%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET002^4 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n027.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 : 300s
% DateTime : Wed Feb 25 09:30:53 AM UTC 2026
% Result : Theorem 2.20s 1.78s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 102 ( 62 unt; 0 typ; 2 def)
% Number of atoms : 627 ( 115 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 958 ( 41 ~; 45 |; 13 &; 795 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 31 usr; 9 con; 0-3 aty)
% ( 40 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 222 ( 196 ^; 26 !; 0 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_16,type,
equal_set: $i > $i > mworld > $o ).
thf(func_def_17,type,
member: $i > $i > mworld > $o ).
thf(func_def_18,type,
subset: $i > $i > mworld > $o ).
thf(func_def_19,type,
singleton: $i > $i ).
thf(func_def_20,type,
product: $i > $i ).
thf(func_def_21,type,
unordered_pair: $i > $i > $i ).
thf(func_def_22,type,
intersection: $i > $i > $i ).
thf(func_def_23,type,
difference: $i > $i > $i ).
thf(func_def_24,type,
sum: $i > $i ).
thf(func_def_25,type,
union: $i > $i > $i ).
thf(func_def_26,type,
power_set: $i > $i ).
thf(func_def_40,type,
sK0: mworld > mworld ).
thf(func_def_45,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f600,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f457,f524,f599]) ).
thf(f599,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f598]) ).
thf(f598,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f585]) ).
thf(f585,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(backward_demodulation,[status(thm)],[f534,f558]) ).
thf(f558,plain,
( ( $false
= ( member @ sK5 @ sK2 @ mactual ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[status(thm)],[f557]) ).
thf(f557,plain,
( ( ( ~ ( member @ sK5 @ sK2 @ mactual ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[status(thm)],[f556]) ).
thf(f556,plain,
( ( ( ~ ( ( member @ sK5 @ sK2 @ mactual )
| ( member @ sK5 @ sK2 @ mactual ) ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[status(thm)],[f553]) ).
thf(f553,plain,
( ( $true
= ( ( ( member @ sK5 @ sK2 @ mactual )
| ( member @ sK5 @ sK2 @ mactual ) )
= $false ) )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f236,f533]) ).
thf(f533,plain,
( ( $false
= ( member @ sK5 @ ( union @ sK2 @ sK2 ) @ mactual ) )
| ~ spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f532]) ).
thf(f532,plain,
( ( $false
= ( ( member @ sK5 @ sK2 @ mactual )
=> ( member @ sK5 @ ( union @ sK2 @ sK2 ) @ mactual ) ) )
| ~ spl1_1 ),
inference(beta_eta_normalization,[status(thm)],[f531]) ).
thf(f531,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( member @ Y0 @ sK2 @ mactual )
=> ( member @ Y0 @ ( union @ sK2 @ sK2 ) @ mactual ) )
@ sK5 ) )
| ~ spl1_1 ),
inference(sigma_clausification,[status(thm)],[f530]) ).
thf(f530,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ sK2 @ mactual )
=> ( member @ Y0 @ ( union @ sK2 @ sK2 ) @ mactual ) ) )
= $false )
| ~ spl1_1 ),
inference(not_proxy_clausification,[status(thm)],[f529]) ).
thf(f529,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ sK2 @ mactual )
=> ( member @ Y0 @ ( union @ sK2 @ sK2 ) @ mactual ) ) ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[status(thm)],[f526]) ).
thf(f526,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ sK2 @ mactual )
=> ( member @ Y0 @ ( union @ sK2 @ sK2 ) @ mactual ) ) )
= $false )
= $true )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f411,f452]) ).
thf(f452,plain,
( ( ( subset @ sK2 @ ( union @ sK2 @ sK2 ) @ mactual )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f450]) ).
thf(f450,definition,
( spl1_1
<=> ( ( subset @ sK2 @ ( union @ sK2 @ sK2 ) @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f411,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) )
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f410]) ).
thf(f410,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) )
= ( subset @ X1 @ Y0 @ mactual ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f409]) ).
thf(f409,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) )
= ( subset @ X1 @ Y0 @ mactual ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f408]) ).
thf(f408,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) )
= ( subset @ Y0 @ Y1 @ mactual ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f407]) ).
thf(f407,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) )
= ( subset @ Y0 @ Y1 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f203]) ).
thf(f203,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
= ( Y2 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f167,f160,f166,f166,f142,f166,f143]) ).
thf(f143,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mimplies_def) ).
thf(f142,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
thf(f95,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f94]) ).
thf(f94,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) )
= mequiv ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mequiv_def) ).
thf(f166,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
thf(f83,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) )
= mforall_di ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] : ( X1 @ X5 @ X2 ) )
= mforall_di ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mforall_di_def) ).
thf(f160,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
thf(f67,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mlocal_def) ).
thf(f167,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f55]) ).
thf(f55,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,axiom,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] :
( mequiv @ ( subset @ X1 @ X3 )
@ ( mforall_di
@ ^ [X5: $i] : ( mimplies @ ( member @ X5 @ X1 ) @ ( member @ X5 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',subset_0) ).
thf(f236,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( member @ X1 @ X2 @ mactual )
| ( member @ X1 @ X3 @ mactual ) )
= ( member @ X1 @ ( union @ X2 @ X3 ) @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f235]) ).
thf(f235,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( member @ X1 @ X2 @ mactual )
| ( member @ X1 @ Y0 @ mactual ) )
= ( member @ X1 @ ( union @ X2 @ Y0 ) @ mactual ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f234]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( member @ X1 @ X2 @ mactual )
| ( member @ X1 @ Y0 @ mactual ) )
= ( member @ X1 @ ( union @ X2 @ Y0 ) @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f233]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( member @ X1 @ Y0 @ mactual )
| ( member @ X1 @ Y1 @ mactual ) )
= ( member @ X1 @ ( union @ Y0 @ Y1 ) @ mactual ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f232]) ).
thf(f232,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( member @ X1 @ Y0 @ mactual )
| ( member @ X1 @ Y1 @ mactual ) )
= ( member @ X1 @ ( union @ Y0 @ Y1 ) @ mactual ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f231]) ).
thf(f231,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( member @ Y0 @ Y1 @ mactual )
| ( member @ Y0 @ Y2 @ mactual ) )
= ( member @ Y0 @ ( union @ Y1 @ Y2 ) @ mactual ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f230]) ).
thf(f230,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( member @ Y0 @ Y1 @ mactual )
| ( member @ Y0 @ Y2 @ mactual ) )
= ( member @ Y0 @ ( union @ Y1 @ Y2 ) @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f193]) ).
thf(f193,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
= ( Y3 @ Y5 ) )
@ ( member @ Y0 @ ( union @ Y1 @ Y2 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( member @ Y0 @ Y1 )
@ ( member @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f154,f160,f166,f166,f166,f142,f177]) ).
thf(f177,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f104]) ).
thf(f104,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mor_def) ).
thf(f154,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( member @ Y0 @ ( union @ Y1 @ Y2 ) ) @ ( mor @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
thf(f89,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( member @ Y0 @ ( union @ Y1 @ Y2 ) ) @ ( mor @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f88]) ).
thf(f88,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mequiv @ ( member @ X0 @ ( union @ X1 @ X2 ) ) @ ( mor @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,axiom,
( mlocal
@ ( mforall_di
@ ^ [X5: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( member @ X5 @ ( union @ X1 @ X3 ) ) @ ( mor @ ( member @ X5 @ X1 ) @ ( member @ X5 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',union_0) ).
thf(f534,plain,
( ( $true
= ( member @ sK5 @ sK2 @ mactual ) )
| ~ spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f532]) ).
thf(f524,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f523]) ).
thf(f523,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f522]) ).
thf(f522,plain,
( ( $false = $true )
| ~ spl1_2 ),
inference(forward_demodulation,[status(thm)],[f508,f474]) ).
thf(f474,plain,
( ( $false
= ( member @ sK4 @ sK2 @ mactual ) )
| ~ spl1_2 ),
inference(binary_proxy_clausification,[status(thm)],[f473]) ).
thf(f473,plain,
( ( ( ( member @ sK4 @ ( union @ sK2 @ sK2 ) @ mactual )
=> ( member @ sK4 @ sK2 @ mactual ) )
= $false )
| ~ spl1_2 ),
inference(beta_eta_normalization,[status(thm)],[f472]) ).
thf(f472,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( member @ Y0 @ ( union @ sK2 @ sK2 ) @ mactual )
=> ( member @ Y0 @ sK2 @ mactual ) )
@ sK4 ) )
| ~ spl1_2 ),
inference(sigma_clausification,[status(thm)],[f471]) ).
thf(f471,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( union @ sK2 @ sK2 ) @ mactual )
=> ( member @ Y0 @ sK2 @ mactual ) ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[status(thm)],[f470]) ).
thf(f470,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( union @ sK2 @ sK2 ) @ mactual )
=> ( member @ Y0 @ sK2 @ mactual ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[status(thm)],[f469]) ).
thf(f469,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( union @ sK2 @ sK2 ) @ mactual )
=> ( member @ Y0 @ sK2 @ mactual ) ) )
= $false ) )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f411,f456]) ).
thf(f456,plain,
( ( $false
= ( subset @ ( union @ sK2 @ sK2 ) @ sK2 @ mactual ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f454]) ).
thf(f454,definition,
( spl1_2
<=> ( $false
= ( subset @ ( union @ sK2 @ sK2 ) @ sK2 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f508,plain,
( ( $true
= ( member @ sK4 @ sK2 @ mactual ) )
| ~ spl1_2 ),
inference(boolean_simplification,[status(thm)],[f507]) ).
thf(f507,plain,
( ( ( ( member @ sK4 @ sK2 @ mactual )
| ( member @ sK4 @ sK2 @ mactual ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[status(thm)],[f495]) ).
thf(f495,plain,
( ( ( ( ( member @ sK4 @ sK2 @ mactual )
| ( member @ sK4 @ sK2 @ mactual ) )
= $true )
= $true )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f236,f475]) ).
thf(f475,plain,
( ( ( member @ sK4 @ ( union @ sK2 @ sK2 ) @ mactual )
= $true )
| ~ spl1_2 ),
inference(binary_proxy_clausification,[status(thm)],[f473]) ).
thf(f457,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f448,f454,f450]) ).
thf(f448,plain,
( ( ( subset @ sK2 @ ( union @ sK2 @ sK2 ) @ mactual )
= $false )
| ( $false
= ( subset @ ( union @ sK2 @ sK2 ) @ sK2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f447]) ).
thf(f447,plain,
( $false
= ( ( subset @ ( union @ sK2 @ sK2 ) @ sK2 @ mactual )
& ( subset @ sK2 @ ( union @ sK2 @ sK2 ) @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f446]) ).
thf(f446,plain,
( ( ~ ( ( subset @ ( union @ sK2 @ sK2 ) @ sK2 @ mactual )
& ( subset @ sK2 @ ( union @ sK2 @ sK2 ) @ mactual ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f445]) ).
thf(f445,plain,
( $true
= ( ( ( subset @ ( union @ sK2 @ sK2 ) @ sK2 @ mactual )
& ( subset @ sK2 @ ( union @ sK2 @ sK2 ) @ mactual ) )
= $false ) ),
inference(superposition,[status(thm)],[f249,f364]) ).
thf(f364,plain,
( $false
= ( equal_set @ ( union @ sK2 @ sK2 ) @ sK2 @ mactual ) ),
inference(beta_eta_normalization,[status(thm)],[f363]) ).
thf(f363,plain,
( ( ^ [Y0: $i] : ( equal_set @ ( union @ Y0 @ Y0 ) @ Y0 @ mactual )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f362]) ).
thf(f362,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( equal_set @ ( union @ Y0 @ Y0 ) @ Y0 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f191]) ).
thf(f191,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] : ( equal_set @ ( union @ Y0 @ Y0 ) @ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f152,f160,f166]) ).
thf(f152,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( equal_set @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f134]) ).
thf(f134,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( equal_set @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(flattening,[status(thm)],[f133]) ).
thf(f133,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( equal_set @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f132]) ).
thf(f132,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( equal_set @ ( union @ X0 @ X0 ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f45]) ).
thf(f45,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X1: $i] : ( equal_set @ ( union @ X1 @ X1 ) @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
thf(f44,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] : ( equal_set @ ( union @ X1 @ X1 ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',thI14) ).
thf(f249,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( ( subset @ X1 @ X2 @ mactual )
& ( subset @ X2 @ X1 @ mactual ) )
= ( equal_set @ X1 @ X2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f248]) ).
thf(f248,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( subset @ X1 @ Y0 @ mactual )
& ( subset @ Y0 @ X1 @ mactual ) )
= ( equal_set @ X1 @ Y0 @ mactual ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f247]) ).
thf(f247,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ X1 @ Y0 @ mactual )
& ( subset @ Y0 @ X1 @ mactual ) )
= ( equal_set @ X1 @ Y0 @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f246]) ).
thf(f246,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) )
= ( equal_set @ Y0 @ Y1 @ mactual ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f245]) ).
thf(f245,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) )
= ( equal_set @ Y0 @ Y1 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f199]) ).
thf(f199,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
= ( Y2 @ Y4 ) )
@ ( equal_set @ Y0 @ Y1 )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f162,f160,f166,f166,f142,f138]) ).
thf(f138,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
thf(f113,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f112]) ).
thf(f112,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mand_def) ).
thf(f162,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
thf(f81,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f80]) ).
thf(f80,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( equal_set @ X0 @ X1 ) @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,axiom,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( equal_set @ X1 @ X3 ) @ ( mand @ ( subset @ X1 @ X3 ) @ ( subset @ X3 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',equal_set_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET002^4 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:48:37 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SET002^4 : TPTP v9.2.1. Released v8.1.0.
% 0.20/0.48 % Domain : Set Theory
% 0.20/0.48 % Problem : TPTP problem SET002+4.p with axiomatized equality
% 0.20/0.48 % Version : [BP13] axioms.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.20/0.48 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.20/0.48 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.20/0.48 % Source : [TPTP]
% 0.20/0.48 % Names : SET002+1 [QMLTP]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0
% 0.20/0.48 % Syntax : Number of formulae : 70 ( 11 unt; 26 typ; 10 def)
% 0.20/0.48 % Number of atoms : 266 ( 10 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 10 ( 6 avg)
% 0.20/0.48 % Number of connectives : 449 ( 1 ~; 1 |; 2 &; 442 @)
% 0.20/0.48 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 14 ( 9 avg)
% 0.20/0.48 % Number of types : 3 ( 1 usr)
% 0.20/0.48 % Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 26 ( 25 usr; 2 con; 0-3 aty)
% 0.20/0.48 % Number of variables : 114 ( 108 ^; 3 !; 3 ?; 114 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.20/0.48 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.20/0.48 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.20/0.48 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.20/0.48 % $modalities == $modal_system_D].
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(mworld,type,
% 0.20/0.48 mworld: $tType ).
% 0.20/0.48
% 0.20/0.48 thf(mrel_type,type,
% 0.20/0.48 mrel: mworld > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mactual_type,type,
% 0.20/0.48 mactual: mworld ).
% 0.20/0.48
% 0.20/0.48 thf(mlocal_type,type,
% 0.20/0.48 mlocal: ( mworld > $o ) > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mlocal_def,definition,
% 0.20/0.48 ( mlocal
% 0.20/0.48 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(mnot_type,type,
% 0.20/0.48 mnot: ( mworld > $o ) > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mand_type,type,
% 0.20/0.48 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mor_type,type,
% 0.20/0.48 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mimplies_type,type,
% 0.20/0.48 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mequiv_type,type,
% 0.20/0.48 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mnot_def,definition,
% 0.20/0.48 ( mnot
% 0.20/0.48 = ( ^ [A: mworld > $o,W: mworld] :
% 0.20/0.48 ~ ( A @ W ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(mand_def,definition,
% 0.20/0.48 ( mand
% 0.20/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.48 ( ( A @ W )
% 0.20/0.48 & ( B @ W ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(mor_def,definition,
% 0.20/0.48 ( mor
% 0.20/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.48 ( ( A @ W )
% 0.20/0.48 | ( B @ W ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(mimplies_def,definition,
% 0.20/0.48 ( mimplies
% 0.20/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.48 ( ( A @ W )
% 0.20/0.48 => ( B @ W ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(mequiv_def,definition,
% 0.20/0.48 ( mequiv
% 0.20/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.48 ( ( A @ W )
% 0.20/0.48 <=> ( B @ W ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(mbox_type,type,
% 0.20/0.48 mbox: ( mworld > $o ) > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mbox_def,definition,
% 0.20/0.48 ( mbox
% 0.20/0.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.48 ! [V: mworld] :
% 0.20/0.48 ( ( mrel @ W @ V )
% 0.20/0.48 => ( Phi @ V ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(mdia_type,type,
% 0.20/0.48 mdia: ( mworld > $o ) > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mdia_def,definition,
% 0.20/0.48 ( mdia
% 0.20/0.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.48 ? [V: mworld] :
% 0.20/0.48 ( ( mrel @ W @ V )
% 0.20/0.48 & ( Phi @ V ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(mrel_serial,axiom,
% 0.20/0.48 ! [W: mworld] :
% 0.20/0.48 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.20/0.48
% 0.20/0.48 thf(mforall_di_type,type,
% 0.20/0.48 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mforall_di_def,definition,
% 0.20/0.48 ( mforall_di
% 0.20/0.48 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.48 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(mexists_di_type,type,
% 0.20/0.48 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(mexists_di_def,definition,
% 0.20/0.48 ( mexists_di
% 0.20/0.48 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.48 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(empty_set_decl,type,
% 0.20/0.48 empty_set: $i ).
% 0.20/0.48
% 0.20/0.48 thf(qmltpeq_decl,type,
% 0.20/0.48 qmltpeq: $i > $i > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(equal_set_decl,type,
% 0.20/0.48 equal_set: $i > $i > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(member_decl,type,
% 0.20/0.48 member: $i > $i > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(subset_decl,type,
% 0.20/0.48 subset: $i > $i > mworld > $o ).
% 0.20/0.48
% 0.20/0.48 thf(singleton_decl,type,
% 0.20/0.48 singleton: $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(product_decl,type,
% 0.20/0.48 product: $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(unordered_pair_decl,type,
% 0.20/0.48 unordered_pair: $i > $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(intersection_decl,type,
% 0.20/0.48 intersection: $i > $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(difference_decl,type,
% 0.20/0.48 difference: $i > $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(sum_decl,type,
% 0.20/0.48 sum: $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(union_decl,type,
% 0.20/0.48 union: $i > $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(power_set_decl,type,
% 0.20/0.48 power_set: $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(reflexivity,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(symmetry,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(transitivity,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [Y: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(difference_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(difference_substitution_2,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(intersection_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(intersection_substitution_2,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(power_set_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(product_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(singleton_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sum_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(union_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(union_substitution_2,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(unordered_pair_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(unordered_pair_substitution_2,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(equal_set_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(equal_set_substitution_2,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(member_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(member_substitution_2,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(subset_substitution_1,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(subset_substitution_2,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(subset_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mequiv @ ( subset @ A @ B )
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(equal_set_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(power_set_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(intersection_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(union_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(empty_set_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(difference_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [B: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(singleton_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(unordered_pair_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sum_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 0.20/0.48 @ ( mexists_di
% 0.20/0.48 @ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(product_0,axiom,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( mforall_di
% 0.20/0.48 @ ^ [A: $i] :
% 0.20/0.48 ( mequiv @ ( member @ X @ ( product @ A ) )
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(thI14,conjecture,
% 0.20/0.48 ( mlocal
% 0.20/0.48 @ ( mforall_di
% 0.20/0.48 @ ^ [A: $i] : ( equal_set @ ( union @ A @ A ) @ A ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 2.02/1.57 ---- Embedded in THF ---
% 2.02/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.02/1.57 %%% Generated on Tue Feb 24 11:48:38 EST 2026
% 2.02/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.02/1.57 %%% Logic specification used:
% 2.02/1.57 %%% thf(spec, logic, $$dhol).
% 2.02/1.57
% 2.02/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2DTF24076.p
% See solution above
% 2.02/1.57 ------------------------
% 2.02/1.58 ---- Cleaned THF ---
% 2.02/1.59 thf(mworld,type,
% 2.02/1.59 mworld: $tType ).
% 2.02/1.59
% 2.02/1.59 thf(mrel_type,type,
% 2.02/1.59 mrel: mworld > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mactual_type,type,
% 2.02/1.59 mactual: mworld ).
% 2.02/1.59
% 2.02/1.59 thf(mlocal_type,type,
% 2.02/1.59 mlocal: ( mworld > $o ) > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mlocal_def,definition,
% 2.02/1.59 ( mlocal
% 2.02/1.59 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(mnot_type,type,
% 2.02/1.59 mnot: ( mworld > $o ) > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mand_type,type,
% 2.02/1.59 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mor_type,type,
% 2.02/1.59 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mimplies_type,type,
% 2.02/1.59 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mequiv_type,type,
% 2.02/1.59 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mnot_def,definition,
% 2.02/1.59 ( mnot
% 2.02/1.59 = ( ^ [A: mworld > $o,W: mworld] :
% 2.02/1.59 ~ ( A @ W ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(mand_def,definition,
% 2.02/1.59 ( mand
% 2.02/1.59 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.02/1.59 ( ( A @ W )
% 2.02/1.59 & ( B @ W ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(mor_def,definition,
% 2.02/1.59 ( mor
% 2.02/1.59 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.02/1.59 ( ( A @ W )
% 2.02/1.59 | ( B @ W ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(mimplies_def,definition,
% 2.02/1.59 ( mimplies
% 2.02/1.59 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.02/1.59 ( ( A @ W )
% 2.02/1.59 => ( B @ W ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(mequiv_def,definition,
% 2.02/1.59 ( mequiv
% 2.02/1.59 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.02/1.59 ( ( A @ W )
% 2.02/1.59 <=> ( B @ W ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(mbox_type,type,
% 2.02/1.59 mbox: ( mworld > $o ) > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mbox_def,definition,
% 2.02/1.59 ( mbox
% 2.02/1.59 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.02/1.59 ! [V: mworld] :
% 2.02/1.59 ( ( mrel @ W @ V )
% 2.02/1.59 => ( Phi @ V ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(mdia_type,type,
% 2.02/1.59 mdia: ( mworld > $o ) > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mdia_def,definition,
% 2.02/1.59 ( mdia
% 2.02/1.59 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.02/1.59 ? [V: mworld] :
% 2.02/1.59 ( ( mrel @ W @ V )
% 2.02/1.59 & ( Phi @ V ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(mrel_serial,axiom,
% 2.02/1.59 ! [W: mworld] :
% 2.02/1.59 ? [V: mworld] : ( mrel @ W @ V ) ).
% 2.02/1.59
% 2.02/1.59 thf(mforall_di_type,type,
% 2.02/1.59 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mforall_di_def,definition,
% 2.02/1.59 ( mforall_di
% 2.02/1.59 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 2.02/1.59 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(mexists_di_type,type,
% 2.02/1.59 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(mexists_di_def,definition,
% 2.02/1.59 ( mexists_di
% 2.02/1.59 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 2.02/1.59 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(empty_set_decl,type,
% 2.02/1.59 empty_set: $i ).
% 2.02/1.59
% 2.02/1.59 thf(qmltpeq_decl,type,
% 2.02/1.59 qmltpeq: $i > $i > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(equal_set_decl,type,
% 2.02/1.59 equal_set: $i > $i > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(member_decl,type,
% 2.02/1.59 member: $i > $i > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(subset_decl,type,
% 2.02/1.59 subset: $i > $i > mworld > $o ).
% 2.02/1.59
% 2.02/1.59 thf(singleton_decl,type,
% 2.02/1.59 singleton: $i > $i ).
% 2.02/1.59
% 2.02/1.59 thf(product_decl,type,
% 2.02/1.59 product: $i > $i ).
% 2.02/1.59
% 2.02/1.59 thf(unordered_pair_decl,type,
% 2.02/1.59 unordered_pair: $i > $i > $i ).
% 2.02/1.59
% 2.02/1.59 thf(intersection_decl,type,
% 2.02/1.59 intersection: $i > $i > $i ).
% 2.02/1.59
% 2.02/1.59 thf(difference_decl,type,
% 2.02/1.59 difference: $i > $i > $i ).
% 2.02/1.59
% 2.02/1.59 thf(sum_decl,type,
% 2.02/1.59 sum: $i > $i ).
% 2.02/1.59
% 2.02/1.59 thf(union_decl,type,
% 2.02/1.59 union: $i > $i > $i ).
% 2.02/1.59
% 2.02/1.59 thf(power_set_decl,type,
% 2.02/1.59 power_set: $i > $i ).
% 2.02/1.59
% 2.02/1.59 thf(reflexivity,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(symmetry,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(transitivity,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [Y: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(difference_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(difference_substitution_2,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(intersection_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(intersection_substitution_2,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(power_set_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(product_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(singleton_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(sum_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(union_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(union_substitution_2,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(unordered_pair_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(unordered_pair_substitution_2,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(equal_set_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(equal_set_substitution_2,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(member_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(member_substitution_2,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(subset_substitution_1,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(subset_substitution_2,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(subset_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mequiv @ ( subset @ A @ B )
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(equal_set_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(power_set_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(intersection_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(union_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(empty_set_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(difference_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [B: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(singleton_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(unordered_pair_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(sum_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 2.02/1.59 @ ( mexists_di
% 2.02/1.59 @ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(product_0,axiom,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [X: $i] :
% 2.02/1.59 ( mforall_di
% 2.02/1.59 @ ^ [A: $i] :
% 2.02/1.59 ( mequiv @ ( member @ X @ ( product @ A ) )
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 2.02/1.59
% 2.02/1.59 thf(thI14,conjecture,
% 2.02/1.59 ( mlocal
% 2.02/1.59 @ ( mforall_di
% 2.02/1.59 @ ^ [A: $i] : ( equal_set @ ( union @ A @ A ) @ A ) ) ) ).
% 2.02/1.59 ------------------------
% 2.20/1.61 % (24179)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/2Mi)
% 2.20/1.61 % (24177)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/27Mi)
% 2.20/1.61 % (24175)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/183Mi)
% 2.20/1.61 % (24180)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/275Mi)
% 2.20/1.61 % (24176)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/4Mi)
% 2.20/1.61 % (24178)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/2Mi)
% 2.20/1.61 % (24181)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/18Mi)
% 2.20/1.61 % (24178)Instruction limit reached!
% 2.20/1.61 % (24178)------------------------------
% 2.20/1.61 % (24178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.61 % (24178)Termination reason: Unknown
% 2.20/1.61 % (24179)Instruction limit reached!
% 2.20/1.61 % (24179)------------------------------
% 2.20/1.61 % (24179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.61 % (24178)Termination phase: shuffling
% 2.20/1.61
% 2.20/1.61 % (24178)Memory used [KB]: 1023
% 2.20/1.61 % (24178)Time elapsed: 0.003 s
% 2.20/1.61 % (24178)Instructions burned: 2 (million)
% 2.20/1.61 % (24178)------------------------------
% 2.20/1.61 % (24178)------------------------------
% 2.20/1.61 % (24179)Termination reason: Unknown
% 2.20/1.61 % (24179)Termination phase: shuffling
% 2.20/1.61
% 2.20/1.61 % (24179)Memory used [KB]: 1023
% 2.20/1.61 % (24179)Time elapsed: 0.003 s
% 2.20/1.61 % (24179)Instructions burned: 3 (million)
% 2.20/1.61 % (24179)------------------------------
% 2.20/1.61 % (24179)------------------------------
% 2.20/1.61 % (24176)Instruction limit reached!
% 2.20/1.61 % (24176)------------------------------
% 2.20/1.61 % (24176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.61 % (24176)Termination reason: Unknown
% 2.20/1.61 % (24176)Termination phase: shuffling
% 2.20/1.61
% 2.20/1.61 % (24176)Memory used [KB]: 1151
% 2.20/1.61 % (24176)Time elapsed: 0.004 s
% 2.20/1.61 % (24176)Instructions burned: 4 (million)
% 2.20/1.61 % (24176)------------------------------
% 2.20/1.61 % (24176)------------------------------
% 2.20/1.61 % (24180)Refutation not found, incomplete strategy
% 2.20/1.61 % (24180)------------------------------
% 2.20/1.61 % (24180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.61 % (24180)Termination reason: Refutation not found, incomplete strategy
% 2.20/1.61
% 2.20/1.61
% 2.20/1.61 % (24180)Memory used [KB]: 5628
% 2.20/1.61 % (24180)Time elapsed: 0.008 s
% 2.20/1.61 % (24180)Instructions burned: 14 (million)
% 2.20/1.61 % (24180)------------------------------
% 2.20/1.61 % (24180)------------------------------
% 2.20/1.62 % (24181)Instruction limit reached!
% 2.20/1.62 % (24181)------------------------------
% 2.20/1.62 % (24181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.62 % (24181)Termination reason: Unknown
% 2.20/1.62 % (24181)Termination phase: Property scanning
% 2.20/1.62
% 2.20/1.62 % (24181)Memory used [KB]: 1151
% 2.20/1.62 % (24181)Time elapsed: 0.010 s
% 2.20/1.62 % (24181)Instructions burned: 19 (million)
% 2.20/1.62 % (24181)------------------------------
% 2.20/1.62 % (24181)------------------------------
% 2.20/1.62 % (24177)Instruction limit reached!
% 2.20/1.62 % (24177)------------------------------
% 2.20/1.62 % (24177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.62 % (24177)Termination reason: Unknown
% 2.20/1.62 % (24177)Termination phase: Saturation
% 2.20/1.62
% 2.20/1.62 % (24177)Memory used [KB]: 5756
% 2.20/1.62 % (24177)Time elapsed: 0.014 s
% 2.20/1.62 % (24177)Instructions burned: 27 (million)
% 2.20/1.62 % (24177)------------------------------
% 2.20/1.62 % (24177)------------------------------
% 2.20/1.63 % (24183)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/37Mi)
% 2.20/1.63 % (24182)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/3Mi)
% 2.20/1.63 % (24184)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/15Mi)
% 2.20/1.63 % (24182)Instruction limit reached!
% 2.20/1.63 % (24182)------------------------------
% 2.20/1.63 % (24182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.63 % (24182)Termination reason: Unknown
% 2.20/1.63 % (24182)Termination phase: shuffling
% 2.20/1.63
% 2.20/1.63 % (24182)Memory used [KB]: 1023
% 2.20/1.63 % (24182)Time elapsed: 0.003 s
% 2.20/1.63 % (24182)Instructions burned: 3 (million)
% 2.20/1.63 % (24182)------------------------------
% 2.20/1.63 % (24182)------------------------------
% 2.20/1.63 % (24185)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/3Mi)
% 2.20/1.63 % (24184)Instruction limit reached!
% 2.20/1.63 % (24184)------------------------------
% 2.20/1.63 % (24184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.63 % (24186)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/1041Mi)
% 2.20/1.63 % (24184)Termination reason: Unknown
% 2.20/1.63 % (24184)Termination phase: Function definition elimination
% 2.20/1.63
% 2.20/1.63 % (24184)Memory used [KB]: 1151
% 2.20/1.63 % (24184)Time elapsed: 0.008 s
% 2.20/1.63 % (24184)Instructions burned: 15 (million)
% 2.20/1.63 % (24184)------------------------------
% 2.20/1.63 % (24184)------------------------------
% 2.20/1.63 % (24185)Instruction limit reached!
% 2.20/1.63 % (24185)------------------------------
% 2.20/1.63 % (24185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.63 % (24185)Termination reason: Unknown
% 2.20/1.63 % (24185)Termination phase: shuffling
% 2.20/1.63
% 2.20/1.63 % (24185)Memory used [KB]: 1023
% 2.20/1.63 % (24185)Time elapsed: 0.003 s
% 2.20/1.63 % (24185)Instructions burned: 3 (million)
% 2.20/1.63 % (24185)------------------------------
% 2.20/1.63 % (24185)------------------------------
% 2.20/1.64 % (24187)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/7Mi)
% 2.20/1.64 % (24187)Instruction limit reached!
% 2.20/1.64 % (24187)------------------------------
% 2.20/1.64 % (24187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.64 % (24187)Termination reason: Unknown
% 2.20/1.64 % (24187)Termination phase: Property scanning
% 2.20/1.64
% 2.20/1.64 % (24187)Memory used [KB]: 1151
% 2.20/1.64 % (24187)Time elapsed: 0.005 s
% 2.20/1.64 % (24187)Instructions burned: 8 (million)
% 2.20/1.64 % (24187)------------------------------
% 2.20/1.64 % (24187)------------------------------
% 2.20/1.64 % (24183)Instruction limit reached!
% 2.20/1.64 % (24183)------------------------------
% 2.20/1.64 % (24183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.64 % (24183)Termination reason: Unknown
% 2.20/1.64 % (24183)Termination phase: Saturation
% 2.20/1.64
% 2.20/1.64 % (24183)Memory used [KB]: 5884
% 2.20/1.64 % (24183)Time elapsed: 0.018 s
% 2.20/1.64 % (24183)Instructions burned: 38 (million)
% 2.20/1.64 % (24183)------------------------------
% 2.20/1.64 % (24183)------------------------------
% 2.20/1.64 % (24188)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/16Mi)
% 2.20/1.65 % (24189)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/3Mi)
% 2.20/1.65 % (24190)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/3Mi)
% 2.20/1.65 % (24189)Instruction limit reached!
% 2.20/1.65 % (24189)------------------------------
% 2.20/1.65 % (24189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.65 % (24189)Termination reason: Unknown
% 2.20/1.65 % (24189)Termination phase: shuffling
% 2.20/1.65
% 2.20/1.65 % (24189)Memory used [KB]: 1023
% 2.20/1.65 % (24189)Time elapsed: 0.003 s
% 2.20/1.65 % (24189)Instructions burned: 3 (million)
% 2.20/1.65 % (24189)------------------------------
% 2.20/1.65 % (24189)------------------------------
% 2.20/1.65 % (24188)Instruction limit reached!
% 2.20/1.65 % (24188)------------------------------
% 2.20/1.65 % (24188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.65 % (24188)Termination reason: Unknown
% 2.20/1.65 % (24190)Instruction limit reached!
% 2.20/1.65 % (24190)------------------------------
% 2.20/1.65 % (24190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.65 % (24190)Termination reason: Unknown
% 2.20/1.65 % (24190)Termination phase: shuffling
% 2.20/1.65
% 2.20/1.65 % (24190)Memory used [KB]: 1023
% 2.20/1.65 % (24190)Time elapsed: 0.003 s
% 2.20/1.65 % (24190)Instructions burned: 4 (million)
% 2.20/1.65 % (24190)------------------------------
% 2.20/1.65 % (24190)------------------------------
% 2.20/1.65 % (24188)Termination phase: Property scanning
% 2.20/1.65
% 2.20/1.65 % (24188)Memory used [KB]: 1151
% 2.20/1.65 % (24188)Time elapsed: 0.009 s
% 2.20/1.65 % (24188)Instructions burned: 17 (million)
% 2.20/1.65 % (24188)------------------------------
% 2.20/1.65 % (24188)------------------------------
% 2.20/1.66 % (24191)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/7Mi)
% 2.20/1.66 % (24192)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/3Mi)
% 2.20/1.66 % (24191)Instruction limit reached!
% 2.20/1.66 % (24191)------------------------------
% 2.20/1.66 % (24191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.66 % (24191)Termination reason: Unknown
% 2.20/1.66 % (24191)Termination phase: Property scanning
% 2.20/1.66
% 2.20/1.66 % (24191)Memory used [KB]: 1151
% 2.20/1.66 % (24191)Time elapsed: 0.005 s
% 2.20/1.66 % (24191)Instructions burned: 8 (million)
% 2.20/1.66 % (24191)------------------------------
% 2.20/1.66 % (24191)------------------------------
% 2.20/1.66 % (24192)Instruction limit reached!
% 2.20/1.66 % (24192)------------------------------
% 2.20/1.66 % (24192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.66 % (24192)Termination reason: Unknown
% 2.20/1.66 % (24192)Termination phase: shuffling
% 2.20/1.66
% 2.20/1.66 % (24192)Memory used [KB]: 1023
% 2.20/1.66 % (24192)Time elapsed: 0.003 s
% 2.20/1.66 % (24192)Instructions burned: 3 (million)
% 2.20/1.66 % (24192)------------------------------
% 2.20/1.66 % (24192)------------------------------
% 2.20/1.67 % (24193)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/4Mi)
% 2.20/1.67 % (24194)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/18Mi)
% 2.20/1.67 % (24195)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/710Mi)
% 2.20/1.67 % (24193)Instruction limit reached!
% 2.20/1.67 % (24193)------------------------------
% 2.20/1.67 % (24193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.67 % (24193)Termination reason: Unknown
% 2.20/1.67 % (24193)Termination phase: shuffling
% 2.20/1.67
% 2.20/1.67 % (24193)Memory used [KB]: 1023
% 2.20/1.67 % (24193)Time elapsed: 0.004 s
% 2.20/1.67 % (24193)Instructions burned: 5 (million)
% 2.20/1.67 % (24193)------------------------------
% 2.20/1.67 % (24193)------------------------------
% 2.20/1.67 % (24194)Instruction limit reached!
% 2.20/1.67 % (24194)------------------------------
% 2.20/1.67 % (24194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.67 % (24194)Termination reason: Unknown
% 2.20/1.67 % (24194)Termination phase: Saturation
% 2.20/1.67
% 2.20/1.67 % (24194)Memory used [KB]: 5628
% 2.20/1.67 % (24194)Time elapsed: 0.010 s
% 2.20/1.67 % (24194)Instructions burned: 18 (million)
% 2.20/1.67 % (24194)------------------------------
% 2.20/1.67 % (24194)------------------------------
% 2.20/1.68 % (24197)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/902Mi)
% 2.20/1.68 % (24196)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/6Mi)
% 2.20/1.68 % (24196)Instruction limit reached!
% 2.20/1.68 % (24196)------------------------------
% 2.20/1.68 % (24196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.68 % (24196)Termination reason: Unknown
% 2.20/1.68 % (24196)Termination phase: shuffling
% 2.20/1.68
% 2.20/1.68 % (24196)Memory used [KB]: 1151
% 2.20/1.68 % (24196)Time elapsed: 0.005 s
% 2.20/1.68 % (24196)Instructions burned: 8 (million)
% 2.20/1.68 % (24196)------------------------------
% 2.20/1.68 % (24196)------------------------------
% 2.20/1.68 % (24197)Refutation not found, incomplete strategy
% 2.20/1.68 % (24197)------------------------------
% 2.20/1.68 % (24197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.68 % (24197)Termination reason: Refutation not found, incomplete strategy
% 2.20/1.68
% 2.20/1.68
% 2.20/1.68 % (24197)Memory used [KB]: 5628
% 2.20/1.68 % (24197)Time elapsed: 0.009 s
% 2.20/1.68 % (24197)Instructions burned: 16 (million)
% 2.20/1.68 % (24197)------------------------------
% 2.20/1.68 % (24197)------------------------------
% 2.20/1.68 % (24198)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/21Mi)
% 2.20/1.69 % (24199)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/5Mi)
% 2.20/1.69 % (24199)Instruction limit reached!
% 2.20/1.69 % (24199)------------------------------
% 2.20/1.69 % (24199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.69 % (24199)Termination reason: Unknown
% 2.20/1.69 % (24199)Termination phase: shuffling
% 2.20/1.69
% 2.20/1.69 % (24199)Memory used [KB]: 1151
% 2.20/1.69 % (24199)Time elapsed: 0.004 s
% 2.20/1.69 % (24199)Instructions burned: 6 (million)
% 2.20/1.69 % (24199)------------------------------
% 2.20/1.69 % (24199)------------------------------
% 2.20/1.69 % (24195)Refutation not found, incomplete strategy
% 2.20/1.69 % (24195)------------------------------
% 2.20/1.69 % (24195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.69 % (24195)Termination reason: Refutation not found, incomplete strategy
% 2.20/1.69
% 2.20/1.69
% 2.20/1.69 % (24195)Memory used [KB]: 5884
% 2.20/1.69 % (24195)Time elapsed: 0.029 s
% 2.20/1.69 % (24198)Instruction limit reached!
% 2.20/1.69 % (24198)------------------------------
% 2.20/1.69 % (24198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.69 % (24195)Instructions burned: 52 (million)
% 2.20/1.69 % (24195)------------------------------
% 2.20/1.69 % (24195)------------------------------
% 2.20/1.69 % (24198)Termination reason: Unknown
% 2.20/1.69 % (24198)Termination phase: Property scanning
% 2.20/1.69
% 2.20/1.69 % (24198)Memory used [KB]: 1151
% 2.20/1.69 % (24198)Time elapsed: 0.011 s
% 2.20/1.69 % (24198)Instructions burned: 22 (million)
% 2.20/1.69 % (24198)------------------------------
% 2.20/1.69 % (24198)------------------------------
% 2.20/1.70 % (24200)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/6Mi)
% 2.20/1.70 % (24200)Instruction limit reached!
% 2.20/1.70 % (24200)------------------------------
% 2.20/1.70 % (24200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.70 % (24200)Termination reason: Unknown
% 2.20/1.70 % (24200)Termination phase: shuffling
% 2.20/1.70
% 2.20/1.70 % (24200)Memory used [KB]: 1151
% 2.20/1.70 % (24200)Time elapsed: 0.004 s
% 2.20/1.70 % (24200)Instructions burned: 6 (million)
% 2.20/1.70 % (24200)------------------------------
% 2.20/1.70 % (24200)------------------------------
% 2.20/1.70 % (24175)Instruction limit reached!
% 2.20/1.70 % (24175)------------------------------
% 2.20/1.70 % (24175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.70 % (24175)Termination reason: Unknown
% 2.20/1.70 % (24175)Termination phase: Saturation
% 2.20/1.70
% 2.20/1.70 % (24175)Memory used [KB]: 6908
% 2.20/1.70 % (24175)Time elapsed: 0.092 s
% 2.20/1.70 % (24175)Instructions burned: 184 (million)
% 2.20/1.70 % (24175)------------------------------
% 2.20/1.70 % (24175)------------------------------
% 2.20/1.70 % (24201)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_24076 for (2999ds/377Mi)
% 2.20/1.71 % (24202)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/779Mi)
% 2.20/1.71 % (24203)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/19Mi)
% 2.20/1.71 % (24204)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/879Mi)
% 2.20/1.71 % (24205)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/17Mi)
% 2.20/1.71 % (24206)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/3Mi)
% 2.20/1.72 % (24206)Instruction limit reached!
% 2.20/1.72 % (24206)------------------------------
% 2.20/1.72 % (24206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.72 % (24206)Termination reason: Unknown
% 2.20/1.72 % (24206)Termination phase: shuffling
% 2.20/1.72
% 2.20/1.72 % (24206)Memory used [KB]: 1023
% 2.20/1.72 % (24206)Time elapsed: 0.003 s
% 2.20/1.72 % (24206)Instructions burned: 4 (million)
% 2.20/1.72 % (24206)------------------------------
% 2.20/1.72 % (24206)------------------------------
% 2.20/1.72 % (24203)Refutation not found, incomplete strategy
% 2.20/1.72 % (24203)------------------------------
% 2.20/1.72 % (24203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.72 % (24203)Termination reason: Refutation not found, incomplete strategy
% 2.20/1.72
% 2.20/1.72
% 2.20/1.72 % (24203)Memory used [KB]: 5628
% 2.20/1.72 % (24203)Time elapsed: 0.009 s
% 2.20/1.72 % (24203)Instructions burned: 16 (million)
% 2.20/1.72 % (24203)------------------------------
% 2.20/1.72 % (24203)------------------------------
% 2.20/1.72 % (24205)Instruction limit reached!
% 2.20/1.72 % (24205)------------------------------
% 2.20/1.72 % (24205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.72 % (24205)Termination reason: Unknown
% 2.20/1.72 % (24205)Termination phase: Property scanning
% 2.20/1.72
% 2.20/1.72 % (24205)Memory used [KB]: 1151
% 2.20/1.72 % (24205)Time elapsed: 0.009 s
% 2.20/1.72 % (24205)Instructions burned: 17 (million)
% 2.20/1.72 % (24205)------------------------------
% 2.20/1.72 % (24205)------------------------------
% 2.20/1.73 % (24207)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/30Mi)
% 2.20/1.73 % (24208)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/127Mi)
% 2.20/1.74 % (24209)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/100Mi)
% 2.20/1.74 % (24202)Refutation not found, incomplete strategy
% 2.20/1.74 % (24202)------------------------------
% 2.20/1.74 % (24202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.74 % (24202)Termination reason: Refutation not found, incomplete strategy
% 2.20/1.74
% 2.20/1.74
% 2.20/1.74 % (24202)Memory used [KB]: 5756
% 2.20/1.74 % (24202)Time elapsed: 0.033 s
% 2.20/1.74 % (24202)Instructions burned: 66 (million)
% 2.20/1.74 % (24202)------------------------------
% 2.20/1.74 % (24202)------------------------------
% 2.20/1.75 % (24207)Instruction limit reached!
% 2.20/1.75 % (24207)------------------------------
% 2.20/1.75 % (24207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.75 % (24207)Termination reason: Unknown
% 2.20/1.75 % (24207)Termination phase: Saturation
% 2.20/1.75
% 2.20/1.75 % (24207)Memory used [KB]: 5756
% 2.20/1.75 % (24207)Time elapsed: 0.015 s
% 2.20/1.75 % (24207)Instructions burned: 30 (million)
% 2.20/1.75 % (24207)------------------------------
% 2.20/1.75 % (24207)------------------------------
% 2.20/1.76 % (24210)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/3Mi)
% 2.20/1.76 % (24210)Instruction limit reached!
% 2.20/1.76 % (24210)------------------------------
% 2.20/1.76 % (24210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.76 % (24210)Termination reason: Unknown
% 2.20/1.76 % (24210)Termination phase: shuffling
% 2.20/1.76
% 2.20/1.76 % (24210)Memory used [KB]: 1151
% 2.20/1.76 % (24210)Time elapsed: 0.004 s
% 2.20/1.76 % (24210)Instructions burned: 5 (million)
% 2.20/1.76 % (24210)------------------------------
% 2.20/1.76 % (24210)------------------------------
% 2.20/1.76 % (24211)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/20Mi)
% 2.20/1.77 % (24211)Instruction limit reached!
% 2.20/1.77 % (24211)------------------------------
% 2.20/1.77 % (24211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.77 % (24211)Termination reason: Unknown
% 2.20/1.77 % (24211)Termination phase: Saturation
% 2.20/1.77
% 2.20/1.77 % (24211)Memory used [KB]: 5628
% 2.20/1.77 % (24211)Time elapsed: 0.011 s
% 2.20/1.77 % (24211)Instructions burned: 20 (million)
% 2.20/1.77 % (24211)------------------------------
% 2.20/1.77 % (24211)------------------------------
% 2.20/1.78 % (24208)First to succeed.
% 2.20/1.78 % (24212)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_24076 for (2998ds/86Mi)
% 2.20/1.78 % (24208)Refutation found. Thanks to Tanya!
% 2.20/1.78 % SZS status Theorem for DTF2THF_24076
% 2.20/1.78 % SZS output start Proof for DTF2THF_24076
% 2.20/1.78 thf(type_def_5, type, mworld: $tType).
% 2.20/1.78 thf(func_def_0, type, mworld: $tType).
% 2.20/1.78 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 2.20/1.78 thf(func_def_2, type, mactual: mworld).
% 2.20/1.78 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 2.20/1.78 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 2.20/1.78 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.20/1.78 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.20/1.78 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.20/1.78 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.20/1.78 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 2.20/1.78 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 2.20/1.78 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 2.20/1.78 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 2.20/1.78 thf(func_def_15, type, qmltpeq: $i > $i > mworld > $o).
% 2.20/1.78 thf(func_def_16, type, equal_set: $i > $i > mworld > $o).
% 2.20/1.78 thf(func_def_17, type, member: $i > $i > mworld > $o).
% 2.20/1.78 thf(func_def_18, type, subset: $i > $i > mworld > $o).
% 2.20/1.78 thf(func_def_19, type, singleton: $i > $i).
% 2.20/1.78 thf(func_def_20, type, product: $i > $i).
% 2.20/1.78 thf(func_def_21, type, unordered_pair: $i > $i > $i).
% 2.20/1.78 thf(func_def_22, type, intersection: $i > $i > $i).
% 2.20/1.78 thf(func_def_23, type, difference: $i > $i > $i).
% 2.20/1.78 thf(func_def_24, type, sum: $i > $i).
% 2.20/1.78 thf(func_def_25, type, union: $i > $i > $i).
% 2.20/1.78 thf(func_def_26, type, power_set: $i > $i).
% 2.20/1.78 thf(func_def_40, type, sK0: mworld > mworld).
% 2.20/1.78 thf(func_def_45, type, ph3: !>[X0: $tType]:(X0)).
% 2.20/1.78 thf(f600,plain,(
% 2.20/1.78 $false),
% 2.20/1.78 inference(avatar_sat_refutation,[status(thm)],[f457,f524,f599])).
% 2.20/1.78 thf(f599,plain,(
% 2.20/1.78 ~spl1_1),
% 2.20/1.78 inference(avatar_contradiction_clause,[status(thm)],[f598])).
% 2.20/1.78 thf(f598,plain,(
% 2.20/1.78 $false | ~spl1_1),
% 2.20/1.78 inference(trivial_inequality_removal,[status(thm)],[f585])).
% 2.20/1.78 thf(f585,plain,(
% 2.20/1.78 ($false = $true) | ~spl1_1),
% 2.20/1.78 inference(backward_demodulation,[status(thm)],[f534,f558])).
% 2.20/1.78 thf(f558,plain,(
% 2.20/1.78 ($false = (member @ sK5 @ sK2 @ mactual)) | ~spl1_1),
% 2.20/1.78 inference(not_proxy_clausification,[status(thm)],[f557])).
% 2.20/1.78 thf(f557,plain,(
% 2.20/1.78 ((~ (member @ sK5 @ sK2 @ mactual)) = $true) | ~spl1_1),
% 2.20/1.78 inference(boolean_simplification,[status(thm)],[f556])).
% 2.20/1.78 thf(f556,plain,(
% 2.20/1.78 ((~ ((member @ sK5 @ sK2 @ mactual) | (member @ sK5 @ sK2 @ mactual))) = $true) | ~spl1_1),
% 2.20/1.78 inference(boolean_simplification,[status(thm)],[f553])).
% 2.20/1.78 thf(f553,plain,(
% 2.20/1.78 ($true = (((member @ sK5 @ sK2 @ mactual) | (member @ sK5 @ sK2 @ mactual)) = $false)) | ~spl1_1),
% 2.20/1.78 inference(superposition,[status(thm)],[f236,f533])).
% 2.20/1.78 thf(f533,plain,(
% 2.20/1.78 ($false = (member @ sK5 @ (union @ sK2 @ sK2) @ mactual)) | ~spl1_1),
% 2.20/1.78 inference(binary_proxy_clausification,[status(thm)],[f532])).
% 2.20/1.78 thf(f532,plain,(
% 2.20/1.78 ($false = ((member @ sK5 @ sK2 @ mactual) => (member @ sK5 @ (union @ sK2 @ sK2) @ mactual))) | ~spl1_1),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f531])).
% 2.20/1.78 thf(f531,plain,(
% 2.20/1.78 ($false = ((^[Y0 : $i]: ((member @ Y0 @ sK2 @ mactual) => (member @ Y0 @ (union @ sK2 @ sK2) @ mactual))) @ sK5)) | ~spl1_1),
% 2.20/1.78 inference(sigma_clausification,[status(thm)],[f530])).
% 2.20/1.78 thf(f530,plain,(
% 2.20/1.78 ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ sK2 @ mactual) => (member @ Y0 @ (union @ sK2 @ sK2) @ mactual)))) = $false) | ~spl1_1),
% 2.20/1.78 inference(not_proxy_clausification,[status(thm)],[f529])).
% 2.20/1.78 thf(f529,plain,(
% 2.20/1.78 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ sK2 @ mactual) => (member @ Y0 @ (union @ sK2 @ sK2) @ mactual)))))) | ~spl1_1),
% 2.20/1.78 inference(boolean_simplification,[status(thm)],[f526])).
% 2.20/1.78 thf(f526,plain,(
% 2.20/1.78 (((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ sK2 @ mactual) => (member @ Y0 @ (union @ sK2 @ sK2) @ mactual)))) = $false) = $true) | ~spl1_1),
% 2.20/1.78 inference(superposition,[status(thm)],[f411,f452])).
% 2.20/1.78 thf(f452,plain,(
% 2.20/1.78 ((subset @ sK2 @ (union @ sK2 @ sK2) @ mactual) = $false) | ~spl1_1),
% 2.20/1.78 inference(avatar_component_clause,[status(thm)],[f450])).
% 2.20/1.78 thf(f450,definition,(
% 2.20/1.78 spl1_1 <=> ((subset @ sK2 @ (union @ sK2 @ sK2) @ mactual) = $false)),
% 2.20/1.78 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 2.20/1.78 thf(f411,plain,(
% 2.20/1.78 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual)))) = (subset @ X1 @ X2 @ mactual)))) )),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f410])).
% 2.20/1.78 thf(f410,plain,(
% 2.20/1.78 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual)))) = (subset @ X1 @ Y0 @ mactual))) @ X2))) )),
% 2.20/1.78 inference(pi_clausification,[status(thm)],[f409])).
% 2.20/1.78 thf(f409,plain,(
% 2.20/1.78 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual)))) = (subset @ X1 @ Y0 @ mactual)))) = $true)) )),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f408])).
% 2.20/1.78 thf(f408,plain,(
% 2.20/1.78 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual)))) = (subset @ Y0 @ Y1 @ mactual))))) @ X1))) )),
% 2.20/1.78 inference(pi_clausification,[status(thm)],[f407])).
% 2.20/1.78 thf(f407,plain,(
% 2.20/1.78 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual)))) = (subset @ Y0 @ Y1 @ mactual)))))) = $true)),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f203])).
% 2.20/1.78 thf(f203,plain,(
% 2.20/1.78 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) = (Y2 @ Y4))))))) @ (subset @ Y0 @ Y1) @ ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 2.20/1.78 inference(definition_unfolding,[status(thm)],[f167,f160,f166,f166,f142,f166,f143])).
% 2.20/1.78 thf(f143,plain,(
% 2.20/1.78 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f60])).
% 2.20/1.78 thf(f60,plain,(
% 2.20/1.78 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f59])).
% 2.20/1.78 thf(f59,plain,(
% 2.20/1.78 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 2.20/1.78 inference(rectify,[status(thm)],[f5])).
% 2.20/1.78 thf(f5,axiom,(
% 2.20/1.78 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mimplies_def)).
% 2.20/1.78 thf(f142,plain,(
% 2.20/1.78 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f95])).
% 2.20/1.78 thf(f95,plain,(
% 2.20/1.78 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f94])).
% 2.20/1.78 thf(f94,plain,(
% 2.20/1.78 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X0 @ X2))) = mequiv)),
% 2.20/1.78 inference(rectify,[status(thm)],[f6])).
% 2.20/1.78 thf(f6,axiom,(
% 2.20/1.78 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) <=> (X1 @ X2))) = mequiv)),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mequiv_def)).
% 2.20/1.78 thf(f166,plain,(
% 2.20/1.78 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f83])).
% 2.20/1.78 thf(f83,plain,(
% 2.20/1.78 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f82])).
% 2.20/1.78 thf(f82,plain,(
% 2.20/1.78 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))) = mforall_di)),
% 2.20/1.78 inference(rectify,[status(thm)],[f10])).
% 2.20/1.78 thf(f10,axiom,(
% 2.20/1.78 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : (X1 @ X5 @ X2))) = mforall_di)),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mforall_di_def)).
% 2.20/1.78 thf(f160,plain,(
% 2.20/1.78 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f67])).
% 2.20/1.78 thf(f67,plain,(
% 2.20/1.78 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f1])).
% 2.20/1.78 thf(f1,axiom,(
% 2.20/1.78 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mlocal_def)).
% 2.20/1.78 thf(f167,plain,(
% 2.20/1.78 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f56])).
% 2.20/1.78 thf(f56,plain,(
% 2.20/1.78 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f55])).
% 2.20/1.78 thf(f55,plain,(
% 2.20/1.78 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (subset @ X0 @ X1) @ (mforall_di @ (^[X2 : $i] : (mimplies @ (member @ X2 @ X0) @ (member @ X2 @ X1))))))))))),
% 2.20/1.78 inference(rectify,[status(thm)],[f33])).
% 2.20/1.78 thf(f33,axiom,(
% 2.20/1.78 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (subset @ X1 @ X3) @ (mforall_di @ (^[X5 : $i] : (mimplies @ (member @ X5 @ X1) @ (member @ X5 @ X3))))))))))),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',subset_0)).
% 2.20/1.78 thf(f236,plain,(
% 2.20/1.78 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((member @ X1 @ X2 @ mactual) | (member @ X1 @ X3 @ mactual)) = (member @ X1 @ (union @ X2 @ X3) @ mactual)) = $true)) )),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f235])).
% 2.20/1.78 thf(f235,plain,(
% 2.20/1.78 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((member @ X1 @ X2 @ mactual) | (member @ X1 @ Y0 @ mactual)) = (member @ X1 @ (union @ X2 @ Y0) @ mactual))) @ X3) = $true)) )),
% 2.20/1.78 inference(pi_clausification,[status(thm)],[f234])).
% 2.20/1.78 thf(f234,plain,(
% 2.20/1.78 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((member @ X1 @ X2 @ mactual) | (member @ X1 @ Y0 @ mactual)) = (member @ X1 @ (union @ X2 @ Y0) @ mactual)))))) )),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f233])).
% 2.20/1.78 thf(f233,plain,(
% 2.20/1.78 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((member @ X1 @ Y0 @ mactual) | (member @ X1 @ Y1 @ mactual)) = (member @ X1 @ (union @ Y0 @ Y1) @ mactual))))) @ X2) = $true)) )),
% 2.20/1.78 inference(pi_clausification,[status(thm)],[f232])).
% 2.20/1.78 thf(f232,plain,(
% 2.20/1.78 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((member @ X1 @ Y0 @ mactual) | (member @ X1 @ Y1 @ mactual)) = (member @ X1 @ (union @ Y0 @ Y1) @ mactual)))))))) )),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f231])).
% 2.20/1.78 thf(f231,plain,(
% 2.20/1.78 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((member @ Y0 @ Y1 @ mactual) | (member @ Y0 @ Y2 @ mactual)) = (member @ Y0 @ (union @ Y1 @ Y2) @ mactual))))))) @ X1))) )),
% 2.20/1.78 inference(pi_clausification,[status(thm)],[f230])).
% 2.20/1.78 thf(f230,plain,(
% 2.20/1.78 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((member @ Y0 @ Y1 @ mactual) | (member @ Y0 @ Y2 @ mactual)) = (member @ Y0 @ (union @ Y1 @ Y2) @ mactual)))))))))),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f193])).
% 2.20/1.78 thf(f193,plain,(
% 2.20/1.78 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y4 @ Y5) = (Y3 @ Y5))))))) @ (member @ Y0 @ (union @ Y1 @ Y2)) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)))))))))) = $true)),
% 2.20/1.78 inference(definition_unfolding,[status(thm)],[f154,f160,f166,f166,f166,f142,f177])).
% 2.20/1.78 thf(f177,plain,(
% 2.20/1.78 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f105])).
% 2.20/1.78 thf(f105,plain,(
% 2.20/1.78 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f104])).
% 2.20/1.78 thf(f104,plain,(
% 2.20/1.78 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 2.20/1.78 inference(rectify,[status(thm)],[f4])).
% 2.20/1.78 thf(f4,axiom,(
% 2.20/1.78 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) | (X1 @ X2))) = mor)),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mor_def)).
% 2.20/1.78 thf(f154,plain,(
% 2.20/1.78 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (member @ Y0 @ (union @ Y1 @ Y2)) @ (mor @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)))))))))))),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f89])).
% 2.20/1.78 thf(f89,plain,(
% 2.20/1.78 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (member @ Y0 @ (union @ Y1 @ Y2)) @ (mor @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)))))))))))),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f88])).
% 2.20/1.78 thf(f88,plain,(
% 2.20/1.78 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X2 : $i] : (mequiv @ (member @ X0 @ (union @ X1 @ X2)) @ (mor @ (member @ X0 @ X1) @ (member @ X0 @ X2))))))))))),
% 2.20/1.78 inference(rectify,[status(thm)],[f37])).
% 2.20/1.78 thf(f37,axiom,(
% 2.20/1.78 (mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (member @ X5 @ (union @ X1 @ X3)) @ (mor @ (member @ X5 @ X1) @ (member @ X5 @ X3))))))))))),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',union_0)).
% 2.20/1.78 thf(f534,plain,(
% 2.20/1.78 ($true = (member @ sK5 @ sK2 @ mactual)) | ~spl1_1),
% 2.20/1.78 inference(binary_proxy_clausification,[status(thm)],[f532])).
% 2.20/1.78 thf(f524,plain,(
% 2.20/1.78 ~spl1_2),
% 2.20/1.78 inference(avatar_contradiction_clause,[status(thm)],[f523])).
% 2.20/1.78 thf(f523,plain,(
% 2.20/1.78 $false | ~spl1_2),
% 2.20/1.78 inference(trivial_inequality_removal,[status(thm)],[f522])).
% 2.20/1.78 thf(f522,plain,(
% 2.20/1.78 ($false = $true) | ~spl1_2),
% 2.20/1.78 inference(forward_demodulation,[status(thm)],[f508,f474])).
% 2.20/1.78 thf(f474,plain,(
% 2.20/1.78 ($false = (member @ sK4 @ sK2 @ mactual)) | ~spl1_2),
% 2.20/1.78 inference(binary_proxy_clausification,[status(thm)],[f473])).
% 2.20/1.78 thf(f473,plain,(
% 2.20/1.78 (((member @ sK4 @ (union @ sK2 @ sK2) @ mactual) => (member @ sK4 @ sK2 @ mactual)) = $false) | ~spl1_2),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f472])).
% 2.20/1.78 thf(f472,plain,(
% 2.20/1.78 ($false = ((^[Y0 : $i]: ((member @ Y0 @ (union @ sK2 @ sK2) @ mactual) => (member @ Y0 @ sK2 @ mactual))) @ sK4)) | ~spl1_2),
% 2.20/1.78 inference(sigma_clausification,[status(thm)],[f471])).
% 2.20/1.78 thf(f471,plain,(
% 2.20/1.78 ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (union @ sK2 @ sK2) @ mactual) => (member @ Y0 @ sK2 @ mactual)))) = $false) | ~spl1_2),
% 2.20/1.78 inference(not_proxy_clausification,[status(thm)],[f470])).
% 2.20/1.78 thf(f470,plain,(
% 2.20/1.78 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (union @ sK2 @ sK2) @ mactual) => (member @ Y0 @ sK2 @ mactual)))))) | ~spl1_2),
% 2.20/1.78 inference(boolean_simplification,[status(thm)],[f469])).
% 2.20/1.78 thf(f469,plain,(
% 2.20/1.78 ($true = ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (union @ sK2 @ sK2) @ mactual) => (member @ Y0 @ sK2 @ mactual)))) = $false)) | ~spl1_2),
% 2.20/1.78 inference(superposition,[status(thm)],[f411,f456])).
% 2.20/1.78 thf(f456,plain,(
% 2.20/1.78 ($false = (subset @ (union @ sK2 @ sK2) @ sK2 @ mactual)) | ~spl1_2),
% 2.20/1.78 inference(avatar_component_clause,[status(thm)],[f454])).
% 2.20/1.78 thf(f454,definition,(
% 2.20/1.78 spl1_2 <=> ($false = (subset @ (union @ sK2 @ sK2) @ sK2 @ mactual))),
% 2.20/1.78 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 2.20/1.78 thf(f508,plain,(
% 2.20/1.78 ($true = (member @ sK4 @ sK2 @ mactual)) | ~spl1_2),
% 2.20/1.78 inference(boolean_simplification,[status(thm)],[f507])).
% 2.20/1.78 thf(f507,plain,(
% 2.20/1.78 (((member @ sK4 @ sK2 @ mactual) | (member @ sK4 @ sK2 @ mactual)) = $true) | ~spl1_2),
% 2.20/1.78 inference(boolean_simplification,[status(thm)],[f495])).
% 2.20/1.78 thf(f495,plain,(
% 2.20/1.78 ((((member @ sK4 @ sK2 @ mactual) | (member @ sK4 @ sK2 @ mactual)) = $true) = $true) | ~spl1_2),
% 2.20/1.78 inference(superposition,[status(thm)],[f236,f475])).
% 2.20/1.78 thf(f475,plain,(
% 2.20/1.78 ((member @ sK4 @ (union @ sK2 @ sK2) @ mactual) = $true) | ~spl1_2),
% 2.20/1.78 inference(binary_proxy_clausification,[status(thm)],[f473])).
% 2.20/1.78 thf(f457,plain,(
% 2.20/1.78 spl1_1 | spl1_2),
% 2.20/1.78 inference(avatar_split_clause,[status(thm)],[f448,f454,f450])).
% 2.20/1.78 thf(f448,plain,(
% 2.20/1.78 ((subset @ sK2 @ (union @ sK2 @ sK2) @ mactual) = $false) | ($false = (subset @ (union @ sK2 @ sK2) @ sK2 @ mactual))),
% 2.20/1.78 inference(binary_proxy_clausification,[status(thm)],[f447])).
% 2.20/1.78 thf(f447,plain,(
% 2.20/1.78 ($false = ((subset @ (union @ sK2 @ sK2) @ sK2 @ mactual) & (subset @ sK2 @ (union @ sK2 @ sK2) @ mactual)))),
% 2.20/1.78 inference(not_proxy_clausification,[status(thm)],[f446])).
% 2.20/1.78 thf(f446,plain,(
% 2.20/1.78 ((~ ((subset @ (union @ sK2 @ sK2) @ sK2 @ mactual) & (subset @ sK2 @ (union @ sK2 @ sK2) @ mactual))) = $true)),
% 2.20/1.78 inference(boolean_simplification,[status(thm)],[f445])).
% 2.20/1.78 thf(f445,plain,(
% 2.20/1.78 ($true = (((subset @ (union @ sK2 @ sK2) @ sK2 @ mactual) & (subset @ sK2 @ (union @ sK2 @ sK2) @ mactual)) = $false))),
% 2.20/1.78 inference(superposition,[status(thm)],[f249,f364])).
% 2.20/1.78 thf(f364,plain,(
% 2.20/1.78 ($false = (equal_set @ (union @ sK2 @ sK2) @ sK2 @ mactual))),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f363])).
% 2.20/1.78 thf(f363,plain,(
% 2.20/1.78 (((^[Y0 : $i]: (equal_set @ (union @ Y0 @ Y0) @ Y0 @ mactual)) @ sK2) = $false)),
% 2.20/1.78 inference(sigma_clausification,[status(thm)],[f362])).
% 2.20/1.78 thf(f362,plain,(
% 2.20/1.78 ($true != (!! @ $i @ (^[Y0 : $i]: (equal_set @ (union @ Y0 @ Y0) @ Y0 @ mactual))))),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f191])).
% 2.20/1.78 thf(f191,plain,(
% 2.20/1.78 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: (equal_set @ (union @ Y0 @ Y0) @ Y0)))))),
% 2.20/1.78 inference(definition_unfolding,[status(thm)],[f152,f160,f166])).
% 2.20/1.78 thf(f152,plain,(
% 2.20/1.78 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (equal_set @ (union @ Y0 @ Y0) @ Y0)))) != $true)),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f134])).
% 2.20/1.78 thf(f134,plain,(
% 2.20/1.78 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (equal_set @ (union @ Y0 @ Y0) @ Y0)))) != $true)),
% 2.20/1.78 inference(flattening,[status(thm)],[f133])).
% 2.20/1.78 thf(f133,plain,(
% 2.20/1.78 ~((mlocal @ (mforall_di @ (^[Y0 : $i]: (equal_set @ (union @ Y0 @ Y0) @ Y0)))) = $true)),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f132])).
% 2.20/1.78 thf(f132,plain,(
% 2.20/1.78 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (equal_set @ (union @ X0 @ X0) @ X0))))),
% 2.20/1.78 inference(rectify,[status(thm)],[f45])).
% 2.20/1.78 thf(f45,negated_conjecture,(
% 2.20/1.78 ~(mlocal @ (mforall_di @ (^[X1 : $i] : (equal_set @ (union @ X1 @ X1) @ X1))))),
% 2.20/1.78 inference(negated_conjecture,[status(cth)],[f44])).
% 2.20/1.78 thf(f44,conjecture,(
% 2.20/1.78 (mlocal @ (mforall_di @ (^[X1 : $i] : (equal_set @ (union @ X1 @ X1) @ X1))))),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',thI14)).
% 2.20/1.78 thf(f249,plain,(
% 2.20/1.78 ( ! [X2 : $i,X1 : $i] : (($true = (((subset @ X1 @ X2 @ mactual) & (subset @ X2 @ X1 @ mactual)) = (equal_set @ X1 @ X2 @ mactual)))) )),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f248])).
% 2.20/1.78 thf(f248,plain,(
% 2.20/1.78 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((subset @ X1 @ Y0 @ mactual) & (subset @ Y0 @ X1 @ mactual)) = (equal_set @ X1 @ Y0 @ mactual))) @ X2))) )),
% 2.20/1.78 inference(pi_clausification,[status(thm)],[f247])).
% 2.20/1.78 thf(f247,plain,(
% 2.20/1.78 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((subset @ X1 @ Y0 @ mactual) & (subset @ Y0 @ X1 @ mactual)) = (equal_set @ X1 @ Y0 @ mactual)))))) )),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f246])).
% 2.20/1.78 thf(f246,plain,(
% 2.20/1.78 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual)) = (equal_set @ Y0 @ Y1 @ mactual))))) @ X1))) )),
% 2.20/1.78 inference(pi_clausification,[status(thm)],[f245])).
% 2.20/1.78 thf(f245,plain,(
% 2.20/1.78 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual)) = (equal_set @ Y0 @ Y1 @ mactual)))))) = $true)),
% 2.20/1.78 inference(beta_eta_normalization,[status(thm)],[f199])).
% 2.20/1.78 thf(f199,plain,(
% 2.20/1.78 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) = (Y2 @ Y4))))))) @ (equal_set @ Y0 @ Y1) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))) = $true)),
% 2.20/1.78 inference(definition_unfolding,[status(thm)],[f162,f160,f166,f166,f142,f138])).
% 2.20/1.78 thf(f138,plain,(
% 2.20/1.78 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f113])).
% 2.20/1.78 thf(f113,plain,(
% 2.20/1.78 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f112])).
% 2.20/1.78 thf(f112,plain,(
% 2.20/1.78 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 2.20/1.78 inference(rectify,[status(thm)],[f3])).
% 2.20/1.78 thf(f3,axiom,(
% 2.20/1.78 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',mand_def)).
% 2.20/1.78 thf(f162,plain,(
% 2.20/1.78 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))))),
% 2.20/1.78 inference(cnf_transformation,[status(thm)],[f81])).
% 2.20/1.78 thf(f81,plain,(
% 2.20/1.78 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))))),
% 2.20/1.78 inference(fool_elimination,[status(thm)],[f80])).
% 2.20/1.78 thf(f80,plain,(
% 2.20/1.78 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (equal_set @ X0 @ X1) @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X0))))))))),
% 2.20/1.78 inference(rectify,[status(thm)],[f34])).
% 2.20/1.78 thf(f34,axiom,(
% 2.20/1.78 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (equal_set @ X1 @ X3) @ (mand @ (subset @ X1 @ X3) @ (subset @ X3 @ X1))))))))),
% 2.20/1.78 file('/export/starexec/sandbox/tmp/tmp.NWwcO6r4c8/DTF2THF_24076.p',equal_set_0)).
% 2.20/1.78 % SZS output end Proof for DTF2THF_24076
% 2.20/1.78 % (24208)------------------------------
% 2.20/1.78 % (24208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.78 % (24208)Termination reason: Refutation
% 2.20/1.78
% 2.20/1.78 % (24208)Memory used [KB]: 6396
% 2.20/1.78 % (24208)Time elapsed: 0.046 s
% 2.20/1.78 % (24208)Instructions burned: 87 (million)
% 2.20/1.78 % (24208)------------------------------
% 2.20/1.78 % (24208)------------------------------
% 2.20/1.78 % (24174)Success in time 0.187 s
%------------------------------------------------------------------------------