset )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[77:[bind(SV16,$thf( sK5_SY30 ))]]) ).
thf(80,plain,
! [SV15: $i] :
( ( ( sK3_SY33 = SV15 )
= $true )
| ( ( ( setadjoin @ SV15 @ emptyset )
= sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[76:[bind(SV16,$thf( sK3_SY33 ))]]) ).
thf(81,plain,
! [SV15: $i] :
( ( ( sK4_SY35 = SV15 )
= $true )
| ( ( ( setadjoin @ SV15 @ emptyset )
= sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[75:[bind(SV16,$thf( sK4_SY35 ))]]) ).
thf(84,plain,
! [SV15: $i,SV16: $i] :
( ( ( ( sK3_SY33 = sK4_SY35 )
= ( SV16 = SV15 ) )
= $false )
| ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= $false ) ),
inference(res,[status(thm)],[56,72]) ).
thf(90,plain,
( ( ( sK3_SY33 = sK4_SY35 )
= ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) ) )
= $false ),
inference(res,[status(thm)],[56,36]) ).
thf(91,plain,
( ( ( sK3_SY33
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK4_SY35
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[90]) ).
thf(92,plain,
( ( ( sK4_SY35
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK3_SY33
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[90]) ).
thf(93,plain,
( ( in @ sK4_SY35 @ ( setadjoin @ sK3_SY33 @ emptyset ) )
= $false ),
inference(extuni,[status(esa)],[84:[bind(SV15,$thf( sK3_SY33 )),bind(SV16,$thf( sK4_SY35 ))]]) ).
thf(94,plain,
( ( in @ sK3_SY33 @ ( setadjoin @ sK4_SY35 @ emptyset ) )
= $false ),
inference(extuni,[status(esa)],[84:[bind(SV15,$thf( sK4_SY35 )),bind(SV16,$thf( sK3_SY33 ))]]) ).
thf(98,plain,
( ( ( in @ sK4_SY35 @ ( setadjoin @ sK3_SY33 @ emptyset ) )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[93,44]) ).
thf(99,plain,
( ( ( in @ sK4_SY35 @ ( setadjoin @ sK3_SY33 @ emptyset ) )
= ( in @ sK3_SY33 @ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[93,38]) ).
thf(100,plain,
( ( ( in @ sK4_SY35 @ ( setadjoin @ sK3_SY33 @ emptyset ) )
= ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= $false ),
inference(res,[status(thm)],[93,37]) ).
thf(102,plain,
( ( ( ( setadjoin @ sK3_SY33 @ emptyset )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false )
| ( ( sK4_SY35 = sK5_SY30 )
= $false ) ),
inference(extuni,[status(esa)],[100]) ).
thf(103,plain,
( ( ( ( setadjoin @ sK3_SY33 @ emptyset )
= sK1_SY0 )
= $false )
| ( ( sK4_SY35 = sK3_SY33 )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(104,plain,
( ( ( setadjoin @ sK3_SY33 @ emptyset )
= sK1_SY0 )
= $false ),
inference(extuni,[status(esa)],[98]) ).
thf(105,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( SV19 @ SV18 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(rename,[status(thm)],[40]) ).
thf(110,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= ( in @ sK4_SY35 @ ( setadjoin @ sK3_SY33 @ emptyset ) ) )
= $false )
| ( ( SV19 @ SV18 )
= $false )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(res,[status(thm)],[105,93]) ).
thf(112,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o,SV15: $i,SV16: $i] :
( ( ( ( SV19 @ SV18 )
= ( SV16 = SV15 ) )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= $false ) ),
inference(res,[status(thm)],[105,72]) ).
thf(113,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o,SV15: $i,SV16: $i] :
( ( ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) ) )
= $false )
| ( ( SV19 @ SV18 )
= $false )
| ( ( in @ SV18 @ SV17 )
= $false )
| ( ( SV16 = SV15 )
= $true ) ),
inference(res,[status(thm)],[105,72]) ).
thf(116,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( SV19 @ SV18 )
= ( sK2_SY24 @ sK4_SY35 ) )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(res,[status(thm)],[105,54]) ).
thf(118,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( SV19 @ SV18 )
= ( sK2_SY24 @ sK3_SY33 ) )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(res,[status(thm)],[105,49]) ).
thf(119,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( in @ SV18 @ SV17 )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false )
| ( ( SV19 @ SV18 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[105,44]) ).
thf(120,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( SV19 @ SV18 )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(res,[status(thm)],[105,44]) ).
thf(121,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( in @ SV18 @ SV17 )
= ( in @ sK3_SY33 @ sK1_SY0 ) )
= $false )
| ( ( SV19 @ SV18 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[105,38]) ).
thf(122,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( SV19 @ SV18 )
= ( in @ sK3_SY33 @ sK1_SY0 ) )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(res,[status(thm)],[105,38]) ).
thf(123,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( in @ SV18 @ SV17 )
= ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= $false )
| ( ( SV19 @ SV18 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[105,37]) ).
thf(124,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( SV19 @ SV18 )
= ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(res,[status(thm)],[105,37]) ).
thf(126,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( SV19 @ SV18 )
= ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) ) )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(res,[status(thm)],[105,36]) ).
thf(127,plain,
! [SV17: $i,SV18: $i] :
( ( $true = $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV19,$thf( ^ [SV35: $i] : $true ))]]) ).
thf(128,plain,
! [SV17: $i,SV18: $i] :
( ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(sim,[status(thm)],[127]) ).
thf(130,plain,
! [SV17: $i,SV18: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV18 ) )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
~ ( SV33 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV19,$thf( ^ [SV32: $i] : ~ ( SV33 @ SV32 ) ))]]) ).
thf(131,plain,
! [SV17: $i,SV18: $i] :
( ( ( SV18 = sK5_SY30 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = sK5_SY30 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV19,$thf( ^ [SV27: $i] : ( SV27 = sK5_SY30 ) ))]]) ).
thf(132,plain,
! [SV17: $i,SV18: $i] :
( ( ( SV18 = emptyset )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV19,$thf( ^ [SV28: $i] : ( SV28 = emptyset ) ))]]) ).
thf(133,plain,
! [SV17: $i,SV18: $i] :
( ( ( SV18 = sK1_SY0 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = sK1_SY0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV19,$thf( ^ [SV29: $i] : ( SV29 = sK1_SY0 ) ))]]) ).
thf(134,plain,
! [SV17: $i,SV18: $i] :
( ( ( SV18 = sK4_SY35 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = sK4_SY35 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV19,$thf( ^ [SV30: $i] : ( SV30 = sK4_SY35 ) ))]]) ).
thf(135,plain,
! [SV17: $i,SV18: $i] :
( ( ( SV18 = sK3_SY33 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = sK3_SY33 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV19,$thf( ^ [SV31: $i] : ( SV31 = sK3_SY33 ) ))]]) ).
thf(136,plain,
! [SV17: $i,SV26: $i > $o,SV18: $i,SV25: $i > $o] :
( ( ( ( SV25 @ SV18 )
| ( SV26 @ SV18 ) )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( SV25 @ SX0 )
| ( SV26 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV19,$thf( ^ [SV24: $i] : ( ( SV25 @ SV24 ) | ( SV26 @ SV24 ) ) ))]]) ).
thf(138,plain,
! [SV93: $i > $i > $i,SV116: $i > $i,SV115: $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ ( SV115 @ SX0 ) @ ( SV116 @ SX0 ) )
= ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV115 @ sK1_SY0 ) @ ( SV116 @ sK1_SY0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV93 @ sK1_SY0
@ ( sK7_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV115 @ SX0 ) @ ( SV116 @ SX0 ) )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK7_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV115 @ SX0 ) @ ( SV116 @ SX0 ) )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ ( SV115 @ SX0 ) @ ( SV116 @ SX0 ) ) = ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(139,plain,
! [SV93: $i > $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK1_SY0
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV93 @ sK1_SY0
@ ( sK7_E @ SV17
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK7_E @ SV17
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(140,plain,
! [SV93: $i > $i > $i,SV122: $i > $i,SV121: $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ ( SV121 @ SX0 ) @ ( SV122 @ SX0 ) )
= ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV121 @ sK1_SY0 ) @ ( SV122 @ sK1_SY0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV93 @ sK1_SY0
@ ( sK7_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV121 @ SX0 ) @ ( SV122 @ SX0 ) )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK7_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV121 @ SX0 ) @ ( SV122 @ SX0 ) )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ ( SV121 @ SX0 ) @ ( SV122 @ SX0 ) ) = ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(141,plain,
! [SV93: $i > $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK1_SY0
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV93 @ sK1_SY0
@ ( sK7_E @ SV17
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK7_E @ SV17
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV93 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(142,plain,
! [SV60: $i > $i > $i,SV80: $i > $i,SV79: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ ( SV79 @ SX0 ) @ ( SV80 @ SX0 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV79 @ SV18 ) @ ( SV80 @ SV18 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV60 @ SV18
@ ( sK6_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV79 @ SX0 ) @ ( SV80 @ SX0 ) )
@ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK6_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV79 @ SX0 ) @ ( SV80 @ SX0 ) )
@ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ ( SV79 @ SX0 ) @ ( SV80 @ SX0 ) ) = ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(143,plain,
! [SV60: $i > $i > $i,SV17: $i] :
( ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset ) @ SV17 )
= $false )
| ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV60 @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( sK6_E @ SV17
@ ^ [SX0: $i] : SX0
@ ( setadjoin @ sK5_SY30 @ emptyset )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK6_E @ SV17
@ ^ [SX0: $i] : SX0
@ ( setadjoin @ sK5_SY30 @ emptyset )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( setadjoin @ sK5_SY30 @ emptyset )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(144,plain,
! [SV60: $i > $i > $i,SV86: $i > $i,SV85: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ ( SV85 @ SX0 ) @ ( SV86 @ SX0 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV85 @ SV18 ) @ ( SV86 @ SV18 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV60 @ SV18
@ ( sK6_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV85 @ SX0 ) @ ( SV86 @ SX0 ) )
@ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK6_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV85 @ SX0 ) @ ( SV86 @ SX0 ) )
@ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ ( SV85 @ SX0 ) @ ( SV86 @ SX0 ) ) = ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(145,plain,
! [SV60: $i > $i > $i,SV17: $i] :
( ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset ) @ SV17 )
= $false )
| ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV60 @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( sK6_E @ SV17
@ ^ [SX0: $i] : SX0
@ ( setadjoin @ sK5_SY30 @ emptyset )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK6_E @ SV17
@ ^ [SX0: $i] : SX0
@ ( setadjoin @ sK5_SY30 @ emptyset )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( setadjoin @ sK5_SY30 @ emptyset )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV60 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(146,plain,
! [SV43: $i > $i > $o,SV42: $i > $i,SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ SX0 @ SX0 )
= ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ) )
= $true )
| ( ( sK5_SY30 = emptyset )
= $false )
| ( ( ( dsetconstr @ ( SV42 @ sK5_SY30 ) @ ( SV43 @ sK5_SY30 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ SX0 @ SX0 ) = ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ))]]) ).
thf(147,plain,
! [SV43: $i > $i > $o,SV42: $i > $i,SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ SX0 @ emptyset )
= ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV42 @ sK5_SY30 ) @ ( SV43 @ sK5_SY30 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ SX0 @ emptyset ) = ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ))]]) ).
thf(148,plain,
! [SV43: $i > $i > $o,SV42: $i > $i,SV17: $i] :
( ( ( in @ emptyset @ SV17 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ sK5_SY30 @ SX0 )
= ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV42 @ emptyset ) @ ( SV43 @ emptyset ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( emptyset )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ sK5_SY30 @ SX0 ) = ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ))]]) ).
thf(149,plain,
! [SV43: $i > $i > $o,SV42: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ sK5_SY30 @ emptyset )
= ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV42 @ SV18 ) @ ( SV43 @ SV18 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ sK5_SY30 @ emptyset ) = ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ))]]) ).
thf(150,plain,
! [SV43: $i > $i > $o,SV42: $i > $i,SV128: $i > $i,SV127: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ ( SV127 @ SX0 ) @ ( SV128 @ SX0 ) )
= ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV127 @ SV18 ) @ ( SV128 @ SV18 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( ( dsetconstr @ ( SV42 @ SV18 ) @ ( SV43 @ SV18 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ ( SV127 @ SX0 ) @ ( SV128 @ SX0 ) ) = ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ))]]) ).
thf(151,plain,
! [SV43: $i > $i > $o,SV42: $i > $i,SV17: $i] :
( ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset ) @ SV17 )
= $false )
| ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV42 @ ( setadjoin @ sK5_SY30 @ emptyset ) ) @ ( SV43 @ ( setadjoin @ sK5_SY30 @ emptyset ) ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( setadjoin @ sK5_SY30 @ emptyset )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ ( SV42 @ SX0 ) @ ( SV43 @ SX0 ) ) ) ))]]) ).
thf(152,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ SX0 @ SX0 )
= SX0 ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= emptyset )
= $false )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= sK5_SY30 )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ SX0 @ SX0 ) = SX0 ) ))]]) ).
thf(153,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ SX0 @ emptyset )
= SX0 ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= sK5_SY30 )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ SX0 @ emptyset ) = SX0 ) ))]]) ).
thf(154,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ sK5_SY30 @ SX0 )
= SX0 ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= emptyset )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ sK5_SY30 @ SX0 ) = SX0 ) ))]]) ).
thf(155,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ sK5_SY30 @ emptyset )
= SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ sK5_SY30 @ emptyset ) = SX0 ) ))]]) ).
thf(156,plain,
! [SV47: $i > $i,SV46: $i > $i,SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( setadjoin @ ( SV46 @ SX0 ) @ ( SV47 @ SX0 ) )
= SX0 ) ) )
= $true )
| ( ( ( setadjoin
@ ( SV46
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
@ ( SV47
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( ( setadjoin @ ( SV46 @ SX0 ) @ ( SV47 @ SX0 ) ) = SX0 ) ))]]) ).
thf(157,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = SX0 ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = SX0 ) ))]]) ).
thf(158,plain,
! [SV211: $i > $i,SV210: $i > $i,SV188: $i > $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) )
= ( setadjoin @ ( SV210 @ SX0 ) @ ( SV211 @ SX0 ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV210 @ sK1_SY0 ) @ ( SV211 @ sK1_SY0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV188 @ sK1_SY0
@ ( sK9_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV210 @ SX0 ) @ ( SV211 @ SX0 ) )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK9_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV210 @ SX0 ) @ ( SV211 @ SX0 ) )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) = ( setadjoin @ ( SV210 @ SX0 ) @ ( SV211 @ SX0 ) ) ) ))]]) ).
thf(159,plain,
! [SV188: $i > $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) )
= SX0 ) ) )
= $true )
| ( ( sK1_SY0
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV188 @ sK1_SY0
@ ( sK9_E @ SV17
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK9_E @ SV17
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) = SX0 ) ))]]) ).
thf(160,plain,
! [SV217: $i > $i,SV216: $i > $i,SV188: $i > $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) )
= ( setadjoin @ ( SV216 @ SX0 ) @ ( SV217 @ SX0 ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV216 @ sK1_SY0 ) @ ( SV217 @ sK1_SY0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV188 @ sK1_SY0
@ ( sK9_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV216 @ SX0 ) @ ( SV217 @ SX0 ) )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK9_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV216 @ SX0 ) @ ( SV217 @ SX0 ) )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) = ( setadjoin @ ( SV216 @ SX0 ) @ ( SV217 @ SX0 ) ) ) ))]]) ).
thf(161,plain,
! [SV188: $i > $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) )
= SX0 ) ) )
= $true )
| ( ( sK1_SY0
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV188 @ sK1_SY0
@ ( sK9_E @ SV17
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK9_E @ SV17
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV188 @ SX0 @ SX1 ) ) ) = SX0 ) ))]]) ).
thf(162,plain,
! [SV175: $i > $i,SV174: $i > $i,SV155: $i > $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) )
= ( setadjoin @ ( SV174 @ SX0 ) @ ( SV175 @ SX0 ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV174 @ SV18 ) @ ( SV175 @ SV18 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV155 @ SV18
@ ( sK8_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV174 @ SX0 ) @ ( SV175 @ SX0 ) )
@ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK8_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV174 @ SX0 ) @ ( SV175 @ SX0 ) )
@ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) = ( setadjoin @ ( SV174 @ SX0 ) @ ( SV175 @ SX0 ) ) ) ))]]) ).
thf(163,plain,
! [SV155: $i > $i > $i,SV17: $i] :
( ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset ) @ SV17 )
= $false )
| ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) )
= SX0 ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV155 @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( sK8_E @ SV17
@ ^ [SX0: $i] : SX0
@ ( setadjoin @ sK5_SY30 @ emptyset )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK8_E @ SV17
@ ^ [SX0: $i] : SX0
@ ( setadjoin @ sK5_SY30 @ emptyset )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( setadjoin @ sK5_SY30 @ emptyset )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) = SX0 ) ))]]) ).
thf(164,plain,
! [SV181: $i > $i,SV180: $i > $i,SV155: $i > $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) )
= ( setadjoin @ ( SV180 @ SX0 ) @ ( SV181 @ SX0 ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV180 @ SV18 ) @ ( SV181 @ SV18 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK2_SY24
@ ( SV155 @ SV18
@ ( sK8_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV180 @ SX0 ) @ ( SV181 @ SX0 ) )
@ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK8_E @ SV17
@ ^ [SX0: $i] : ( setadjoin @ ( SV180 @ SX0 ) @ ( SV181 @ SX0 ) )
@ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) = ( setadjoin @ ( SV180 @ SX0 ) @ ( SV181 @ SX0 ) ) ) ))]]) ).
thf(165,plain,
! [SV155: $i > $i > $i,SV17: $i] :
( ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset ) @ SV17 )
= $false )
| ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) )
= SX0 ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV155 @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( sK8_E @ SV17
@ ^ [SX0: $i] : SX0
@ ( setadjoin @ sK5_SY30 @ emptyset )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK8_E @ SV17
@ ^ [SX0: $i] : SX0
@ ( setadjoin @ sK5_SY30 @ emptyset )
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( setadjoin @ sK5_SY30 @ emptyset )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV155 @ SX0 @ SX1 ) ) ) = SX0 ) ))]]) ).
thf(166,plain,
! [SV138: $i > $i > $o,SV137: $i > $i,SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) )
= ( setadjoin @ SX0 @ SX0 ) ) ) )
= $true )
| ( ( sK5_SY30 = emptyset )
= $false )
| ( ( ( dsetconstr @ ( SV137 @ sK5_SY30 ) @ ( SV138 @ sK5_SY30 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) ) = ( setadjoin @ SX0 @ SX0 ) ) ))]]) ).
thf(167,plain,
! [SV138: $i > $i > $o,SV137: $i > $i,SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV137 @ sK5_SY30 ) @ ( SV138 @ sK5_SY30 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) ) = ( setadjoin @ SX0 @ emptyset ) ) ))]]) ).
thf(168,plain,
! [SV138: $i > $i > $o,SV137: $i > $i,SV17: $i] :
( ( ( in @ emptyset @ SV17 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ SX0 ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV137 @ emptyset ) @ ( SV138 @ emptyset ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( emptyset )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) ) = ( setadjoin @ sK5_SY30 @ SX0 ) ) ))]]) ).
thf(169,plain,
! [SV138: $i > $i > $o,SV137: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV137 @ SV18 ) @ ( SV138 @ SV18 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) ) = ( setadjoin @ sK5_SY30 @ emptyset ) ) ))]]) ).
thf(170,plain,
! [SV223: $i > $i,SV222: $i > $i,SV138: $i > $i > $o,SV137: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) )
= ( setadjoin @ ( SV222 @ SX0 ) @ ( SV223 @ SX0 ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( SV222 @ SV18 ) @ ( SV223 @ SV18 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( ( dsetconstr @ ( SV137 @ SV18 ) @ ( SV138 @ SV18 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) ) = ( setadjoin @ ( SV222 @ SX0 ) @ ( SV223 @ SX0 ) ) ) ))]]) ).
thf(171,plain,
! [SV138: $i > $i > $o,SV137: $i > $i,SV17: $i] :
( ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset ) @ SV17 )
= $false )
| ( ( in @ ( setadjoin @ sK5_SY30 @ emptyset )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) )
= SX0 ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV137 @ ( setadjoin @ sK5_SY30 @ emptyset ) ) @ ( SV138 @ ( setadjoin @ sK5_SY30 @ emptyset ) ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( setadjoin @ sK5_SY30 @ emptyset )),bind(SV19,$thf( ^ [SX0: $i] : ( ( dsetconstr @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) ) = SX0 ) ))]]) ).
thf(172,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( setadjoin @ SX0 @ SX0 ) ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= emptyset )
= $false )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= sK5_SY30 )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( setadjoin @ SX0 @ SX0 ) ) ))]]) ).
thf(173,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= sK5_SY30 )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( setadjoin @ SX0 @ emptyset ) ) ))]]) ).
thf(174,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( setadjoin @ sK5_SY30 @ SX0 ) ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= emptyset )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( setadjoin @ sK5_SY30 @ SX0 ) ) ))]]) ).
thf(175,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( setadjoin @ sK5_SY30 @ emptyset ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( setadjoin @ sK5_SY30 @ emptyset ) ) ))]]) ).
thf(176,plain,
! [SV142: $i > $i,SV141: $i > $i,SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( SX0
= ( setadjoin @ ( SV141 @ SX0 ) @ ( SV142 @ SX0 ) ) ) ) )
= $true )
| ( ( ( setadjoin
@ ( SV141
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
@ ( SV142
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = ( setadjoin @ ( SV141 @ SX0 ) @ ( SV142 @ SX0 ) ) ) ))]]) ).
thf(177,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = SX0 ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( SX0 = SX0 ) ))]]) ).
thf(178,plain,
! [SV39: $i > $i,SV38: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( SV38 @ SX0 )
= ( SV39 @ SX0 ) ) ) )
= $true )
| ( ( ( SV38 @ SV18 )
= ( SV39 @ SV18 ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $true ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( SV38 @ SX0 ) = ( SV39 @ SX0 ) ) ))]]) ).
thf(179,plain,
! [SV39: $i > $i,SV38: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( SV38 @ SX0 )
= ( SV39 @ SX0 ) ) ) )
= $true )
| ( ( ( SV38 @ SV18 )
= ( SV39 @ SV18 ) )
= $false )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[126:[bind(SV19,$thf( ^ [SX0: $i] : ( ( SV38 @ SX0 ) = ( SV39 @ SX0 ) ) ))]]) ).
thf(180,plain,
! [SV286: $i > $i > $i,SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( in @ SX0
@ ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV286 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV286 @ sK5_SY30
@ ( sK13_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV286 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK13_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV286 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( sK5_SY30 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV286 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(181,plain,
! [SV286: $i > $i > $i,SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( in @ SX0
@ ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV286 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV286 @ sK5_SY30
@ ( sK13_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV286 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK13_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV286 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( sK5_SY30 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV286 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(182,plain,
! [SV275: $i > $i > $i,SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( in @ SX0
@ ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV275 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV275 @ sK5_SY30
@ ( sK12_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV275 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK12_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV275 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[124:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV275 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(183,plain,
! [SV275: $i > $i > $i,SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( in @ SX0
@ ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV275 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV275 @ sK5_SY30
@ ( sK12_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV275 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK12_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV275 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV275 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(184,plain,
! [SV268: $i > $i > $o,SV267: $i > $i,SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ SX0 @ ( dsetconstr @ ( SV267 @ SX0 ) @ ( SV268 @ SX0 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV267 @ sK5_SY30 ) @ ( SV268 @ sK5_SY30 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ ( dsetconstr @ ( SV267 @ SX0 ) @ ( SV268 @ SX0 ) ) ) ))]]) ).
thf(185,plain,
! [SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ SX0 @ SX0 ) ) )
= $true )
| ( ( sK5_SY30
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV18,$thf( sK5_SY30 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ SX0 ) ))]]) ).
thf(186,plain,
! [SV258: $i > $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( in @ sK5_SY30
@ ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV258 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV258 @ sK1_SY0
@ ( sK11_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV258 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK11_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV258 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[124:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK5_SY30 @ ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV258 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(187,plain,
! [SV258: $i > $i > $i,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( in @ sK5_SY30
@ ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV258 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV258 @ sK1_SY0
@ ( sK11_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV258 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK11_E @ SV17
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV258 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK5_SY30 @ ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV258 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(188,plain,
! [SV246: $i > $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV246 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV246 @ SV18
@ ( sK10_E @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV246 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( sK10_E @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV246 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[124:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK5_SY30 @ ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV246 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(189,plain,
! [SV246: $i > $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY24 @ ( SV246 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY24
@ ( SV246 @ SV18
@ ( sK10_E @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV246 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY24
@ ( sK10_E @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY24 @ ( SV246 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK5_SY30 @ ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY24 @ ( SV246 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(190,plain,
! [SV239: $i > $i > $o,SV238: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ sK5_SY30 @ ( dsetconstr @ ( SV238 @ SX0 ) @ ( SV239 @ SX0 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV238 @ SV18 ) @ ( SV239 @ SV18 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK5_SY30 @ ( dsetconstr @ ( SV238 @ SX0 ) @ ( SV239 @ SX0 ) ) ) ))]]) ).
thf(191,plain,
! [SV17: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ SV17 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ sK5_SY30 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[124:[bind(SV18,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK5_SY30 @ SX0 ) ))]]) ).
thf(192,plain,
! [SV233: $i > $i,SV232: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ ( SV232 @ SX0 ) @ ( SV233 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV232 @ SV18 ) @ ( SV233 @ SV18 ) )
= $true )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[124:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ ( SV232 @ SX0 ) @ ( SV233 @ SX0 ) ) ))]]) ).
thf(193,plain,
! [SV233: $i > $i,SV232: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ ( SV232 @ SX0 ) @ ( SV233 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV232 @ SV18 ) @ ( SV233 @ SV18 ) )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ ( SV232 @ SX0 ) @ ( SV233 @ SX0 ) ) ))]]) ).
thf(194,plain,
! [SV19: $i > $o] :
( ( ( in @ sK5_SY30
@ ( dsetconstr
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( SV19 @ sK5_SY30 )
= $false ) ),
inference(extuni,[status(esa)],[123:[bind(SV17,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )),bind(SV18,$thf( sK5_SY30 ))]]) ).
thf(195,plain,
! [SV17: $i] :
( ( ( in @ sK3_SY33 @ SV17 )
= $false )
| ( ( in @ sK3_SY33
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ SX0 @ SX0 ) ) )
= $true )
| ( ( sK3_SY33 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[122:[bind(SV18,$thf( sK3_SY33 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ SX0 ) ))]]) ).
thf(196,plain,
! [SV17: $i] :
( ( ( in @ sK3_SY33 @ SV17 )
= $false )
| ( ( in @ sK3_SY33
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ SX0 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[122:[bind(SV18,$thf( sK3_SY33 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ sK1_SY0 ) ))]]) ).
thf(197,plain,
! [SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ sK3_SY33 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[122:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK3_SY33 @ SX0 ) ))]]) ).
thf(198,plain,
! [SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ sK3_SY33 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[122:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK3_SY33 @ sK1_SY0 ) ))]]) ).
thf(199,plain,
! [SV296: $i > $i,SV295: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ ( SV295 @ SX0 ) @ ( SV296 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV295 @ SV18 ) @ ( SV296 @ SV18 ) )
= $true )
| ( ( in @ sK3_SY33 @ sK1_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[122:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ ( SV295 @ SX0 ) @ ( SV296 @ SX0 ) ) ))]]) ).
thf(200,plain,
! [SV296: $i > $i,SV295: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ ( SV295 @ SX0 ) @ ( SV296 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV295 @ SV18 ) @ ( SV296 @ SV18 ) )
= $false )
| ( ( in @ sK3_SY33 @ sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[122:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ ( SV295 @ SX0 ) @ ( SV296 @ SX0 ) ) ))]]) ).
thf(201,plain,
! [SV19: $i > $o] :
( ( ( in @ sK3_SY33
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( SV19 @ sK3_SY33 )
= $false ) ),
inference(extuni,[status(esa)],[121:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK3_SY33 ))]]) ).
thf(202,plain,
! [SV17: $i] :
( ( ( in @ sK4_SY35 @ SV17 )
= $false )
| ( ( in @ sK4_SY35
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ SX0 @ SX0 ) ) )
= $true )
| ( ( sK4_SY35 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[120:[bind(SV18,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ SX0 ) ))]]) ).
thf(203,plain,
! [SV17: $i] :
( ( ( in @ sK4_SY35 @ SV17 )
= $false )
| ( ( in @ sK4_SY35
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ SX0 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[120:[bind(SV18,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ SX0 @ sK1_SY0 ) ))]]) ).
thf(204,plain,
! [SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ sK4_SY35 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[120:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK4_SY35 @ SX0 ) ))]]) ).
thf(205,plain,
! [SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ sK4_SY35 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[120:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ sK4_SY35 @ sK1_SY0 ) ))]]) ).
thf(206,plain,
! [SV306: $i > $i,SV305: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ ( SV305 @ SX0 ) @ ( SV306 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV305 @ SV18 ) @ ( SV306 @ SV18 ) )
= $true )
| ( ( in @ sK4_SY35 @ sK1_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[120:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ ( SV305 @ SX0 ) @ ( SV306 @ SX0 ) ) ))]]) ).
thf(207,plain,
! [SV306: $i > $i,SV305: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( in @ ( SV305 @ SX0 ) @ ( SV306 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV305 @ SV18 ) @ ( SV306 @ SV18 ) )
= $false )
| ( ( in @ sK4_SY35 @ sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[120:[bind(SV19,$thf( ^ [SX0: $i] : ( in @ ( SV305 @ SX0 ) @ ( SV306 @ SX0 ) ) ))]]) ).
thf(208,plain,
! [SV19: $i > $o] :
( ( ( in @ sK4_SY35
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $true )
| ( ( SV19 @ sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[119:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK4_SY35 ))]]) ).
thf(209,plain,
! [SV17: $i] :
( ( ( in @ sK3_SY33 @ SV17 )
= $false )
| ( ( in @ sK3_SY33
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[118:[bind(SV18,$thf( sK3_SY33 )),bind(SV19,$thf( ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ))]]) ).
thf(210,plain,
! [SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( sK2_SY24 @ sK3_SY33 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[118:[bind(SV19,$thf( ^ [SX0: $i] : ( sK2_SY24 @ sK3_SY33 ) ))]]) ).
thf(211,plain,
! [SV315: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( sK2_SY24 @ ( SV315 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY24 @ ( SV315 @ SV18 ) )
= $true )
| ( ( sK2_SY24 @ sK3_SY33 )
= $true ) ),
inference(extuni,[status(esa)],[118:[bind(SV19,$thf( ^ [SX0: $i] : ( sK2_SY24 @ ( SV315 @ SX0 ) ) ))]]) ).
thf(212,plain,
! [SV315: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( sK2_SY24 @ ( SV315 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY24 @ ( SV315 @ SV18 ) )
= $false )
| ( ( sK2_SY24 @ sK3_SY33 )
= $false ) ),
inference(extuni,[status(esa)],[118:[bind(SV19,$thf( ^ [SX0: $i] : ( sK2_SY24 @ ( SV315 @ SX0 ) ) ))]]) ).
thf(213,plain,
! [SV17: $i] :
( ( ( in @ sK4_SY35 @ SV17 )
= $false )
| ( ( in @ sK4_SY35
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[116:[bind(SV18,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ))]]) ).
thf(214,plain,
! [SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( sK2_SY24 @ sK4_SY35 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[116:[bind(SV19,$thf( ^ [SX0: $i] : ( sK2_SY24 @ sK4_SY35 ) ))]]) ).
thf(215,plain,
! [SV320: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( sK2_SY24 @ ( SV320 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY24 @ ( SV320 @ SV18 ) )
= $true )
| ( ( sK2_SY24 @ sK4_SY35 )
= $true ) ),
inference(extuni,[status(esa)],[116:[bind(SV19,$thf( ^ [SX0: $i] : ( sK2_SY24 @ ( SV320 @ SX0 ) ) ))]]) ).
thf(216,plain,
! [SV320: $i > $i,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( sK2_SY24 @ ( SV320 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY24 @ ( SV320 @ SV18 ) )
= $false )
| ( ( sK2_SY24 @ sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[116:[bind(SV19,$thf( ^ [SX0: $i] : ( sK2_SY24 @ ( SV320 @ SX0 ) ) ))]]) ).
thf(217,plain,
! [SV19: $i > $o,SV17: $i,SV15: $i,SV16: $i] :
( ( ( SV16 = SV15 )
= $true )
| ( ( in @ SV16 @ SV17 )
= $false )
| ( ( SV19 @ SV16 )
= $false )
| ( ( ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) )
= ( setadjoin @ SV15 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[113:[bind(SV18,$thf( SV16 ))]]) ).
thf(218,plain,
! [SV17: $i,SV325: $i > $i,SV18: $i,SV326: $i > $i] :
( ( ( in @ ( SV326 @ SV18 ) @ ( setadjoin @ ( SV325 @ SV18 ) @ emptyset ) )
= $false )
| ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( SV325 @ SX0 )
= ( SV326 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[112:[bind(SV15,$thf( SV325 @ SV18 )),bind(SV16,$thf( SV326 @ SV18 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( SV325 @ SX0 ) = ( SV326 @ SX0 ) ) ))]]) ).
thf(219,plain,
! [SV17: $i,SV326: $i > $i,SV18: $i,SV325: $i > $i] :
( ( ( in @ ( SV325 @ SV18 ) @ ( setadjoin @ ( SV326 @ SV18 ) @ emptyset ) )
= $false )
| ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( SV325 @ SX0 )
= ( SV326 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[112:[bind(SV15,$thf( SV326 @ SV18 )),bind(SV16,$thf( SV325 @ SV18 )),bind(SV19,$thf( ^ [SX0: $i] : ( ( SV325 @ SX0 ) = ( SV326 @ SX0 ) ) ))]]) ).
thf(220,plain,
! [SV326: $i > $i,SV325: $i > $i,SV17: $i,SV18: $i,SV15: $i,SV16: $i] :
( ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= $false )
| ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( SV325 @ SX0 )
= ( SV326 @ SX0 ) ) ) )
= $true )
| ( ( ( SV325 @ SV18 )
= ( SV326 @ SV18 ) )
= $true )
| ( ( SV16 = SV15 )
= $true ) ),
inference(extuni,[status(esa)],[112:[bind(SV19,$thf( ^ [SX0: $i] : ( ( SV325 @ SX0 ) = ( SV326 @ SX0 ) ) ))]]) ).
thf(221,plain,
! [SV326: $i > $i,SV325: $i > $i,SV17: $i,SV18: $i,SV15: $i,SV16: $i] :
( ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= $false )
| ( ( in @ SV18 @ SV17 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( SV325 @ SX0 )
= ( SV326 @ SX0 ) ) ) )
= $true )
| ( ( ( SV325 @ SV18 )
= ( SV326 @ SV18 ) )
= $false )
| ( ( SV16 = SV15 )
= $false ) ),
inference(extuni,[status(esa)],[112:[bind(SV19,$thf( ^ [SX0: $i] : ( ( SV325 @ SX0 ) = ( SV326 @ SX0 ) ) ))]]) ).
thf(222,plain,
! [SV19: $i > $o,SV17: $i] :
( ( ( in @ sK4_SY35 @ SV17 )
= $false )
| ( ( SV19 @ sK4_SY35 )
= $false )
| ( ( ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) )
= ( setadjoin @ sK3_SY33 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[110:[bind(SV18,$thf( sK4_SY35 ))]]) ).
thf(225,plain,
! [SV17: $i] :
( ( ( in @ sK5_SY30 @ SV17 )
= $false )
| ( ( in @ sK5_SY30
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = sK5_SY30 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[131:[bind(SV18,$thf( sK5_SY30 ))]]) ).
thf(226,plain,
! [SV17: $i] :
( ( ( in @ emptyset @ SV17 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(extuni,[status(esa)],[132:[bind(SV18,$thf( emptyset ))]]) ).
thf(227,plain,
! [SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[133:[bind(SV18,$thf( sK1_SY0 ))]]) ).
thf(228,plain,
! [SV17: $i] :
( ( ( in @ sK4_SY35 @ SV17 )
= $false )
| ( ( in @ sK4_SY35
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = sK4_SY35 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[134:[bind(SV18,$thf( sK4_SY35 ))]]) ).
thf(229,plain,
! [SV17: $i] :
( ( ( in @ sK3_SY33 @ SV17 )
= $false )
| ( ( in @ sK3_SY33
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SX0 = sK3_SY33 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[135:[bind(SV18,$thf( sK3_SY33 ))]]) ).
thf(230,plain,
! [SV17: $i,SV18: $i,SV33: $i > $o] :
( ( ( SV33 @ SV18 )
= $true )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
~ ( SV33 @ SX0 ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(231,plain,
! [SV26: $i > $o,SV17: $i,SV18: $i,SV25: $i > $o] :
( ( ( SV25 @ SV18 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( SV25 @ SX0 )
| ( SV26 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(232,plain,
! [SV25: $i > $o,SV17: $i,SV18: $i,SV26: $i > $o] :
( ( ( SV26 @ SV18 )
= $false )
| ( ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] :
( ( SV25 @ SX0 )
| ( SV26 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(233,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( in @ sK3_SY33 @ ( setadjoin @ sK4_SY35 @ emptyset ) )
= ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) ) )
= $false )
| ( ( SV19 @ SV18 )
= $false )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(res,[status(thm)],[94,105]) ).
thf(237,plain,
( ( ( in @ sK3_SY33 @ ( setadjoin @ sK4_SY35 @ emptyset ) )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[94,44]) ).
thf(238,plain,
( ( ( in @ sK3_SY33 @ ( setadjoin @ sK4_SY35 @ emptyset ) )
= ( in @ sK3_SY33 @ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[94,38]) ).
thf(239,plain,
( ( ( in @ sK3_SY33 @ ( setadjoin @ sK4_SY35 @ emptyset ) )
= ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= $false ),
inference(res,[status(thm)],[94,37]) ).
thf(241,plain,
( ( ( ( setadjoin @ sK4_SY35 @ emptyset )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false )
| ( ( sK3_SY33 = sK5_SY30 )
= $false ) ),
inference(extuni,[status(esa)],[239]) ).
thf(242,plain,
( ( ( setadjoin @ sK4_SY35 @ emptyset )
= sK1_SY0 )
= $false ),
inference(extuni,[status(esa)],[238]) ).
thf(243,plain,
( ( ( ( setadjoin @ sK4_SY35 @ emptyset )
= sK1_SY0 )
= $false )
| ( ( sK3_SY33 = sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[237]) ).
thf(244,plain,
! [SV19: $i > $o,SV17: $i] :
( ( ( in @ sK3_SY33 @ SV17 )
= $false )
| ( ( SV19 @ sK3_SY33 )
= $false )
| ( ( ( setadjoin @ sK4_SY35 @ emptyset )
= ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[233:[bind(SV18,$thf( sK3_SY33 ))]]) ).
thf(246,plain,
! [SV15: $i,SV16: $i] :
( ( ( ( ( setadjoin @ sK3_SY33 @ emptyset )
= sK1_SY0 )
= ( SV16 = SV15 ) )
= $false )
| ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= $false ) ),
inference(res,[status(thm)],[104,72]) ).
thf(252,plain,
( ( ( ( setadjoin @ sK3_SY33 @ emptyset )
= sK1_SY0 )
= ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) ) )
= $false ),
inference(res,[status(thm)],[104,36]) ).
thf(253,plain,
( ( ( sK3_SY33 = sK5_SY30 )
= $false )
| ( ( sK1_SY0
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[252]) ).
thf(254,plain,
( ( ( ( setadjoin @ sK3_SY33 @ emptyset )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK1_SY0
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[252]) ).
thf(255,plain,
( ( ( sK1_SY0
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( ( setadjoin @ sK3_SY33 @ emptyset )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[252]) ).
thf(256,plain,
( ( in @ sK1_SY0 @ ( setadjoin @ ( setadjoin @ sK3_SY33 @ emptyset ) @ emptyset ) )
= $false ),
inference(extuni,[status(esa)],[246:[bind(SV15,$thf( setadjoin @ sK3_SY33 @ emptyset )),bind(SV16,$thf( sK1_SY0 ))]]) ).
thf(257,plain,
( ( in @ ( setadjoin @ sK3_SY33 @ emptyset ) @ ( setadjoin @ sK1_SY0 @ emptyset ) )
= $false ),
inference(extuni,[status(esa)],[246:[bind(SV15,$thf( sK1_SY0 )),bind(SV16,$thf( setadjoin @ sK3_SY33 @ emptyset ))]]) ).
thf(259,plain,
! [SV15: $i,SV16: $i] :
( ( ( ( ( setadjoin @ sK4_SY35 @ emptyset )
= sK1_SY0 )
= ( SV16 = SV15 ) )
= $false )
| ( ( in @ SV16 @ ( setadjoin @ SV15 @ emptyset ) )
= $false ) ),
inference(res,[status(thm)],[242,72]) ).
thf(265,plain,
( ( ( ( setadjoin @ sK4_SY35 @ emptyset )
= sK1_SY0 )
= ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) )
= ( setadjoin @ sK5_SY30 @ emptyset ) ) )
= $false ),
inference(res,[status(thm)],[242,36]) ).
thf(266,plain,
( ( ( sK4_SY35 = sK5_SY30 )
= $false )
| ( ( sK1_SY0
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[265]) ).
thf(267,plain,
( ( ( ( setadjoin @ sK4_SY35 @ emptyset )
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( sK1_SY0
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[265]) ).
thf(268,plain,
( ( ( sK1_SY0
= ( setadjoin @ sK5_SY30 @ emptyset ) )
= $false )
| ( ( ( setadjoin @ sK4_SY35 @ emptyset )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[265]) ).
thf(269,plain,
( ( in @ sK1_SY0 @ ( setadjoin @ ( setadjoin @ sK4_SY35 @ emptyset ) @ emptyset ) )
= $false ),
inference(extuni,[status(esa)],[259:[bind(SV15,$thf( setadjoin @ sK4_SY35 @ emptyset )),bind(SV16,$thf( sK1_SY0 ))]]) ).
thf(270,plain,
( ( in @ ( setadjoin @ sK4_SY35 @ emptyset ) @ ( setadjoin @ sK1_SY0 @ emptyset ) )
= $false ),
inference(extuni,[status(esa)],[259:[bind(SV15,$thf( sK1_SY0 )),bind(SV16,$thf( setadjoin @ sK4_SY35 @ emptyset ))]]) ).
thf(271,plain,
! [SV17: $i,SV18: $i,SV19: $i > $o] :
( ( ( ( in @ sK1_SY0 @ ( setadjoin @ ( setadjoin @ sK3_SY33 @ emptyset ) @ emptyset ) )
= ( in @ SV18
@ ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) ) )
= $false )
| ( ( SV19 @ SV18 )
= $false )
| ( ( in @ SV18 @ SV17 )
= $false ) ),
inference(res,[status(thm)],[256,105]) ).
thf(275,plain,
( ( ( in @ sK1_SY0 @ ( setadjoin @ ( setadjoin @ sK3_SY33 @ emptyset ) @ emptyset ) )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[256,44]) ).
thf(276,plain,
( ( ( in @ sK1_SY0 @ ( setadjoin @ ( setadjoin @ sK3_SY33 @ emptyset ) @ emptyset ) )
= ( in @ sK3_SY33 @ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[256,38]) ).
thf(277,plain,
( ( ( in @ sK1_SY0 @ ( setadjoin @ ( setadjoin @ sK3_SY33 @ emptyset ) @ emptyset ) )
= ( in @ sK5_SY30
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) ) )
= $false ),
inference(res,[status(thm)],[256,37]) ).
thf(279,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK3_SY33 @ emptyset ) @ emptyset )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY24 @ SX0 ) ) )
= $false )
| ( ( sK1_SY0 = sK5_SY30 )
= $false ) ),
inference(extuni,[status(esa)],[277]) ).
thf(280,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK3_SY33 @ emptyset ) @ emptyset )
= sK1_SY0 )
= $false )
| ( ( sK1_SY0 = sK3_SY33 )
= $false ) ),
inference(extuni,[status(esa)],[276]) ).
thf(281,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK3_SY33 @ emptyset ) @ emptyset )
= sK1_SY0 )
= $false )
| ( ( sK1_SY0 = sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[275]) ).
thf(282,plain,
! [SV19: $i > $o,SV17: $i] :
( ( ( in @ sK1_SY0 @ SV17 )
= $false )
| ( ( SV19 @ sK1_SY0 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ sK3_SY33 @ emptyset ) @ emptyset )
= ( dsetconstr @ SV17
@ ^ [SX0: $i] : ( SV19 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[271:[bind(SV18,$thf( sK1_SY0 ))]]) ).
thf(283,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,282,281,280,279,270,269,268,267,266,257,256,255,254,253,244,243,242,241,232,231,230,229,228,227,226,225,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,128,105,104,103,102,94,93,92,91,81,80,79,72,71,70,69,68,67,66,65,56,54,49,44,38,37]) ).
thf(284,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU683^2 : 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
% 0.08/0.20 % Computer : n010.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 15:31:40 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.24/1.28
% 5.24/1.28 No.of.Axioms: 0
% 5.24/1.28
% 5.24/1.28 Length.of.Defs: 757
% 5.24/1.28
% 5.24/1.28 Contains.Choice.Funs: false
% 5.24/1.28 .......
% 5.24/1.28
% 5.24/1.28 ********************************
% 5.24/1.28 * All subproblems solved! *
% 5.24/1.28 ********************************
% 5.24/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:283,loop_count:15,foatp_calls:4,translation:fof_experiment)
% 5.24/1.28
% 5.24/1.28 %**** Beginning of derivation protocol ****
% 5.24/1.28 % SZS output start CNFRefutation
% See solution above
% 5.24/1.28
% 5.24/1.28 %**** End of derivation protocol ****
% 5.24/1.28 %**** no. of clauses in derivation: 236 ****
% 5.24/1.28 %**** clause counter: 283 ****
% 5.24/1.28
% 5.24/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:283,loop_count:15,foatp_calls:4,translation:fof_experiment)
%------------------------------------------------------------------------------