TSTP Solution File: SEU510^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU510^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:12:27 EDT 2022
% Result : Theorem 10.38s 10.62s
% Output : CNFRefutation 10.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 198 ( 42 unt; 13 typ; 3 def)
% Number of atoms : 1564 ( 598 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 2124 ( 103 ~; 322 |; 4 &;1670 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 175 ( 175 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 723 ( 286 ^ 437 !; 0 ?; 723 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i > $o ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_E,type,
sK4_E: $i > ( $i > $i ) > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: $i > ( $i > $i ) > ( $i > $i > $o ) > $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(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/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(1,conjecture,
( dsetconstrI
=> ( emptysetE
=> ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(2,negated_conjecture,
( ( dsetconstrI
=> ( emptysetE
=> ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ 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] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ! [SY0: $i,SY1: $i > $o,SY2: $i] :
( ( in @ SY2 @ SY0 )
=> ( ( SY1 @ SY2 )
=> ( ( dsetconstr @ SY0
@ ^ [Xy: $i] : ( SY1 @ Xy ) )
!= emptyset ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,dsetconstrI,emptysetE,nonempty]) ).
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] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY0: $i,SY1: $i > $o,SY2: $i] :
( ( in @ SY2 @ SY0 )
=> ( ( SY1 @ SY2 )
=> ( ( dsetconstr @ SY0
@ ^ [Xy: $i] : ( SY1 @ Xy ) )
!= emptyset ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [SY0: $i,SY1: $i > $o,SY2: $i] :
( ( in @ SY2 @ SY0 )
=> ( ( SY1 @ SY2 )
=> ( ( dsetconstr @ SY0
@ ^ [Xy: $i] : ( SY1 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( in @ sK3_SY17 @ sK1_SY0 )
& ( sK2_SY14 @ sK3_SY17 )
& ( ( dsetconstr @ sK1_SY0
@ ^ [SY18: $i] : ( sK2_SY14 @ SY18 ) )
= emptyset ) )
= $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] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $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,
( ( ( in @ sK3_SY17 @ sK1_SY0 )
& ( sK2_SY14 @ sK3_SY17 )
& ( ( dsetconstr @ sK1_SY0
@ ^ [SY18: $i] : ( sK2_SY14 @ SY18 ) )
= emptyset ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ( in @ sK3_SY17 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY14 @ sK3_SY17 )
| ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
!= emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,dsetconstrI,emptysetE,nonempty]) ).
thf(15,plain,
( ( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV1: $i] :
( ( ! [SY20: $i > $o,SY21: $i] :
( ~ ( in @ SY21 @ SV1 )
| ~ ( SY20 @ SY21 )
| ( in @ SY21
@ ( dsetconstr @ SV1
@ ^ [Xy: $i] : ( SY20 @ Xy ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( in @ sK3_SY17 @ sK1_SY0 )
| ~ ~ ( ~ ( sK2_SY14 @ sK3_SY17 )
| ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
!= emptyset ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i] :
( ( ( ~ ( in @ SV2 @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV3: $i > $o,SV1: $i] :
( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ SV1 )
| ~ ( SV3 @ SY23 )
| ( in @ SY23
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV3 @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( sK2_SY14 @ sK3_SY17 )
| ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
!= emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: $i] :
( ( ( in @ SV2 @ emptyset )
= $false )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: $i > $o,SV1: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV1 )
| ~ ( SV3 @ SV4 )
| ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV3 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( in @ sK3_SY17 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( sK2_SY14 @ sK3_SY17 )
| ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i,SV5: $o] :
( ( SV5 = $true )
| ( ( in @ SV2 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV2: $i] :
( ( $false = $true )
| ( ( in @ SV2 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV3: $i > $o,SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV1 ) )
= $true )
| ( ( ~ ( SV3 @ SV4 )
| ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV3 @ SY24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(30,plain,
( ( ~ ( sK2_SY14 @ sK3_SY17 )
| ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
!= emptyset ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV3: $i > $o,SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ SV1 )
= $false )
| ( ( ~ ( SV3 @ SV4 )
| ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV3 @ SY24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ( sK2_SY14 @ sK3_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(33,plain,
( ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
!= emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV1: $i,SV4: $i,SV3: $i > $o] :
( ( ( ~ ( SV3 @ SV4 ) )
= $true )
| ( ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV3 @ SY24 ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( sK2_SY14 @ sK3_SY17 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
= emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: $i,SV4: $i,SV3: $i > $o] :
( ( ( SV3 @ SV4 )
= $false )
| ( ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV3 @ SY24 ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV2: $i] :
( ( $false = $true )
| ( ( in @ SV2 @ emptyset )
= $false ) ),
inference(prim_subst,[status(thm)],[26:[bind(SV5,$thf( $false ))]]) ).
thf(41,plain,
! [SV1: $i,SV4: $i] :
( ( $true = $false )
| ( ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV9: $i] : $true ))]]) ).
thf(43,plain,
! [SV1: $i,SV4: $i,SV7: $i > $o] :
( ( ( ~ ( SV7 @ SV4 ) )
= $false )
| ( ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( SV7 @ SX0 ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV6: $i] : ~ ( SV7 @ SV6 ) ))]]) ).
thf(44,plain,
! [SV1: $i,SV4: $i] :
( ( ( SV4 = emptyset )
= $false )
| ( ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV10: $i] : ( SV10 = emptyset ) ))]]) ).
thf(45,plain,
! [SV1: $i,SV4: $i] :
( ( ( SV4 = sK1_SY0 )
= $false )
| ( ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] : ( SX0 = sK1_SY0 ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV11: $i] : ( SV11 = sK1_SY0 ) ))]]) ).
thf(46,plain,
! [SV1: $i,SV4: $i] :
( ( ( SV4 = sK3_SY17 )
= $false )
| ( ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] : ( SX0 = sK3_SY17 ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV12: $i] : ( SV12 = sK3_SY17 ) ))]]) ).
thf(47,plain,
! [SV2: $i,SV5: $o] :
( ( SV5 = $true )
| ( ( SV5
= ( ~ ( in @ SV2 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[26]) ).
thf(48,plain,
! [SV2: $i,SV5: $o] :
( ( ( ~ ( SV5
| ~ ( in @ SV2 @ emptyset ) )
| ~ ( ~ SV5
| ~ ~ ( in @ SV2 @ emptyset ) ) )
= $false )
| ( SV5 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[47]) ).
thf(49,plain,
! [SV2: $i,SV5: $o] :
( ( ( SV5
= ( ~ ( in @ SV2 @ emptyset ) ) )
= $false )
| ( SV5 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[47]) ).
thf(50,plain,
! [SV2: $i,SV5: $o] :
( ( ( ~ ( SV5
| ~ ( in @ SV2 @ emptyset ) ) )
= $false )
| ( SV5 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
! [SV2: $i,SV5: $o] :
( ( ( SV5
| ~ ( in @ SV2 @ emptyset ) )
= $true )
| ( SV5 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV2: $i,SV5: $o] :
( ( SV5 = $true )
| ( ( ~ ( in @ SV2 @ emptyset ) )
= $true )
| ( SV5 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV5: $o,SV2: $i] :
( ( ( in @ SV2 @ emptyset )
= $false )
| ( SV5 = $true )
| ( SV5 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV2: $i] :
( ( ~ ( in @ SV2 @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[49:[bind(SV5,$thf( ~ ( in @ SV2 @ emptyset ) ))]]) ).
thf(61,plain,
! [SV2: $i] :
( ( in @ SV2 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV1: $i,SV4: $i,SV7: $i > $o] :
( ( ( SV7 @ SV4 )
= $true )
| ( ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( SV7 @ SX0 ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(64,plain,
! [SV1: $i] :
( ( ( in @ emptyset @ SV1 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(extuni,[status(esa)],[44:[bind(SV4,$thf( emptyset ))]]) ).
thf(65,plain,
! [SV1: $i] :
( ( ( in @ sK1_SY0 @ SV1 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] : ( SX0 = sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[45:[bind(SV4,$thf( sK1_SY0 ))]]) ).
thf(66,plain,
! [SV1: $i] :
( ( ( in @ sK3_SY17 @ SV1 )
= $false )
| ( ( in @ sK3_SY17
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] : ( SX0 = sK3_SY17 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[46:[bind(SV4,$thf( sK3_SY17 ))]]) ).
thf(67,plain,
! [SV2: $i] :
( ( in @ SV2 @ emptyset )
= $false ),
inference(sim,[status(thm)],[28]) ).
thf(68,plain,
! [SV5: $o,SV2: $i] :
( ( ( in @ SV2 @ emptyset )
= $false )
| ( SV5 = $true ) ),
inference(sim,[status(thm)],[56]) ).
thf(69,plain,
! [SV2: $i] :
( ( in @ SV2 @ emptyset )
= $false ),
inference(sim,[status(thm)],[28]) ).
thf(70,plain,
! [SV2: $i] :
( ( in @ SV2 @ emptyset )
= $false ),
inference(sim,[status(thm)],[39]) ).
thf(71,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(sim,[status(thm)],[41]) ).
thf(72,plain,
! [SV14: $i,SV15: $o] :
( ( SV15 = $true )
| ( ( in @ SV14 @ emptyset )
= $false ) ),
inference(rename,[status(thm)],[26]) ).
thf(75,plain,
! [SV14: $i,SV15: $o] :
( ( ( ( in @ SV14 @ emptyset )
= ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false )
| ( SV15 = $true ) ),
inference(res,[status(thm)],[72,24]) ).
thf(77,plain,
! [SV14: $i] :
( ( $false = $true )
| ( ( in @ SV14 @ emptyset )
= $false ) ),
inference(prim_subst,[status(thm)],[72:[bind(SV15,$thf( $false ))]]) ).
thf(78,plain,
! [SV14: $i] :
( ( in @ SV14 @ emptyset )
= $false ),
inference(sim,[status(thm)],[77]) ).
thf(79,plain,
! [SV14: $i,SV16: $o] :
( ( ( ~ SV16 )
= $true )
| ( ( in @ SV14 @ emptyset )
= $false ) ),
inference(prim_subst,[status(thm)],[72:[bind(SV15,$thf( ~ ( SV16 ) ))]]) ).
thf(80,plain,
! [SV14: $i,SV20: $o,SV19: $o] :
( ( ( SV19
| SV20 )
= $true )
| ( ( in @ SV14 @ emptyset )
= $false ) ),
inference(prim_subst,[status(thm)],[72:[bind(SV15,$thf( SV19 | SV20 ))]]) ).
thf(81,plain,
! [SV14: $i,SV18: $i,SV17: $i] :
( ( ( SV17 = SV18 )
= $true )
| ( ( in @ SV14 @ emptyset )
= $false ) ),
inference(prim_subst,[status(thm)],[72:[bind(SV15,$thf( SV17 = SV18 ))]]) ).
thf(82,plain,
! [SV14: $i,SV15: $o] :
( ( SV15 = $true )
| ( ( SV15
= ( ~ ( in @ SV14 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[72]) ).
thf(83,plain,
! [SV15: $o] :
( ( SV15 = $true )
| ( ( emptyset = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[75:[bind(SV14,$thf( sK3_SY17 ))]]) ).
thf(86,plain,
! [SV14: $i] :
( ( ~ ( in @ SV14 @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[82:[bind(SV15,$thf( ~ ( in @ SV14 @ emptyset ) ))]]) ).
thf(87,plain,
! [SV14: $i,SV16: $o] :
( ( SV16 = $false )
| ( ( in @ SV14 @ emptyset )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV14: $i,SV20: $o,SV19: $o] :
( ( SV19 = $true )
| ( SV20 = $true )
| ( ( in @ SV14 @ emptyset )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV14: $i] :
( ( in @ SV14 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(rename,[status(thm)],[37]) ).
thf(97,plain,
! [SV33: $i,SV34: $i,SV35: $i > $o,SV14: $i,SV15: $o] :
( ( ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= ( in @ SV14 @ emptyset ) )
= $false )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34 @ SV33 )
= $false )
| ( SV15 = $true ) ),
inference(res,[status(thm)],[92,72]) ).
thf(98,plain,
! [SV33: $i,SV34: $i,SV35: $i > $o,SV14: $i,SV15: $o] :
( ( ( ( in @ SV34 @ SV33 )
= SV15 )
= $false )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( in @ SV14 @ emptyset )
= $false ) ),
inference(res,[status(thm)],[92,72]) ).
thf(99,plain,
! [SV33: $i,SV34: $i,SV35: $i > $o,SV14: $i,SV15: $o] :
( ( ( ( SV35 @ SV34 )
= SV15 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV14 @ emptyset )
= $false ) ),
inference(res,[status(thm)],[92,72]) ).
thf(101,plain,
! [SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( SV35 @ SV34 )
= ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
= emptyset ) )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(res,[status(thm)],[92,36]) ).
thf(103,plain,
! [SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( SV35 @ SV34 )
= ( sK2_SY14 @ sK3_SY17 ) )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(res,[status(thm)],[92,35]) ).
thf(104,plain,
! [SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( in @ SV34 @ SV33 )
= ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[92,24]) ).
thf(105,plain,
! [SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( SV35 @ SV34 )
= ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(res,[status(thm)],[92,24]) ).
thf(106,plain,
! [SV33: $i,SV34: $i] :
( ( $true = $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV35,$thf( ^ [SV39: $i] : $true ))]]) ).
thf(107,plain,
! [SV33: $i,SV34: $i] :
( ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : $true ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(sim,[status(thm)],[106]) ).
thf(109,plain,
! [SV33: $i,SV34: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ SV34 ) )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
~ ( SV37 @ SX0 ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV35,$thf( ^ [SV36: $i] : ~ ( SV37 @ SV36 ) ))]]) ).
thf(110,plain,
! [SV33: $i,SV34: $i] :
( ( ( SV34 = sK3_SY17 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SX0 = sK3_SY17 ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV35,$thf( ^ [SV40: $i] : ( SV40 = sK3_SY17 ) ))]]) ).
thf(111,plain,
! [SV33: $i,SV34: $i] :
( ( ( SV34 = emptyset )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV35,$thf( ^ [SV41: $i] : ( SV41 = emptyset ) ))]]) ).
thf(112,plain,
! [SV33: $i,SV34: $i] :
( ( ( SV34 = sK1_SY0 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SX0 = sK1_SY0 ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV35,$thf( ^ [SV42: $i] : ( SV42 = sK1_SY0 ) ))]]) ).
thf(113,plain,
! [SV33: $i,SV49: $i > $o,SV34: $i,SV48: $i > $o] :
( ( ( ( SV48 @ SV34 )
| ( SV49 @ SV34 ) )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( SV48 @ SX0 )
| ( SV49 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV35,$thf( ^ [SV47: $i] : ( ( SV48 @ SV47 ) | ( SV49 @ SV47 ) ) ))]]) ).
thf(115,plain,
! [SV33: $i] :
( ( ( in @ sK3_SY17 @ SV33 )
= $false )
| ( ( in @ sK3_SY17
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( in @ SX0 @ SX0 ) ) )
= $true )
| ( ( sK3_SY17 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[105:[bind(SV34,$thf( sK3_SY17 )),bind(SV35,$thf( ^ [SX0: $i] : ( in @ SX0 @ SX0 ) ))]]) ).
thf(116,plain,
! [SV33: $i] :
( ( ( in @ sK3_SY17 @ SV33 )
= $false )
| ( ( in @ sK3_SY17
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( in @ SX0 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[105:[bind(SV34,$thf( sK3_SY17 )),bind(SV35,$thf( ^ [SX0: $i] : ( in @ SX0 @ sK1_SY0 ) ))]]) ).
thf(117,plain,
! [SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( in @ sK3_SY17 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[105:[bind(SV34,$thf( sK1_SY0 )),bind(SV35,$thf( ^ [SX0: $i] : ( in @ sK3_SY17 @ SX0 ) ))]]) ).
thf(118,plain,
! [SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( in @ sK3_SY17 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[105:[bind(SV35,$thf( ^ [SX0: $i] : ( in @ sK3_SY17 @ sK1_SY0 ) ))]]) ).
thf(119,plain,
! [SV72: $i > $i,SV71: $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( in @ ( SV71 @ SX0 ) @ ( SV72 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV71 @ SV34 ) @ ( SV72 @ SV34 ) )
= $true )
| ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[105:[bind(SV35,$thf( ^ [SX0: $i] : ( in @ ( SV71 @ SX0 ) @ ( SV72 @ SX0 ) ) ))]]) ).
thf(120,plain,
! [SV72: $i > $i,SV71: $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( in @ ( SV71 @ SX0 ) @ ( SV72 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV71 @ SV34 ) @ ( SV72 @ SV34 ) )
= $false )
| ( ( in @ sK3_SY17 @ sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[105:[bind(SV35,$thf( ^ [SX0: $i] : ( in @ ( SV71 @ SX0 ) @ ( SV72 @ SX0 ) ) ))]]) ).
thf(121,plain,
! [SV35: $i > $o] :
( ( ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( SV35 @ sK3_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[104:[bind(SV33,$thf( sK1_SY0 )),bind(SV34,$thf( sK3_SY17 ))]]) ).
thf(122,plain,
! [SV33: $i] :
( ( ( in @ sK3_SY17 @ SV33 )
= $false )
| ( ( in @ sK3_SY17
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[103:[bind(SV34,$thf( sK3_SY17 )),bind(SV35,$thf( ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) ))]]) ).
thf(123,plain,
! [SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( sK2_SY14 @ sK3_SY17 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[103:[bind(SV35,$thf( ^ [SX0: $i] : ( sK2_SY14 @ sK3_SY17 ) ))]]) ).
thf(124,plain,
! [SV81: $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( sK2_SY14 @ ( SV81 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY14 @ ( SV81 @ SV34 ) )
= $true )
| ( ( sK2_SY14 @ sK3_SY17 )
= $true ) ),
inference(extuni,[status(esa)],[103:[bind(SV35,$thf( ^ [SX0: $i] : ( sK2_SY14 @ ( SV81 @ SX0 ) ) ))]]) ).
thf(125,plain,
! [SV81: $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( sK2_SY14 @ ( SV81 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY14 @ ( SV81 @ SV34 ) )
= $false )
| ( ( sK2_SY14 @ sK3_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[103:[bind(SV35,$thf( ^ [SX0: $i] : ( sK2_SY14 @ ( SV81 @ SX0 ) ) ))]]) ).
thf(126,plain,
! [SV121: $i > $i > $i,SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK1_SY0 = emptyset )
= $false )
| ( ( sK2_SY14
@ ( SV121 @ sK1_SY0
@ ( sK5_E @ SV33
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( sK5_E @ SV33
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( sK1_SY0 )),bind(SV35,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(127,plain,
! [SV121: $i > $i > $i,SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( emptyset
= ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV121 @ sK1_SY0
@ ( sK5_E @ SV33
@ ^ [SX0: $i] : emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( sK5_E @ SV33
@ ^ [SX0: $i] : emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( sK1_SY0 )),bind(SV35,$thf( ^ [SX0: $i] : ( emptyset = ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(128,plain,
! [SV121: $i > $i > $i,SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK1_SY0 = emptyset )
= $false )
| ( ( sK2_SY14
@ ( SV121 @ sK1_SY0
@ ( sK5_E @ SV33
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY14
@ ( sK5_E @ SV33
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( sK1_SY0 )),bind(SV35,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(129,plain,
! [SV121: $i > $i > $i,SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( emptyset
= ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV121 @ sK1_SY0
@ ( sK5_E @ SV33
@ ^ [SX0: $i] : emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY14
@ ( sK5_E @ SV33
@ ^ [SX0: $i] : emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( sK1_SY0 )),bind(SV35,$thf( ^ [SX0: $i] : ( emptyset = ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV121 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(130,plain,
! [SV100: $i > $i > $i,SV33: $i] :
( ( ( in @ emptyset @ SV33 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV100 @ emptyset
@ ( sK4_E @ SV33
@ ^ [SX0: $i] : SX0
@ emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( sK4_E @ SV33
@ ^ [SX0: $i] : SX0
@ emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( emptyset )),bind(SV35,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(131,plain,
! [SV100: $i > $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( emptyset
= ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV100 @ SV34
@ ( sK4_E @ SV33
@ ^ [SX0: $i] : emptyset
@ SV34
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( sK4_E @ SV33
@ ^ [SX0: $i] : emptyset
@ SV34
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV35,$thf( ^ [SX0: $i] : ( emptyset = ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(132,plain,
! [SV100: $i > $i > $i,SV33: $i] :
( ( ( in @ emptyset @ SV33 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV100 @ emptyset
@ ( sK4_E @ SV33
@ ^ [SX0: $i] : SX0
@ emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY14
@ ( sK4_E @ SV33
@ ^ [SX0: $i] : SX0
@ emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( emptyset )),bind(SV35,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(133,plain,
! [SV100: $i > $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( emptyset
= ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV100 @ SV34
@ ( sK4_E @ SV33
@ ^ [SX0: $i] : emptyset
@ SV34
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY14
@ ( sK4_E @ SV33
@ ^ [SX0: $i] : emptyset
@ SV34
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV35,$thf( ^ [SX0: $i] : ( emptyset = ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV100 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(134,plain,
! [SV91: $i > $i > $o,SV90: $i > $i,SV33: $i] :
( ( ( in @ emptyset @ SV33 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( SX0
= ( dsetconstr @ ( SV90 @ SX0 ) @ ( SV91 @ SX0 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV90 @ emptyset ) @ ( SV91 @ emptyset ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( emptyset )),bind(SV35,$thf( ^ [SX0: $i] : ( SX0 = ( dsetconstr @ ( SV90 @ SX0 ) @ ( SV91 @ SX0 ) ) ) ))]]) ).
thf(135,plain,
! [SV91: $i > $i > $o,SV90: $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( emptyset
= ( dsetconstr @ ( SV90 @ SX0 ) @ ( SV91 @ SX0 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV90 @ SV34 ) @ ( SV91 @ SV34 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV35,$thf( ^ [SX0: $i] : ( emptyset = ( dsetconstr @ ( SV90 @ SX0 ) @ ( SV91 @ SX0 ) ) ) ))]]) ).
thf(136,plain,
! [SV33: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
@ SV33 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SX0 = SX0 ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
= emptyset )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )),bind(SV35,$thf( ^ [SX0: $i] : ( SX0 = SX0 ) ))]]) ).
thf(137,plain,
! [SV33: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
@ SV33 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( emptyset = SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )),bind(SV35,$thf( ^ [SX0: $i] : ( emptyset = SX0 ) ))]]) ).
thf(138,plain,
! [SV174: $i > $i > $i,SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) )
= SX0 ) ) )
= $true )
| ( ( sK1_SY0 = emptyset )
= $false )
| ( ( sK2_SY14
@ ( SV174 @ sK1_SY0
@ ( sK7_E @ SV33
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( sK7_E @ SV33
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( sK1_SY0 )),bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) = SX0 ) ))]]) ).
thf(139,plain,
! [SV174: $i > $i > $i,SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) )
= emptyset ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV174 @ sK1_SY0
@ ( sK7_E @ SV33
@ ^ [SX0: $i] : emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( sK7_E @ SV33
@ ^ [SX0: $i] : emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( sK1_SY0 )),bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) = emptyset ) ))]]) ).
thf(140,plain,
! [SV174: $i > $i > $i,SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) )
= SX0 ) ) )
= $true )
| ( ( sK1_SY0 = emptyset )
= $false )
| ( ( sK2_SY14
@ ( SV174 @ sK1_SY0
@ ( sK7_E @ SV33
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY14
@ ( sK7_E @ SV33
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( sK1_SY0 )),bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) = SX0 ) ))]]) ).
thf(141,plain,
! [SV174: $i > $i > $i,SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) )
= emptyset ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV174 @ sK1_SY0
@ ( sK7_E @ SV33
@ ^ [SX0: $i] : emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY14
@ ( sK7_E @ SV33
@ ^ [SX0: $i] : emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( sK1_SY0 )),bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ SX0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV174 @ SX0 @ SX1 ) ) ) = emptyset ) ))]]) ).
thf(142,plain,
! [SV153: $i > $i > $i,SV33: $i] :
( ( ( in @ emptyset @ SV33 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) )
= SX0 ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV153 @ emptyset
@ ( sK6_E @ SV33
@ ^ [SX0: $i] : SX0
@ emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( sK6_E @ SV33
@ ^ [SX0: $i] : SX0
@ emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( emptyset )),bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) = SX0 ) ))]]) ).
thf(143,plain,
! [SV153: $i > $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) )
= emptyset ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV153 @ SV34
@ ( sK6_E @ SV33
@ ^ [SX0: $i] : emptyset
@ SV34
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( sK2_SY14
@ ( sK6_E @ SV33
@ ^ [SX0: $i] : emptyset
@ SV34
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) = emptyset ) ))]]) ).
thf(144,plain,
! [SV153: $i > $i > $i,SV33: $i] :
( ( ( in @ emptyset @ SV33 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) )
= SX0 ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV153 @ emptyset
@ ( sK6_E @ SV33
@ ^ [SX0: $i] : SX0
@ emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY14
@ ( sK6_E @ SV33
@ ^ [SX0: $i] : SX0
@ emptyset
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( emptyset )),bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) = SX0 ) ))]]) ).
thf(145,plain,
! [SV153: $i > $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ sK1_SY0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) )
= emptyset ) ) )
= $true )
| ( ( sK2_SY14
@ ( SV153 @ SV34
@ ( sK6_E @ SV33
@ ^ [SX0: $i] : emptyset
@ SV34
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( sK2_SY14
@ ( sK6_E @ SV33
@ ^ [SX0: $i] : emptyset
@ SV34
@ ^ [SX0: $i,SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ sK1_SY0 @ ^ [SX1: $i] : ( sK2_SY14 @ ( SV153 @ SX0 @ SX1 ) ) ) = emptyset ) ))]]) ).
thf(146,plain,
! [SV144: $i > $i > $o,SV143: $i > $i,SV33: $i] :
( ( ( in @ emptyset @ SV33 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ ( SV143 @ SX0 ) @ ( SV144 @ SX0 ) )
= SX0 ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV143 @ emptyset ) @ ( SV144 @ emptyset ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( emptyset )),bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ ( SV143 @ SX0 ) @ ( SV144 @ SX0 ) ) = SX0 ) ))]]) ).
thf(147,plain,
! [SV144: $i > $i > $o,SV143: $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( dsetconstr @ ( SV143 @ SX0 ) @ ( SV144 @ SX0 ) )
= emptyset ) ) )
= $true )
| ( ( ( dsetconstr @ ( SV143 @ SV34 ) @ ( SV144 @ SV34 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV35,$thf( ^ [SX0: $i] : ( ( dsetconstr @ ( SV143 @ SX0 ) @ ( SV144 @ SX0 ) ) = emptyset ) ))]]) ).
thf(148,plain,
! [SV33: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
@ SV33 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SX0 = SX0 ) ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
= emptyset )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )),bind(SV35,$thf( ^ [SX0: $i] : ( SX0 = SX0 ) ))]]) ).
thf(149,plain,
! [SV33: $i] :
( ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
@ SV33 )
= $false )
| ( ( in
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV34,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )),bind(SV35,$thf( ^ [SX0: $i] : ( SX0 = emptyset ) ))]]) ).
thf(150,plain,
! [SV87: $i > $i,SV86: $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( SV86 @ SX0 )
= ( SV87 @ SX0 ) ) ) )
= $true )
| ( ( ( SV86 @ SV34 )
= ( SV87 @ SV34 ) )
= $true )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
= emptyset )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV35,$thf( ^ [SX0: $i] : ( ( SV86 @ SX0 ) = ( SV87 @ SX0 ) ) ))]]) ).
thf(151,plain,
! [SV87: $i > $i,SV86: $i > $i,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( SV86 @ SX0 )
= ( SV87 @ SX0 ) ) ) )
= $true )
| ( ( ( SV86 @ SV34 )
= ( SV87 @ SV34 ) )
= $false )
| ( ( ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( sK2_SY14 @ SX0 ) )
= emptyset )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV35,$thf( ^ [SX0: $i] : ( ( SV86 @ SX0 ) = ( SV87 @ SX0 ) ) ))]]) ).
thf(152,plain,
! [SV35: $i > $o,SV33: $i,SV34: $i,SV14: $i] :
( ( ( in @ SV14 @ emptyset )
= $false )
| ( ( in @ SV34 @ SV33 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[99:[bind(SV15,$thf( SV35 @ SV34 ))]]) ).
thf(153,plain,
! [SV35: $i > $o,SV33: $i,SV34: $i,SV14: $i] :
( ( ( in @ SV14 @ emptyset )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( SV35 @ SV34 )
= $false ) ),
inference(extuni,[status(esa)],[98:[bind(SV15,$thf( in @ SV34 @ SV33 ))]]) ).
thf(154,plain,
! [SV35: $i > $o,SV33: $i,SV14: $i,SV15: $o] :
( ( SV15 = $true )
| ( ( in @ SV14 @ SV33 )
= $false )
| ( ( SV35 @ SV14 )
= $false )
| ( ( ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) )
= emptyset )
= $false ) ),
inference(extuni,[status(esa)],[97:[bind(SV34,$thf( SV14 ))]]) ).
thf(157,plain,
! [SV33: $i] :
( ( ( in @ sK3_SY17 @ SV33 )
= $false )
| ( ( in @ sK3_SY17
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SX0 = sK3_SY17 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[110:[bind(SV34,$thf( sK3_SY17 ))]]) ).
thf(158,plain,
! [SV33: $i] :
( ( ( in @ emptyset @ SV33 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(extuni,[status(esa)],[111:[bind(SV34,$thf( emptyset ))]]) ).
thf(159,plain,
! [SV33: $i] :
( ( ( in @ sK1_SY0 @ SV33 )
= $false )
| ( ( in @ sK1_SY0
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SX0 = sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[112:[bind(SV34,$thf( sK1_SY0 ))]]) ).
thf(160,plain,
! [SV33: $i,SV34: $i,SV37: $i > $o] :
( ( ( SV37 @ SV34 )
= $true )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
~ ( SV37 @ SX0 ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(161,plain,
! [SV49: $i > $o,SV33: $i,SV34: $i,SV48: $i > $o] :
( ( ( SV48 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( SV48 @ SX0 )
| ( SV49 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(162,plain,
! [SV48: $i > $o,SV33: $i,SV34: $i,SV49: $i > $o] :
( ( ( SV49 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] :
( ( SV48 @ SX0 )
| ( SV49 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(163,plain,
! [SV198: $i] :
( ( in @ SV198 @ emptyset )
= $false ),
inference(rename,[status(thm)],[61]) ).
thf(164,plain,
! [SV198: $i,SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( in @ SV198 @ emptyset )
= ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) ) )
= $false )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(res,[status(thm)],[163,92]) ).
thf(167,plain,
! [SV198: $i] :
( ( ( in @ SV198 @ emptyset )
= ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[163,24]) ).
thf(168,plain,
( ( emptyset = sK1_SY0 )
= $false ),
inference(extuni,[status(esa)],[167:[bind(SV198,$thf( sK3_SY17 ))]]) ).
thf(169,plain,
! [SV35: $i > $o,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( SV35 @ SV34 )
= $false )
| ( ( emptyset
= ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[164:[bind(SV198,$thf( SV34 ))]]) ).
thf(171,plain,
! [SV201: $i,SV202: $i,SV203: $i > $o] :
( ( ( SV203 @ SV202 )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(rename,[status(thm)],[63]) ).
thf(176,plain,
! [SV201: $i,SV202: $i,SV203: $i > $o,SV198: $i] :
( ( ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= ( in @ SV198 @ emptyset ) )
= $false )
| ( ( SV203 @ SV202 )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(res,[status(thm)],[171,163]) ).
thf(177,plain,
! [SV201: $i,SV202: $i,SV203: $i > $o,SV198: $i] :
( ( ( ( SV203 @ SV202 )
= ( in @ SV198 @ emptyset ) )
= $false )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(res,[status(thm)],[171,163]) ).
thf(178,plain,
! [SV201: $i,SV202: $i,SV203: $i > $o,SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= ( in @ SV34 @ SV33 ) )
= $false )
| ( ( SV203 @ SV202 )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[171,92]) ).
thf(179,plain,
! [SV201: $i,SV202: $i,SV203: $i > $o,SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( SV203 @ SV202 )
= ( in @ SV34 @ SV33 ) )
= $false )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[171,92]) ).
thf(180,plain,
! [SV201: $i,SV202: $i,SV203: $i > $o,SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( in @ SV202 @ SV201 )
= ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) ) )
= $false )
| ( ( SV203 @ SV202 )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= $true )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(res,[status(thm)],[171,92]) ).
thf(185,plain,
! [SV201: $i,SV202: $i,SV203: $i > $o] :
( ( ( ( in @ SV202 @ SV201 )
= ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false )
| ( ( SV203 @ SV202 )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[171,24]) ).
thf(187,plain,
! [SV201: $i,SV202: $i] :
( ( $false = $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] : ~ $false ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(prim_subst,[status(thm)],[171:[bind(SV203,$thf( ^ [SV206: $i] : $false ))]]) ).
thf(188,plain,
! [SV201: $i,SV202: $i] :
( ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] : ~ $false ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(sim,[status(thm)],[187]) ).
thf(189,plain,
! [SV201: $i,SV202: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ SV202 ) )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ~ ( SV205 @ SX0 ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(prim_subst,[status(thm)],[171:[bind(SV203,$thf( ^ [SV204: $i] : ~ ( SV205 @ SV204 ) ))]]) ).
thf(190,plain,
! [SV201: $i,SV202: $i] :
( ( ( SV202 = sK1_SY0 )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] : ( SX0 != sK1_SY0 ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(prim_subst,[status(thm)],[171:[bind(SV203,$thf( ^ [SV208: $i] : ( SV208 = sK1_SY0 ) ))]]) ).
thf(191,plain,
! [SV201: $i,SV202: $i] :
( ( ( SV202 = sK3_SY17 )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] : ( SX0 != sK3_SY17 ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(prim_subst,[status(thm)],[171:[bind(SV203,$thf( ^ [SV209: $i] : ( SV209 = sK3_SY17 ) ))]]) ).
thf(192,plain,
! [SV201: $i,SV202: $i] :
( ( ( SV202 = emptyset )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] : ( SX0 != emptyset ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(prim_subst,[status(thm)],[171:[bind(SV203,$thf( ^ [SV210: $i] : ( SV210 = emptyset ) ))]]) ).
thf(193,plain,
! [SV201: $i,SV217: $i > $o,SV202: $i,SV216: $i > $o] :
( ( ( ( SV216 @ SV202 )
| ( SV217 @ SV202 ) )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( ( SV216 @ SX0 )
| ( SV217 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(prim_subst,[status(thm)],[171:[bind(SV203,$thf( ^ [SV215: $i] : ( ( SV216 @ SV215 ) | ( SV217 @ SV215 ) ) ))]]) ).
thf(194,plain,
! [SV201: $i,SV214: $i > $i,SV202: $i,SV213: $i > $i] :
( ( ( ( SV213 @ SV202 )
= ( SV214 @ SV202 ) )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
( ( SV213 @ SX0 )
!= ( SV214 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(prim_subst,[status(thm)],[171:[bind(SV203,$thf( ^ [SV212: $i] : ( ( SV213 @ SV212 ) = ( SV214 @ SV212 ) ) ))]]) ).
thf(195,plain,
! [SV203: $i > $o] :
( ( ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= $true )
| ( ( SV203 @ sK3_SY17 )
= $true ) ),
inference(extuni,[status(esa)],[185:[bind(SV201,$thf( sK1_SY0 )),bind(SV202,$thf( sK3_SY17 ))]]) ).
thf(196,plain,
! [SV203: $i > $o,SV35: $i > $o,SV33: $i,SV34: $i] :
( ( ( in @ SV34 @ SV33 )
= $false )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) )
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= $true )
| ( ( SV203 @ SV34 )
= $true ) ),
inference(extuni,[status(esa)],[180:[bind(SV201,$thf( dsetconstr @ SV33 @ ^ [SX0: $i] : ( SV35 @ SX0 ) )),bind(SV202,$thf( SV34 ))]]) ).
thf(197,plain,
! [SV201: $i,SV35: $i > $o,SV240: $i > $i,SV202: $i,SV239: $i > $i] :
( ( ( in @ ( SV239 @ SV202 )
@ ( dsetconstr @ ( SV240 @ SV202 )
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( SV35 @ ( SV239 @ SV202 ) )
= $false )
| ( ( in @ SV202 @ SV201 )
= $false )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( in @ ( SV239 @ SX0 ) @ ( SV240 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[179:[bind(SV33,$thf( SV240 @ SV202 )),bind(SV34,$thf( SV239 @ SV202 )),bind(SV203,$thf( ^ [SX0: $i] : ( in @ ( SV239 @ SX0 ) @ ( SV240 @ SX0 ) ) ))]]) ).
thf(198,plain,
! [SV240: $i > $i,SV239: $i > $i,SV201: $i,SV202: $i,SV35: $i > $o,SV33: $i,SV34: $i] :
( ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV202 @ SV201 )
= $false )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( in @ ( SV239 @ SX0 ) @ ( SV240 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV239 @ SV202 ) @ ( SV240 @ SV202 ) )
= $true )
| ( ( in @ SV34 @ SV33 )
= $true ) ),
inference(extuni,[status(esa)],[179:[bind(SV203,$thf( ^ [SX0: $i] : ( in @ ( SV239 @ SX0 ) @ ( SV240 @ SX0 ) ) ))]]) ).
thf(199,plain,
! [SV240: $i > $i,SV239: $i > $i,SV201: $i,SV202: $i,SV35: $i > $o,SV33: $i,SV34: $i] :
( ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV202 @ SV201 )
= $false )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( in @ ( SV239 @ SX0 ) @ ( SV240 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV239 @ SV202 ) @ ( SV240 @ SV202 ) )
= $false )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(extuni,[status(esa)],[179:[bind(SV203,$thf( ^ [SX0: $i] : ( in @ ( SV239 @ SX0 ) @ ( SV240 @ SX0 ) ) ))]]) ).
thf(200,plain,
! [SV35: $i > $o,SV203: $i > $o,SV201: $i,SV34: $i] :
( ( ( in @ SV34
@ ( dsetconstr
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) )
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34 @ SV201 )
= $false )
| ( ( SV203 @ SV34 )
= $true ) ),
inference(extuni,[status(esa)],[178:[bind(SV33,$thf( dsetconstr @ SV201 @ ^ [SX0: $i] : ~ ( SV203 @ SX0 ) )),bind(SV202,$thf( SV34 ))]]) ).
thf(201,plain,
! [SV243: $i > $i,SV201: $i] :
( ( ( in @ emptyset @ SV201 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( in @ ( SV243 @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[177:[bind(SV202,$thf( emptyset )),bind(SV198,$thf( SV243 @ emptyset )),bind(SV203,$thf( ^ [SX0: $i] : ( in @ ( SV243 @ SX0 ) @ SX0 ) ))]]) ).
thf(202,plain,
! [SV243: $i > $i,SV201: $i,SV202: $i] :
( ( ( in @ SV202 @ SV201 )
= $false )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( in @ ( SV243 @ SX0 ) @ emptyset ) ) )
= $true ) ),
inference(extuni,[status(esa)],[177:[bind(SV198,$thf( SV243 @ SV202 )),bind(SV203,$thf( ^ [SX0: $i] : ( in @ ( SV243 @ SX0 ) @ emptyset ) ))]]) ).
thf(203,plain,
! [SV198: $i,SV244: $i > $i,SV243: $i > $i,SV201: $i,SV202: $i] :
( ( ( in @ SV202 @ SV201 )
= $false )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( in @ ( SV243 @ SX0 ) @ ( SV244 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV243 @ SV202 ) @ ( SV244 @ SV202 ) )
= $true )
| ( ( in @ SV198 @ emptyset )
= $true ) ),
inference(extuni,[status(esa)],[177:[bind(SV203,$thf( ^ [SX0: $i] : ( in @ ( SV243 @ SX0 ) @ ( SV244 @ SX0 ) ) ))]]) ).
thf(204,plain,
! [SV198: $i,SV244: $i > $i,SV243: $i > $i,SV201: $i,SV202: $i] :
( ( ( in @ SV202 @ SV201 )
= $false )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( in @ ( SV243 @ SX0 ) @ ( SV244 @ SX0 ) ) ) )
= $true )
| ( ( in @ ( SV243 @ SV202 ) @ ( SV244 @ SV202 ) )
= $false )
| ( ( in @ SV198 @ emptyset )
= $false ) ),
inference(extuni,[status(esa)],[177:[bind(SV203,$thf( ^ [SX0: $i] : ( in @ ( SV243 @ SX0 ) @ ( SV244 @ SX0 ) ) ))]]) ).
thf(205,plain,
! [SV203: $i > $o,SV201: $i,SV198: $i] :
( ( ( in @ SV198 @ SV201 )
= $false )
| ( ( SV203 @ SV198 )
= $true )
| ( ( ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) )
= emptyset )
= $false ) ),
inference(extuni,[status(esa)],[176:[bind(SV202,$thf( SV198 ))]]) ).
thf(208,plain,
! [SV201: $i,SV202: $i,SV205: $i > $o] :
( ( ( SV205 @ SV202 )
= $false )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ~ ( SV205 @ SX0 ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(209,plain,
! [SV201: $i,SV217: $i > $o,SV202: $i,SV216: $i > $o] :
( ( ( SV216 @ SV202 )
= $true )
| ( ( SV217 @ SV202 )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( ( SV216 @ SX0 )
| ( SV217 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(210,plain,
! [SV251: $i] :
( ( ( in @ emptyset @ SV251 )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(rename,[status(thm)],[64]) ).
thf(213,plain,
! [SV251: $i,SV201: $i,SV202: $i,SV203: $i > $o] :
( ( ( ( in @ emptyset
@ ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= ( in @ SV202 @ SV201 ) )
= $false )
| ( ( in @ emptyset @ SV251 )
= $false )
| ( ( SV203 @ SV202 )
= $true )
| ( ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[210,171]) ).
thf(214,plain,
! [SV251: $i,SV201: $i,SV202: $i,SV203: $i > $o] :
( ( ( ( in @ emptyset @ SV251 )
= ( in @ SV202
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) ) )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true )
| ( ( SV203 @ SV202 )
= $true )
| ( ( in @ SV202 @ SV201 )
= $false ) ),
inference(res,[status(thm)],[210,171]) ).
thf(216,plain,
! [SV251: $i,SV198: $i] :
( ( ( ( in @ emptyset
@ ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= ( in @ SV198 @ emptyset ) )
= $false )
| ( ( in @ emptyset @ SV251 )
= $false ) ),
inference(res,[status(thm)],[210,163]) ).
thf(217,plain,
! [SV251: $i,SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( in @ emptyset
@ ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= ( in @ SV34 @ SV33 ) )
= $false )
| ( ( in @ emptyset @ SV251 )
= $false )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[210,92]) ).
thf(218,plain,
! [SV251: $i,SV33: $i,SV34: $i,SV35: $i > $o] :
( ( ( ( in @ emptyset @ SV251 )
= ( in @ SV34
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) ) )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true )
| ( ( SV35 @ SV34 )
= $false )
| ( ( in @ SV34 @ SV33 )
= $false ) ),
inference(res,[status(thm)],[210,92]) ).
thf(222,plain,
! [SV251: $i] :
( ( ( ( in @ emptyset @ SV251 )
= ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(res,[status(thm)],[210,24]) ).
thf(223,plain,
( ( ( in @ emptyset
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true )
| ( ( emptyset = sK3_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[222:[bind(SV251,$thf( sK1_SY0 ))]]) ).
thf(224,plain,
! [SV35: $i > $o,SV33: $i] :
( ( ( in @ emptyset @ SV33 )
= $false )
| ( ( SV35 @ emptyset )
= $false )
| ( ( in @ emptyset
@ ( dsetconstr
@ ( dsetconstr @ SV33
@ ^ [SX0: $i] : ( SV35 @ SX0 ) )
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(extuni,[status(esa)],[218:[bind(SV251,$thf( dsetconstr @ SV33 @ ^ [SX0: $i] : ( SV35 @ SX0 ) )),bind(SV34,$thf( emptyset ))]]) ).
thf(225,plain,
! [SV35: $i > $o,SV251: $i] :
( ( ( in @ emptyset
@ ( dsetconstr
@ ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
@ ^ [SX0: $i] : ( SV35 @ SX0 ) ) )
= $true )
| ( ( SV35 @ emptyset )
= $false )
| ( ( in @ emptyset @ SV251 )
= $false ) ),
inference(extuni,[status(esa)],[217:[bind(SV33,$thf( dsetconstr @ SV251 @ ^ [SX0: $i] : ( SX0 = emptyset ) )),bind(SV34,$thf( emptyset ))]]) ).
thf(226,plain,
! [SV251: $i] :
( ( ( in @ emptyset @ SV251 )
= $false )
| ( ( ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
= emptyset )
= $false ) ),
inference(extuni,[status(esa)],[216:[bind(SV198,$thf( emptyset ))]]) ).
thf(227,plain,
! [SV203: $i > $o,SV201: $i] :
( ( ( in @ emptyset @ SV201 )
= $false )
| ( ( SV203 @ emptyset )
= $true )
| ( ( in @ emptyset
@ ( dsetconstr
@ ( dsetconstr @ SV201
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) )
@ ^ [SX0: $i] : ( SX0 = emptyset ) ) )
= $true ) ),
inference(extuni,[status(esa)],[214:[bind(SV251,$thf( dsetconstr @ SV201 @ ^ [SX0: $i] : ~ ( SV203 @ SX0 ) )),bind(SV202,$thf( emptyset ))]]) ).
thf(228,plain,
! [SV203: $i > $o,SV251: $i] :
( ( ( in @ emptyset
@ ( dsetconstr
@ ( dsetconstr @ SV251
@ ^ [SX0: $i] : ( SX0 = emptyset ) )
@ ^ [SX0: $i] :
~ ( SV203 @ SX0 ) ) )
= $true )
| ( ( SV203 @ emptyset )
= $true )
| ( ( in @ emptyset @ SV251 )
= $false ) ),
inference(extuni,[status(esa)],[213:[bind(SV201,$thf( dsetconstr @ SV251 @ ^ [SX0: $i] : ( SX0 = emptyset ) )),bind(SV202,$thf( emptyset ))]]) ).
thf(229,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,228,227,226,225,224,223,210,209,208,205,204,203,202,201,200,199,198,197,196,195,194,192,191,190,188,171,169,168,163,162,161,160,159,158,157,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,107,92,89,88,87,83,81,78,71,70,69,68,67,66,65,36,35]) ).
thf(230,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU510^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 20:48:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 531
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:0,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.18/0.51
% 0.18/0.51 Prim_subst applied to clause
% 0.18/0.51
% 0.18/0.51 72:[ 0:<SV15 = $true>-w(1)-i() 1:<(in@SV14)@emptyset = $false>-w(1)-i() ]-mln(2)-w(2)-i(rename 26)-o(AXIOM)-fv([ SV14 SV15 ])
% 0.39/0.57 .
% 0.39/0.59
% 0.39/0.59 Prim_subst applied to clause
% 0.39/0.59
% 0.39/0.59 92:[ 0:<SV35@SV34 = $false>-w(1)-i() 1:<(in@SV34)@((dsetconstr@SV33)@(^[SX0:$i]: (SV35@SX0))) = $true>-w(1)-i() 2:<(in@SV34)@SV33 = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 37)-o(AXIOM)-fv([ SV33 SV34 SV35 ])
% 0.80/1.01 ..
% 5.59/5.84
% 5.59/5.84 Prim_subst applied to clause
% 5.59/5.84
% 5.59/5.84 171:[ 0:<SV203@SV202 = $true>-w(1)-i() 1:<(in@SV202)@((dsetconstr@SV201)@(^[SX0:$i]: (~ (SV203@SX0)))) = $true>-w(1)-i() 2:<(in@SV202)@SV201 = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 63)-o(AXIOM)-fv([ SV201 SV202 SV203 ])
% 5.89/6.11 ..
% 10.38/10.62
% 10.38/10.62 ********************************
% 10.38/10.62 * All subproblems solved! *
% 10.38/10.62 ********************************
% 10.38/10.62 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:229,loop_count:10,foatp_calls:3,translation:fof_full)
% 10.38/10.65
% 10.38/10.65 %**** Beginning of derivation protocol ****
% 10.38/10.65 % SZS output start CNFRefutation
% See solution above
% 10.38/10.65
% 10.38/10.65 %**** End of derivation protocol ****
% 10.38/10.65 %**** no. of clauses in derivation: 182 ****
% 10.38/10.65 %**** clause counter: 229 ****
% 10.38/10.65
% 10.38/10.65 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:229,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------