%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU820^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:29 AM UTC 2026
% Result : Theorem 1.72s 1.40s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 148 ( 62 unt; 0 typ; 8 def)
% Number of atoms : 1631 ( 230 equ; 0 cnn)
% Maximal formula atoms : 5 ( 11 avg)
% Number of connectives : 2767 ( 149 ~; 172 |; 123 &;1694 @)
% ( 8 <=>; 358 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 27 usr; 22 con; 0-2 aty)
% ( 240 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 367 ( 309 ^; 56 !; 2 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
nonempty: $i > $o ).
thf(func_def_6,type,
subset: $i > $i > $o ).
thf(func_def_9,type,
transitiveset: $i > $o ).
thf(func_def_10,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_11,type,
wellorderedByIn: $i > $o ).
thf(func_def_12,type,
ordinal: $i > $o ).
thf(func_def_28,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f272,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f76,f88,f117,f127,f137,f173,f210,f232,f271]) ).
thf(f271,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f270]) ).
thf(f270,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f269]) ).
thf(f269,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f268]) ).
thf(f268,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f261,f249]) ).
thf(f249,plain,
( ! [X0: $i > $o] :
( $true
= ( X0 @ sK8 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f247]) ).
thf(f247,plain,
( ! [X0: $i > $o] :
( $true
= ( $true
=> ( X0 @ sK8 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f61,f238]) ).
thf(f238,plain,
( ( $true
= ( in @ sK8 @ emptyset ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f236]) ).
thf(f236,plain,
( ( ( ( in @ sK8 @ emptyset )
=> ( subset @ sK8 @ emptyset ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f235]) ).
thf(f235,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK8 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f71]) ).
thf(f71,definition,
( spl0_1
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f61,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ( in @ X1 @ emptyset )
=> ( X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X1 @ emptyset )
=> ( Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ emptyset )
=> ( Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y3 @ Y4 )
| ( Y3 = Y4 ) ) ) )
& ( in @ Y3 @ Y2 ) ) ) ) ) ) )
@ Y0 ) )
@ emptyset ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f37,f33,f35,f34,f39]) ).
thf(f39,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y3 @ Y4 )
| ( Y3 = Y4 ) ) ) )
& ( in @ Y3 @ Y2 ) ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f29,f36,f38]) ).
thf(f38,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 )
| ( in @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y3 @ Y4 ) )
=> ( in @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
@ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( ^ [Y2: $i] : ( emptyset != Y2 )
@ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f32,f31,f30]) ).
thf(f30,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( nonempty
= ( ^ [X0: $i] : ( emptyset != X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',nonempty) ).
thf(f31,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X1 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ X5 @ X4 )
| ( in @ X4 @ X5 )
| ( X4 = X5 ) ) ) )
& ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ~ ( in @ X6 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( stricttotalorderedByIn
= ( ^ [X2: $i] :
( ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( ( in @ X4 @ X5 )
& ( in @ X0 @ X4 ) )
=> ( in @ X0 @ X5 ) ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ X5 @ X4 )
| ( in @ X4 @ X5 )
| ( X4 = X5 ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ~ ( in @ X4 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',stricttotalorderedByIn) ).
thf(f32,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ( in @ X2 @ X1 )
& ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 = X3 )
| ( in @ X2 @ X3 ) ) ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) )
= wellorderedByIn ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X2: $i] :
( ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( ( nonempty @ X4 )
=> ? [X0: $i] :
( ( in @ X0 @ X4 )
& ! [X5: $i] :
( ( in @ X5 @ X4 )
=> ( ( X0 = X5 )
| ( in @ X0 @ X5 ) ) ) ) ) )
& ( stricttotalorderedByIn @ X2 ) ) )
= wellorderedByIn ),
file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',wellorderedByIn) ).
thf(f36,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X2: $i] :
! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( subset @ X4 @ X2 ) ) )
= transitiveset ),
file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',transitiveset) ).
thf(f29,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',ordinal) ).
thf(f34,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= powersetE1 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: $i,X2: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( subset @ X3 @ X2 ) )
= powersetE1 ),
file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',powersetE1) ).
thf(f35,plain,
( subsetemptysetimpeq
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( subsetemptysetimpeq
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
( subsetemptysetimpeq
= ( ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( emptyset = X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( subsetemptysetimpeq
= ( ! [X2: $i] :
( ( subset @ X2 @ emptyset )
=> ( emptyset = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',subsetemptysetimpeq) ).
thf(f33,plain,
( vacuousDall
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( vacuousDall
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( vacuousDall
= ( ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( vacuousDall
= ( ! [X1: $i > $o,X0: $i] :
( ( in @ X0 @ emptyset )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',vacuousDall) ).
thf(f37,plain,
( $true
= ( ~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( ~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,negated_conjecture,
~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f9,conjecture,
( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',emptysetOrdinal) ).
thf(f261,plain,
( ! [X3: $i > $o] :
( $true
= ( ~ ( X3 @ sK8 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f256]) ).
thf(f256,plain,
( ! [X3: $i > $o] :
( $true
= ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ sK8 ) )
| ~ spl0_1 ),
inference(primitive_instantiation,[status(thm)],[f249]) ).
thf(f232,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[status(thm)],[f231]) ).
thf(f231,plain,
( $false
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f230]) ).
thf(f230,plain,
( ( $true = $false )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f229]) ).
thf(f229,plain,
( ( $false
= ( ( in @ sK7 @ emptyset )
=> $true ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f228]) ).
thf(f228,plain,
( ( $false
= ( ( in @ sK7 @ emptyset )
=> ( ( sK6 = sK7 )
| ( in @ sK6 @ sK7 )
| $true ) ) )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f223,f226]) ).
thf(f226,plain,
( ! [X0: $i > $o] :
( $true
= ( X0 @ sK6 ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f224]) ).
thf(f224,plain,
( ! [X0: $i > $o] :
( $true
= ( $true
=> ( X0 @ sK6 ) ) )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f61,f219]) ).
thf(f219,plain,
( ( $true
= ( in @ sK6 @ emptyset ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
( ( ( ( in @ sK6 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK6 = Y0 )
| ( in @ sK6 @ Y0 )
| ( in @ Y0 @ sK6 ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f216]) ).
thf(f216,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) )
@ sK6 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f135,definition,
( spl0_8
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f223,plain,
( ( $false
= ( ( in @ sK7 @ emptyset )
=> ( ( sK6 = sK7 )
| ( in @ sK6 @ sK7 )
| ( in @ sK7 @ sK6 ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK6 = Y0 )
| ( in @ sK6 @ Y0 )
| ( in @ Y0 @ sK6 ) ) )
@ sK7 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f221]) ).
thf(f221,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK6 = Y0 )
| ( in @ sK6 @ Y0 )
| ( in @ Y0 @ sK6 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f220]) ).
thf(f220,plain,
( ( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK6 = Y0 )
| ( in @ sK6 @ Y0 )
| ( in @ Y0 @ sK6 ) ) ) ) ) )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f217,f219]) ).
thf(f210,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[status(thm)],[f209]) ).
thf(f209,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f208]) ).
thf(f208,plain,
( ( $true = $false )
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f207]) ).
thf(f207,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f199,f189]) ).
thf(f189,plain,
( ! [X0: $i > $o] :
( $true
= ( X0 @ sK5 ) )
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f187]) ).
thf(f187,plain,
( ! [X0: $i > $o] :
( $true
= ( $true
=> ( X0 @ sK5 ) ) )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f61,f182]) ).
thf(f182,plain,
( ( $true
= ( in @ sK5 @ emptyset ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
( ( ( ( in @ sK5 @ emptyset )
=> ~ ( in @ sK5 @ sK5 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f179]) ).
thf(f179,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) )
@ sK5 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f133]) ).
thf(f133,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f132]) ).
thf(f132,definition,
( spl0_7
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f199,plain,
( ! [X3: $i > $o] :
( $true
= ( ~ ( X3 @ sK5 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f195]) ).
thf(f195,plain,
( ! [X3: $i > $o] :
( $true
= ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ sK5 ) )
| ~ spl0_7 ),
inference(primitive_instantiation,[status(thm)],[f189]) ).
thf(f173,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[status(thm)],[f172]) ).
thf(f172,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
( ( $true = $false )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f170]) ).
thf(f170,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f167,f150]) ).
thf(f150,plain,
( ! [X0: $i > $o] :
( $true
= ( X0 @ sK3 ) )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f148]) ).
thf(f148,plain,
( ! [X0: $i > $o] :
( $true
= ( $true
=> ( X0 @ sK3 ) ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f61,f143]) ).
thf(f143,plain,
( ( $true
= ( in @ sK3 @ emptyset ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK3 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK3 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f140]) ).
thf(f140,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) )
@ sK3 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f125]) ).
thf(f125,definition,
( spl0_6
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f167,plain,
( ! [X3: $i > $o] :
( $true
= ( ~ ( X3 @ sK3 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f158]) ).
thf(f158,plain,
( ! [X3: $i > $o] :
( $true
= ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ sK3 ) )
| ~ spl0_6 ),
inference(primitive_instantiation,[status(thm)],[f150]) ).
thf(f137,plain,
( spl0_7
| spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f130,f122,f135,f132]) ).
thf(f122,definition,
( spl0_5
<=> ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f130,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f127,plain,
( spl0_5
| spl0_6
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f120,f86,f125,f122]) ).
thf(f86,definition,
( spl0_4
<=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f120,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f117,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f116]) ).
thf(f116,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $true = $false )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f114]) ).
thf(f114,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f109,f112]) ).
thf(f112,plain,
( ( $true
= ( subset @ sK2 @ emptyset ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $true
= ( $true
=> ( subset @ sK2 @ emptyset ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f80,f95]) ).
thf(f95,plain,
( ( $true
= ( in @ sK2 @ ( powerset @ emptyset ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $false
= ( ( in @ sK2 @ ( powerset @ emptyset ) )
=> ( ( emptyset != sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) )
& ( in @ Y0 @ sK2 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) )
@ sK2 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl0_3
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f80,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( subset @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f42,f46]) ).
thf(f109,plain,
( ( $true
= ( ~ ( subset @ sK2 @ emptyset ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $true
= ( ( subset @ sK2 @ emptyset )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f56,f102]) ).
thf(f102,plain,
( ( $false
= ( emptyset = sK2 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $false
= ( ~ ( ( emptyset != sK2 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( ( emptyset != sK2 )
=> $false )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f97,f98]) ).
thf(f98,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) )
& ( in @ Y0 @ sK2 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $false
= ( ( emptyset != sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) )
& ( in @ Y0 @ sK2 ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $false
= ( $true
=> ( ( emptyset != sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) )
& ( in @ Y0 @ sK2 ) ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f93,f95]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( ( subset @ X1 @ emptyset )
=> ( emptyset = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f88,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f81,f74,f86,f83]) ).
thf(f74,definition,
( spl0_2
<=> ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f81,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f76,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f69,f74,f71]) ).
thf(f69,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f49,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU820^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.35 % Computer : n027.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 12:35:22 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEU820^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.47 % Domain : Set Theory
% 0.27/0.47 % Problem : Ordinals
% 0.27/0.47 % Version : Especial > Reduced > Especial.
% 0.27/0.47 % English : ordinal emptyset
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.47 % Source : [Bro08]
% 0.27/0.47 % Names : ZFC322l [Bro08]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.27/0.47 % Syntax : Number of formulae : 21 ( 8 unt; 12 typ; 8 def)
% 0.27/0.47 % Number of atoms : 50 ( 12 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 4 ( 5 avg)
% 0.27/0.47 % Number of connectives : 80 ( 2 ~; 3 |; 6 &; 52 @)
% 0.27/0.47 % ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 5 ( 1 avg)
% 0.27/0.47 % Number of types : 2 ( 0 usr)
% 0.27/0.47 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 13 ( 12 usr; 4 con; 0-2 aty)
% 0.27/0.47 % Number of variables : 20 ( 5 ^; 14 !; 1 ?; 20 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : http://mathgate.info/detsetitem.php?id=517
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(in_type,type,
% 0.27/0.47 in: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptyset_type,type,
% 0.27/0.47 emptyset: $i ).
% 0.27/0.47
% 0.27/0.47 thf(powerset_type,type,
% 0.27/0.47 powerset: $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(nonempty_type,type,
% 0.27/0.47 nonempty: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(nonempty,definition,
% 0.27/0.47 ( nonempty
% 0.27/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(vacuousDall_type,type,
% 0.27/0.47 vacuousDall: $o ).
% 0.27/0.47
% 0.27/0.47 thf(vacuousDall,definition,
% 0.27/0.47 ( vacuousDall
% 0.27/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ emptyset )
% 0.27/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subset_type,type,
% 0.27/0.47 subset: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetemptysetimpeq_type,type,
% 0.27/0.47 subsetemptysetimpeq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetemptysetimpeq,definition,
% 0.27/0.47 ( subsetemptysetimpeq
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ( subset @ A @ emptyset )
% 0.27/0.47 => ( A = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetE1_type,type,
% 0.27/0.47 powersetE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetE1,definition,
% 0.27/0.47 ( powersetE1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(transitiveset_type,type,
% 0.27/0.47 transitiveset: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(transitiveset,definition,
% 0.27/0.47 ( transitiveset
% 0.27/0.47 = ( ^ [A: $i] :
% 0.27/0.47 ! [X: $i] :
% 0.27/0.47 ( ( in @ X @ A )
% 0.27/0.47 => ( subset @ X @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(stricttotalorderedByIn_type,type,
% 0.27/0.47 stricttotalorderedByIn: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(stricttotalorderedByIn,definition,
% 0.27/0.47 ( stricttotalorderedByIn
% 0.27/0.47 = ( ^ [A: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [X: $i] :
% 0.27/0.47 ( ( in @ X @ A )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ A )
% 0.27/0.47 => ( ( ( in @ Xx @ X )
% 0.27/0.47 & ( in @ X @ Y ) )
% 0.27/0.47 => ( in @ Xx @ Y ) ) ) ) )
% 0.27/0.47 & ! [X: $i] :
% 0.27/0.47 ( ( in @ X @ A )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ A )
% 0.27/0.47 => ( ( X = Y )
% 0.27/0.47 | ( in @ X @ Y )
% 0.27/0.47 | ( in @ Y @ X ) ) ) )
% 0.27/0.47 & ! [X: $i] :
% 0.27/0.47 ( ( in @ X @ A )
% 0.27/0.47 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(wellorderedByIn_type,type,
% 0.27/0.47 wellorderedByIn: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(wellorderedByIn,definition,
% 0.27/0.47 ( wellorderedByIn
% 0.27/0.47 = ( ^ [A: $i] :
% 0.27/0.47 ( ( stricttotalorderedByIn @ A )
% 0.27/0.47 & ! [X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ( ( nonempty @ X )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ X )
% 0.27/0.47 & ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ X )
% 0.27/0.47 => ( ( Xx = Y )
% 0.27/0.47 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ordinal_type,type,
% 0.27/0.47 ordinal: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(ordinal,definition,
% 0.27/0.47 ( ordinal
% 0.27/0.47 = ( ^ [Xx: $i] :
% 0.27/0.47 ( ( transitiveset @ Xx )
% 0.27/0.47 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetOrdinal,conjecture,
% 0.27/0.47 ( vacuousDall
% 0.27/0.47 => ( subsetemptysetimpeq
% 0.27/0.47 => ( powersetE1
% 0.27/0.47 => ( ordinal @ emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.69/1.30 ---- Embedded in THF ---
% 1.69/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.69/1.31 %%% Generated on Tue Feb 24 12:35:23 EST 2026
% 1.69/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.69/1.31 %%% Logic specification used:
% 1.69/1.31 %%% thf(spec, logic, $$dhol).
% 1.69/1.31
% 1.69/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2DTF1367.p
% See solution above
% 1.69/1.31 ------------------------
% 1.69/1.32 ---- Cleaned THF ---
% 1.69/1.32 thf(in_type,type,
% 1.69/1.32 in: $i > $i > $o ).
% 1.69/1.32
% 1.69/1.32 thf(emptyset_type,type,
% 1.69/1.32 emptyset: $i ).
% 1.69/1.32
% 1.69/1.32 thf(powerset_type,type,
% 1.69/1.32 powerset: $i > $i ).
% 1.69/1.32
% 1.69/1.32 thf(nonempty_type,type,
% 1.69/1.32 nonempty: $i > $o ).
% 1.69/1.32
% 1.69/1.32 thf(nonempty,definition,
% 1.69/1.32 ( nonempty
% 1.69/1.32 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(vacuousDall_type,type,
% 1.69/1.32 vacuousDall: $o ).
% 1.69/1.32
% 1.69/1.32 thf(vacuousDall,definition,
% 1.69/1.32 ( vacuousDall
% 1.69/1.32 = ( ! [Xphi: $i > $o,Xx: $i] :
% 1.69/1.32 ( ( in @ Xx @ emptyset )
% 1.69/1.32 => ( Xphi @ Xx ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(subset_type,type,
% 1.69/1.32 subset: $i > $i > $o ).
% 1.69/1.32
% 1.69/1.32 thf(subsetemptysetimpeq_type,type,
% 1.69/1.32 subsetemptysetimpeq: $o ).
% 1.69/1.32
% 1.69/1.32 thf(subsetemptysetimpeq,definition,
% 1.69/1.32 ( subsetemptysetimpeq
% 1.69/1.32 = ( ! [A: $i] :
% 1.69/1.32 ( ( subset @ A @ emptyset )
% 1.69/1.32 => ( A = emptyset ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(powersetE1_type,type,
% 1.69/1.32 powersetE1: $o ).
% 1.69/1.32
% 1.69/1.32 thf(powersetE1,definition,
% 1.69/1.32 ( powersetE1
% 1.69/1.32 = ( ! [A: $i,B: $i] :
% 1.69/1.32 ( ( in @ B @ ( powerset @ A ) )
% 1.69/1.32 => ( subset @ B @ A ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(transitiveset_type,type,
% 1.69/1.32 transitiveset: $i > $o ).
% 1.69/1.32
% 1.69/1.32 thf(transitiveset,definition,
% 1.69/1.32 ( transitiveset
% 1.69/1.32 = ( ^ [A: $i] :
% 1.69/1.32 ! [X: $i] :
% 1.69/1.32 ( ( in @ X @ A )
% 1.69/1.32 => ( subset @ X @ A ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(stricttotalorderedByIn_type,type,
% 1.69/1.32 stricttotalorderedByIn: $i > $o ).
% 1.69/1.32
% 1.69/1.32 thf(stricttotalorderedByIn,definition,
% 1.69/1.32 ( stricttotalorderedByIn
% 1.69/1.32 = ( ^ [A: $i] :
% 1.69/1.32 ( ! [Xx: $i] :
% 1.69/1.32 ( ( in @ Xx @ A )
% 1.69/1.32 => ! [X: $i] :
% 1.69/1.32 ( ( in @ X @ A )
% 1.69/1.32 => ! [Y: $i] :
% 1.69/1.32 ( ( in @ Y @ A )
% 1.69/1.32 => ( ( ( in @ Xx @ X )
% 1.69/1.32 & ( in @ X @ Y ) )
% 1.69/1.32 => ( in @ Xx @ Y ) ) ) ) )
% 1.69/1.32 & ! [X: $i] :
% 1.69/1.32 ( ( in @ X @ A )
% 1.69/1.32 => ! [Y: $i] :
% 1.69/1.32 ( ( in @ Y @ A )
% 1.69/1.32 => ( ( X = Y )
% 1.69/1.32 | ( in @ X @ Y )
% 1.69/1.32 | ( in @ Y @ X ) ) ) )
% 1.69/1.32 & ! [X: $i] :
% 1.69/1.32 ( ( in @ X @ A )
% 1.69/1.32 => ~ ( in @ X @ X ) ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(wellorderedByIn_type,type,
% 1.69/1.32 wellorderedByIn: $i > $o ).
% 1.69/1.32
% 1.69/1.32 thf(wellorderedByIn,definition,
% 1.69/1.32 ( wellorderedByIn
% 1.69/1.32 = ( ^ [A: $i] :
% 1.69/1.32 ( ( stricttotalorderedByIn @ A )
% 1.69/1.32 & ! [X: $i] :
% 1.69/1.32 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.32 => ( ( nonempty @ X )
% 1.69/1.32 => ? [Xx: $i] :
% 1.69/1.32 ( ( in @ Xx @ X )
% 1.69/1.32 & ! [Y: $i] :
% 1.69/1.32 ( ( in @ Y @ X )
% 1.69/1.32 => ( ( Xx = Y )
% 1.69/1.32 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(ordinal_type,type,
% 1.69/1.32 ordinal: $i > $o ).
% 1.69/1.32
% 1.69/1.32 thf(ordinal,definition,
% 1.69/1.32 ( ordinal
% 1.69/1.32 = ( ^ [Xx: $i] :
% 1.69/1.32 ( ( transitiveset @ Xx )
% 1.69/1.32 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(emptysetOrdinal,conjecture,
% 1.69/1.32 ( vacuousDall
% 1.69/1.32 => ( subsetemptysetimpeq
% 1.69/1.32 => ( powersetE1
% 1.69/1.32 => ( ordinal @ emptyset ) ) ) ) ).
% 1.69/1.32 ------------------------
% 1.69/1.33 % (1591)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_1367 for (2999ds/275Mi)
% 1.69/1.33 % (1588)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_1367 for (2999ds/27Mi)
% 1.69/1.34 % (1591)Refutation not found, incomplete strategy
% 1.69/1.34 % (1591)------------------------------
% 1.69/1.34 % (1591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1591)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.34
% 1.69/1.34
% 1.69/1.34 % (1591)Memory used [KB]: 5500
% 1.69/1.34 % (1591)Time elapsed: 0.003 s
% 1.69/1.34 % (1591)Instructions burned: 5 (million)
% 1.69/1.34 % (1591)------------------------------
% 1.69/1.34 % (1591)------------------------------
% 1.69/1.34 % (1586)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/183Mi)
% 1.69/1.34 % (1587)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_1367 for (2999ds/4Mi)
% 1.69/1.34 % (1589)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/2Mi)
% 1.69/1.34 % (1590)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_1367 for (2999ds/2Mi)
% 1.69/1.34 % (1592)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/18Mi)
% 1.69/1.34 % (1588)Instruction limit reached!
% 1.69/1.34 % (1588)------------------------------
% 1.69/1.34 % (1588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1588)Termination reason: Unknown
% 1.69/1.34 % (1588)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (1588)Memory used [KB]: 5628
% 1.69/1.34 % (1588)Time elapsed: 0.009 s
% 1.69/1.34 % (1588)Instructions burned: 27 (million)
% 1.69/1.34 % (1588)------------------------------
% 1.69/1.34 % (1588)------------------------------
% 1.69/1.34 % (1589)Instruction limit reached!
% 1.69/1.34 % (1589)------------------------------
% 1.69/1.34 % (1589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1589)Termination reason: Unknown
% 1.69/1.34 % (1589)Termination phase: shuffling
% 1.69/1.34
% 1.69/1.34 % (1589)Memory used [KB]: 1023
% 1.69/1.34 % (1589)Time elapsed: 0.003 s
% 1.69/1.34 % (1589)Instructions burned: 2 (million)
% 1.69/1.34 % (1589)------------------------------
% 1.69/1.34 % (1589)------------------------------
% 1.69/1.34 % (1590)Instruction limit reached!
% 1.69/1.34 % (1590)------------------------------
% 1.69/1.34 % (1590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1590)Termination reason: Unknown
% 1.69/1.34 % (1590)Termination phase: shuffling
% 1.69/1.34
% 1.69/1.34 % (1590)Memory used [KB]: 1023
% 1.69/1.34 % (1590)Time elapsed: 0.003 s
% 1.69/1.34 % (1590)Instructions burned: 2 (million)
% 1.69/1.34 % (1590)------------------------------
% 1.69/1.34 % (1590)------------------------------
% 1.69/1.34 % (1587)Instruction limit reached!
% 1.69/1.34 % (1587)------------------------------
% 1.69/1.34 % (1587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1587)Termination reason: Unknown
% 1.69/1.34 % (1587)Termination phase: Property scanning
% 1.69/1.34
% 1.69/1.34 % (1587)Memory used [KB]: 1023
% 1.69/1.34 % (1587)Time elapsed: 0.004 s
% 1.69/1.34 % (1587)Instructions burned: 4 (million)
% 1.69/1.34 % (1587)------------------------------
% 1.69/1.34 % (1587)------------------------------
% 1.69/1.35 % (1593)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/3Mi)
% 1.69/1.35 % (1593)Instruction limit reached!
% 1.69/1.35 % (1593)------------------------------
% 1.69/1.35 % (1593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (1593)Termination reason: Unknown
% 1.69/1.35 % (1593)Termination phase: Property scanning
% 1.69/1.35
% 1.69/1.35 % (1593)Memory used [KB]: 1023
% 1.69/1.35 % (1593)Time elapsed: 0.002 s
% 1.69/1.35 % (1593)Instructions burned: 3 (million)
% 1.69/1.35 % (1593)------------------------------
% 1.69/1.35 % (1593)------------------------------
% 1.69/1.35 % (1592)Instruction limit reached!
% 1.69/1.35 % (1592)------------------------------
% 1.69/1.35 % (1592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (1592)Termination reason: Unknown
% 1.69/1.35 % (1592)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (1592)Memory used [KB]: 5500
% 1.69/1.35 % (1592)Time elapsed: 0.012 s
% 1.69/1.35 % (1592)Instructions burned: 19 (million)
% 1.69/1.35 % (1592)------------------------------
% 1.69/1.35 % (1592)------------------------------
% 1.69/1.35 % (1594)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_1367 for (2999ds/37Mi)
% 1.69/1.36 % (1598)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/7Mi)
% 1.69/1.36 % (1598)Instruction limit reached!
% 1.69/1.36 % (1598)------------------------------
% 1.69/1.36 % (1598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (1598)Termination reason: Unknown
% 1.69/1.36 % (1598)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (1598)Memory used [KB]: 1023
% 1.69/1.36 % (1598)Time elapsed: 0.003 s
% 1.69/1.36 % (1598)Instructions burned: 7 (million)
% 1.69/1.36 % (1598)------------------------------
% 1.69/1.36 % (1598)------------------------------
% 1.69/1.36 % (1596)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_1367 for (2999ds/3Mi)
% 1.69/1.36 % (1595)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_1367 for (2999ds/15Mi)
% 1.69/1.36 % (1597)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_1367 for (2999ds/1041Mi)
% 1.69/1.36 % (1596)Instruction limit reached!
% 1.69/1.36 % (1596)------------------------------
% 1.69/1.36 % (1596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (1596)Termination reason: Unknown
% 1.69/1.36 % (1596)Termination phase: Property scanning
% 1.69/1.36
% 1.69/1.36 % (1596)Memory used [KB]: 1023
% 1.69/1.36 % (1596)Time elapsed: 0.003 s
% 1.69/1.36 % (1596)Instructions burned: 3 (million)
% 1.69/1.36 % (1596)------------------------------
% 1.69/1.36 % (1596)------------------------------
% 1.69/1.36 % (1594)Instruction limit reached!
% 1.69/1.36 % (1594)------------------------------
% 1.69/1.36 % (1594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (1594)Termination reason: Unknown
% 1.69/1.36 % (1594)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (1594)Memory used [KB]: 5628
% 1.69/1.36 % (1594)Time elapsed: 0.014 s
% 1.69/1.36 % (1594)Instructions burned: 38 (million)
% 1.69/1.36 % (1594)------------------------------
% 1.69/1.36 % (1594)------------------------------
% 1.69/1.37 % (1600)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_1367 for (2999ds/3Mi)
% 1.69/1.37 % (1595)Instruction limit reached!
% 1.69/1.37 % (1595)------------------------------
% 1.69/1.37 % (1595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (1595)Termination reason: Unknown
% 1.69/1.37 % (1595)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (1595)Memory used [KB]: 5628
% 1.69/1.37 % (1595)Time elapsed: 0.010 s
% 1.69/1.37 % (1595)Instructions burned: 16 (million)
% 1.69/1.37 % (1595)------------------------------
% 1.69/1.37 % (1595)------------------------------
% 1.69/1.37 % (1600)Instruction limit reached!
% 1.69/1.37 % (1600)------------------------------
% 1.69/1.37 % (1600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (1600)Termination reason: Unknown
% 1.69/1.37 % (1600)Termination phase: Property scanning
% 1.69/1.37
% 1.69/1.37 % (1600)Memory used [KB]: 1023
% 1.69/1.37 % (1600)Time elapsed: 0.002 s
% 1.69/1.37 % (1600)Instructions burned: 4 (million)
% 1.69/1.37 % (1600)------------------------------
% 1.69/1.37 % (1600)------------------------------
% 1.69/1.37 % (1599)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/16Mi)
% 1.69/1.37 % (1601)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_1367 for (2999ds/3Mi)
% 1.69/1.37 % (1601)Instruction limit reached!
% 1.69/1.37 % (1601)------------------------------
% 1.69/1.37 % (1601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (1601)Termination reason: Unknown
% 1.69/1.37 % (1601)Termination phase: Function definition elimination
% 1.69/1.37
% 1.69/1.37 % (1601)Memory used [KB]: 1023
% 1.69/1.37 % (1601)Time elapsed: 0.003 s
% 1.69/1.37 % (1601)Instructions burned: 5 (million)
% 1.69/1.37 % (1601)------------------------------
% 1.69/1.37 % (1601)------------------------------
% 1.69/1.37 % (1602)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/7Mi)
% 1.69/1.38 % (1602)Instruction limit reached!
% 1.69/1.38 % (1602)------------------------------
% 1.69/1.38 % (1602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (1602)Termination reason: Unknown
% 1.69/1.38 % (1602)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (1602)Memory used [KB]: 5500
% 1.69/1.38 % (1602)Time elapsed: 0.004 s
% 1.69/1.38 % (1602)Instructions burned: 8 (million)
% 1.69/1.38 % (1602)------------------------------
% 1.69/1.38 % (1602)------------------------------
% 1.69/1.38 % (1604)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/4Mi)
% 1.69/1.38 % (1604)Instruction limit reached!
% 1.69/1.38 % (1604)------------------------------
% 1.69/1.38 % (1604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (1604)Termination reason: Unknown
% 1.69/1.38 % (1604)Termination phase: Property scanning
% 1.69/1.38
% 1.69/1.38 % (1604)Memory used [KB]: 1023
% 1.69/1.38 % (1604)Time elapsed: 0.002 s
% 1.69/1.38 % (1604)Instructions burned: 4 (million)
% 1.69/1.38 % (1604)------------------------------
% 1.69/1.38 % (1604)------------------------------
% 1.69/1.38 % (1599)Instruction limit reached!
% 1.69/1.38 % (1599)------------------------------
% 1.69/1.38 % (1599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (1599)Termination reason: Unknown
% 1.69/1.38 % (1599)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (1599)Memory used [KB]: 5756
% 1.69/1.38 % (1599)Time elapsed: 0.012 s
% 1.69/1.38 % (1599)Instructions burned: 16 (million)
% 1.69/1.38 % (1599)------------------------------
% 1.69/1.38 % (1599)------------------------------
% 1.69/1.38 % (1605)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/18Mi)
% 1.69/1.38 % (1603)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/3Mi)
% 1.69/1.39 % (1606)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/710Mi)
% 1.69/1.39 % (1603)Instruction limit reached!
% 1.69/1.39 % (1603)------------------------------
% 1.69/1.39 % (1603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (1603)Termination reason: Unknown
% 1.69/1.39 % (1603)Termination phase: Property scanning
% 1.69/1.39
% 1.69/1.39 % (1603)Memory used [KB]: 1023
% 1.69/1.39 % (1603)Time elapsed: 0.004 s
% 1.69/1.39 % (1603)Instructions burned: 4 (million)
% 1.69/1.39 % (1603)------------------------------
% 1.69/1.39 % (1603)------------------------------
% 1.69/1.39 % (1607)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/6Mi)
% 1.69/1.39 % (1606)Refutation not found, incomplete strategy
% 1.69/1.39 % (1606)------------------------------
% 1.69/1.39 % (1606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (1606)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.39
% 1.69/1.39
% 1.69/1.39 % (1606)Memory used [KB]: 5500
% 1.69/1.39 % (1606)Time elapsed: 0.003 s
% 1.69/1.39 % (1606)Instructions burned: 4 (million)
% 1.69/1.39 % (1606)------------------------------
% 1.69/1.39 % (1606)------------------------------
% 1.69/1.39 % (1607)Instruction limit reached!
% 1.69/1.39 % (1607)------------------------------
% 1.69/1.39 % (1607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (1607)Termination reason: Unknown
% 1.69/1.39 % (1607)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (1607)Memory used [KB]: 5500
% 1.69/1.39 % (1607)Time elapsed: 0.003 s
% 1.69/1.39 % (1607)Instructions burned: 8 (million)
% 1.69/1.39 % (1607)------------------------------
% 1.69/1.39 % (1607)------------------------------
% 1.69/1.39 % (1605)Instruction limit reached!
% 1.69/1.39 % (1605)------------------------------
% 1.69/1.39 % (1605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (1605)Termination reason: Unknown
% 1.69/1.39 % (1605)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (1605)Memory used [KB]: 5628
% 1.69/1.39 % (1605)Time elapsed: 0.008 s
% 1.69/1.39 % (1605)Instructions burned: 19 (million)
% 1.69/1.39 % (1605)------------------------------
% 1.69/1.39 % (1605)------------------------------
% 1.69/1.39 % (1597)First to succeed.
% 1.69/1.40 % (1608)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_1367 for (2999ds/902Mi)
% 1.72/1.40 % (1610)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1367 for (2999ds/5Mi)
% 1.72/1.40 % (1611)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_1367 for (2999ds/6Mi)
% 1.72/1.40 % (1608)Refutation not found, incomplete strategy
% 1.72/1.40 % (1608)------------------------------
% 1.72/1.40 % (1608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (1608)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.40
% 1.72/1.40
% 1.72/1.40 % (1608)Memory used [KB]: 5500
% 1.72/1.40 % (1608)Time elapsed: 0.005 s
% 1.72/1.40 % (1608)Instructions burned: 4 (million)
% 1.72/1.40 % (1608)------------------------------
% 1.72/1.40 % (1608)------------------------------
% 1.72/1.40 % (1597)Refutation found. Thanks to Tanya!
% 1.72/1.40 % SZS status Theorem for DTF2THF_1367
% 1.72/1.40 % SZS output start Proof for DTF2THF_1367
% 1.72/1.40 thf(func_def_0, type, in: $i > $i > $o).
% 1.72/1.40 thf(func_def_2, type, powerset: $i > $i).
% 1.72/1.40 thf(func_def_3, type, nonempty: $i > $o).
% 1.72/1.40 thf(func_def_6, type, subset: $i > $i > $o).
% 1.72/1.40 thf(func_def_9, type, transitiveset: $i > $o).
% 1.72/1.40 thf(func_def_10, type, stricttotalorderedByIn: $i > $o).
% 1.72/1.40 thf(func_def_11, type, wellorderedByIn: $i > $o).
% 1.72/1.40 thf(func_def_12, type, ordinal: $i > $o).
% 1.72/1.40 thf(func_def_28, type, ph1: !>[X0: $tType]:(X0)).
% 1.72/1.40 thf(f272,plain,(
% 1.72/1.40 $false),
% 1.72/1.40 inference(avatar_sat_refutation,[status(thm)],[f76,f88,f117,f127,f137,f173,f210,f232,f271])).
% 1.72/1.40 thf(f271,plain,(
% 1.72/1.40 ~spl0_1),
% 1.72/1.40 inference(avatar_contradiction_clause,[status(thm)],[f270])).
% 1.72/1.40 thf(f270,plain,(
% 1.72/1.40 $false | ~spl0_1),
% 1.72/1.40 inference(trivial_inequality_removal,[status(thm)],[f269])).
% 1.72/1.40 thf(f269,plain,(
% 1.72/1.40 ($true = $false) | ~spl0_1),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f268])).
% 1.72/1.40 thf(f268,plain,(
% 1.72/1.40 ($true = (~ $true)) | ~spl0_1),
% 1.72/1.40 inference(forward_demodulation,[status(thm)],[f261,f249])).
% 1.72/1.40 thf(f249,plain,(
% 1.72/1.40 ( ! [X0 : $i > $o] : (($true = (X0 @ sK8))) ) | ~spl0_1),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f247])).
% 1.72/1.40 thf(f247,plain,(
% 1.72/1.40 ( ! [X0 : $i > $o] : (($true = ($true => (X0 @ sK8)))) ) | ~spl0_1),
% 1.72/1.40 inference(superposition,[status(thm)],[f61,f238])).
% 1.72/1.40 thf(f238,plain,(
% 1.72/1.40 ($true = (in @ sK8 @ emptyset)) | ~spl0_1),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 1.72/1.40 thf(f236,plain,(
% 1.72/1.40 (((in @ sK8 @ emptyset) => (subset @ sK8 @ emptyset)) = $false) | ~spl0_1),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f235])).
% 1.72/1.40 thf(f235,plain,(
% 1.72/1.40 (((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset))) @ sK8) = $false) | ~spl0_1),
% 1.72/1.40 inference(sigma_clausification,[status(thm)],[f72])).
% 1.72/1.40 thf(f72,plain,(
% 1.72/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset))))) | ~spl0_1),
% 1.72/1.40 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.72/1.40 thf(f71,definition,(
% 1.72/1.40 spl0_1 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset)))))),
% 1.72/1.40 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.72/1.40 thf(f61,plain,(
% 1.72/1.40 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((in @ X1 @ emptyset) => (X2 @ X1)))) )),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.72/1.40 thf(f60,plain,(
% 1.72/1.40 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X1 @ emptyset) => (Y0 @ X1))) @ X2))) )),
% 1.72/1.40 inference(pi_clausification,[status(thm)],[f59])).
% 1.72/1.40 thf(f59,plain,(
% 1.72/1.40 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ emptyset) => (Y0 @ X1)))))) )),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.72/1.40 thf(f58,plain,(
% 1.72/1.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0))))) @ X1))) )),
% 1.72/1.40 inference(pi_clausification,[status(thm)],[f46])).
% 1.72/1.40 thf(f46,plain,(
% 1.72/1.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))))),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.72/1.40 thf(f42,plain,(
% 1.72/1.40 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset)))) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))))))))))),
% 1.72/1.40 inference(not_proxy_clausification,[status(thm)],[f41])).
% 1.72/1.40 thf(f41,plain,(
% 1.72/1.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset)))) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))))))))),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.72/1.40 thf(f40,plain,(
% 1.72/1.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((^[Y0 : $i]: (((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ Y0) & ((^[Y1 : $i]: (((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (~ (in @ Y3 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (((Y3 = Y4) | (in @ Y3 @ Y4)) | (in @ Y4 @ Y3))))))))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => (((in @ Y3 @ Y4) & (in @ Y4 @ Y5)) => (in @ Y3 @ Y5))))))))))))) @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (((^[Y3 : $i]: (~ (emptyset = Y3))) @ Y2) => (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ Y3 @ Y4) | (Y3 = Y4))))) & (in @ Y3 @ Y2)))))))))) @ Y0))) @ emptyset))))))),
% 1.72/1.40 inference(definition_unfolding,[status(thm)],[f37,f33,f35,f34,f39])).
% 1.72/1.40 thf(f39,plain,(
% 1.72/1.40 (ordinal = (^[Y0 : $i]: (((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ Y0) & ((^[Y1 : $i]: (((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (~ (in @ Y3 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (((Y3 = Y4) | (in @ Y3 @ Y4)) | (in @ Y4 @ Y3))))))))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => (((in @ Y3 @ Y4) & (in @ Y4 @ Y5)) => (in @ Y3 @ Y5))))))))))))) @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (((^[Y3 : $i]: (~ (emptyset = Y3))) @ Y2) => (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ Y3 @ Y4) | (Y3 = Y4))))) & (in @ Y3 @ Y2)))))))))) @ Y0))))),
% 1.72/1.40 inference(definition_unfolding,[status(thm)],[f29,f36,f38])).
% 1.72/1.40 thf(f38,plain,(
% 1.72/1.40 (wellorderedByIn = (^[Y0 : $i]: (((^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (in @ Y2 @ Y2))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (((Y2 = Y3) | (in @ Y2 @ Y3)) | (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (((in @ Y2 @ Y3) & (in @ Y3 @ Y4)) => (in @ Y2 @ Y4))))))))))))) @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (((^[Y2 : $i]: (~ (emptyset = Y2))) @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))))),
% 1.72/1.40 inference(definition_unfolding,[status(thm)],[f32,f31,f30])).
% 1.72/1.40 thf(f30,plain,(
% 1.72/1.40 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 1.72/1.40 inference(cnf_transformation,[status(thm)],[f18])).
% 1.72/1.40 thf(f18,plain,(
% 1.72/1.40 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 1.72/1.40 inference(fool_elimination,[status(thm)],[f1])).
% 1.72/1.40 thf(f1,axiom,(
% 1.72/1.40 (nonempty = (^[X0 : $i] : ((emptyset != X0))))),
% 1.72/1.40 file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',nonempty)).
% 1.72/1.40 thf(f31,plain,(
% 1.72/1.40 (stricttotalorderedByIn = (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((Y1 = Y2) | (in @ Y1 @ Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))))))),
% 1.72/1.40 inference(cnf_transformation,[status(thm)],[f22])).
% 1.72/1.40 thf(f22,plain,(
% 1.72/1.40 (stricttotalorderedByIn = (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((Y1 = Y2) | (in @ Y1 @ Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))))))),
% 1.72/1.40 inference(fool_elimination,[status(thm)],[f21])).
% 1.72/1.40 thf(f21,plain,(
% 1.72/1.40 (stricttotalorderedByIn = (^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (((in @ X2 @ X3) & (in @ X1 @ X2)) => (in @ X1 @ X3))))) & ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ X5 @ X4) | (in @ X4 @ X5) | (X4 = X5)))) & ! [X6 : $i] : ((in @ X6 @ X0) => ~(in @ X6 @ X6)))))),
% 1.72/1.40 inference(rectify,[status(thm)],[f6])).
% 1.72/1.40 thf(f6,axiom,(
% 1.72/1.40 (stricttotalorderedByIn = (^[X2 : $i] : (! [X0 : $i] : ((in @ X0 @ X2) => ! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X2) => (((in @ X4 @ X5) & (in @ X0 @ X4)) => (in @ X0 @ X5))))) & ! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ X5 @ X4) | (in @ X4 @ X5) | (X4 = X5)))) & ! [X4 : $i] : ((in @ X4 @ X2) => ~(in @ X4 @ X4)))))),
% 1.72/1.40 file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',stricttotalorderedByIn)).
% 1.72/1.40 thf(f32,plain,(
% 1.72/1.40 (wellorderedByIn = (^[Y0 : $i]: ((stricttotalorderedByIn @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))))),
% 1.72/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.72/1.40 thf(f17,plain,(
% 1.72/1.40 (wellorderedByIn = (^[Y0 : $i]: ((stricttotalorderedByIn @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))))),
% 1.72/1.40 inference(fool_elimination,[status(thm)],[f16])).
% 1.72/1.40 thf(f16,plain,(
% 1.72/1.40 ((^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((nonempty @ X1) => ? [X2 : $i] : ((in @ X2 @ X1) & ! [X3 : $i] : ((in @ X3 @ X1) => ((X2 = X3) | (in @ X2 @ X3)))))) & (stricttotalorderedByIn @ X0))) = wellorderedByIn)),
% 1.72/1.40 inference(rectify,[status(thm)],[f7])).
% 1.72/1.40 thf(f7,axiom,(
% 1.72/1.40 ((^[X2 : $i] : (! [X4 : $i] : ((in @ X4 @ (powerset @ X2)) => ((nonempty @ X4) => ? [X0 : $i] : ((in @ X0 @ X4) & ! [X5 : $i] : ((in @ X5 @ X4) => ((X0 = X5) | (in @ X0 @ X5)))))) & (stricttotalorderedByIn @ X2))) = wellorderedByIn)),
% 1.72/1.40 file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',wellorderedByIn)).
% 1.72/1.40 thf(f36,plain,(
% 1.72/1.40 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.72/1.40 inference(cnf_transformation,[status(thm)],[f13])).
% 1.72/1.40 thf(f13,plain,(
% 1.72/1.40 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.72/1.40 inference(fool_elimination,[status(thm)],[f12])).
% 1.72/1.40 thf(f12,plain,(
% 1.72/1.40 ((^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))) = transitiveset)),
% 1.72/1.40 inference(rectify,[status(thm)],[f5])).
% 1.72/1.40 thf(f5,axiom,(
% 1.72/1.40 ((^[X2 : $i] : (! [X4 : $i] : ((in @ X4 @ X2) => (subset @ X4 @ X2)))) = transitiveset)),
% 1.72/1.40 file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',transitiveset)).
% 1.72/1.40 thf(f29,plain,(
% 1.72/1.40 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & (wellorderedByIn @ Y0))))),
% 1.72/1.40 inference(cnf_transformation,[status(thm)],[f20])).
% 1.72/1.40 thf(f20,plain,(
% 1.72/1.40 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & (wellorderedByIn @ Y0))))),
% 1.72/1.40 inference(fool_elimination,[status(thm)],[f19])).
% 1.72/1.40 thf(f19,plain,(
% 1.72/1.40 (ordinal = (^[X0 : $i] : ((wellorderedByIn @ X0) & (transitiveset @ X0))))),
% 1.72/1.40 inference(rectify,[status(thm)],[f8])).
% 1.72/1.40 thf(f8,axiom,(
% 1.72/1.40 (ordinal = (^[X0 : $i] : ((wellorderedByIn @ X0) & (transitiveset @ X0))))),
% 1.72/1.40 file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',ordinal)).
% 1.72/1.40 thf(f34,plain,(
% 1.72/1.40 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 1.72/1.40 inference(cnf_transformation,[status(thm)],[f26])).
% 1.72/1.40 thf(f26,plain,(
% 1.72/1.40 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 1.72/1.40 inference(fool_elimination,[status(thm)],[f25])).
% 1.72/1.40 thf(f25,plain,(
% 1.72/1.40 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)) = powersetE1)),
% 1.72/1.40 inference(rectify,[status(thm)],[f4])).
% 1.72/1.40 thf(f4,axiom,(
% 1.72/1.40 (! [X3 : $i,X2 : $i] : ((in @ X3 @ (powerset @ X2)) => (subset @ X3 @ X2)) = powersetE1)),
% 1.72/1.40 file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',powersetE1)).
% 1.72/1.40 thf(f35,plain,(
% 1.72/1.40 (subsetemptysetimpeq = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))))),
% 1.72/1.40 inference(cnf_transformation,[status(thm)],[f28])).
% 1.72/1.40 thf(f28,plain,(
% 1.72/1.40 (subsetemptysetimpeq = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))))),
% 1.72/1.40 inference(fool_elimination,[status(thm)],[f27])).
% 1.72/1.40 thf(f27,plain,(
% 1.72/1.40 (subsetemptysetimpeq = ! [X0 : $i] : ((subset @ X0 @ emptyset) => (emptyset = X0)))),
% 1.72/1.40 inference(rectify,[status(thm)],[f3])).
% 1.72/1.40 thf(f3,axiom,(
% 1.72/1.40 (subsetemptysetimpeq = ! [X2 : $i] : ((subset @ X2 @ emptyset) => (emptyset = X2)))),
% 1.72/1.40 file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',subsetemptysetimpeq)).
% 1.72/1.40 thf(f33,plain,(
% 1.72/1.40 (vacuousDall = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))))),
% 1.72/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.72/1.40 thf(f15,plain,(
% 1.72/1.40 (vacuousDall = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))))),
% 1.72/1.40 inference(fool_elimination,[status(thm)],[f14])).
% 1.72/1.40 thf(f14,plain,(
% 1.72/1.40 (vacuousDall = ! [X0 : $i > $o,X1 : $i] : ((in @ X1 @ emptyset) => (X0 @ X1)))),
% 1.72/1.40 inference(rectify,[status(thm)],[f2])).
% 1.72/1.40 thf(f2,axiom,(
% 1.72/1.40 (vacuousDall = ! [X1 : $i > $o,X0 : $i] : ((in @ X0 @ emptyset) => (X1 @ X0)))),
% 1.72/1.40 file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',vacuousDall)).
% 1.72/1.40 thf(f37,plain,(
% 1.72/1.40 ($true = (~ (vacuousDall => (subsetemptysetimpeq => (powersetE1 => (ordinal @ emptyset))))))),
% 1.72/1.40 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.40 thf(f24,plain,(
% 1.72/1.40 ($true = (~ (vacuousDall => (subsetemptysetimpeq => (powersetE1 => (ordinal @ emptyset))))))),
% 1.72/1.40 inference(fool_elimination,[status(thm)],[f23])).
% 1.72/1.40 thf(f23,plain,(
% 1.72/1.40 ~(vacuousDall => (subsetemptysetimpeq => (powersetE1 => (ordinal @ emptyset))))),
% 1.72/1.40 inference(rectify,[status(thm)],[f10])).
% 1.72/1.40 thf(f10,negated_conjecture,(
% 1.72/1.40 ~(vacuousDall => (subsetemptysetimpeq => (powersetE1 => (ordinal @ emptyset))))),
% 1.72/1.40 inference(negated_conjecture,[status(cth)],[f9])).
% 1.72/1.40 thf(f9,conjecture,(
% 1.72/1.40 vacuousDall => (subsetemptysetimpeq => (powersetE1 => (ordinal @ emptyset)))),
% 1.72/1.40 file('/export/starexec/sandbox2/tmp/tmp.EwVXU3TaNk/DTF2THF_1367.p',emptysetOrdinal)).
% 1.72/1.40 thf(f261,plain,(
% 1.72/1.40 ( ! [X3 : $i > $o] : (($true = (~ (X3 @ sK8)))) ) | ~spl0_1),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f256])).
% 1.72/1.40 thf(f256,plain,(
% 1.72/1.40 ( ! [X3 : $i > $o] : (($true = ((^[Y0 : $i]: (~ (X3 @ Y0))) @ sK8))) ) | ~spl0_1),
% 1.72/1.40 inference(primitive_instantiation,[status(thm)],[f249])).
% 1.72/1.40 thf(f232,plain,(
% 1.72/1.40 ~spl0_8),
% 1.72/1.40 inference(avatar_contradiction_clause,[status(thm)],[f231])).
% 1.72/1.40 thf(f231,plain,(
% 1.72/1.40 $false | ~spl0_8),
% 1.72/1.40 inference(trivial_inequality_removal,[status(thm)],[f230])).
% 1.72/1.40 thf(f230,plain,(
% 1.72/1.40 ($true = $false) | ~spl0_8),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f229])).
% 1.72/1.40 thf(f229,plain,(
% 1.72/1.40 ($false = ((in @ sK7 @ emptyset) => $true)) | ~spl0_8),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f228])).
% 1.72/1.40 thf(f228,plain,(
% 1.72/1.40 ($false = ((in @ sK7 @ emptyset) => (((sK6 = sK7) | (in @ sK6 @ sK7)) | $true))) | ~spl0_8),
% 1.72/1.40 inference(backward_demodulation,[status(thm)],[f223,f226])).
% 1.72/1.40 thf(f226,plain,(
% 1.72/1.40 ( ! [X0 : $i > $o] : (($true = (X0 @ sK6))) ) | ~spl0_8),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f224])).
% 1.72/1.40 thf(f224,plain,(
% 1.72/1.40 ( ! [X0 : $i > $o] : (($true = ($true => (X0 @ sK6)))) ) | ~spl0_8),
% 1.72/1.40 inference(superposition,[status(thm)],[f61,f219])).
% 1.72/1.40 thf(f219,plain,(
% 1.72/1.40 ($true = (in @ sK6 @ emptyset)) | ~spl0_8),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f217])).
% 1.72/1.40 thf(f217,plain,(
% 1.72/1.40 (((in @ sK6 @ emptyset) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (((sK6 = Y0) | (in @ sK6 @ Y0)) | (in @ Y0 @ sK6)))))) = $false) | ~spl0_8),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f216])).
% 1.72/1.40 thf(f216,plain,(
% 1.72/1.40 ($false = ((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))) @ sK6)) | ~spl0_8),
% 1.72/1.40 inference(sigma_clausification,[status(thm)],[f136])).
% 1.72/1.40 thf(f136,plain,(
% 1.72/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) | ~spl0_8),
% 1.72/1.40 inference(avatar_component_clause,[status(thm)],[f135])).
% 1.72/1.40 thf(f135,definition,(
% 1.72/1.40 spl0_8 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0)))))))))),
% 1.72/1.40 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.72/1.40 thf(f223,plain,(
% 1.72/1.40 ($false = ((in @ sK7 @ emptyset) => (((sK6 = sK7) | (in @ sK6 @ sK7)) | (in @ sK7 @ sK6)))) | ~spl0_8),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f222])).
% 1.72/1.40 thf(f222,plain,(
% 1.72/1.40 ($false = ((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (((sK6 = Y0) | (in @ sK6 @ Y0)) | (in @ Y0 @ sK6)))) @ sK7)) | ~spl0_8),
% 1.72/1.40 inference(sigma_clausification,[status(thm)],[f221])).
% 1.72/1.40 thf(f221,plain,(
% 1.72/1.40 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (((sK6 = Y0) | (in @ sK6 @ Y0)) | (in @ Y0 @ sK6))))) = $false) | ~spl0_8),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f220])).
% 1.72/1.40 thf(f220,plain,(
% 1.72/1.40 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (((sK6 = Y0) | (in @ sK6 @ Y0)) | (in @ Y0 @ sK6))))))) | ~spl0_8),
% 1.72/1.40 inference(backward_demodulation,[status(thm)],[f217,f219])).
% 1.72/1.40 thf(f210,plain,(
% 1.72/1.40 ~spl0_7),
% 1.72/1.40 inference(avatar_contradiction_clause,[status(thm)],[f209])).
% 1.72/1.40 thf(f209,plain,(
% 1.72/1.40 $false | ~spl0_7),
% 1.72/1.40 inference(trivial_inequality_removal,[status(thm)],[f208])).
% 1.72/1.40 thf(f208,plain,(
% 1.72/1.40 ($true = $false) | ~spl0_7),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f207])).
% 1.72/1.40 thf(f207,plain,(
% 1.72/1.40 ($true = (~ $true)) | ~spl0_7),
% 1.72/1.40 inference(forward_demodulation,[status(thm)],[f199,f189])).
% 1.72/1.40 thf(f189,plain,(
% 1.72/1.40 ( ! [X0 : $i > $o] : (($true = (X0 @ sK5))) ) | ~spl0_7),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f187])).
% 1.72/1.40 thf(f187,plain,(
% 1.72/1.40 ( ! [X0 : $i > $o] : (($true = ($true => (X0 @ sK5)))) ) | ~spl0_7),
% 1.72/1.40 inference(superposition,[status(thm)],[f61,f182])).
% 1.72/1.40 thf(f182,plain,(
% 1.72/1.40 ($true = (in @ sK5 @ emptyset)) | ~spl0_7),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f180])).
% 1.72/1.40 thf(f180,plain,(
% 1.72/1.40 (((in @ sK5 @ emptyset) => (~ (in @ sK5 @ sK5))) = $false) | ~spl0_7),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f179])).
% 1.72/1.40 thf(f179,plain,(
% 1.72/1.40 ($false = ((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0)))) @ sK5)) | ~spl0_7),
% 1.72/1.40 inference(sigma_clausification,[status(thm)],[f133])).
% 1.72/1.40 thf(f133,plain,(
% 1.72/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0)))))) | ~spl0_7),
% 1.72/1.40 inference(avatar_component_clause,[status(thm)],[f132])).
% 1.72/1.40 thf(f132,definition,(
% 1.72/1.40 spl0_7 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))))),
% 1.72/1.40 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.72/1.40 thf(f199,plain,(
% 1.72/1.40 ( ! [X3 : $i > $o] : (($true = (~ (X3 @ sK5)))) ) | ~spl0_7),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f195])).
% 1.72/1.40 thf(f195,plain,(
% 1.72/1.40 ( ! [X3 : $i > $o] : (($true = ((^[Y0 : $i]: (~ (X3 @ Y0))) @ sK5))) ) | ~spl0_7),
% 1.72/1.40 inference(primitive_instantiation,[status(thm)],[f189])).
% 1.72/1.40 thf(f173,plain,(
% 1.72/1.40 ~spl0_6),
% 1.72/1.40 inference(avatar_contradiction_clause,[status(thm)],[f172])).
% 1.72/1.40 thf(f172,plain,(
% 1.72/1.40 $false | ~spl0_6),
% 1.72/1.40 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 1.72/1.40 thf(f171,plain,(
% 1.72/1.40 ($true = $false) | ~spl0_6),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f170])).
% 1.72/1.40 thf(f170,plain,(
% 1.72/1.40 ($true = (~ $true)) | ~spl0_6),
% 1.72/1.40 inference(forward_demodulation,[status(thm)],[f167,f150])).
% 1.72/1.40 thf(f150,plain,(
% 1.72/1.40 ( ! [X0 : $i > $o] : (($true = (X0 @ sK3))) ) | ~spl0_6),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f148])).
% 1.72/1.40 thf(f148,plain,(
% 1.72/1.40 ( ! [X0 : $i > $o] : (($true = ($true => (X0 @ sK3)))) ) | ~spl0_6),
% 1.72/1.40 inference(superposition,[status(thm)],[f61,f143])).
% 1.72/1.40 thf(f143,plain,(
% 1.72/1.40 ($true = (in @ sK3 @ emptyset)) | ~spl0_6),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f141])).
% 1.72/1.40 thf(f141,plain,(
% 1.72/1.40 (((in @ sK3 @ emptyset) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((in @ sK3 @ Y0) & (in @ Y0 @ Y1)) => (in @ sK3 @ Y1))))))))) = $false) | ~spl0_6),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f140])).
% 1.72/1.40 thf(f140,plain,(
% 1.72/1.40 ($false = ((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))) @ sK3)) | ~spl0_6),
% 1.72/1.40 inference(sigma_clausification,[status(thm)],[f126])).
% 1.72/1.40 thf(f126,plain,(
% 1.72/1.40 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) = $false) | ~spl0_6),
% 1.72/1.40 inference(avatar_component_clause,[status(thm)],[f125])).
% 1.72/1.40 thf(f125,definition,(
% 1.72/1.40 spl0_6 <=> ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) = $false)),
% 1.72/1.40 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.72/1.40 thf(f167,plain,(
% 1.72/1.40 ( ! [X3 : $i > $o] : (($true = (~ (X3 @ sK3)))) ) | ~spl0_6),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f158])).
% 1.72/1.40 thf(f158,plain,(
% 1.72/1.40 ( ! [X3 : $i > $o] : (($true = ((^[Y0 : $i]: (~ (X3 @ Y0))) @ sK3))) ) | ~spl0_6),
% 1.72/1.40 inference(primitive_instantiation,[status(thm)],[f150])).
% 1.72/1.40 thf(f137,plain,(
% 1.72/1.40 spl0_7 | spl0_8 | ~spl0_5),
% 1.72/1.40 inference(avatar_split_clause,[status(thm)],[f130,f122,f135,f132])).
% 1.72/1.40 thf(f122,definition,(
% 1.72/1.40 spl0_5 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))))),
% 1.72/1.40 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.72/1.40 thf(f130,plain,(
% 1.72/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0)))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) | ~spl0_5),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.72/1.40 thf(f123,plain,(
% 1.72/1.40 ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0)))))))))) | ~spl0_5),
% 1.72/1.40 inference(avatar_component_clause,[status(thm)],[f122])).
% 1.72/1.40 thf(f127,plain,(
% 1.72/1.40 spl0_5 | spl0_6 | ~spl0_4),
% 1.72/1.40 inference(avatar_split_clause,[status(thm)],[f120,f86,f125,f122])).
% 1.72/1.40 thf(f86,definition,(
% 1.72/1.40 spl0_4 <=> ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) = $false)),
% 1.72/1.40 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.72/1.40 thf(f120,plain,(
% 1.72/1.40 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0)))))))))) | ~spl0_4),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.72/1.40 thf(f87,plain,(
% 1.72/1.40 ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) = $false) | ~spl0_4),
% 1.72/1.40 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.72/1.40 thf(f117,plain,(
% 1.72/1.40 ~spl0_3),
% 1.72/1.40 inference(avatar_contradiction_clause,[status(thm)],[f116])).
% 1.72/1.40 thf(f116,plain,(
% 1.72/1.40 $false | ~spl0_3),
% 1.72/1.40 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.72/1.40 thf(f115,plain,(
% 1.72/1.40 ($true = $false) | ~spl0_3),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f114])).
% 1.72/1.40 thf(f114,plain,(
% 1.72/1.40 ($true = (~ $true)) | ~spl0_3),
% 1.72/1.40 inference(backward_demodulation,[status(thm)],[f109,f112])).
% 1.72/1.40 thf(f112,plain,(
% 1.72/1.40 ($true = (subset @ sK2 @ emptyset)) | ~spl0_3),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f110])).
% 1.72/1.40 thf(f110,plain,(
% 1.72/1.40 ($true = ($true => (subset @ sK2 @ emptyset))) | ~spl0_3),
% 1.72/1.40 inference(superposition,[status(thm)],[f80,f95])).
% 1.72/1.40 thf(f95,plain,(
% 1.72/1.40 ($true = (in @ sK2 @ (powerset @ emptyset))) | ~spl0_3),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.72/1.40 thf(f93,plain,(
% 1.72/1.40 ($false = ((in @ sK2 @ (powerset @ emptyset)) => ((~ (emptyset = sK2)) => (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) | (Y0 = Y1))))) & (in @ Y0 @ sK2))))))) | ~spl0_3),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.72/1.40 thf(f92,plain,(
% 1.72/1.40 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))) @ sK2)) | ~spl0_3),
% 1.72/1.40 inference(sigma_clausification,[status(thm)],[f84])).
% 1.72/1.40 thf(f84,plain,(
% 1.72/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))))) | ~spl0_3),
% 1.72/1.40 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.72/1.40 thf(f83,definition,(
% 1.72/1.40 spl0_3 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))),
% 1.72/1.40 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.72/1.40 thf(f80,plain,(
% 1.72/1.40 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (powerset @ X1)) => (subset @ X2 @ X1)))) )),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.72/1.40 thf(f79,plain,(
% 1.72/1.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (subset @ Y0 @ X1))) @ X2))) )),
% 1.72/1.40 inference(pi_clausification,[status(thm)],[f68])).
% 1.72/1.40 thf(f68,plain,(
% 1.72/1.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (subset @ Y0 @ X1)))) = $true)) )),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.72/1.40 thf(f67,plain,(
% 1.72/1.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0))))) @ X1))) )),
% 1.72/1.40 inference(pi_clausification,[status(thm)],[f64])).
% 1.72/1.40 thf(f64,plain,(
% 1.72/1.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.72/1.40 thf(f49,plain,(
% 1.72/1.40 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset)))) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))))))))),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.72/1.40 thf(f48,plain,(
% 1.72/1.40 (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset)))) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))))) = $false)),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f47])).
% 1.72/1.40 thf(f47,plain,(
% 1.72/1.40 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset)))) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))))))))))),
% 1.72/1.40 inference(backward_demodulation,[status(thm)],[f42,f46])).
% 1.72/1.40 thf(f109,plain,(
% 1.72/1.40 ($true = (~ (subset @ sK2 @ emptyset))) | ~spl0_3),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f106])).
% 1.72/1.40 thf(f106,plain,(
% 1.72/1.40 ($true = ((subset @ sK2 @ emptyset) => $false)) | ~spl0_3),
% 1.72/1.40 inference(superposition,[status(thm)],[f56,f102])).
% 1.72/1.40 thf(f102,plain,(
% 1.72/1.40 ($false = (emptyset = sK2)) | ~spl0_3),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f101])).
% 1.72/1.40 thf(f101,plain,(
% 1.72/1.40 ($false = (~ (~ (emptyset = sK2)))) | ~spl0_3),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f100])).
% 1.72/1.40 thf(f100,plain,(
% 1.72/1.40 (((~ (emptyset = sK2)) => $false) = $false) | ~spl0_3),
% 1.72/1.40 inference(backward_demodulation,[status(thm)],[f97,f98])).
% 1.72/1.40 thf(f98,plain,(
% 1.72/1.40 ($false = (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) | (Y0 = Y1))))) & (in @ Y0 @ sK2))))) | ~spl0_3),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.72/1.40 thf(f97,plain,(
% 1.72/1.40 ($false = ((~ (emptyset = sK2)) => (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) | (Y0 = Y1))))) & (in @ Y0 @ sK2)))))) | ~spl0_3),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f96])).
% 1.72/1.40 thf(f96,plain,(
% 1.72/1.40 ($false = ($true => ((~ (emptyset = sK2)) => (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) | (Y0 = Y1))))) & (in @ Y0 @ sK2))))))) | ~spl0_3),
% 1.72/1.40 inference(backward_demodulation,[status(thm)],[f93,f95])).
% 1.72/1.40 thf(f56,plain,(
% 1.72/1.40 ( ! [X1 : $i] : (($true = ((subset @ X1 @ emptyset) => (emptyset = X1)))) )),
% 1.72/1.40 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.72/1.40 thf(f55,plain,(
% 1.72/1.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0))) @ X1))) )),
% 1.72/1.40 inference(pi_clausification,[status(thm)],[f50])).
% 1.72/1.40 thf(f50,plain,(
% 1.72/1.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))))),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.72/1.40 thf(f88,plain,(
% 1.72/1.40 spl0_3 | spl0_4 | ~spl0_2),
% 1.72/1.40 inference(avatar_split_clause,[status(thm)],[f81,f74,f86,f83])).
% 1.72/1.40 thf(f74,definition,(
% 1.72/1.40 spl0_2 <=> ($false = ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))))))),
% 1.72/1.40 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.72/1.40 thf(f81,plain,(
% 1.72/1.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))))) | ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) = $false) | ~spl0_2),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.72/1.40 thf(f75,plain,(
% 1.72/1.40 ($false = ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))) | ~spl0_2),
% 1.72/1.40 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.72/1.40 thf(f76,plain,(
% 1.72/1.40 spl0_1 | spl0_2),
% 1.72/1.40 inference(avatar_split_clause,[status(thm)],[f69,f74,f71])).
% 1.72/1.40 thf(f69,plain,(
% 1.72/1.40 ($false = ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset)))))),
% 1.72/1.40 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.72/1.40 thf(f66,plain,(
% 1.72/1.40 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset)))) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))) = $false)),
% 1.72/1.40 inference(boolean_simplification,[status(thm)],[f65])).
% 1.72/1.40 thf(f65,plain,(
% 1.72/1.40 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset)))) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (((Y0 = Y1) | (in @ Y0 @ Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ emptyset) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ emptyset)) => ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))))))))),
% 1.72/1.40 inference(backward_demodulation,[status(thm)],[f49,f64])).
% 1.72/1.40 % SZS output end Proof for DTF2THF_1367
% 1.72/1.40 % (1597)------------------------------
% 1.72/1.40 % (1597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (1597)Termination reason: Refutation
% 1.72/1.40
% 1.72/1.40 % (1597)Memory used [KB]: 5756
% 1.72/1.40 % (1597)Time elapsed: 0.040 s
% 1.72/1.40 % (1597)Instructions burned: 53 (million)
% 1.72/1.40 % (1597)------------------------------
% 1.72/1.40 % (1597)------------------------------
% 1.72/1.40 % (1585)Success in time 0.065 s
%------------------------------------------------------------------------------