%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET579^3 : 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 : n029.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 09:31:47 AM UTC 2026
% Result : Theorem 1.84s 1.47s
% Output : Refutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 144 ( 78 unt; 0 typ; 4 def)
% Number of atoms : 1038 ( 172 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 1568 ( 99 ~; 58 |; 41 &;1265 @)
% ( 6 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 94 ( 94 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 27 usr; 13 con; 0-3 aty)
% ( 65 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 316 ( 280 ^; 36 !; 0 ?; 316 :)
% 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_14,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_15,type,
member: $i > $i > mworld > $o ).
thf(func_def_16,type,
subset: $i > $i > mworld > $o ).
thf(func_def_17,type,
difference: $i > $i > $i ).
thf(func_def_32,type,
sK0: mworld > mworld ).
thf(func_def_39,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f688,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f271,f468,f516,f598,f683]) ).
thf(f683,plain,
( ~ spl1_2
| ~ spl1_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f682]) ).
thf(f682,plain,
( $false
| ~ spl1_2
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f667]) ).
thf(f667,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_8 ),
inference(backward_demodulation,[status(thm)],[f515,f491]) ).
thf(f491,plain,
( ( $false
= ( member @ sK8 @ sK4 @ mactual ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[status(thm)],[f490]) ).
thf(f490,plain,
( ( ( ~ ( member @ sK8 @ sK4 @ mactual ) )
= $true )
| ~ spl1_2 ),
inference(binary_proxy_clausification,[status(thm)],[f488]) ).
thf(f488,plain,
( ( $true
= ( ~ ( member @ sK8 @ sK4 @ mactual )
& ( member @ sK8 @ sK3 @ mactual ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[status(thm)],[f484]) ).
thf(f484,plain,
( ( ( ( ~ ( member @ sK8 @ sK4 @ mactual )
& ( member @ sK8 @ sK3 @ mactual ) )
= $true )
= $true )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f174,f480]) ).
thf(f480,plain,
( ( $true
= ( member @ sK8 @ sK2 @ mactual ) )
| ~ spl1_2 ),
inference(binary_proxy_clausification,[status(thm)],[f478]) ).
thf(f478,plain,
( ( ( ( member @ sK8 @ sK2 @ mactual )
=> ( member @ sK8 @ ( difference @ sK3 @ sK4 ) @ mactual ) )
= $false )
| ~ spl1_2 ),
inference(beta_eta_normalization,[status(thm)],[f477]) ).
thf(f477,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( member @ Y0 @ sK2 @ mactual )
=> ( member @ Y0 @ ( difference @ sK3 @ sK4 ) @ mactual ) )
@ sK8 ) )
| ~ spl1_2 ),
inference(sigma_clausification,[status(thm)],[f476]) ).
thf(f476,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ sK2 @ mactual )
=> ( member @ Y0 @ ( difference @ sK3 @ sK4 ) @ mactual ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[status(thm)],[f475]) ).
thf(f475,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ sK2 @ mactual )
=> ( member @ Y0 @ ( difference @ sK3 @ sK4 ) @ mactual ) ) ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[status(thm)],[f469]) ).
thf(f469,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ sK2 @ mactual )
=> ( member @ Y0 @ ( difference @ sK3 @ sK4 ) @ mactual ) ) )
= $false ) )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f141,f261]) ).
thf(f261,plain,
( ( $false
= ( subset @ sK2 @ ( difference @ sK3 @ sK4 ) @ mactual ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f259]) ).
thf(f259,definition,
( spl1_2
<=> ( $false
= ( subset @ sK2 @ ( difference @ sK3 @ sK4 ) @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f141,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) )
= ( subset @ X1 @ X2 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f140]) ).
thf(f140,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)],[f139]) ).
thf(f139,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)],[f138]) ).
thf(f138,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)],[f137]) ).
thf(f137,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)],[f113]) ).
thf(f113,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)],[f95,f97,f92,f92,f85,f92,f80]) ).
thf(f80,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
thf(f70,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f69]) ).
thf(f69,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.PwGLKcqaSk/DTF2THF_6202.p',mimplies_def) ).
thf(f85,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f44]) ).
thf(f44,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( mequiv
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',mequiv_def) ).
thf(f92,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
thf(f63,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f62]) ).
thf(f62,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.PwGLKcqaSk/DTF2THF_6202.p',mforall_di_def) ).
thf(f97,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
thf(f66,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.PwGLKcqaSk/DTF2THF_6202.p',mlocal_def) ).
thf(f95,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)],[f59]) ).
thf(f59,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)],[f58]) ).
thf(f58,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)],[f23]) ).
thf(f23,axiom,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X8: $i] :
( mequiv @ ( subset @ X3 @ X8 )
@ ( mforall_di
@ ^ [X9: $i] : ( mimplies @ ( member @ X9 @ X3 ) @ ( member @ X9 @ X8 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',subset_defn) ).
thf(f174,plain,
! [X1: $i] :
( $true
= ( ( ~ ( member @ X1 @ sK4 @ mactual )
& ( member @ X1 @ sK3 @ mactual ) )
= ( member @ X1 @ sK2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f173]) ).
thf(f173,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ~ ( member @ Y0 @ sK4 @ mactual )
& ( member @ Y0 @ sK3 @ mactual ) )
= ( member @ Y0 @ sK2 @ mactual ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( member @ Y0 @ sK4 @ mactual )
& ( member @ Y0 @ sK3 @ mactual ) )
= ( member @ Y0 @ sK2 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( member @ Y0 @ sK4 @ mactual )
& ( member @ Y0 @ sK3 @ mactual ) )
= ( member @ Y0 @ sK2 @ mactual ) ) )
=> ( qmltpeq @ sK2 @ ( difference @ sK3 @ sK4 ) @ mactual ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f169]) ).
thf(f169,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( member @ Y1 @ Y0 @ mactual )
& ( member @ Y1 @ sK3 @ mactual ) )
= ( member @ Y1 @ sK2 @ mactual ) ) )
=> ( qmltpeq @ sK2 @ ( difference @ sK3 @ Y0 ) @ mactual ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( member @ Y1 @ Y0 @ mactual )
& ( member @ Y1 @ sK3 @ mactual ) )
= ( member @ Y1 @ sK2 @ mactual ) ) )
=> ( qmltpeq @ sK2 @ ( difference @ sK3 @ Y0 ) @ mactual ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f167]) ).
thf(f167,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( ~ ( member @ Y2 @ Y1 @ mactual )
& ( member @ Y2 @ Y0 @ mactual ) )
= ( member @ Y2 @ sK2 @ mactual ) ) )
=> ( qmltpeq @ sK2 @ ( difference @ Y0 @ Y1 ) @ mactual ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( ~ ( member @ Y2 @ Y1 @ mactual )
& ( member @ Y2 @ Y0 @ mactual ) )
= ( member @ Y2 @ sK2 @ mactual ) ) )
=> ( qmltpeq @ sK2 @ ( difference @ Y0 @ Y1 ) @ mactual ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f165]) ).
thf(f165,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ~ ( member @ Y3 @ Y2 @ mactual )
& ( member @ Y3 @ Y1 @ mactual ) )
= ( member @ Y3 @ Y0 @ mactual ) ) )
=> ( qmltpeq @ Y0 @ ( difference @ Y1 @ Y2 ) @ mactual ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ~ ( member @ Y3 @ Y2 @ mactual )
& ( member @ Y3 @ Y1 @ mactual ) )
= ( member @ Y3 @ Y0 @ mactual ) ) )
=> ( qmltpeq @ Y0 @ ( difference @ Y1 @ Y2 ) @ mactual ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f118]) ).
thf(f118,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] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > mworld > $o,Y4: mworld] :
( !! @ $i
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: $i] :
( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y5 @ Y6 )
= ( Y4 @ Y6 ) )
@ ( member @ Y3 @ Y0 )
@ ( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ ( member @ Y3 @ Y1 )
@ ( ^ [Y4: mworld > $o,Y5: mworld] :
~ ( Y4 @ Y5 )
@ ( member @ Y3 @ Y2 ) ) ) ) )
@ ( qmltpeq @ Y0 @ ( difference @ Y1 @ Y2 ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f103,f97,f92,f92,f92,f80,f92,f85,f104,f84]) ).
thf(f84,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) )
= mnot ),
file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',mnot_def) ).
thf(f104,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f38]) ).
thf(f38,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',mand_def) ).
thf(f103,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] :
( mimplies
@ ( mforall_di
@ ^ [Y3: $i] : ( mequiv @ ( member @ Y3 @ Y0 ) @ ( mand @ ( member @ Y3 @ Y1 ) @ ( mnot @ ( member @ Y3 @ Y2 ) ) ) ) )
@ ( qmltpeq @ Y0 @ ( difference @ Y1 @ Y2 ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f77]) ).
thf(f77,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] :
( mimplies
@ ( mforall_di
@ ^ [Y3: $i] : ( mequiv @ ( member @ Y3 @ Y0 ) @ ( mand @ ( member @ Y3 @ Y1 ) @ ( mnot @ ( member @ Y3 @ Y2 ) ) ) ) )
@ ( qmltpeq @ Y0 @ ( difference @ Y1 @ Y2 ) ) ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f76]) ).
thf(f76,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] :
( mimplies
@ ( mforall_di
@ ^ [Y3: $i] : ( mequiv @ ( member @ Y3 @ Y0 ) @ ( mand @ ( member @ Y3 @ Y1 ) @ ( mnot @ ( member @ Y3 @ Y2 ) ) ) ) )
@ ( qmltpeq @ Y0 @ ( difference @ Y1 @ Y2 ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f75]) ).
thf(f75,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] :
( mimplies
@ ( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( member @ X3 @ X0 ) @ ( mand @ ( member @ X3 @ X1 ) @ ( mnot @ ( member @ X3 @ X2 ) ) ) ) )
@ ( qmltpeq @ X0 @ ( difference @ X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X8: $i] :
( mforall_di
@ ^ [X9: $i] :
( mimplies
@ ( mforall_di
@ ^ [X10: $i] : ( mequiv @ ( member @ X10 @ X3 ) @ ( mand @ ( member @ X10 @ X8 ) @ ( mnot @ ( member @ X10 @ X9 ) ) ) ) )
@ ( qmltpeq @ X3 @ ( difference @ X8 @ X9 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
thf(f25,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X8: $i] :
( mforall_di
@ ^ [X9: $i] :
( mimplies
@ ( mforall_di
@ ^ [X10: $i] : ( mequiv @ ( member @ X10 @ X3 ) @ ( mand @ ( member @ X10 @ X8 ) @ ( mnot @ ( member @ X10 @ X9 ) ) ) ) )
@ ( qmltpeq @ X3 @ ( difference @ X8 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',prove_th20) ).
thf(f515,plain,
( ( $true
= ( member @ sK8 @ sK4 @ mactual ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f513]) ).
thf(f513,definition,
( spl1_8
<=> ( $true
= ( member @ sK8 @ sK4 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition]) ).
thf(f598,plain,
( ~ spl1_2
| ~ spl1_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f597]) ).
thf(f597,plain,
( $false
| ~ spl1_2
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f596]) ).
thf(f596,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_7 ),
inference(forward_demodulation,[status(thm)],[f489,f511]) ).
thf(f511,plain,
( ( ( member @ sK8 @ sK3 @ mactual )
= $false )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f509]) ).
thf(f509,definition,
( spl1_7
<=> ( ( member @ sK8 @ sK3 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f489,plain,
( ( ( member @ sK8 @ sK3 @ mactual )
= $true )
| ~ spl1_2 ),
inference(binary_proxy_clausification,[status(thm)],[f488]) ).
thf(f516,plain,
( spl1_7
| spl1_8
| ~ spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f502,f259,f513,f509]) ).
thf(f502,plain,
( ( $true
= ( member @ sK8 @ sK4 @ mactual ) )
| ( ( member @ sK8 @ sK3 @ mactual )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[status(thm)],[f501]) ).
thf(f501,plain,
( ( ( ~ ( member @ sK8 @ sK4 @ mactual ) )
= $false )
| ( ( member @ sK8 @ sK3 @ mactual )
= $false )
| ~ spl1_2 ),
inference(binary_proxy_clausification,[status(thm)],[f500]) ).
thf(f500,plain,
( ( $false
= ( ~ ( member @ sK8 @ sK4 @ mactual )
& ( member @ sK8 @ sK3 @ mactual ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[status(thm)],[f499]) ).
thf(f499,plain,
( ( $true
= ( ~ ( ~ ( member @ sK8 @ sK4 @ mactual )
& ( member @ sK8 @ sK3 @ mactual ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[status(thm)],[f496]) ).
thf(f496,plain,
( ( $true
= ( ( ~ ( member @ sK8 @ sK4 @ mactual )
& ( member @ sK8 @ sK3 @ mactual ) )
= $false ) )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f160,f479]) ).
thf(f479,plain,
( ( $false
= ( member @ sK8 @ ( difference @ sK3 @ sK4 ) @ mactual ) )
| ~ spl1_2 ),
inference(binary_proxy_clausification,[status(thm)],[f478]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( member @ X3 @ X2 @ mactual )
& ( member @ X3 @ X1 @ mactual ) )
= ( member @ X3 @ ( difference @ X1 @ X2 ) @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f159]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ~ ( member @ Y0 @ X2 @ mactual )
& ( member @ Y0 @ X1 @ mactual ) )
= ( member @ Y0 @ ( difference @ X1 @ X2 ) @ mactual ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( member @ Y0 @ X2 @ mactual )
& ( member @ Y0 @ X1 @ mactual ) )
= ( member @ Y0 @ ( difference @ X1 @ X2 ) @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f157]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( member @ Y1 @ Y0 @ mactual )
& ( member @ Y1 @ X1 @ mactual ) )
= ( member @ Y1 @ ( difference @ X1 @ Y0 ) @ mactual ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( member @ Y1 @ Y0 @ mactual )
& ( member @ Y1 @ X1 @ mactual ) )
= ( member @ Y1 @ ( difference @ X1 @ Y0 ) @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f155]) ).
thf(f155,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ~ ( member @ Y2 @ Y1 @ mactual )
& ( member @ Y2 @ Y0 @ mactual ) )
= ( member @ Y2 @ ( difference @ Y0 @ Y1 ) @ mactual ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ~ ( member @ Y2 @ Y1 @ mactual )
& ( member @ Y2 @ Y0 @ mactual ) )
= ( member @ Y2 @ ( difference @ Y0 @ Y1 ) @ mactual ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f112]) ).
thf(f112,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 @ Y2 @ ( difference @ Y0 @ Y1 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( member @ Y2 @ Y0 )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f94,f97,f92,f92,f92,f85,f104,f84]) ).
thf(f94,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( member @ Y2 @ ( difference @ Y0 @ Y1 ) ) @ ( mand @ ( member @ Y2 @ Y0 ) @ ( mnot @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( member @ Y2 @ ( difference @ Y0 @ Y1 ) ) @ ( mand @ ( member @ Y2 @ Y0 ) @ ( mnot @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f54]) ).
thf(f54,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mequiv @ ( member @ X2 @ ( difference @ X0 @ X1 ) ) @ ( mand @ ( member @ X2 @ X0 ) @ ( mnot @ ( member @ X2 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X8: $i] :
( mforall_di
@ ^ [X9: $i] : ( mequiv @ ( member @ X9 @ ( difference @ X3 @ X8 ) ) @ ( mand @ ( member @ X9 @ X3 ) @ ( mnot @ ( member @ X9 @ X8 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',difference_defn) ).
thf(f468,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f467]) ).
thf(f467,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f466]) ).
thf(f466,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(forward_demodulation,[status(thm)],[f465,f358]) ).
thf(f358,plain,
( ( ( member @ sK7 @ sK2 @ mactual )
= $false )
| ~ spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f357]) ).
thf(f357,plain,
( ( $false
= ( ( member @ sK7 @ ( difference @ sK3 @ sK4 ) @ mactual )
=> ( member @ sK7 @ sK2 @ mactual ) ) )
| ~ spl1_1 ),
inference(beta_eta_normalization,[status(thm)],[f356]) ).
thf(f356,plain,
( ( ( ^ [Y0: $i] :
( ( member @ Y0 @ ( difference @ sK3 @ sK4 ) @ mactual )
=> ( member @ Y0 @ sK2 @ mactual ) )
@ sK7 )
= $false )
| ~ spl1_1 ),
inference(sigma_clausification,[status(thm)],[f355]) ).
thf(f355,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( difference @ sK3 @ sK4 ) @ mactual )
=> ( member @ Y0 @ sK2 @ mactual ) ) )
= $false )
| ~ spl1_1 ),
inference(not_proxy_clausification,[status(thm)],[f354]) ).
thf(f354,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( difference @ sK3 @ sK4 ) @ mactual )
=> ( member @ Y0 @ sK2 @ mactual ) ) ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[status(thm)],[f351]) ).
thf(f351,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( difference @ sK3 @ sK4 ) @ mactual )
=> ( member @ Y0 @ sK2 @ mactual ) ) )
= $false ) )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f141,f257]) ).
thf(f257,plain,
( ( ( subset @ ( difference @ sK3 @ sK4 ) @ sK2 @ mactual )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f255]) ).
thf(f255,definition,
( spl1_1
<=> ( ( subset @ ( difference @ sK3 @ sK4 ) @ sK2 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f465,plain,
( ( ( member @ sK7 @ sK2 @ mactual )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[status(thm)],[f464]) ).
thf(f464,plain,
( ( ( $true
= ( member @ sK7 @ sK2 @ mactual ) )
= $true )
| ~ spl1_1 ),
inference(forward_demodulation,[status(thm)],[f460,f402]) ).
thf(f402,plain,
( ( $true
= ( member @ sK7 @ sK3 @ mactual ) )
| ~ spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f401]) ).
thf(f401,plain,
( ( ( ~ ( member @ sK7 @ sK4 @ mactual )
& ( member @ sK7 @ sK3 @ mactual ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[status(thm)],[f398]) ).
thf(f398,plain,
( ( ( ( ~ ( member @ sK7 @ sK4 @ mactual )
& ( member @ sK7 @ sK3 @ mactual ) )
= $true )
= $true )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f160,f359]) ).
thf(f359,plain,
( ( $true
= ( member @ sK7 @ ( difference @ sK3 @ sK4 ) @ mactual ) )
| ~ spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f357]) ).
thf(f460,plain,
( ( $true
= ( ( member @ sK7 @ sK3 @ mactual )
= ( member @ sK7 @ sK2 @ mactual ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[status(thm)],[f459]) ).
thf(f459,plain,
( ( $true
= ( ( $true
& ( member @ sK7 @ sK3 @ mactual ) )
= ( member @ sK7 @ sK2 @ mactual ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[status(thm)],[f452]) ).
thf(f452,plain,
( ( $true
= ( ( ~ $false
& ( member @ sK7 @ sK3 @ mactual ) )
= ( member @ sK7 @ sK2 @ mactual ) ) )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f174,f404]) ).
thf(f404,plain,
( ( $false
= ( member @ sK7 @ sK4 @ mactual ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[status(thm)],[f403]) ).
thf(f403,plain,
( ( $true
= ( ~ ( member @ sK7 @ sK4 @ mactual ) ) )
| ~ spl1_1 ),
inference(binary_proxy_clausification,[status(thm)],[f401]) ).
thf(f271,plain,
( spl1_2
| spl1_1 ),
inference(avatar_split_clause,[status(thm)],[f268,f255,f259]) ).
thf(f268,plain,
( ( $false
= ( subset @ sK2 @ ( difference @ sK3 @ sK4 ) @ mactual ) )
| ( ( subset @ ( difference @ sK3 @ sK4 ) @ sK2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f267]) ).
thf(f267,plain,
( $false
= ( ( subset @ sK2 @ ( difference @ sK3 @ sK4 ) @ mactual )
& ( subset @ ( difference @ sK3 @ sK4 ) @ sK2 @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f266]) ).
thf(f266,plain,
( ( ~ ( ( subset @ sK2 @ ( difference @ sK3 @ sK4 ) @ mactual )
& ( subset @ ( difference @ sK3 @ sK4 ) @ sK2 @ mactual ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f264]) ).
thf(f264,plain,
( ( ( ( subset @ sK2 @ ( difference @ sK3 @ sK4 ) @ mactual )
& ( subset @ ( difference @ sK3 @ sK4 ) @ sK2 @ mactual ) )
= $false )
= $true ),
inference(superposition,[status(thm)],[f219,f231]) ).
thf(f231,plain,
( $false
= ( qmltpeq @ ( difference @ sK3 @ sK4 ) @ sK2 @ mactual ) ),
inference(trivial_inequality_removal,[status(thm)],[f230]) ).
thf(f230,plain,
( ( $false = $true )
| ( $false
= ( qmltpeq @ ( difference @ sK3 @ sK4 ) @ sK2 @ mactual ) ) ),
inference(superposition,[status(thm)],[f205,f171]) ).
thf(f171,plain,
( ( qmltpeq @ sK2 @ ( difference @ sK3 @ sK4 ) @ mactual )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f170]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( ( qmltpeq @ X1 @ X2 @ mactual )
= $false )
| ( $true
= ( qmltpeq @ X2 @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f204]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( ( qmltpeq @ X1 @ X2 @ mactual )
=> ( qmltpeq @ X2 @ X1 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f203]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( qmltpeq @ X1 @ Y0 @ mactual )
=> ( qmltpeq @ Y0 @ X1 @ mactual ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f202]) ).
thf(f202,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( qmltpeq @ X1 @ Y0 @ mactual )
=> ( qmltpeq @ Y0 @ X1 @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f201]) ).
thf(f201,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( qmltpeq @ Y0 @ Y1 @ mactual )
=> ( qmltpeq @ Y1 @ Y0 @ mactual ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f200]) ).
thf(f200,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( qmltpeq @ Y0 @ Y1 @ mactual )
=> ( qmltpeq @ Y1 @ Y0 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,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] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( qmltpeq @ Y0 @ Y1 )
@ ( qmltpeq @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f90,f97,f92,f92,f80]) ).
thf(f90,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( qmltpeq @ Y0 @ Y1 ) @ ( qmltpeq @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( qmltpeq @ Y0 @ Y1 ) @ ( qmltpeq @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mimplies @ ( qmltpeq @ X0 @ X1 ) @ ( qmltpeq @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( mlocal
@ ( mforall_di
@ ^ [X5: $i] :
( mforall_di
@ ^ [X6: $i] : ( mimplies @ ( qmltpeq @ X5 @ X6 ) @ ( qmltpeq @ X6 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',symmetry) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( ( ( subset @ X2 @ X1 @ mactual )
& ( subset @ X1 @ X2 @ mactual ) )
= ( qmltpeq @ X1 @ X2 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f218]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( subset @ Y0 @ X1 @ mactual )
& ( subset @ X1 @ Y0 @ mactual ) )
= ( qmltpeq @ X1 @ Y0 @ mactual ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ Y0 @ X1 @ mactual )
& ( subset @ X1 @ Y0 @ mactual ) )
= ( qmltpeq @ X1 @ Y0 @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f216]) ).
thf(f216,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y1 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) )
= ( qmltpeq @ Y0 @ Y1 @ mactual ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f215]) ).
thf(f215,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y1 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) )
= ( qmltpeq @ Y0 @ Y1 @ mactual ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f107]) ).
thf(f107,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 ) )
@ ( qmltpeq @ Y0 @ Y1 )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f87,f97,f92,f92,f85,f104]) ).
thf(f87,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ X0 @ X1 ) @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,axiom,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X8: $i] : ( mequiv @ ( qmltpeq @ X3 @ X8 ) @ ( mand @ ( subset @ X3 @ X8 ) @ ( subset @ X8 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',equal_defn) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET579^3 : TPTP v9.2.1. Released v8.1.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n029.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 11:59:29 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SET579^3 : TPTP v9.2.1. Released v8.1.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : TPTP problem SET579+3.p with axiomatized equality
% 0.20/0.46 % Version : [BP13] axioms.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.20/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.20/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.20/0.46 % Source : [TPTP]
% 0.20/0.46 % Names : SET579+1 [QMLTP]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0
% 0.20/0.46 % Syntax : Number of formulae : 42 ( 11 unt; 17 typ; 10 def)
% 0.20/0.46 % Number of atoms : 134 ( 10 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 13 ( 5 avg)
% 0.20/0.46 % Number of connectives : 210 ( 1 ~; 1 |; 2 &; 203 @)
% 0.20/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 17 ( 7 avg)
% 0.20/0.46 % Number of types : 3 ( 1 usr)
% 0.20/0.46 % Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 17 ( 16 usr; 1 con; 0-3 aty)
% 0.20/0.46 % Number of variables : 66 ( 60 ^; 3 !; 3 ?; 66 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.20/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.20/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.20/0.46 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.20/0.46 % $modalities == $modal_system_D].
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(mworld,type,
% 0.20/0.46 mworld: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(mrel_type,type,
% 0.20/0.46 mrel: mworld > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mactual_type,type,
% 0.20/0.46 mactual: mworld ).
% 0.20/0.46
% 0.20/0.46 thf(mlocal_type,type,
% 0.20/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mlocal_def,definition,
% 0.20/0.46 ( mlocal
% 0.20/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mnot_type,type,
% 0.20/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mand_type,type,
% 0.20/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mor_type,type,
% 0.20/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mimplies_type,type,
% 0.20/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mequiv_type,type,
% 0.20/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mnot_def,definition,
% 0.20/0.46 ( mnot
% 0.20/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.20/0.46 ~ ( A @ W ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mand_def,definition,
% 0.20/0.46 ( mand
% 0.20/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.46 ( ( A @ W )
% 0.20/0.46 & ( B @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mor_def,definition,
% 0.20/0.46 ( mor
% 0.20/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.46 ( ( A @ W )
% 0.20/0.46 | ( B @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mimplies_def,definition,
% 0.20/0.46 ( mimplies
% 0.20/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.46 ( ( A @ W )
% 0.20/0.46 => ( B @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mequiv_def,definition,
% 0.20/0.46 ( mequiv
% 0.20/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.46 ( ( A @ W )
% 0.20/0.46 <=> ( B @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mbox_type,type,
% 0.20/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mbox_def,definition,
% 0.20/0.46 ( mbox
% 0.20/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.46 ! [V: mworld] :
% 0.20/0.46 ( ( mrel @ W @ V )
% 0.20/0.46 => ( Phi @ V ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mdia_type,type,
% 0.20/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mdia_def,definition,
% 0.20/0.46 ( mdia
% 0.20/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.46 ? [V: mworld] :
% 0.20/0.46 ( ( mrel @ W @ V )
% 0.20/0.46 & ( Phi @ V ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mrel_serial,axiom,
% 0.20/0.46 ! [W: mworld] :
% 0.20/0.46 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.20/0.46
% 0.20/0.46 thf(mforall_di_type,type,
% 0.20/0.46 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mforall_di_def,definition,
% 0.20/0.46 ( mforall_di
% 0.20/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.46 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mexists_di_type,type,
% 0.20/0.46 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mexists_di_def,definition,
% 0.20/0.46 ( mexists_di
% 0.20/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.46 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(qmltpeq_decl,type,
% 0.20/0.46 qmltpeq: $i > $i > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(member_decl,type,
% 0.20/0.46 member: $i > $i > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(subset_decl,type,
% 0.20/0.46 subset: $i > $i > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(difference_decl,type,
% 0.20/0.46 difference: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(reflexivity,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symmetry,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [X: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(transitivity,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [X: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [Y: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(difference_substitution_1,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [A: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(difference_substitution_2,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [A: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(member_substitution_1,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [A: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(member_substitution_2,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [A: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset_substitution_1,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [A: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset_substitution_2,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [A: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(difference_defn,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [D: $i] : ( mequiv @ ( member @ D @ ( difference @ B @ C ) ) @ ( mand @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(equal_defn,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset_defn,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] :
% 0.20/0.46 ( mequiv @ ( subset @ B @ C )
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(reflexivity_of_subset,axiom,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [B: $i] : ( subset @ B @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(prove_th20,conjecture,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [B: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [C: $i] :
% 0.20/0.46 ( mforall_di
% 0.20/0.46 @ ^ [D: $i] :
% 0.20/0.46 ( mimplies
% 0.20/0.46 @ ( mforall_di
% 0.20/0.46 @ ^ [E: $i] : ( mequiv @ ( member @ E @ B ) @ ( mand @ ( member @ E @ C ) @ ( mnot @ ( member @ E @ D ) ) ) ) )
% 0.20/0.46 @ ( qmltpeq @ B @ ( difference @ C @ D ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 11:59:30 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2DTF6202.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.32 ---- Cleaned THF ---
% 0.31/1.32 thf(mworld,type,
% 0.31/1.32 mworld: $tType ).
% 0.31/1.32
% 0.31/1.32 thf(mrel_type,type,
% 0.31/1.32 mrel: mworld > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mactual_type,type,
% 0.31/1.32 mactual: mworld ).
% 0.31/1.32
% 0.31/1.32 thf(mlocal_type,type,
% 0.31/1.32 mlocal: ( mworld > $o ) > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mlocal_def,definition,
% 0.31/1.32 ( mlocal
% 0.31/1.32 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(mnot_type,type,
% 0.31/1.32 mnot: ( mworld > $o ) > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mand_type,type,
% 0.31/1.32 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mor_type,type,
% 0.31/1.32 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mimplies_type,type,
% 0.31/1.32 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mequiv_type,type,
% 0.31/1.32 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mnot_def,definition,
% 0.31/1.32 ( mnot
% 0.31/1.32 = ( ^ [A: mworld > $o,W: mworld] :
% 0.31/1.32 ~ ( A @ W ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(mand_def,definition,
% 0.31/1.32 ( mand
% 0.31/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.32 ( ( A @ W )
% 0.31/1.32 & ( B @ W ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(mor_def,definition,
% 0.31/1.32 ( mor
% 0.31/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.32 ( ( A @ W )
% 0.31/1.32 | ( B @ W ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(mimplies_def,definition,
% 0.31/1.32 ( mimplies
% 0.31/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.32 ( ( A @ W )
% 0.31/1.32 => ( B @ W ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(mequiv_def,definition,
% 0.31/1.32 ( mequiv
% 0.31/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.32 ( ( A @ W )
% 0.31/1.32 <=> ( B @ W ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(mbox_type,type,
% 0.31/1.32 mbox: ( mworld > $o ) > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mbox_def,definition,
% 0.31/1.32 ( mbox
% 0.31/1.32 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/1.32 ! [V: mworld] :
% 0.31/1.32 ( ( mrel @ W @ V )
% 0.31/1.32 => ( Phi @ V ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(mdia_type,type,
% 0.31/1.32 mdia: ( mworld > $o ) > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mdia_def,definition,
% 0.31/1.32 ( mdia
% 0.31/1.32 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/1.32 ? [V: mworld] :
% 0.31/1.32 ( ( mrel @ W @ V )
% 0.31/1.32 & ( Phi @ V ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(mrel_serial,axiom,
% 0.31/1.32 ! [W: mworld] :
% 0.31/1.32 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.31/1.32
% 0.31/1.32 thf(mforall_di_type,type,
% 0.31/1.32 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mforall_di_def,definition,
% 0.31/1.32 ( mforall_di
% 0.31/1.32 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/1.32 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(mexists_di_type,type,
% 0.31/1.32 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(mexists_di_def,definition,
% 0.31/1.32 ( mexists_di
% 0.31/1.32 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/1.32 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(qmltpeq_decl,type,
% 0.31/1.32 qmltpeq: $i > $i > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(member_decl,type,
% 0.31/1.32 member: $i > $i > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(subset_decl,type,
% 0.31/1.32 subset: $i > $i > mworld > $o ).
% 0.31/1.32
% 0.31/1.32 thf(difference_decl,type,
% 0.31/1.32 difference: $i > $i > $i ).
% 0.31/1.32
% 0.31/1.32 thf(reflexivity,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(symmetry,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [X: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(transitivity,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [X: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [Y: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(difference_substitution_1,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [A: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(difference_substitution_2,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [A: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(member_substitution_1,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [A: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(member_substitution_2,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [A: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(subset_substitution_1,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [A: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(subset_substitution_2,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [A: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(difference_defn,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [D: $i] : ( mequiv @ ( member @ D @ ( difference @ B @ C ) ) @ ( mand @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(equal_defn,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(subset_defn,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] :
% 0.31/1.32 ( mequiv @ ( subset @ B @ C )
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(reflexivity_of_subset,axiom,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [B: $i] : ( subset @ B @ B ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(prove_th20,conjecture,
% 0.31/1.32 ( mlocal
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [B: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [C: $i] :
% 0.31/1.32 ( mforall_di
% 0.31/1.32 @ ^ [D: $i] :
% 0.31/1.32 ( mimplies
% 0.31/1.32 @ ( mforall_di
% 0.31/1.32 @ ^ [E: $i] : ( mequiv @ ( member @ E @ B ) @ ( mand @ ( member @ E @ C ) @ ( mnot @ ( member @ E @ D ) ) ) ) )
% 0.31/1.32 @ ( qmltpeq @ B @ ( difference @ C @ D ) ) ) ) ) ) ) ).
% 0.31/1.32 ------------------------
% 0.31/1.33 % (6533)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/2Mi)
% 0.31/1.33 % (6533)Instruction limit reached!
% 0.31/1.33 % (6533)------------------------------
% 0.31/1.33 % (6533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (6533)Termination reason: Unknown
% 0.31/1.33 % (6533)Termination phase: shuffling
% 0.31/1.33
% 0.31/1.33 % (6533)Memory used [KB]: 1023
% 0.31/1.33 % (6533)Time elapsed: 0.002 s
% 0.31/1.33 % (6533)Instructions burned: 3 (million)
% 0.31/1.33 % (6533)------------------------------
% 0.31/1.33 % (6533)------------------------------
% 0.31/1.34 % (6530)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/183Mi)
% 0.31/1.34 % (6531)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_6202 for (2999ds/4Mi)
% 0.31/1.34 % (6532)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_6202 for (2999ds/27Mi)
% 0.31/1.34 % (6534)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_6202 for (2999ds/2Mi)
% 0.31/1.34 % (6535)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_6202 for (2999ds/275Mi)
% 0.31/1.34 % (6536)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/18Mi)
% 0.31/1.34 % (6534)Instruction limit reached!
% 0.31/1.34 % (6534)------------------------------
% 0.31/1.34 % (6534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (6534)Termination reason: Unknown
% 0.31/1.34 % (6534)Termination phase: shuffling
% 0.31/1.34
% 0.31/1.34 % (6534)Memory used [KB]: 1023
% 0.31/1.34 % (6534)Time elapsed: 0.003 s
% 0.31/1.34 % (6534)Instructions burned: 2 (million)
% 0.31/1.34 % (6534)------------------------------
% 0.31/1.34 % (6534)------------------------------
% 0.31/1.34 % (6531)Instruction limit reached!
% 0.31/1.34 % (6531)------------------------------
% 0.31/1.34 % (6531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (6531)Termination reason: Unknown
% 0.31/1.34 % (6531)Termination phase: Property scanning
% 0.31/1.34
% 0.31/1.34 % (6531)Memory used [KB]: 1023
% 0.31/1.34 % (6531)Time elapsed: 0.004 s
% 0.31/1.34 % (6531)Instructions burned: 4 (million)
% 0.31/1.34 % (6531)------------------------------
% 0.31/1.34 % (6531)------------------------------
% 0.31/1.34 % (6537)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/3Mi)
% 0.31/1.34 % (6535)Refutation not found, incomplete strategy
% 0.31/1.34 % (6535)------------------------------
% 0.31/1.34 % (6535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (6537)Instruction limit reached!
% 0.31/1.34 % (6537)------------------------------
% 0.31/1.34 % (6537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (6537)Termination reason: Unknown
% 0.31/1.34 % (6535)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.34
% 0.31/1.34 % (6537)Termination phase: Property scanning
% 0.31/1.34
% 0.31/1.34
% 0.31/1.34 % (6537)Memory used [KB]: 1023
% 0.31/1.34 % (6537)Time elapsed: 0.003 s
% 0.31/1.34 % (6535)Memory used [KB]: 5500
% 0.31/1.34 % (6537)Instructions burned: 5 (million)
% 0.31/1.34 % (6537)------------------------------
% 0.31/1.34 % (6537)------------------------------
% 0.31/1.34 % (6535)Time elapsed: 0.007 s
% 0.31/1.34 % (6535)Instructions burned: 9 (million)
% 0.31/1.34 % (6535)------------------------------
% 0.31/1.34 % (6535)------------------------------
% 0.31/1.35 % (6536)Instruction limit reached!
% 0.31/1.35 % (6536)------------------------------
% 0.31/1.35 % (6536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (6536)Termination reason: Unknown
% 0.31/1.35 % (6536)Termination phase: Saturation
% 0.31/1.35
% 0.31/1.35 % (6536)Memory used [KB]: 5628
% 0.31/1.35 % (6536)Time elapsed: 0.011 s
% 0.31/1.35 % (6536)Instructions burned: 18 (million)
% 0.31/1.35 % (6536)------------------------------
% 0.31/1.35 % (6536)------------------------------
% 0.31/1.35 % (6532)Instruction limit reached!
% 0.31/1.35 % (6532)------------------------------
% 0.31/1.35 % (6532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (6532)Termination reason: Unknown
% 0.31/1.35 % (6532)Termination phase: Saturation
% 0.31/1.35
% 0.31/1.35 % (6532)Memory used [KB]: 5756
% 0.31/1.35 % (6532)Time elapsed: 0.016 s
% 0.31/1.35 % (6532)Instructions burned: 27 (million)
% 0.31/1.35 % (6532)------------------------------
% 0.31/1.35 % (6532)------------------------------
% 0.31/1.35 % (6540)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_6202 for (2999ds/3Mi)
% 0.31/1.35 % (6540)Instruction limit reached!
% 0.31/1.35 % (6540)------------------------------
% 0.31/1.35 % (6540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (6540)Termination reason: Unknown
% 0.31/1.35 % (6540)Termination phase: Property scanning
% 0.31/1.35
% 0.31/1.35 % (6540)Memory used [KB]: 1023
% 0.31/1.35 % (6540)Time elapsed: 0.003 s
% 0.31/1.35 % (6540)Instructions burned: 5 (million)
% 0.31/1.35 % (6540)------------------------------
% 0.31/1.35 % (6540)------------------------------
% 0.31/1.36 % (6538)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_6202 for (2999ds/37Mi)
% 0.31/1.36 % (6539)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_6202 for (2999ds/15Mi)
% 0.31/1.36 % (6541)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_6202 for (2999ds/1041Mi)
% 0.31/1.36 % (6539)Instruction limit reached!
% 0.31/1.36 % (6539)------------------------------
% 0.31/1.36 % (6539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.36 % (6539)Termination reason: Unknown
% 0.31/1.36 % (6539)Termination phase: Saturation
% 0.31/1.36
% 0.31/1.36 % (6539)Memory used [KB]: 1151
% 0.31/1.36 % (6539)Time elapsed: 0.009 s
% 0.31/1.36 % (6539)Instructions burned: 16 (million)
% 0.31/1.36 % (6539)------------------------------
% 0.31/1.36 % (6539)------------------------------
% 0.31/1.36 % (6542)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/7Mi)
% 0.31/1.36 % (6544)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_6202 for (2999ds/3Mi)
% 0.31/1.37 % (6544)Instruction limit reached!
% 0.31/1.37 % (6544)------------------------------
% 0.31/1.37 % (6544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.37 % (6544)Termination reason: Unknown
% 0.31/1.37 % (6544)Termination phase: Property scanning
% 0.31/1.37
% 0.31/1.37 % (6544)Memory used [KB]: 1023
% 0.31/1.37 % (6544)Time elapsed: 0.003 s
% 0.31/1.37 % (6544)Instructions burned: 5 (million)
% 0.31/1.37 % (6544)------------------------------
% 0.31/1.37 % (6544)------------------------------
% 0.31/1.37 % (6542)Instruction limit reached!
% 0.31/1.37 % (6542)------------------------------
% 0.31/1.37 % (6542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.37 % (6542)Termination reason: Unknown
% 0.31/1.37 % (6542)Termination phase: Function definition elimination
% 0.31/1.37
% 0.31/1.37 % (6542)Memory used [KB]: 1023
% 0.31/1.37 % (6542)Time elapsed: 0.006 s
% 0.31/1.37 % (6542)Instructions burned: 8 (million)
% 0.31/1.37 % (6542)------------------------------
% 0.31/1.37 % (6542)------------------------------
% 0.31/1.37 % (6543)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/16Mi)
% 0.31/1.37 % (6545)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_6202 for (2999ds/3Mi)
% 0.31/1.37 % (6545)Instruction limit reached!
% 0.31/1.37 % (6545)------------------------------
% 0.31/1.37 % (6545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.37 % (6545)Termination reason: Unknown
% 0.31/1.37 % (6545)Termination phase: shuffling
% 0.31/1.37
% 0.31/1.37 % (6545)Memory used [KB]: 1023
% 0.31/1.37 % (6545)Time elapsed: 0.002 s
% 0.31/1.37 % (6545)Instructions burned: 3 (million)
% 0.31/1.37 % (6545)------------------------------
% 0.31/1.37 % (6545)------------------------------
% 0.31/1.38 % (6546)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/7Mi)
% 0.31/1.38 % (6538)Instruction limit reached!
% 0.31/1.38 % (6538)------------------------------
% 0.31/1.38 % (6538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.38 % (6538)Termination reason: Unknown
% 0.31/1.38 % (6538)Termination phase: Saturation
% 0.31/1.38
% 0.31/1.38 % (6538)Memory used [KB]: 5884
% 0.31/1.38 % (6538)Time elapsed: 0.022 s
% 0.31/1.38 % (6538)Instructions burned: 38 (million)
% 0.31/1.38 % (6538)------------------------------
% 0.31/1.38 % (6538)------------------------------
% 0.31/1.38 % (6543)Instruction limit reached!
% 0.31/1.38 % (6543)------------------------------
% 0.31/1.38 % (6543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.38 % (6543)Termination reason: Unknown
% 0.31/1.38 % (6543)Termination phase: Saturation
% 0.31/1.38
% 0.31/1.38 % (6543)Memory used [KB]: 5628
% 0.31/1.38 % (6543)Time elapsed: 0.010 s
% 0.31/1.38 % (6543)Instructions burned: 16 (million)
% 0.31/1.38 % (6543)------------------------------
% 0.31/1.38 % (6543)------------------------------
% 0.31/1.38 % (6546)Instruction limit reached!
% 0.31/1.38 % (6546)------------------------------
% 0.31/1.38 % (6546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.38 % (6546)Termination reason: Unknown
% 0.31/1.38 % (6546)Termination phase: Function definition elimination
% 0.31/1.38
% 0.31/1.38 % (6546)Memory used [KB]: 1023
% 0.31/1.38 % (6546)Time elapsed: 0.004 s
% 0.31/1.38 % (6546)Instructions burned: 8 (million)
% 0.31/1.38 % (6546)------------------------------
% 0.31/1.38 % (6546)------------------------------
% 0.31/1.38 % (6548)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/4Mi)
% 0.31/1.38 % (6548)Instruction limit reached!
% 0.31/1.38 % (6548)------------------------------
% 0.31/1.38 % (6548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.38 % (6548)Termination reason: Unknown
% 0.31/1.38 % (6548)Termination phase: shuffling
% 0.31/1.38
% 0.31/1.38 % (6548)Memory used [KB]: 1023
% 0.31/1.38 % (6548)Time elapsed: 0.002 s
% 0.31/1.38 % (6548)Instructions burned: 4 (million)
% 0.31/1.38 % (6548)------------------------------
% 0.31/1.38 % (6548)------------------------------
% 0.31/1.39 % (6547)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/3Mi)
% 0.31/1.39 % (6547)Instruction limit reached!
% 0.31/1.39 % (6547)------------------------------
% 0.31/1.39 % (6547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.39 % (6547)Termination reason: Unknown
% 0.31/1.39 % (6547)Termination phase: Property scanning
% 0.31/1.39
% 0.31/1.39 % (6547)Memory used [KB]: 1023
% 0.31/1.39 % (6547)Time elapsed: 0.004 s
% 0.31/1.39 % (6547)Instructions burned: 4 (million)
% 0.31/1.39 % (6547)------------------------------
% 0.31/1.39 % (6547)------------------------------
% 0.31/1.39 % (6551)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/6Mi)
% 0.31/1.39 % (6551)Instruction limit reached!
% 0.31/1.39 % (6551)------------------------------
% 0.31/1.39 % (6551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.39 % (6551)Termination reason: Unknown
% 0.31/1.39 % (6551)Termination phase: Function definition elimination
% 0.31/1.39
% 0.31/1.39 % (6551)Memory used [KB]: 1023
% 0.31/1.39 % (6551)Time elapsed: 0.004 s
% 0.31/1.39 % (6551)Instructions burned: 8 (million)
% 0.31/1.39 % (6551)------------------------------
% 0.31/1.39 % (6551)------------------------------
% 0.31/1.39 % (6549)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/18Mi)
% 0.31/1.39 % (6552)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_6202 for (2999ds/902Mi)
% 0.31/1.39 % (6550)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/710Mi)
% 0.31/1.40 % (6552)Refutation not found, incomplete strategy
% 0.31/1.40 % (6552)------------------------------
% 0.31/1.40 % (6552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.40 % (6552)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.40
% 0.31/1.40
% 0.31/1.40 % (6552)Memory used [KB]: 5628
% 0.31/1.40 % (6552)Time elapsed: 0.003 s
% 0.31/1.40 % (6552)Instructions burned: 7 (million)
% 0.31/1.40 % (6552)------------------------------
% 0.31/1.40 % (6552)------------------------------
% 1.84/1.40 % (6554)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/5Mi)
% 1.84/1.40 % (6554)Instruction limit reached!
% 1.84/1.40 % (6554)------------------------------
% 1.84/1.40 % (6554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.40 % (6554)Termination reason: Unknown
% 1.84/1.40 % (6554)Termination phase: Property scanning
% 1.84/1.40
% 1.84/1.40 % (6554)Memory used [KB]: 1023
% 1.84/1.40 % (6554)Time elapsed: 0.003 s
% 1.84/1.40 % (6554)Instructions burned: 5 (million)
% 1.84/1.40 % (6554)------------------------------
% 1.84/1.40 % (6554)------------------------------
% 1.84/1.40 % (6549)Instruction limit reached!
% 1.84/1.40 % (6549)------------------------------
% 1.84/1.40 % (6549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.40 % (6549)Termination reason: Unknown
% 1.84/1.40 % (6549)Termination phase: Saturation
% 1.84/1.40
% 1.84/1.40 % (6549)Memory used [KB]: 5628
% 1.84/1.40 % (6549)Time elapsed: 0.012 s
% 1.84/1.40 % (6549)Instructions burned: 18 (million)
% 1.84/1.40 % (6549)------------------------------
% 1.84/1.40 % (6549)------------------------------
% 1.84/1.40 % (6553)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_6202 for (2999ds/21Mi)
% 1.84/1.41 % (6555)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_6202 for (2999ds/6Mi)
% 1.84/1.41 % (6555)Instruction limit reached!
% 1.84/1.41 % (6555)------------------------------
% 1.84/1.41 % (6555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (6555)Termination reason: Unknown
% 1.84/1.41 % (6555)Termination phase: Property scanning
% 1.84/1.41
% 1.84/1.41 % (6555)Memory used [KB]: 1023
% 1.84/1.41 % (6555)Time elapsed: 0.003 s
% 1.84/1.41 % (6555)Instructions burned: 8 (million)
% 1.84/1.41 % (6555)------------------------------
% 1.84/1.41 % (6555)------------------------------
% 1.84/1.41 % (6556)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/377Mi)
% 1.84/1.41 % (6530)Instruction limit reached!
% 1.84/1.41 % (6530)------------------------------
% 1.84/1.41 % (6530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (6530)Termination reason: Unknown
% 1.84/1.41 % (6530)Termination phase: Saturation
% 1.84/1.41
% 1.84/1.41 % (6530)Memory used [KB]: 6524
% 1.84/1.41 % (6530)Time elapsed: 0.079 s
% 1.84/1.41 % (6530)Instructions burned: 183 (million)
% 1.84/1.41 % (6530)------------------------------
% 1.84/1.41 % (6530)------------------------------
% 1.84/1.41 % (6553)Instruction limit reached!
% 1.84/1.41 % (6553)------------------------------
% 1.84/1.41 % (6553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (6553)Termination reason: Unknown
% 1.84/1.41 % (6553)Termination phase: Saturation
% 1.84/1.41
% 1.84/1.41 % (6553)Memory used [KB]: 5628
% 1.84/1.41 % (6553)Time elapsed: 0.012 s
% 1.84/1.41 % (6553)Instructions burned: 21 (million)
% 1.84/1.41 % (6553)------------------------------
% 1.84/1.41 % (6553)------------------------------
% 1.84/1.42 % (6557)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_6202 for (2999ds/779Mi)
% 1.84/1.42 % (6558)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_6202 for (2999ds/19Mi)
% 1.84/1.42 % (6558)Refutation not found, incomplete strategy
% 1.84/1.42 % (6558)------------------------------
% 1.84/1.42 % (6558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.42 % (6558)Termination reason: Refutation not found, incomplete strategy
% 1.84/1.42
% 1.84/1.42
% 1.84/1.42 % (6558)Memory used [KB]: 5628
% 1.84/1.42 % (6558)Time elapsed: 0.004 s
% 1.84/1.42 % (6558)Instructions burned: 11 (million)
% 1.84/1.42 % (6558)------------------------------
% 1.84/1.42 % (6558)------------------------------
% 1.84/1.42 % (6559)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/879Mi)
% 1.84/1.43 % (6560)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/17Mi)
% 1.84/1.43 % (6557)Refutation not found, incomplete strategy
% 1.84/1.43 % (6557)------------------------------
% 1.84/1.43 % (6557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.43 % (6557)Termination reason: Refutation not found, incomplete strategy
% 1.84/1.43
% 1.84/1.43
% 1.84/1.43 % (6557)Memory used [KB]: 5628
% 1.84/1.43 % (6557)Time elapsed: 0.032 s
% 1.84/1.43 % (6557)Instructions burned: 28 (million)
% 1.84/1.43 % (6557)------------------------------
% 1.84/1.43 % (6557)------------------------------
% 1.84/1.43 % (6560)Instruction limit reached!
% 1.84/1.43 % (6560)------------------------------
% 1.84/1.43 % (6560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.43 % (6560)Termination reason: Unknown
% 1.84/1.43 % (6560)Termination phase: Saturation
% 1.84/1.43
% 1.84/1.43 % (6560)Memory used [KB]: 5628
% 1.84/1.43 % (6560)Time elapsed: 0.006 s
% 1.84/1.43 % (6560)Instructions burned: 17 (million)
% 1.84/1.43 % (6560)------------------------------
% 1.84/1.43 % (6560)------------------------------
% 1.84/1.43 % (6561)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/3Mi)
% 1.84/1.43 % (6561)Instruction limit reached!
% 1.84/1.43 % (6561)------------------------------
% 1.84/1.43 % (6561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.43 % (6561)Termination reason: Unknown
% 1.84/1.43 % (6561)Termination phase: shuffling
% 1.84/1.43
% 1.84/1.43 % (6561)Memory used [KB]: 1023
% 1.84/1.43 % (6561)Time elapsed: 0.002 s
% 1.84/1.43 % (6561)Instructions burned: 4 (million)
% 1.84/1.43 % (6561)------------------------------
% 1.84/1.43 % (6561)------------------------------
% 1.84/1.44 % (6562)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/30Mi)
% 1.84/1.44 % (6563)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/127Mi)
% 1.84/1.44 % (6564)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_6202 for (2999ds/100Mi)
% 1.84/1.45 % (6562)Instruction limit reached!
% 1.84/1.45 % (6562)------------------------------
% 1.84/1.45 % (6562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.45 % (6562)Termination reason: Unknown
% 1.84/1.45 % (6562)Termination phase: Saturation
% 1.84/1.45
% 1.84/1.45 % (6562)Memory used [KB]: 5756
% 1.84/1.45 % (6562)Time elapsed: 0.033 s
% 1.84/1.45 % (6562)Instructions burned: 32 (million)
% 1.84/1.45 % (6562)------------------------------
% 1.84/1.45 % (6562)------------------------------
% 1.84/1.46 % (6565)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_6202 for (2998ds/3Mi)
% 1.84/1.46 % (6565)Instruction limit reached!
% 1.84/1.46 % (6565)------------------------------
% 1.84/1.46 % (6565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.46 % (6565)Termination reason: Unknown
% 1.84/1.46 % (6565)Termination phase: Property scanning
% 1.84/1.46
% 1.84/1.46 % (6565)Memory used [KB]: 1023
% 1.84/1.46 % (6565)Time elapsed: 0.003 s
% 1.84/1.46 % (6565)Instructions burned: 5 (million)
% 1.84/1.46 % (6565)------------------------------
% 1.84/1.46 % (6565)------------------------------
% 1.84/1.47 % (6566)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_6202 for (2998ds/20Mi)
% 1.84/1.47 % (6564)Instruction limit reached!
% 1.84/1.47 % (6564)------------------------------
% 1.84/1.47 % (6564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.47 % (6564)Termination reason: Unknown
% 1.84/1.47 % (6564)Termination phase: Saturation
% 1.84/1.47
% 1.84/1.47 % (6564)Memory used [KB]: 6012
% 1.84/1.47 % (6564)Time elapsed: 0.055 s
% 1.84/1.47 % (6564)Instructions burned: 101 (million)
% 1.84/1.47 % (6564)------------------------------
% 1.84/1.47 % (6564)------------------------------
% 1.84/1.47 % (6563)First to succeed.
% 1.84/1.47 % (6566)Refutation not found, incomplete strategy
% 1.84/1.47 % (6566)------------------------------
% 1.84/1.47 % (6566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.47 % (6566)Termination reason: Refutation not found, incomplete strategy
% 1.84/1.47
% 1.84/1.47
% 1.84/1.47 % (6566)Memory used [KB]: 5628
% 1.84/1.47 % (6566)Time elapsed: 0.007 s
% 1.84/1.47 % (6566)Instructions burned: 17 (million)
% 1.84/1.47 % (6566)------------------------------
% 1.84/1.47 % (6566)------------------------------
% 1.84/1.47 % (6563)Refutation found. Thanks to Tanya!
% 1.84/1.47 % SZS status Theorem for DTF2THF_6202
% 1.84/1.47 % SZS output start Proof for DTF2THF_6202
% 1.84/1.47 thf(type_def_5, type, mworld: $tType).
% 1.84/1.47 thf(func_def_0, type, mworld: $tType).
% 1.84/1.47 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.84/1.47 thf(func_def_2, type, mactual: mworld).
% 1.84/1.47 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.84/1.47 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.84/1.47 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.84/1.47 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.84/1.47 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.84/1.47 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.84/1.47 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.84/1.47 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.84/1.47 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.84/1.47 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.84/1.47 thf(func_def_14, type, qmltpeq: $i > $i > mworld > $o).
% 1.84/1.47 thf(func_def_15, type, member: $i > $i > mworld > $o).
% 1.84/1.47 thf(func_def_16, type, subset: $i > $i > mworld > $o).
% 1.84/1.47 thf(func_def_17, type, difference: $i > $i > $i).
% 1.84/1.47 thf(func_def_32, type, sK0: mworld > mworld).
% 1.84/1.47 thf(func_def_39, type, ph5: !>[X0: $tType]:(X0)).
% 1.84/1.47 thf(f688,plain,(
% 1.84/1.47 $false),
% 1.84/1.47 inference(avatar_sat_refutation,[status(thm)],[f271,f468,f516,f598,f683])).
% 1.84/1.47 thf(f683,plain,(
% 1.84/1.47 ~spl1_2 | ~spl1_8),
% 1.84/1.47 inference(avatar_contradiction_clause,[status(thm)],[f682])).
% 1.84/1.47 thf(f682,plain,(
% 1.84/1.47 $false | (~spl1_2 | ~spl1_8)),
% 1.84/1.47 inference(trivial_inequality_removal,[status(thm)],[f667])).
% 1.84/1.47 thf(f667,plain,(
% 1.84/1.47 ($false = $true) | (~spl1_2 | ~spl1_8)),
% 1.84/1.47 inference(backward_demodulation,[status(thm)],[f515,f491])).
% 1.84/1.47 thf(f491,plain,(
% 1.84/1.47 ($false = (member @ sK8 @ sK4 @ mactual)) | ~spl1_2),
% 1.84/1.47 inference(not_proxy_clausification,[status(thm)],[f490])).
% 1.84/1.47 thf(f490,plain,(
% 1.84/1.47 ((~ (member @ sK8 @ sK4 @ mactual)) = $true) | ~spl1_2),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f488])).
% 1.84/1.47 thf(f488,plain,(
% 1.84/1.47 ($true = ((~ (member @ sK8 @ sK4 @ mactual)) & (member @ sK8 @ sK3 @ mactual))) | ~spl1_2),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f484])).
% 1.84/1.47 thf(f484,plain,(
% 1.84/1.47 ((((~ (member @ sK8 @ sK4 @ mactual)) & (member @ sK8 @ sK3 @ mactual)) = $true) = $true) | ~spl1_2),
% 1.84/1.47 inference(superposition,[status(thm)],[f174,f480])).
% 1.84/1.47 thf(f480,plain,(
% 1.84/1.47 ($true = (member @ sK8 @ sK2 @ mactual)) | ~spl1_2),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f478])).
% 1.84/1.47 thf(f478,plain,(
% 1.84/1.47 (((member @ sK8 @ sK2 @ mactual) => (member @ sK8 @ (difference @ sK3 @ sK4) @ mactual)) = $false) | ~spl1_2),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f477])).
% 1.84/1.47 thf(f477,plain,(
% 1.84/1.47 ($false = ((^[Y0 : $i]: ((member @ Y0 @ sK2 @ mactual) => (member @ Y0 @ (difference @ sK3 @ sK4) @ mactual))) @ sK8)) | ~spl1_2),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f476])).
% 1.84/1.47 thf(f476,plain,(
% 1.84/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ sK2 @ mactual) => (member @ Y0 @ (difference @ sK3 @ sK4) @ mactual))))) | ~spl1_2),
% 1.84/1.47 inference(not_proxy_clausification,[status(thm)],[f475])).
% 1.84/1.47 thf(f475,plain,(
% 1.84/1.47 ((~ (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ sK2 @ mactual) => (member @ Y0 @ (difference @ sK3 @ sK4) @ mactual))))) = $true) | ~spl1_2),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f469])).
% 1.84/1.47 thf(f469,plain,(
% 1.84/1.47 ($true = ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ sK2 @ mactual) => (member @ Y0 @ (difference @ sK3 @ sK4) @ mactual)))) = $false)) | ~spl1_2),
% 1.84/1.47 inference(superposition,[status(thm)],[f141,f261])).
% 1.84/1.47 thf(f261,plain,(
% 1.84/1.47 ($false = (subset @ sK2 @ (difference @ sK3 @ sK4) @ mactual)) | ~spl1_2),
% 1.84/1.47 inference(avatar_component_clause,[status(thm)],[f259])).
% 1.84/1.47 thf(f259,definition,(
% 1.84/1.47 spl1_2 <=> ($false = (subset @ sK2 @ (difference @ sK3 @ sK4) @ mactual))),
% 1.84/1.47 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.84/1.47 thf(f141,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual)))) = (subset @ X1 @ X2 @ mactual)) = $true)) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f140])).
% 1.84/1.47 thf(f140,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual)))) = (subset @ X1 @ Y0 @ mactual))) @ X2))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f139])).
% 1.84/1.47 thf(f139,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual)))) = (subset @ X1 @ Y0 @ mactual)))) = $true)) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f138])).
% 1.84/1.47 thf(f138,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual)))) = (subset @ Y0 @ Y1 @ mactual))))) @ X1))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f137])).
% 1.84/1.47 thf(f137,plain,(
% 1.84/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual)))) = (subset @ Y0 @ Y1 @ mactual)))))) = $true)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f113])).
% 1.84/1.47 thf(f113,plain,(
% 1.84/1.47 (((^[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)),
% 1.84/1.47 inference(definition_unfolding,[status(thm)],[f95,f97,f92,f92,f85,f92,f80])).
% 1.84/1.47 thf(f80,plain,(
% 1.84/1.47 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f70])).
% 1.84/1.47 thf(f70,plain,(
% 1.84/1.47 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f69])).
% 1.84/1.47 thf(f69,plain,(
% 1.84/1.47 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.84/1.47 inference(rectify,[status(thm)],[f5])).
% 1.84/1.47 thf(f5,axiom,(
% 1.84/1.47 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.84/1.47 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',mimplies_def)).
% 1.84/1.47 thf(f85,plain,(
% 1.84/1.47 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f45])).
% 1.84/1.47 thf(f45,plain,(
% 1.84/1.47 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f44])).
% 1.84/1.47 thf(f44,plain,(
% 1.84/1.47 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X0 @ X2))))),
% 1.84/1.47 inference(rectify,[status(thm)],[f6])).
% 1.84/1.47 thf(f6,axiom,(
% 1.84/1.47 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) <=> (X1 @ X2))))),
% 1.84/1.47 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',mequiv_def)).
% 1.84/1.47 thf(f92,plain,(
% 1.84/1.47 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f63])).
% 1.84/1.47 thf(f63,plain,(
% 1.84/1.47 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f62])).
% 1.84/1.47 thf(f62,plain,(
% 1.84/1.47 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))) = mforall_di)),
% 1.84/1.47 inference(rectify,[status(thm)],[f10])).
% 1.84/1.47 thf(f10,axiom,(
% 1.84/1.47 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : (X1 @ X5 @ X2))) = mforall_di)),
% 1.84/1.47 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',mforall_di_def)).
% 1.84/1.47 thf(f97,plain,(
% 1.84/1.47 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f66])).
% 1.84/1.47 thf(f66,plain,(
% 1.84/1.47 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f1])).
% 1.84/1.47 thf(f1,axiom,(
% 1.84/1.47 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.84/1.47 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',mlocal_def)).
% 1.84/1.47 thf(f95,plain,(
% 1.84/1.47 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f59])).
% 1.84/1.47 thf(f59,plain,(
% 1.84/1.47 ($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)))))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f58])).
% 1.84/1.47 thf(f58,plain,(
% 1.84/1.47 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (subset @ X0 @ X1) @ (mforall_di @ (^[X2 : $i] : (mimplies @ (member @ X2 @ X0) @ (member @ X2 @ X1))))))))))),
% 1.84/1.47 inference(rectify,[status(thm)],[f23])).
% 1.84/1.47 thf(f23,axiom,(
% 1.84/1.47 (mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X8 : $i] : (mequiv @ (subset @ X3 @ X8) @ (mforall_di @ (^[X9 : $i] : (mimplies @ (member @ X9 @ X3) @ (member @ X9 @ X8))))))))))),
% 1.84/1.47 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',subset_defn)).
% 1.84/1.47 thf(f174,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = (((~ (member @ X1 @ sK4 @ mactual)) & (member @ X1 @ sK3 @ mactual)) = (member @ X1 @ sK2 @ mactual)))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f173])).
% 1.84/1.47 thf(f173,plain,(
% 1.84/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((~ (member @ Y0 @ sK4 @ mactual)) & (member @ Y0 @ sK3 @ mactual)) = (member @ Y0 @ sK2 @ mactual))) @ X1) = $true)) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f172])).
% 1.84/1.47 thf(f172,plain,(
% 1.84/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: (((~ (member @ Y0 @ sK4 @ mactual)) & (member @ Y0 @ sK3 @ mactual)) = (member @ Y0 @ sK2 @ mactual)))))),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f170])).
% 1.84/1.47 thf(f170,plain,(
% 1.84/1.47 (((!! @ $i @ (^[Y0 : $i]: (((~ (member @ Y0 @ sK4 @ mactual)) & (member @ Y0 @ sK3 @ mactual)) = (member @ Y0 @ sK2 @ mactual)))) => (qmltpeq @ sK2 @ (difference @ sK3 @ sK4) @ mactual)) = $false)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f169])).
% 1.84/1.47 thf(f169,plain,(
% 1.84/1.47 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((~ (member @ Y1 @ Y0 @ mactual)) & (member @ Y1 @ sK3 @ mactual)) = (member @ Y1 @ sK2 @ mactual)))) => (qmltpeq @ sK2 @ (difference @ sK3 @ Y0) @ mactual))) @ sK4) = $false)),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f168])).
% 1.84/1.47 thf(f168,plain,(
% 1.84/1.47 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((~ (member @ Y1 @ Y0 @ mactual)) & (member @ Y1 @ sK3 @ mactual)) = (member @ Y1 @ sK2 @ mactual)))) => (qmltpeq @ sK2 @ (difference @ sK3 @ Y0) @ mactual)))) = $false)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f167])).
% 1.84/1.47 thf(f167,plain,(
% 1.84/1.47 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (((~ (member @ Y2 @ Y1 @ mactual)) & (member @ Y2 @ Y0 @ mactual)) = (member @ Y2 @ sK2 @ mactual)))) => (qmltpeq @ sK2 @ (difference @ Y0 @ Y1) @ mactual))))) @ sK3) = $false)),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f166])).
% 1.84/1.47 thf(f166,plain,(
% 1.84/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (((~ (member @ Y2 @ Y1 @ mactual)) & (member @ Y2 @ Y0 @ mactual)) = (member @ Y2 @ sK2 @ mactual)))) => (qmltpeq @ sK2 @ (difference @ Y0 @ Y1) @ mactual)))))) = $false)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f165])).
% 1.84/1.47 thf(f165,plain,(
% 1.84/1.47 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((~ (member @ Y3 @ Y2 @ mactual)) & (member @ Y3 @ Y1 @ mactual)) = (member @ Y3 @ Y0 @ mactual)))) => (qmltpeq @ Y0 @ (difference @ Y1 @ Y2) @ mactual))))))) @ sK2))),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f164])).
% 1.84/1.47 thf(f164,plain,(
% 1.84/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((~ (member @ Y3 @ Y2 @ mactual)) & (member @ Y3 @ Y1 @ mactual)) = (member @ Y3 @ Y0 @ mactual)))) => (qmltpeq @ Y0 @ (difference @ Y1 @ Y2) @ mactual)))))))) != $true)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f118])).
% 1.84/1.47 thf(f118,plain,(
% 1.84/1.47 (((^[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]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ ((^[Y3 : $i > mworld > $o]: ((^[Y4 : mworld]: (!! @ $i @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))) @ (^[Y3 : $i]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y5 @ Y6) = (Y4 @ Y6))))))) @ (member @ Y3 @ Y0) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ (member @ Y3 @ Y1) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: (~ (Y4 @ Y5))))) @ (member @ Y3 @ Y2)))))) @ (qmltpeq @ Y0 @ (difference @ Y1 @ Y2)))))))))) != $true)),
% 1.84/1.47 inference(definition_unfolding,[status(thm)],[f103,f97,f92,f92,f92,f80,f92,f85,f104,f84])).
% 1.84/1.47 thf(f84,plain,(
% 1.84/1.47 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f53])).
% 1.84/1.47 thf(f53,plain,(
% 1.84/1.47 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f52])).
% 1.84/1.47 thf(f52,plain,(
% 1.84/1.47 ((^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))) = mnot)),
% 1.84/1.47 inference(rectify,[status(thm)],[f2])).
% 1.84/1.47 thf(f2,axiom,(
% 1.84/1.47 ((^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))) = mnot)),
% 1.84/1.47 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',mnot_def)).
% 1.84/1.47 thf(f104,plain,(
% 1.84/1.47 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f39])).
% 1.84/1.47 thf(f39,plain,(
% 1.84/1.47 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f38])).
% 1.84/1.47 thf(f38,plain,(
% 1.84/1.47 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))))),
% 1.84/1.47 inference(rectify,[status(thm)],[f3])).
% 1.84/1.47 thf(f3,axiom,(
% 1.84/1.47 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))))),
% 1.84/1.47 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',mand_def)).
% 1.84/1.47 thf(f103,plain,(
% 1.84/1.47 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mforall_di @ (^[Y3 : $i]: (mequiv @ (member @ Y3 @ Y0) @ (mand @ (member @ Y3 @ Y1) @ (mnot @ (member @ Y3 @ Y2)))))) @ (qmltpeq @ Y0 @ (difference @ Y1 @ Y2)))))))))) != $true)),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f77])).
% 1.84/1.47 thf(f77,plain,(
% 1.84/1.47 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mforall_di @ (^[Y3 : $i]: (mequiv @ (member @ Y3 @ Y0) @ (mand @ (member @ Y3 @ Y1) @ (mnot @ (member @ Y3 @ Y2)))))) @ (qmltpeq @ Y0 @ (difference @ Y1 @ Y2)))))))))) != $true)),
% 1.84/1.47 inference(flattening,[status(thm)],[f76])).
% 1.84/1.47 thf(f76,plain,(
% 1.84/1.47 ~((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mforall_di @ (^[Y3 : $i]: (mequiv @ (member @ Y3 @ Y0) @ (mand @ (member @ Y3 @ Y1) @ (mnot @ (member @ Y3 @ Y2)))))) @ (qmltpeq @ Y0 @ (difference @ Y1 @ Y2)))))))))) = $true)),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f75])).
% 1.84/1.47 thf(f75,plain,(
% 1.84/1.47 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X2 : $i] : (mimplies @ (mforall_di @ (^[X3 : $i] : (mequiv @ (member @ X3 @ X0) @ (mand @ (member @ X3 @ X1) @ (mnot @ (member @ X3 @ X2)))))) @ (qmltpeq @ X0 @ (difference @ X1 @ X2))))))))))),
% 1.84/1.47 inference(rectify,[status(thm)],[f26])).
% 1.84/1.47 thf(f26,negated_conjecture,(
% 1.84/1.47 ~(mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X8 : $i] : (mforall_di @ (^[X9 : $i] : (mimplies @ (mforall_di @ (^[X10 : $i] : (mequiv @ (member @ X10 @ X3) @ (mand @ (member @ X10 @ X8) @ (mnot @ (member @ X10 @ X9)))))) @ (qmltpeq @ X3 @ (difference @ X8 @ X9))))))))))),
% 1.84/1.47 inference(negated_conjecture,[status(cth)],[f25])).
% 1.84/1.47 thf(f25,conjecture,(
% 1.84/1.47 (mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X8 : $i] : (mforall_di @ (^[X9 : $i] : (mimplies @ (mforall_di @ (^[X10 : $i] : (mequiv @ (member @ X10 @ X3) @ (mand @ (member @ X10 @ X8) @ (mnot @ (member @ X10 @ X9)))))) @ (qmltpeq @ X3 @ (difference @ X8 @ X9))))))))))),
% 1.84/1.47 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',prove_th20)).
% 1.84/1.47 thf(f515,plain,(
% 1.84/1.47 ($true = (member @ sK8 @ sK4 @ mactual)) | ~spl1_8),
% 1.84/1.47 inference(avatar_component_clause,[status(thm)],[f513])).
% 1.84/1.47 thf(f513,definition,(
% 1.84/1.47 spl1_8 <=> ($true = (member @ sK8 @ sK4 @ mactual))),
% 1.84/1.47 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.84/1.47 thf(f598,plain,(
% 1.84/1.47 ~spl1_2 | ~spl1_7),
% 1.84/1.47 inference(avatar_contradiction_clause,[status(thm)],[f597])).
% 1.84/1.47 thf(f597,plain,(
% 1.84/1.47 $false | (~spl1_2 | ~spl1_7)),
% 1.84/1.47 inference(trivial_inequality_removal,[status(thm)],[f596])).
% 1.84/1.47 thf(f596,plain,(
% 1.84/1.47 ($false = $true) | (~spl1_2 | ~spl1_7)),
% 1.84/1.47 inference(forward_demodulation,[status(thm)],[f489,f511])).
% 1.84/1.47 thf(f511,plain,(
% 1.84/1.47 ((member @ sK8 @ sK3 @ mactual) = $false) | ~spl1_7),
% 1.84/1.47 inference(avatar_component_clause,[status(thm)],[f509])).
% 1.84/1.47 thf(f509,definition,(
% 1.84/1.47 spl1_7 <=> ((member @ sK8 @ sK3 @ mactual) = $false)),
% 1.84/1.47 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.84/1.47 thf(f489,plain,(
% 1.84/1.47 ((member @ sK8 @ sK3 @ mactual) = $true) | ~spl1_2),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f488])).
% 1.84/1.47 thf(f516,plain,(
% 1.84/1.47 spl1_7 | spl1_8 | ~spl1_2),
% 1.84/1.47 inference(avatar_split_clause,[status(thm)],[f502,f259,f513,f509])).
% 1.84/1.47 thf(f502,plain,(
% 1.84/1.47 ($true = (member @ sK8 @ sK4 @ mactual)) | ((member @ sK8 @ sK3 @ mactual) = $false) | ~spl1_2),
% 1.84/1.47 inference(not_proxy_clausification,[status(thm)],[f501])).
% 1.84/1.47 thf(f501,plain,(
% 1.84/1.47 ((~ (member @ sK8 @ sK4 @ mactual)) = $false) | ((member @ sK8 @ sK3 @ mactual) = $false) | ~spl1_2),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f500])).
% 1.84/1.47 thf(f500,plain,(
% 1.84/1.47 ($false = ((~ (member @ sK8 @ sK4 @ mactual)) & (member @ sK8 @ sK3 @ mactual))) | ~spl1_2),
% 1.84/1.47 inference(not_proxy_clausification,[status(thm)],[f499])).
% 1.84/1.47 thf(f499,plain,(
% 1.84/1.47 ($true = (~ ((~ (member @ sK8 @ sK4 @ mactual)) & (member @ sK8 @ sK3 @ mactual)))) | ~spl1_2),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f496])).
% 1.84/1.47 thf(f496,plain,(
% 1.84/1.47 ($true = (((~ (member @ sK8 @ sK4 @ mactual)) & (member @ sK8 @ sK3 @ mactual)) = $false)) | ~spl1_2),
% 1.84/1.47 inference(superposition,[status(thm)],[f160,f479])).
% 1.84/1.47 thf(f479,plain,(
% 1.84/1.47 ($false = (member @ sK8 @ (difference @ sK3 @ sK4) @ mactual)) | ~spl1_2),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f478])).
% 1.84/1.47 thf(f160,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((~ (member @ X3 @ X2 @ mactual)) & (member @ X3 @ X1 @ mactual)) = (member @ X3 @ (difference @ X1 @ X2) @ mactual)) = $true)) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f159])).
% 1.84/1.47 thf(f159,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((~ (member @ Y0 @ X2 @ mactual)) & (member @ Y0 @ X1 @ mactual)) = (member @ Y0 @ (difference @ X1 @ X2) @ mactual))) @ X3) = $true)) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f158])).
% 1.84/1.47 thf(f158,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((~ (member @ Y0 @ X2 @ mactual)) & (member @ Y0 @ X1 @ mactual)) = (member @ Y0 @ (difference @ X1 @ X2) @ mactual)))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f157])).
% 1.84/1.47 thf(f157,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (member @ Y1 @ Y0 @ mactual)) & (member @ Y1 @ X1 @ mactual)) = (member @ Y1 @ (difference @ X1 @ Y0) @ mactual))))) @ X2))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f156])).
% 1.84/1.47 thf(f156,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (member @ Y1 @ Y0 @ mactual)) & (member @ Y1 @ X1 @ mactual)) = (member @ Y1 @ (difference @ X1 @ Y0) @ mactual)))))) = $true)) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f155])).
% 1.84/1.47 thf(f155,plain,(
% 1.84/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (member @ Y2 @ Y1 @ mactual)) & (member @ Y2 @ Y0 @ mactual)) = (member @ Y2 @ (difference @ Y0 @ Y1) @ mactual))))))) @ X1) = $true)) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f154])).
% 1.84/1.47 thf(f154,plain,(
% 1.84/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (member @ Y2 @ Y1 @ mactual)) & (member @ Y2 @ Y0 @ mactual)) = (member @ Y2 @ (difference @ Y0 @ Y1) @ mactual)))))))) = $true)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f112])).
% 1.84/1.47 thf(f112,plain,(
% 1.84/1.47 (((^[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 @ Y2 @ (difference @ Y0 @ Y1)) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y4 @ Y5) & (Y3 @ Y5))))))) @ (member @ Y2 @ Y0) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (~ (Y3 @ Y4))))) @ (member @ Y2 @ Y1))))))))))) = $true)),
% 1.84/1.47 inference(definition_unfolding,[status(thm)],[f94,f97,f92,f92,f92,f85,f104,f84])).
% 1.84/1.47 thf(f94,plain,(
% 1.84/1.47 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (member @ Y2 @ (difference @ Y0 @ Y1)) @ (mand @ (member @ Y2 @ Y0) @ (mnot @ (member @ Y2 @ Y1))))))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f55])).
% 1.84/1.47 thf(f55,plain,(
% 1.84/1.47 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (member @ Y2 @ (difference @ Y0 @ Y1)) @ (mand @ (member @ Y2 @ Y0) @ (mnot @ (member @ Y2 @ Y1))))))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f54])).
% 1.84/1.47 thf(f54,plain,(
% 1.84/1.47 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X2 : $i] : (mequiv @ (member @ X2 @ (difference @ X0 @ X1)) @ (mand @ (member @ X2 @ X0) @ (mnot @ (member @ X2 @ X1)))))))))))),
% 1.84/1.47 inference(rectify,[status(thm)],[f21])).
% 1.84/1.47 thf(f21,axiom,(
% 1.84/1.47 (mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X8 : $i] : (mforall_di @ (^[X9 : $i] : (mequiv @ (member @ X9 @ (difference @ X3 @ X8)) @ (mand @ (member @ X9 @ X3) @ (mnot @ (member @ X9 @ X8)))))))))))),
% 1.84/1.47 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',difference_defn)).
% 1.84/1.47 thf(f468,plain,(
% 1.84/1.47 ~spl1_1),
% 1.84/1.47 inference(avatar_contradiction_clause,[status(thm)],[f467])).
% 1.84/1.47 thf(f467,plain,(
% 1.84/1.47 $false | ~spl1_1),
% 1.84/1.47 inference(trivial_inequality_removal,[status(thm)],[f466])).
% 1.84/1.47 thf(f466,plain,(
% 1.84/1.47 ($false = $true) | ~spl1_1),
% 1.84/1.47 inference(forward_demodulation,[status(thm)],[f465,f358])).
% 1.84/1.47 thf(f358,plain,(
% 1.84/1.47 ((member @ sK7 @ sK2 @ mactual) = $false) | ~spl1_1),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f357])).
% 1.84/1.47 thf(f357,plain,(
% 1.84/1.47 ($false = ((member @ sK7 @ (difference @ sK3 @ sK4) @ mactual) => (member @ sK7 @ sK2 @ mactual))) | ~spl1_1),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f356])).
% 1.84/1.47 thf(f356,plain,(
% 1.84/1.47 (((^[Y0 : $i]: ((member @ Y0 @ (difference @ sK3 @ sK4) @ mactual) => (member @ Y0 @ sK2 @ mactual))) @ sK7) = $false) | ~spl1_1),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f355])).
% 1.84/1.47 thf(f355,plain,(
% 1.84/1.47 ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (difference @ sK3 @ sK4) @ mactual) => (member @ Y0 @ sK2 @ mactual)))) = $false) | ~spl1_1),
% 1.84/1.47 inference(not_proxy_clausification,[status(thm)],[f354])).
% 1.84/1.47 thf(f354,plain,(
% 1.84/1.47 ((~ (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (difference @ sK3 @ sK4) @ mactual) => (member @ Y0 @ sK2 @ mactual))))) = $true) | ~spl1_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f351])).
% 1.84/1.47 thf(f351,plain,(
% 1.84/1.47 ($true = ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (difference @ sK3 @ sK4) @ mactual) => (member @ Y0 @ sK2 @ mactual)))) = $false)) | ~spl1_1),
% 1.84/1.47 inference(superposition,[status(thm)],[f141,f257])).
% 1.84/1.47 thf(f257,plain,(
% 1.84/1.47 ((subset @ (difference @ sK3 @ sK4) @ sK2 @ mactual) = $false) | ~spl1_1),
% 1.84/1.47 inference(avatar_component_clause,[status(thm)],[f255])).
% 1.84/1.47 thf(f255,definition,(
% 1.84/1.47 spl1_1 <=> ((subset @ (difference @ sK3 @ sK4) @ sK2 @ mactual) = $false)),
% 1.84/1.47 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.84/1.47 thf(f465,plain,(
% 1.84/1.47 ((member @ sK7 @ sK2 @ mactual) = $true) | ~spl1_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f464])).
% 1.84/1.47 thf(f464,plain,(
% 1.84/1.47 (($true = (member @ sK7 @ sK2 @ mactual)) = $true) | ~spl1_1),
% 1.84/1.47 inference(forward_demodulation,[status(thm)],[f460,f402])).
% 1.84/1.47 thf(f402,plain,(
% 1.84/1.47 ($true = (member @ sK7 @ sK3 @ mactual)) | ~spl1_1),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f401])).
% 1.84/1.47 thf(f401,plain,(
% 1.84/1.47 (((~ (member @ sK7 @ sK4 @ mactual)) & (member @ sK7 @ sK3 @ mactual)) = $true) | ~spl1_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f398])).
% 1.84/1.47 thf(f398,plain,(
% 1.84/1.47 ((((~ (member @ sK7 @ sK4 @ mactual)) & (member @ sK7 @ sK3 @ mactual)) = $true) = $true) | ~spl1_1),
% 1.84/1.47 inference(superposition,[status(thm)],[f160,f359])).
% 1.84/1.47 thf(f359,plain,(
% 1.84/1.47 ($true = (member @ sK7 @ (difference @ sK3 @ sK4) @ mactual)) | ~spl1_1),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f357])).
% 1.84/1.47 thf(f460,plain,(
% 1.84/1.47 ($true = ((member @ sK7 @ sK3 @ mactual) = (member @ sK7 @ sK2 @ mactual))) | ~spl1_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f459])).
% 1.84/1.47 thf(f459,plain,(
% 1.84/1.47 ($true = (($true & (member @ sK7 @ sK3 @ mactual)) = (member @ sK7 @ sK2 @ mactual))) | ~spl1_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f452])).
% 1.84/1.47 thf(f452,plain,(
% 1.84/1.47 ($true = (((~ $false) & (member @ sK7 @ sK3 @ mactual)) = (member @ sK7 @ sK2 @ mactual))) | ~spl1_1),
% 1.84/1.47 inference(superposition,[status(thm)],[f174,f404])).
% 1.84/1.47 thf(f404,plain,(
% 1.84/1.47 ($false = (member @ sK7 @ sK4 @ mactual)) | ~spl1_1),
% 1.84/1.47 inference(not_proxy_clausification,[status(thm)],[f403])).
% 1.84/1.47 thf(f403,plain,(
% 1.84/1.47 ($true = (~ (member @ sK7 @ sK4 @ mactual))) | ~spl1_1),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f401])).
% 1.84/1.47 thf(f271,plain,(
% 1.84/1.47 spl1_2 | spl1_1),
% 1.84/1.47 inference(avatar_split_clause,[status(thm)],[f268,f255,f259])).
% 1.84/1.47 thf(f268,plain,(
% 1.84/1.47 ($false = (subset @ sK2 @ (difference @ sK3 @ sK4) @ mactual)) | ((subset @ (difference @ sK3 @ sK4) @ sK2 @ mactual) = $false)),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f267])).
% 1.84/1.47 thf(f267,plain,(
% 1.84/1.47 ($false = ((subset @ sK2 @ (difference @ sK3 @ sK4) @ mactual) & (subset @ (difference @ sK3 @ sK4) @ sK2 @ mactual)))),
% 1.84/1.47 inference(not_proxy_clausification,[status(thm)],[f266])).
% 1.84/1.47 thf(f266,plain,(
% 1.84/1.47 ((~ ((subset @ sK2 @ (difference @ sK3 @ sK4) @ mactual) & (subset @ (difference @ sK3 @ sK4) @ sK2 @ mactual))) = $true)),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f264])).
% 1.84/1.47 thf(f264,plain,(
% 1.84/1.47 ((((subset @ sK2 @ (difference @ sK3 @ sK4) @ mactual) & (subset @ (difference @ sK3 @ sK4) @ sK2 @ mactual)) = $false) = $true)),
% 1.84/1.47 inference(superposition,[status(thm)],[f219,f231])).
% 1.84/1.47 thf(f231,plain,(
% 1.84/1.47 ($false = (qmltpeq @ (difference @ sK3 @ sK4) @ sK2 @ mactual))),
% 1.84/1.47 inference(trivial_inequality_removal,[status(thm)],[f230])).
% 1.84/1.47 thf(f230,plain,(
% 1.84/1.47 ($false = $true) | ($false = (qmltpeq @ (difference @ sK3 @ sK4) @ sK2 @ mactual))),
% 1.84/1.47 inference(superposition,[status(thm)],[f205,f171])).
% 1.84/1.47 thf(f171,plain,(
% 1.84/1.47 ((qmltpeq @ sK2 @ (difference @ sK3 @ sK4) @ mactual) = $false)),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f170])).
% 1.84/1.47 thf(f205,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : (((qmltpeq @ X1 @ X2 @ mactual) = $false) | ($true = (qmltpeq @ X2 @ X1 @ mactual))) )),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f204])).
% 1.84/1.47 thf(f204,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : ((((qmltpeq @ X1 @ X2 @ mactual) => (qmltpeq @ X2 @ X1 @ mactual)) = $true)) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f203])).
% 1.84/1.47 thf(f203,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((qmltpeq @ X1 @ Y0 @ mactual) => (qmltpeq @ Y0 @ X1 @ mactual))) @ X2) = $true)) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f202])).
% 1.84/1.47 thf(f202,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((qmltpeq @ X1 @ Y0 @ mactual) => (qmltpeq @ Y0 @ X1 @ mactual)))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f201])).
% 1.84/1.47 thf(f201,plain,(
% 1.84/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((qmltpeq @ Y0 @ Y1 @ mactual) => (qmltpeq @ Y1 @ Y0 @ mactual))))) @ X1) = $true)) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f200])).
% 1.84/1.47 thf(f200,plain,(
% 1.84/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((qmltpeq @ Y0 @ Y1 @ mactual) => (qmltpeq @ Y1 @ Y0 @ mactual)))))) = $true)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f109])).
% 1.84/1.47 thf(f109,plain,(
% 1.84/1.47 (((^[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]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ (qmltpeq @ Y0 @ Y1) @ (qmltpeq @ Y1 @ Y0))))))) = $true)),
% 1.84/1.47 inference(definition_unfolding,[status(thm)],[f90,f97,f92,f92,f80])).
% 1.84/1.47 thf(f90,plain,(
% 1.84/1.47 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (qmltpeq @ Y0 @ Y1) @ (qmltpeq @ Y1 @ Y0))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f31])).
% 1.84/1.47 thf(f31,plain,(
% 1.84/1.48 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (qmltpeq @ Y0 @ Y1) @ (qmltpeq @ Y1 @ Y0))))))))),
% 1.84/1.48 inference(fool_elimination,[status(thm)],[f30])).
% 1.84/1.48 thf(f30,plain,(
% 1.84/1.48 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mimplies @ (qmltpeq @ X0 @ X1) @ (qmltpeq @ X1 @ X0)))))))),
% 1.84/1.48 inference(rectify,[status(thm)],[f13])).
% 1.84/1.48 thf(f13,axiom,(
% 1.84/1.48 (mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X6 : $i] : (mimplies @ (qmltpeq @ X5 @ X6) @ (qmltpeq @ X6 @ X5)))))))),
% 1.84/1.48 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',symmetry)).
% 1.84/1.48 thf(f219,plain,(
% 1.84/1.48 ( ! [X2 : $i,X1 : $i] : (((((subset @ X2 @ X1 @ mactual) & (subset @ X1 @ X2 @ mactual)) = (qmltpeq @ X1 @ X2 @ mactual)) = $true)) )),
% 1.84/1.48 inference(beta_eta_normalization,[status(thm)],[f218])).
% 1.84/1.48 thf(f218,plain,(
% 1.84/1.48 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((subset @ Y0 @ X1 @ mactual) & (subset @ X1 @ Y0 @ mactual)) = (qmltpeq @ X1 @ Y0 @ mactual))) @ X2))) )),
% 1.84/1.48 inference(pi_clausification,[status(thm)],[f217])).
% 1.84/1.48 thf(f217,plain,(
% 1.84/1.48 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((subset @ Y0 @ X1 @ mactual) & (subset @ X1 @ Y0 @ mactual)) = (qmltpeq @ X1 @ Y0 @ mactual)))))) )),
% 1.84/1.48 inference(beta_eta_normalization,[status(thm)],[f216])).
% 1.84/1.48 thf(f216,plain,(
% 1.84/1.48 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ Y0 @ mactual) & (subset @ Y0 @ Y1 @ mactual)) = (qmltpeq @ Y0 @ Y1 @ mactual))))) @ X1) = $true)) )),
% 1.84/1.48 inference(pi_clausification,[status(thm)],[f215])).
% 1.84/1.48 thf(f215,plain,(
% 1.84/1.48 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ Y0 @ mactual) & (subset @ Y0 @ Y1 @ mactual)) = (qmltpeq @ Y0 @ Y1 @ mactual)))))))),
% 1.84/1.48 inference(beta_eta_normalization,[status(thm)],[f107])).
% 1.84/1.48 thf(f107,plain,(
% 1.84/1.48 (((^[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))))))) @ (qmltpeq @ Y0 @ Y1) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))) = $true)),
% 1.84/1.48 inference(definition_unfolding,[status(thm)],[f87,f97,f92,f92,f85,f104])).
% 1.84/1.48 thf(f87,plain,(
% 1.84/1.48 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))))),
% 1.84/1.48 inference(cnf_transformation,[status(thm)],[f41])).
% 1.84/1.48 thf(f41,plain,(
% 1.84/1.48 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))))),
% 1.84/1.48 inference(fool_elimination,[status(thm)],[f40])).
% 1.84/1.48 thf(f40,plain,(
% 1.84/1.48 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (qmltpeq @ X0 @ X1) @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X0))))))))),
% 1.84/1.48 inference(rectify,[status(thm)],[f22])).
% 1.84/1.48 thf(f22,axiom,(
% 1.84/1.48 (mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X8 : $i] : (mequiv @ (qmltpeq @ X3 @ X8) @ (mand @ (subset @ X3 @ X8) @ (subset @ X8 @ X3))))))))),
% 1.84/1.48 file('/export/starexec/sandbox/tmp/tmp.PwGLKcqaSk/DTF2THF_6202.p',equal_defn)).
% 1.84/1.48 % SZS output end Proof for DTF2THF_6202
% 1.84/1.48 % (6563)------------------------------
% 1.84/1.48 % (6563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.48 % (6563)Termination reason: Refutation
% 1.84/1.48
% 1.84/1.48 % (6563)Memory used [KB]: 6268
% 1.84/1.48 % (6563)Time elapsed: 0.059 s
% 1.84/1.48 % (6563)Instructions burned: 92 (million)
% 1.84/1.48 % (6563)------------------------------
% 1.84/1.48 % (6563)------------------------------
% 1.84/1.48 % (6529)Success in time 0.156 s
%------------------------------------------------------------------------------