%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU637^2 : 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 : n015.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 09:35:49 AM UTC 2026
% Result : Theorem 1.68s 1.39s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 10
% Syntax : Number of formulae : 152 ( 113 unt; 0 typ; 2 def)
% Number of atoms : 1450 ( 265 equ; 0 cnn)
% Maximal formula atoms : 11 ( 9 avg)
% Number of connectives : 2740 ( 45 ~; 36 |; 53 &;1864 @)
% ( 2 <=>; 424 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 120 ( 120 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 17 con; 0-2 aty)
% ( 274 !!; 42 ??; 0 @@+; 0 @@-)
% Number of variables : 483 ( 365 ^; 113 !; 5 ?; 483 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_11,type,
singleton: $i > $o ).
thf(func_def_26,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
sK3: $i > $o ).
thf(f608,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f363,f486,f607]) ).
thf(f607,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f606]) ).
thf(f606,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f605]) ).
thf(f605,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f604]) ).
thf(f604,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f574,f603]) ).
thf(f603,plain,
( ( ( sK4 = sK6 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f602]) ).
thf(f602,plain,
( ( ( $true
=> ( sK4 = sK6 ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f567,f598]) ).
thf(f598,plain,
( ( ( in @ sK6 @ sK2 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f586]) ).
thf(f586,plain,
( ( ( $true
=> ( in @ sK6 @ sK2 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f55,f554]) ).
thf(f554,plain,
( ( ( in @ sK6 @ ( dsetconstr @ sK2 @ sK3 ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f550]) ).
thf(f550,plain,
( ( $false
= ( ( in @ sK6 @ ( dsetconstr @ sK2 @ sK3 ) )
=> ( in @ sK6 @ ( setadjoin @ sK4 @ emptyset ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f546]) ).
thf(f546,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) )
@ sK6 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f534]) ).
thf(f534,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f359]) ).
thf(f359,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f358]) ).
thf(f358,definition,
( spl0_1
<=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f55,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) )
=> ( in @ X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ X2 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( in @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( in @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f37,f41]) ).
thf(f41,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( $false
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ~ ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ~ ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f31,f34,f27,f30,f29,f28,f33,f32]) ).
thf(f32,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= X0 )
& ( in @ X1 @ X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: $i] :
? [X2: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= X0 )
& ( in @ X2 @ X0 ) ) )
= singleton ),
file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',singleton) ).
thf(f33,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= eqinunit ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X3: $i,X2: $i] :
( ( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= eqinunit ),
file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',eqinunit) ).
thf(f28,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) )
= uniqinunit ),
file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',uniqinunit) ).
thf(f29,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X0 ) )
=> ( X0 = X1 ) ) )
= setext ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $i,X4: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X4 ) ) )
= setext ),
file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',setext) ).
thf(f30,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',dsetconstrER) ).
thf(f27,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( dsetconstrEL
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( dsetconstrEL
= ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',dsetconstrEL) ).
thf(f34,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',dsetconstrI) ).
thf(f31,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X0: $i > $o,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( X0 @ X4 )
& ( in @ X4 @ X1 ) )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X5: $i] : ( X0 @ X5 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X1: $i > $o,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X1: $i > $o,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',singletonprop) ).
thf(f567,plain,
( ( ( ( in @ sK6 @ sK2 )
=> ( sK4 = sK6 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f562]) ).
thf(f562,plain,
( ( ( ( in @ sK6 @ sK2 )
=> ( $true
=> ( sK4 = sK6 ) ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f197,f557]) ).
thf(f557,plain,
( ( ( sK3 @ sK6 )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f556]) ).
thf(f556,plain,
( ( $false = $true )
| ( ( sK3 @ sK6 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f555]) ).
thf(f555,plain,
( ( $false
= ( $false
=> ( in @ sK6 @ ( setadjoin @ sK4 @ emptyset ) ) ) )
| ( ( sK3 @ sK6 )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f550,f76]) ).
thf(f76,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
= $false )
| ( ( X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
=> ( X3 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f197,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( ( sK3 @ X1 )
=> ( sK4 = X1 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f196]) ).
thf(f196,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( $true
=> ( ( sK3 @ X1 )
=> ( sK4 = X1 ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f195,f124]) ).
thf(f124,plain,
( ( sK3 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
( ( ( in @ sK4 @ sK2 )
& ( sK3 @ sK4 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
& ( sK3 @ Y0 ) )
@ sK4 )
= $true ),
inference(sigma_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
& ( sK3 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
& ( sK3 @ Y0 ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
& ( sK3 @ Y0 ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f108,f111]) ).
thf(f111,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( sK3 @ Y0 )
=> ( ( sK3 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( sK3 @ Y0 )
=> ( ( sK3 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
& ( sK3 @ Y0 ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f107]) ).
thf(f107,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
& ( Y0 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ sK2 @ Y0 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2 @ Y0 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
& ( Y0 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ sK2 @ Y0 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f83,f98]) ).
thf(f98,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f79]) ).
thf(f79,plain,
( $false
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f64,f78]) ).
thf(f78,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( Y1 @ Y2 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f195,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( ( sK3 @ sK4 )
=> ( ( sK3 @ X1 )
=> ( sK4 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f192]) ).
thf(f192,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK3 @ sK4 )
=> ( ( sK3 @ Y0 )
=> ( sK4 = Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK3 @ sK4 )
=> ( ( sK3 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f182]) ).
thf(f182,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK3 @ sK4 )
=> ( ( sK3 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f115,f127]) ).
thf(f127,plain,
( ( in @ sK4 @ sK2 )
= $true ),
inference(boolean_simplification,[status(thm)],[f126]) ).
thf(f126,plain,
( ( ( in @ sK4 @ sK2 )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f123,f124]) ).
thf(f115,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK3 @ X1 )
=> ( ( sK3 @ Y0 )
=> ( X1 = Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f114]) ).
thf(f114,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( sK3 @ Y0 )
=> ( ( sK3 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f111]) ).
thf(f574,plain,
( ( ( sK4 != sK6 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f568]) ).
thf(f568,plain,
( ( ( ( sK4 = sK6 )
=> $false )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f106,f553]) ).
thf(f553,plain,
( ( ( in @ sK6 @ ( setadjoin @ sK4 @ emptyset ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f550]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
=> ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f101]) ).
thf(f101,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f98]) ).
thf(f486,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f485]) ).
thf(f485,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f484]) ).
thf(f484,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f144,f474]) ).
thf(f474,plain,
( ( $false
= ( in @ sK4 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f434,f456]) ).
thf(f456,plain,
( ( sK4 = sK5 )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[status(thm)],[f454]) ).
thf(f454,plain,
( ( ( sK5 = sK4 )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f445]) ).
thf(f445,plain,
( ( ( $true
=> ( sK5 = sK4 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f92,f435]) ).
thf(f435,plain,
( ( ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f432]) ).
thf(f432,plain,
( ( ( ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ sK5 @ ( dsetconstr @ sK2 @ sK3 ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f427]) ).
thf(f427,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
@ sK5 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f362]) ).
thf(f362,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f361]) ).
thf(f361,definition,
( spl0_2
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f434,plain,
( ( ( in @ sK5 @ ( dsetconstr @ sK2 @ sK3 ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f432]) ).
thf(f144,plain,
( ( in @ sK4 @ ( dsetconstr @ sK2 @ sK3 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( $true
=> ( in @ sK4 @ ( dsetconstr @ sK2 @ sK3 ) ) )
= $true ),
inference(superposition,[status(thm)],[f138,f124]) ).
thf(f138,plain,
! [X0: $i > $o] :
( ( ( X0 @ sK4 )
=> ( in @ sK4 @ ( dsetconstr @ sK2 @ X0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f132]) ).
thf(f132,plain,
! [X0: $i > $o] :
( ( $true
=> ( ( X0 @ sK4 )
=> ( in @ sK4 @ ( dsetconstr @ sK2 @ X0 ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f62,f127]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X3 @ X2 )
=> ( ( X1 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f363,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f356,f361,f358]) ).
thf(f356,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f174]) ).
thf(f174,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f170]) ).
thf(f170,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) )
=> $false ) )
= $true ),
inference(superposition,[status(thm)],[f95,f166]) ).
thf(f166,plain,
( $false
= ( ( setadjoin @ sK4 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) ),
inference(boolean_simplification,[status(thm)],[f165]) ).
thf(f165,plain,
( $false
= ( $true
& ( ( setadjoin @ sK4 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) ) ),
inference(superposition,[status(thm)],[f146,f144]) ).
thf(f146,plain,
! [X1: $i] :
( $false
= ( ( in @ X1 @ ( dsetconstr @ sK2 @ sK3 ) )
& ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f145]) ).
thf(f145,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU637^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:29:31 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU637^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Ordered Pairs - Singletons
% 0.29/0.46 % Version : Especial > Reduced > Especial.
% 0.29/0.46 % English : (! A:i.! phi:i>o.(! x:i.in x A -> (! y:i.in y A -> phi x ->
% 0.29/0.46 % phi y -> x = y)) -> (? x:i.in x A & phi x) -> singleton
% 0.29/0.46 % (dsetconstr A (^ x:i.phi x)))
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC139l [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.57 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.57 v6.1.0, 0.86 v6.0.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 19 ( 7 unt; 11 typ; 7 def)
% 0.29/0.46 % Number of atoms : 41 ( 12 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 11 ( 5 avg)
% 0.29/0.46 % Number of connectives : 78 ( 0 ~; 0 |; 2 &; 54 @)
% 0.29/0.46 % ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 17 ( 3 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 12 ( 11 usr; 7 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 28 ( 5 ^; 21 !; 2 ?; 28 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=469
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI_type,type,
% 0.29/0.46 dsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI,definition,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL_type,type,
% 0.29/0.46 dsetconstrEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL,definition,
% 0.29/0.46 ( dsetconstrEL
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER_type,type,
% 0.29/0.46 dsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER,definition,
% 0.29/0.46 ( dsetconstrER
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setext_type,type,
% 0.29/0.46 setext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setext,definition,
% 0.29/0.46 ( setext
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit_type,type,
% 0.29/0.46 uniqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit,definition,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit_type,type,
% 0.29/0.46 eqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit,definition,
% 0.29/0.46 ( eqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singleton_type,type,
% 0.29/0.46 singleton: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(singleton,definition,
% 0.29/0.46 ( singleton
% 0.29/0.46 = ( ^ [A: $i] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( A
% 0.29/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop,conjecture,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 => ( dsetconstrEL
% 0.29/0.46 => ( dsetconstrER
% 0.29/0.46 => ( setext
% 0.29/0.46 => ( uniqinunit
% 0.29/0.46 => ( eqinunit
% 0.29/0.46 => ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.28 %%% Generated on Tue Feb 24 12:29:32 EST 2026
% 1.49/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.28 %%% Logic specification used:
% 1.49/1.28 %%% thf(spec, logic, $$dhol).
% 1.49/1.28
% 1.49/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2DTF1177.p
% See solution above
% 1.49/1.28 ------------------------
% 1.49/1.29 ---- Cleaned THF ---
% 1.49/1.29 thf(in_type,type,
% 1.49/1.29 in: $i > $i > $o ).
% 1.49/1.29
% 1.49/1.29 thf(emptyset_type,type,
% 1.49/1.29 emptyset: $i ).
% 1.49/1.29
% 1.49/1.29 thf(setadjoin_type,type,
% 1.49/1.29 setadjoin: $i > $i > $i ).
% 1.49/1.29
% 1.49/1.29 thf(dsetconstr_type,type,
% 1.49/1.29 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.49/1.29
% 1.49/1.29 thf(dsetconstrI_type,type,
% 1.49/1.29 dsetconstrI: $o ).
% 1.49/1.29
% 1.49/1.29 thf(dsetconstrI,definition,
% 1.49/1.29 ( dsetconstrI
% 1.49/1.29 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.49/1.29 ( ( in @ Xx @ A )
% 1.49/1.29 => ( ( Xphi @ Xx )
% 1.49/1.29 => ( in @ Xx
% 1.49/1.29 @ ( dsetconstr @ A
% 1.49/1.29 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.49/1.29
% 1.49/1.29 thf(dsetconstrEL_type,type,
% 1.49/1.29 dsetconstrEL: $o ).
% 1.49/1.29
% 1.49/1.29 thf(dsetconstrEL,definition,
% 1.49/1.29 ( dsetconstrEL
% 1.49/1.29 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.49/1.29 ( ( in @ Xx
% 1.49/1.29 @ ( dsetconstr @ A
% 1.49/1.29 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.49/1.29 => ( in @ Xx @ A ) ) ) ) ).
% 1.49/1.29
% 1.49/1.29 thf(dsetconstrER_type,type,
% 1.49/1.29 dsetconstrER: $o ).
% 1.49/1.29
% 1.49/1.29 thf(dsetconstrER,definition,
% 1.49/1.29 ( dsetconstrER
% 1.49/1.29 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.49/1.29 ( ( in @ Xx
% 1.49/1.29 @ ( dsetconstr @ A
% 1.49/1.29 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.49/1.29 => ( Xphi @ Xx ) ) ) ) ).
% 1.49/1.29
% 1.49/1.29 thf(setext_type,type,
% 1.49/1.29 setext: $o ).
% 1.49/1.29
% 1.49/1.29 thf(setext,definition,
% 1.49/1.29 ( setext
% 1.49/1.29 = ( ! [A: $i,B: $i] :
% 1.49/1.29 ( ! [Xx: $i] :
% 1.49/1.29 ( ( in @ Xx @ A )
% 1.49/1.29 => ( in @ Xx @ B ) )
% 1.49/1.29 => ( ! [Xx: $i] :
% 1.49/1.29 ( ( in @ Xx @ B )
% 1.49/1.29 => ( in @ Xx @ A ) )
% 1.49/1.29 => ( A = B ) ) ) ) ) ).
% 1.49/1.29
% 1.49/1.29 thf(uniqinunit_type,type,
% 1.49/1.29 uniqinunit: $o ).
% 1.49/1.29
% 1.49/1.29 thf(uniqinunit,definition,
% 1.49/1.29 ( uniqinunit
% 1.49/1.29 = ( ! [Xx: $i,Xy: $i] :
% 1.49/1.29 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.49/1.29 => ( Xx = Xy ) ) ) ) ).
% 1.49/1.29
% 1.49/1.29 thf(eqinunit_type,type,
% 1.49/1.29 eqinunit: $o ).
% 1.49/1.29
% 1.49/1.29 thf(eqinunit,definition,
% 1.49/1.29 ( eqinunit
% 1.49/1.29 = ( ! [Xx: $i,Xy: $i] :
% 1.49/1.29 ( ( Xx = Xy )
% 1.49/1.29 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.49/1.29
% 1.49/1.29 thf(singleton_type,type,
% 1.49/1.29 singleton: $i > $o ).
% 1.49/1.29
% 1.49/1.29 thf(singleton,definition,
% 1.49/1.29 ( singleton
% 1.49/1.29 = ( ^ [A: $i] :
% 1.49/1.29 ? [Xx: $i] :
% 1.49/1.29 ( ( in @ Xx @ A )
% 1.49/1.29 & ( A
% 1.49/1.29 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.49/1.29
% 1.49/1.29 thf(singletonprop,conjecture,
% 1.49/1.29 ( dsetconstrI
% 1.49/1.29 => ( dsetconstrEL
% 1.49/1.29 => ( dsetconstrER
% 1.49/1.29 => ( setext
% 1.49/1.29 => ( uniqinunit
% 1.49/1.29 => ( eqinunit
% 1.49/1.29 => ! [A: $i,Xphi: $i > $o] :
% 1.49/1.29 ( ! [Xx: $i] :
% 1.49/1.29 ( ( in @ Xx @ A )
% 1.49/1.29 => ! [Xy: $i] :
% 1.49/1.29 ( ( in @ Xy @ A )
% 1.49/1.29 => ( ( Xphi @ Xx )
% 1.49/1.29 => ( ( Xphi @ Xy )
% 1.49/1.29 => ( Xx = Xy ) ) ) ) )
% 1.49/1.29 => ( ? [Xx: $i] :
% 1.49/1.29 ( ( in @ Xx @ A )
% 1.49/1.29 & ( Xphi @ Xx ) )
% 1.49/1.29 => ( singleton
% 1.49/1.29 @ ( dsetconstr @ A
% 1.49/1.29 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ).
% 1.49/1.29 ------------------------
% 1.68/1.30 % (1450)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/183Mi)
% 1.68/1.30 % (1456)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/18Mi)
% 1.68/1.31 % (1456)Instruction limit reached!
% 1.68/1.31 % (1456)------------------------------
% 1.68/1.31 % (1456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.31 % (1456)Termination reason: Unknown
% 1.68/1.31 % (1456)Termination phase: Saturation
% 1.68/1.31
% 1.68/1.31 % (1456)Memory used [KB]: 5628
% 1.68/1.31 % (1451)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_1177 for (2999ds/4Mi)
% 1.68/1.31 % (1456)Time elapsed: 0.008 s
% 1.68/1.31 % (1456)Instructions burned: 19 (million)
% 1.68/1.31 % (1456)------------------------------
% 1.68/1.31 % (1456)------------------------------
% 1.68/1.31 % (1453)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/2Mi)
% 1.68/1.31 % (1452)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_1177 for (2999ds/27Mi)
% 1.68/1.31 % (1454)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_1177 for (2999ds/2Mi)
% 1.68/1.31 % (1455)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_1177 for (2999ds/275Mi)
% 1.68/1.31 % (1453)Instruction limit reached!
% 1.68/1.31 % (1453)------------------------------
% 1.68/1.31 % (1453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.31 % (1453)Termination reason: Unknown
% 1.68/1.31 % (1453)Termination phase: shuffling
% 1.68/1.31
% 1.68/1.31 % (1453)Memory used [KB]: 1023
% 1.68/1.31 % (1453)Time elapsed: 0.003 s
% 1.68/1.31 % (1453)Instructions burned: 2 (million)
% 1.68/1.31 % (1453)------------------------------
% 1.68/1.31 % (1453)------------------------------
% 1.68/1.31 % (1454)Instruction limit reached!
% 1.68/1.31 % (1454)------------------------------
% 1.68/1.31 % (1454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.31 % (1454)Termination reason: Unknown
% 1.68/1.31 % (1454)Termination phase: shuffling
% 1.68/1.31
% 1.68/1.31 % (1454)Memory used [KB]: 1023
% 1.68/1.31 % (1454)Time elapsed: 0.003 s
% 1.68/1.31 % (1454)Instructions burned: 2 (million)
% 1.68/1.31 % (1454)------------------------------
% 1.68/1.31 % (1454)------------------------------
% 1.68/1.31 % (1451)Instruction limit reached!
% 1.68/1.31 % (1451)------------------------------
% 1.68/1.31 % (1451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.31 % (1451)Termination reason: Unknown
% 1.68/1.31 % (1451)Termination phase: Saturation
% 1.68/1.31
% 1.68/1.31 % (1451)Memory used [KB]: 5500
% 1.68/1.31 % (1451)Time elapsed: 0.005 s
% 1.68/1.31 % (1451)Instructions burned: 5 (million)
% 1.68/1.31 % (1451)------------------------------
% 1.68/1.31 % (1451)------------------------------
% 1.68/1.32 % (1457)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/3Mi)
% 1.68/1.32 % (1457)Instruction limit reached!
% 1.68/1.32 % (1457)------------------------------
% 1.68/1.32 % (1457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (1457)Termination reason: Unknown
% 1.68/1.32 % (1457)Termination phase: Saturation
% 1.68/1.32
% 1.68/1.32 % (1457)Memory used [KB]: 1023
% 1.68/1.32 % (1457)Time elapsed: 0.003 s
% 1.68/1.32 % (1457)Instructions burned: 4 (million)
% 1.68/1.32 % (1457)------------------------------
% 1.68/1.32 % (1457)------------------------------
% 1.68/1.33 % (1452)Instruction limit reached!
% 1.68/1.33 % (1452)------------------------------
% 1.68/1.33 % (1452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (1452)Termination reason: Unknown
% 1.68/1.33 % (1452)Termination phase: Saturation
% 1.68/1.33
% 1.68/1.33 % (1452)Memory used [KB]: 5628
% 1.68/1.33 % (1452)Time elapsed: 0.019 s
% 1.68/1.33 % (1452)Instructions burned: 28 (million)
% 1.68/1.33 % (1452)------------------------------
% 1.68/1.33 % (1452)------------------------------
% 1.68/1.33 % (1458)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_1177 for (2999ds/37Mi)
% 1.68/1.33 % (1459)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_1177 for (2999ds/15Mi)
% 1.68/1.33 % (1460)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_1177 for (2999ds/3Mi)
% 1.68/1.33 % (1461)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_1177 for (2999ds/1041Mi)
% 1.68/1.33 % (1460)Instruction limit reached!
% 1.68/1.33 % (1460)------------------------------
% 1.68/1.33 % (1460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (1460)Termination reason: Unknown
% 1.68/1.33 % (1460)Termination phase: Function definition elimination
% 1.68/1.33
% 1.68/1.33 % (1460)Memory used [KB]: 1023
% 1.68/1.33 % (1460)Time elapsed: 0.004 s
% 1.68/1.33 % (1460)Instructions burned: 4 (million)
% 1.68/1.33 % (1460)------------------------------
% 1.68/1.33 % (1460)------------------------------
% 1.68/1.34 % (1459)Instruction limit reached!
% 1.68/1.34 % (1459)------------------------------
% 1.68/1.34 % (1459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (1459)Termination reason: Unknown
% 1.68/1.34 % (1459)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (1459)Memory used [KB]: 5628
% 1.68/1.34 % (1459)Time elapsed: 0.012 s
% 1.68/1.34 % (1459)Instructions burned: 16 (million)
% 1.68/1.34 % (1459)------------------------------
% 1.68/1.34 % (1459)------------------------------
% 1.68/1.34 % (1462)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/7Mi)
% 1.68/1.34 % (1462)Instruction limit reached!
% 1.68/1.34 % (1462)------------------------------
% 1.68/1.34 % (1462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (1462)Termination reason: Unknown
% 1.68/1.34 % (1462)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (1462)Memory used [KB]: 1023
% 1.68/1.34 % (1462)Time elapsed: 0.004 s
% 1.68/1.34 % (1462)Instructions burned: 7 (million)
% 1.68/1.34 % (1462)------------------------------
% 1.68/1.34 % (1462)------------------------------
% 1.68/1.35 % (1458)Instruction limit reached!
% 1.68/1.35 % (1458)------------------------------
% 1.68/1.35 % (1458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.35 % (1458)Termination reason: Unknown
% 1.68/1.35 % (1458)Termination phase: Saturation
% 1.68/1.35
% 1.68/1.35 % (1458)Memory used [KB]: 5756
% 1.68/1.35 % (1458)Time elapsed: 0.019 s
% 1.68/1.35 % (1458)Instructions burned: 39 (million)
% 1.68/1.35 % (1458)------------------------------
% 1.68/1.35 % (1458)------------------------------
% 1.68/1.35 % (1463)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/16Mi)
% 1.68/1.35 % (1465)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_1177 for (2999ds/3Mi)
% 1.68/1.35 % (1465)Instruction limit reached!
% 1.68/1.35 % (1465)------------------------------
% 1.68/1.35 % (1465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.35 % (1465)Termination reason: Unknown
% 1.68/1.35 % (1465)Termination phase: Function definition elimination
% 1.68/1.35
% 1.68/1.35 % (1465)Memory used [KB]: 1023
% 1.68/1.35 % (1465)Time elapsed: 0.003 s
% 1.68/1.35 % (1465)Instructions burned: 5 (million)
% 1.68/1.35 % (1465)------------------------------
% 1.68/1.35 % (1465)------------------------------
% 1.68/1.36 % (1466)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/7Mi)
% 1.68/1.36 % (1464)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_1177 for (2999ds/3Mi)
% 1.68/1.36 % (1466)Refutation not found, incomplete strategy
% 1.68/1.36 % (1466)------------------------------
% 1.68/1.36 % (1466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (1466)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.36
% 1.68/1.36
% 1.68/1.36 % (1466)Memory used [KB]: 5500
% 1.68/1.36 % (1466)Time elapsed: 0.004 s
% 1.68/1.36 % (1466)Instructions burned: 5 (million)
% 1.68/1.36 % (1466)------------------------------
% 1.68/1.36 % (1466)------------------------------
% 1.68/1.36 % (1464)Instruction limit reached!
% 1.68/1.36 % (1464)------------------------------
% 1.68/1.36 % (1464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (1464)Termination reason: Unknown
% 1.68/1.36 % (1464)Termination phase: Property scanning
% 1.68/1.36
% 1.68/1.36 % (1464)Memory used [KB]: 1023
% 1.68/1.36 % (1464)Time elapsed: 0.004 s
% 1.68/1.36 % (1464)Instructions burned: 4 (million)
% 1.68/1.36 % (1464)------------------------------
% 1.68/1.36 % (1464)------------------------------
% 1.68/1.36 % (1463)Instruction limit reached!
% 1.68/1.36 % (1463)------------------------------
% 1.68/1.36 % (1463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (1463)Termination reason: Unknown
% 1.68/1.36 % (1463)Termination phase: Saturation
% 1.68/1.36
% 1.68/1.36 % (1463)Memory used [KB]: 5884
% 1.68/1.36 % (1463)Time elapsed: 0.012 s
% 1.68/1.36 % (1463)Instructions burned: 16 (million)
% 1.68/1.36 % (1463)------------------------------
% 1.68/1.36 % (1463)------------------------------
% 1.68/1.36 % (1450)Instruction limit reached!
% 1.68/1.36 % (1450)------------------------------
% 1.68/1.36 % (1450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (1450)Termination reason: Unknown
% 1.68/1.36 % (1450)Termination phase: Saturation
% 1.68/1.36
% 1.68/1.36 % (1450)Memory used [KB]: 6268
% 1.68/1.36 % (1450)Time elapsed: 0.060 s
% 1.68/1.36 % (1450)Instructions burned: 183 (million)
% 1.68/1.36 % (1450)------------------------------
% 1.68/1.36 % (1450)------------------------------
% 1.68/1.36 % (1467)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/3Mi)
% 1.68/1.37 % (1467)Instruction limit reached!
% 1.68/1.37 % (1467)------------------------------
% 1.68/1.37 % (1467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (1467)Termination reason: Unknown
% 1.68/1.37 % (1467)Termination phase: Property scanning
% 1.68/1.37
% 1.68/1.37 % (1467)Memory used [KB]: 1023
% 1.68/1.37 % (1467)Time elapsed: 0.003 s
% 1.68/1.37 % (1467)Instructions burned: 5 (million)
% 1.68/1.37 % (1467)------------------------------
% 1.68/1.37 % (1467)------------------------------
% 1.68/1.37 % (1468)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/4Mi)
% 1.68/1.37 % (1468)Instruction limit reached!
% 1.68/1.37 % (1468)------------------------------
% 1.68/1.37 % (1468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (1468)Termination reason: Unknown
% 1.68/1.37 % (1468)Termination phase: Property scanning
% 1.68/1.37
% 1.68/1.37 % (1468)Memory used [KB]: 1023
% 1.68/1.37 % (1468)Time elapsed: 0.003 s
% 1.68/1.37 % (1468)Instructions burned: 5 (million)
% 1.68/1.37 % (1468)------------------------------
% 1.68/1.37 % (1468)------------------------------
% 1.68/1.37 % (1471)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/6Mi)
% 1.68/1.37 % (1471)Instruction limit reached!
% 1.68/1.37 % (1471)------------------------------
% 1.68/1.37 % (1471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (1471)Termination reason: Unknown
% 1.68/1.37 % (1471)Termination phase: Saturation
% 1.68/1.37
% 1.68/1.37 % (1471)Memory used [KB]: 5500
% 1.68/1.37 % (1471)Time elapsed: 0.003 s
% 1.68/1.37 % (1471)Instructions burned: 7 (million)
% 1.68/1.37 % (1471)------------------------------
% 1.68/1.37 % (1471)------------------------------
% 1.68/1.38 % (1472)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_1177 for (2999ds/902Mi)
% 1.68/1.38 % (1469)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/18Mi)
% 1.68/1.38 % (1470)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/710Mi)
% 1.68/1.38 % (1473)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/21Mi)
% 1.68/1.38 % (1461)First to succeed.
% 1.68/1.38 % (1474)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1177 for (2999ds/5Mi)
% 1.68/1.38 % (1474)Instruction limit reached!
% 1.68/1.38 % (1474)------------------------------
% 1.68/1.38 % (1474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (1474)Termination reason: Unknown
% 1.68/1.38 % (1474)Termination phase: Saturation
% 1.68/1.38
% 1.68/1.38 % (1474)Memory used [KB]: 5500
% 1.68/1.38 % (1474)Time elapsed: 0.003 s
% 1.68/1.38 % (1474)Instructions burned: 7 (million)
% 1.68/1.38 % (1474)------------------------------
% 1.68/1.38 % (1474)------------------------------
% 1.68/1.39 % (1461)Refutation found. Thanks to Tanya!
% 1.68/1.39 % SZS status Theorem for DTF2THF_1177
% 1.68/1.39 % SZS output start Proof for DTF2THF_1177
% 1.68/1.39 thf(func_def_0, type, in: $i > $i > $o).
% 1.68/1.39 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.68/1.39 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.68/1.39 thf(func_def_11, type, singleton: $i > $o).
% 1.68/1.39 thf(func_def_26, type, ph1: !>[X0: $tType]:(X0)).
% 1.68/1.39 thf(func_def_28, type, sK3: $i > $o).
% 1.68/1.39 thf(f608,plain,(
% 1.68/1.39 $false),
% 1.68/1.39 inference(avatar_sat_refutation,[status(thm)],[f363,f486,f607])).
% 1.68/1.39 thf(f607,plain,(
% 1.68/1.39 ~spl0_1),
% 1.68/1.39 inference(avatar_contradiction_clause,[status(thm)],[f606])).
% 1.68/1.39 thf(f606,plain,(
% 1.68/1.39 $false | ~spl0_1),
% 1.68/1.39 inference(trivial_inequality_removal,[status(thm)],[f605])).
% 1.68/1.39 thf(f605,plain,(
% 1.68/1.39 ($false = $true) | ~spl0_1),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f604])).
% 1.68/1.39 thf(f604,plain,(
% 1.68/1.39 ((~ $true) = $true) | ~spl0_1),
% 1.68/1.39 inference(backward_demodulation,[status(thm)],[f574,f603])).
% 1.68/1.39 thf(f603,plain,(
% 1.68/1.39 ((sK4 = sK6) = $true) | ~spl0_1),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f602])).
% 1.68/1.39 thf(f602,plain,(
% 1.68/1.39 (($true => (sK4 = sK6)) = $true) | ~spl0_1),
% 1.68/1.39 inference(backward_demodulation,[status(thm)],[f567,f598])).
% 1.68/1.39 thf(f598,plain,(
% 1.68/1.39 ((in @ sK6 @ sK2) = $true) | ~spl0_1),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f586])).
% 1.68/1.39 thf(f586,plain,(
% 1.68/1.39 (($true => (in @ sK6 @ sK2)) = $true) | ~spl0_1),
% 1.68/1.39 inference(superposition,[status(thm)],[f55,f554])).
% 1.68/1.39 thf(f554,plain,(
% 1.68/1.39 ((in @ sK6 @ (dsetconstr @ sK2 @ sK3)) = $true) | ~spl0_1),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f550])).
% 1.68/1.39 thf(f550,plain,(
% 1.68/1.39 ($false = ((in @ sK6 @ (dsetconstr @ sK2 @ sK3)) => (in @ sK6 @ (setadjoin @ sK4 @ emptyset)))) | ~spl0_1),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f546])).
% 1.68/1.39 thf(f546,plain,(
% 1.68/1.39 (((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))) @ sK6) = $false) | ~spl0_1),
% 1.68/1.39 inference(sigma_clausification,[status(thm)],[f534])).
% 1.68/1.39 thf(f534,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))) = $false) | ~spl0_1),
% 1.68/1.39 inference(not_proxy_clausification,[status(thm)],[f359])).
% 1.68/1.39 thf(f359,plain,(
% 1.68/1.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) = $true) | ~spl0_1),
% 1.68/1.39 inference(avatar_component_clause,[status(thm)],[f358])).
% 1.68/1.39 thf(f358,definition,(
% 1.68/1.39 spl0_1 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) = $true)),
% 1.68/1.39 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.68/1.39 thf(f55,plain,(
% 1.68/1.39 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X2 @ (dsetconstr @ X1 @ X3)) => (in @ X2 @ X1)) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.68/1.39 thf(f54,plain,(
% 1.68/1.39 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (in @ X2 @ X1))) @ X3) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f53])).
% 1.68/1.39 thf(f53,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (in @ X2 @ X1)))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.68/1.39 thf(f52,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (in @ Y0 @ X1))))) @ X2) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f51])).
% 1.68/1.39 thf(f51,plain,(
% 1.68/1.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (in @ Y0 @ X1)))))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.68/1.39 thf(f50,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0))))))) @ X1) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f45])).
% 1.68/1.39 thf(f45,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.68/1.39 thf(f43,plain,(
% 1.68/1.39 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))))))),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f42])).
% 1.68/1.39 thf(f42,plain,(
% 1.68/1.39 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))))))))) = $false)),
% 1.68/1.39 inference(backward_demodulation,[status(thm)],[f37,f41])).
% 1.68/1.39 thf(f41,plain,(
% 1.68/1.39 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.68/1.39 thf(f37,plain,(
% 1.68/1.39 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))))))))))),
% 1.68/1.39 inference(not_proxy_clausification,[status(thm)],[f36])).
% 1.68/1.39 thf(f36,plain,(
% 1.68/1.39 ((~ ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))))))) = $true)),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.68/1.39 thf(f35,plain,(
% 1.68/1.39 ((~ ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))))))) = $true)),
% 1.68/1.39 inference(definition_unfolding,[status(thm)],[f31,f34,f27,f30,f29,f28,f33,f32])).
% 1.68/1.39 thf(f32,plain,(
% 1.68/1.39 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.68/1.39 inference(cnf_transformation,[status(thm)],[f16])).
% 1.68/1.39 thf(f16,plain,(
% 1.68/1.39 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.68/1.39 inference(fool_elimination,[status(thm)],[f15])).
% 1.68/1.39 thf(f15,plain,(
% 1.68/1.39 ((^[X0 : $i] : (? [X1 : $i] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))) = singleton)),
% 1.68/1.39 inference(rectify,[status(thm)],[f7])).
% 1.68/1.39 thf(f7,axiom,(
% 1.68/1.39 ((^[X0 : $i] : (? [X2 : $i] : (((setadjoin @ X2 @ emptyset) = X0) & (in @ X2 @ X0)))) = singleton)),
% 1.68/1.39 file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',singleton)).
% 1.68/1.39 thf(f33,plain,(
% 1.68/1.39 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.68/1.39 inference(cnf_transformation,[status(thm)],[f18])).
% 1.68/1.39 thf(f18,plain,(
% 1.68/1.39 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.68/1.39 inference(fool_elimination,[status(thm)],[f17])).
% 1.68/1.39 thf(f17,plain,(
% 1.68/1.39 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X1 @ (setadjoin @ X0 @ emptyset))) = eqinunit)),
% 1.68/1.39 inference(rectify,[status(thm)],[f6])).
% 1.68/1.39 thf(f6,axiom,(
% 1.68/1.39 (! [X3 : $i,X2 : $i] : ((X2 = X3) => (in @ X2 @ (setadjoin @ X3 @ emptyset))) = eqinunit)),
% 1.68/1.39 file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',eqinunit)).
% 1.68/1.39 thf(f28,plain,(
% 1.68/1.39 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.68/1.39 inference(cnf_transformation,[status(thm)],[f14])).
% 1.68/1.39 thf(f14,plain,(
% 1.68/1.39 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.68/1.39 inference(fool_elimination,[status(thm)],[f13])).
% 1.68/1.39 thf(f13,plain,(
% 1.68/1.39 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.68/1.39 inference(rectify,[status(thm)],[f5])).
% 1.68/1.39 thf(f5,axiom,(
% 1.68/1.39 (! [X2 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X3 @ emptyset)) => (X2 = X3)) = uniqinunit)),
% 1.68/1.39 file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',uniqinunit)).
% 1.68/1.39 thf(f29,plain,(
% 1.68/1.39 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.68/1.39 inference(cnf_transformation,[status(thm)],[f24])).
% 1.68/1.39 thf(f24,plain,(
% 1.68/1.39 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.68/1.39 inference(fool_elimination,[status(thm)],[f23])).
% 1.68/1.39 thf(f23,plain,(
% 1.68/1.39 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))) = setext)),
% 1.68/1.39 inference(rectify,[status(thm)],[f4])).
% 1.68/1.39 thf(f4,axiom,(
% 1.68/1.39 (! [X0 : $i,X4 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X4)) => (! [X2 : $i] : ((in @ X2 @ X4) => (in @ X2 @ X0)) => (X0 = X4))) = setext)),
% 1.68/1.39 file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',setext)).
% 1.68/1.39 thf(f30,plain,(
% 1.68/1.39 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 1.68/1.39 inference(cnf_transformation,[status(thm)],[f22])).
% 1.68/1.39 thf(f22,plain,(
% 1.68/1.39 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 1.68/1.39 inference(fool_elimination,[status(thm)],[f21])).
% 1.68/1.39 thf(f21,plain,(
% 1.68/1.39 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 1.68/1.39 inference(rectify,[status(thm)],[f3])).
% 1.68/1.39 thf(f3,axiom,(
% 1.68/1.39 (! [X1 : $i > $o,X0 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.68/1.39 file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',dsetconstrER)).
% 1.68/1.39 thf(f27,plain,(
% 1.68/1.39 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y1 @ Y0)))))))))),
% 1.68/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.68/1.39 thf(f12,plain,(
% 1.68/1.39 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y1 @ Y0)))))))))),
% 1.68/1.39 inference(fool_elimination,[status(thm)],[f11])).
% 1.68/1.39 thf(f11,plain,(
% 1.68/1.39 (dsetconstrEL = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (in @ X1 @ X2)))),
% 1.68/1.39 inference(rectify,[status(thm)],[f2])).
% 1.68/1.39 thf(f2,axiom,(
% 1.68/1.39 (dsetconstrEL = ! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)))),
% 1.68/1.39 file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',dsetconstrEL)).
% 1.68/1.39 thf(f34,plain,(
% 1.68/1.39 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.68/1.39 inference(cnf_transformation,[status(thm)],[f20])).
% 1.68/1.39 thf(f20,plain,(
% 1.68/1.39 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.68/1.39 inference(fool_elimination,[status(thm)],[f19])).
% 1.68/1.39 thf(f19,plain,(
% 1.68/1.39 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))))) = dsetconstrI)),
% 1.68/1.39 inference(rectify,[status(thm)],[f1])).
% 1.68/1.39 thf(f1,axiom,(
% 1.68/1.39 (! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 1.68/1.39 file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',dsetconstrI)).
% 1.68/1.39 thf(f31,plain,(
% 1.68/1.39 ((~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))))))) = $true)),
% 1.68/1.39 inference(cnf_transformation,[status(thm)],[f26])).
% 1.68/1.39 thf(f26,plain,(
% 1.68/1.39 ((~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))))))) = $true)),
% 1.68/1.39 inference(fool_elimination,[status(thm)],[f25])).
% 1.68/1.39 thf(f25,plain,(
% 1.68/1.39 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X0 : $i > $o,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X0 @ X4) & (in @ X4 @ X1)) => (singleton @ (dsetconstr @ X1 @ (^[X5 : $i] : (X0 @ X5))))))))))))),
% 1.68/1.39 inference(rectify,[status(thm)],[f9])).
% 1.68/1.39 thf(f9,negated_conjecture,(
% 1.68/1.39 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X1 : $i > $o,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))))))))),
% 1.68/1.39 inference(negated_conjecture,[status(cth)],[f8])).
% 1.68/1.39 thf(f8,conjecture,(
% 1.68/1.39 dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X1 : $i > $o,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2)))))))))))),
% 1.68/1.39 file('/export/starexec/sandbox2/tmp/tmp.6JlMGmXHfo/DTF2THF_1177.p',singletonprop)).
% 1.68/1.39 thf(f567,plain,(
% 1.68/1.39 (((in @ sK6 @ sK2) => (sK4 = sK6)) = $true) | ~spl0_1),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f562])).
% 1.68/1.39 thf(f562,plain,(
% 1.68/1.39 (((in @ sK6 @ sK2) => ($true => (sK4 = sK6))) = $true) | ~spl0_1),
% 1.68/1.39 inference(superposition,[status(thm)],[f197,f557])).
% 1.68/1.39 thf(f557,plain,(
% 1.68/1.39 ((sK3 @ sK6) = $true) | ~spl0_1),
% 1.68/1.39 inference(trivial_inequality_removal,[status(thm)],[f556])).
% 1.68/1.39 thf(f556,plain,(
% 1.68/1.39 ($false = $true) | ((sK3 @ sK6) = $true) | ~spl0_1),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f555])).
% 1.68/1.39 thf(f555,plain,(
% 1.68/1.39 ($false = ($false => (in @ sK6 @ (setadjoin @ sK4 @ emptyset)))) | ((sK3 @ sK6) = $true) | ~spl0_1),
% 1.68/1.39 inference(superposition,[status(thm)],[f550,f76])).
% 1.68/1.39 thf(f76,plain,(
% 1.68/1.39 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ X3)) = $false) | ((X3 @ X1) = $true)) )),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.68/1.39 thf(f75,plain,(
% 1.68/1.39 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X1 @ (dsetconstr @ X2 @ X3)) => (X3 @ X1)) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.68/1.39 thf(f74,plain,(
% 1.68/1.39 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1))) @ X3) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f73])).
% 1.68/1.39 thf(f73,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1)))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.68/1.39 thf(f72,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1))))) @ X2) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f71])).
% 1.68/1.39 thf(f71,plain,(
% 1.68/1.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1)))))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.68/1.39 thf(f70,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0))))))) @ X1) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f65])).
% 1.68/1.39 thf(f65,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.68/1.39 thf(f44,plain,(
% 1.68/1.39 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))))))) = $false)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.68/1.39 thf(f197,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ((sK3 @ X1) => (sK4 = X1))) = $true)) )),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f196])).
% 1.68/1.39 thf(f196,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ($true => ((sK3 @ X1) => (sK4 = X1)))) = $true)) )),
% 1.68/1.39 inference(forward_demodulation,[status(thm)],[f195,f124])).
% 1.68/1.39 thf(f124,plain,(
% 1.68/1.39 ((sK3 @ sK4) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.68/1.39 thf(f123,plain,(
% 1.68/1.39 (((in @ sK4 @ sK2) & (sK3 @ sK4)) = $true)),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f122])).
% 1.68/1.39 thf(f122,plain,(
% 1.68/1.39 (((^[Y0 : $i]: ((in @ Y0 @ sK2) & (sK3 @ Y0))) @ sK4) = $true)),
% 1.68/1.39 inference(sigma_clausification,[status(thm)],[f117])).
% 1.68/1.39 thf(f117,plain,(
% 1.68/1.39 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) & (sK3 @ Y0)))) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.68/1.39 thf(f113,plain,(
% 1.68/1.39 ($false = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) & (sK3 @ Y0)))) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3)))))))),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f112])).
% 1.68/1.39 thf(f112,plain,(
% 1.68/1.39 (($true => ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) & (sK3 @ Y0)))) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3))))))) = $false)),
% 1.68/1.39 inference(backward_demodulation,[status(thm)],[f108,f111])).
% 1.68/1.39 thf(f111,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((sK3 @ Y0) => ((sK3 @ Y1) => (Y0 = Y1))))))))) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.68/1.39 thf(f108,plain,(
% 1.68/1.39 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((sK3 @ Y0) => ((sK3 @ Y1) => (Y0 = Y1))))))))) => ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) & (sK3 @ Y0)))) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3))))))) = $false)),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f107])).
% 1.68/1.39 thf(f107,plain,(
% 1.68/1.39 ($false = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((Y0 @ Y1) => ((Y0 @ Y2) => (Y1 = Y2))))))))) => ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ Y0)) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ Y0)))))))) @ sK3))),
% 1.68/1.39 inference(sigma_clausification,[status(thm)],[f104])).
% 1.68/1.39 thf(f104,plain,(
% 1.68/1.39 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((Y0 @ Y1) => ((Y0 @ Y2) => (Y1 = Y2))))))))) => ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ Y0)) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ Y0))))))))) = $false)),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f103])).
% 1.68/1.39 thf(f103,plain,(
% 1.68/1.39 ($false = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))) @ sK2))),
% 1.68/1.39 inference(sigma_clausification,[status(thm)],[f100])).
% 1.68/1.39 thf(f100,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) = $false)),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f99])).
% 1.68/1.39 thf(f99,plain,(
% 1.68/1.39 (($true => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))) = $false)),
% 1.68/1.39 inference(backward_demodulation,[status(thm)],[f83,f98])).
% 1.68/1.39 thf(f98,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.68/1.39 thf(f83,plain,(
% 1.68/1.39 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))) = $false)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.68/1.39 thf(f80,plain,(
% 1.68/1.39 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))))) = $false)),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f79])).
% 1.68/1.39 thf(f79,plain,(
% 1.68/1.39 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))))),
% 1.68/1.39 inference(backward_demodulation,[status(thm)],[f64,f78])).
% 1.68/1.39 thf(f78,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.68/1.39 thf(f64,plain,(
% 1.68/1.39 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))) = $false)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.68/1.39 thf(f195,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ((sK3 @ sK4) => ((sK3 @ X1) => (sK4 = X1)))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f192])).
% 1.68/1.39 thf(f192,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK3 @ sK4) => ((sK3 @ Y0) => (sK4 = Y0))))) @ X1) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f183])).
% 1.68/1.39 thf(f183,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK3 @ sK4) => ((sK3 @ Y0) => (sK4 = Y0)))))) = $true)),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f182])).
% 1.68/1.39 thf(f182,plain,(
% 1.68/1.39 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK3 @ sK4) => ((sK3 @ Y0) => (sK4 = Y0))))))) = $true)),
% 1.68/1.39 inference(superposition,[status(thm)],[f115,f127])).
% 1.68/1.39 thf(f127,plain,(
% 1.68/1.39 ((in @ sK4 @ sK2) = $true)),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f126])).
% 1.68/1.39 thf(f126,plain,(
% 1.68/1.39 (((in @ sK4 @ sK2) & $true) = $true)),
% 1.68/1.39 inference(backward_demodulation,[status(thm)],[f123,f124])).
% 1.68/1.39 thf(f115,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK3 @ X1) => ((sK3 @ Y0) => (X1 = Y0))))))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f114])).
% 1.68/1.39 thf(f114,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((sK3 @ Y0) => ((sK3 @ Y1) => (Y0 = Y1)))))))) @ X1) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f111])).
% 1.68/1.39 thf(f574,plain,(
% 1.68/1.39 ((~ (sK4 = sK6)) = $true) | ~spl0_1),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f568])).
% 1.68/1.39 thf(f568,plain,(
% 1.68/1.39 (((sK4 = sK6) => $false) = $true) | ~spl0_1),
% 1.68/1.39 inference(superposition,[status(thm)],[f106,f553])).
% 1.68/1.39 thf(f553,plain,(
% 1.68/1.39 ((in @ sK6 @ (setadjoin @ sK4 @ emptyset)) = $false) | ~spl0_1),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f550])).
% 1.68/1.39 thf(f106,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : ((((X2 = X1) => (in @ X1 @ (setadjoin @ X2 @ emptyset))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.68/1.39 thf(f105,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((Y0 = X1) => (in @ X1 @ (setadjoin @ Y0 @ emptyset)))) @ X2) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f102])).
% 1.68/1.39 thf(f102,plain,(
% 1.68/1.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => (in @ X1 @ (setadjoin @ Y0 @ emptyset))))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f101])).
% 1.68/1.39 thf(f101,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ X1) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f98])).
% 1.68/1.39 thf(f486,plain,(
% 1.68/1.39 ~spl0_2),
% 1.68/1.39 inference(avatar_contradiction_clause,[status(thm)],[f485])).
% 1.68/1.39 thf(f485,plain,(
% 1.68/1.39 $false | ~spl0_2),
% 1.68/1.39 inference(trivial_inequality_removal,[status(thm)],[f484])).
% 1.68/1.39 thf(f484,plain,(
% 1.68/1.39 ($false = $true) | ~spl0_2),
% 1.68/1.39 inference(backward_demodulation,[status(thm)],[f144,f474])).
% 1.68/1.39 thf(f474,plain,(
% 1.68/1.39 ($false = (in @ sK4 @ (dsetconstr @ sK2 @ sK3))) | ~spl0_2),
% 1.68/1.39 inference(backward_demodulation,[status(thm)],[f434,f456])).
% 1.68/1.39 thf(f456,plain,(
% 1.68/1.39 (sK4 = sK5) | ~spl0_2),
% 1.68/1.39 inference(equality_proxy_clausification,[status(thm)],[f454])).
% 1.68/1.39 thf(f454,plain,(
% 1.68/1.39 ((sK5 = sK4) = $true) | ~spl0_2),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f445])).
% 1.68/1.39 thf(f445,plain,(
% 1.68/1.39 (($true => (sK5 = sK4)) = $true) | ~spl0_2),
% 1.68/1.39 inference(superposition,[status(thm)],[f92,f435])).
% 1.68/1.39 thf(f435,plain,(
% 1.68/1.39 ((in @ sK5 @ (setadjoin @ sK4 @ emptyset)) = $true) | ~spl0_2),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f432])).
% 1.68/1.39 thf(f432,plain,(
% 1.68/1.39 (((in @ sK5 @ (setadjoin @ sK4 @ emptyset)) => (in @ sK5 @ (dsetconstr @ sK2 @ sK3))) = $false) | ~spl0_2),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f427])).
% 1.68/1.39 thf(f427,plain,(
% 1.68/1.39 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3)))) @ sK5)) | ~spl0_2),
% 1.68/1.39 inference(sigma_clausification,[status(thm)],[f362])).
% 1.68/1.39 thf(f362,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3))))) = $false) | ~spl0_2),
% 1.68/1.39 inference(avatar_component_clause,[status(thm)],[f361])).
% 1.68/1.39 thf(f361,definition,(
% 1.68/1.39 spl0_2 <=> ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3))))) = $false)),
% 1.68/1.39 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.68/1.39 thf(f92,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.68/1.39 thf(f91,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f90])).
% 1.68/1.39 thf(f90,plain,(
% 1.68/1.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.68/1.39 thf(f89,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f84])).
% 1.68/1.39 thf(f84,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.68/1.39 thf(f434,plain,(
% 1.68/1.39 ((in @ sK5 @ (dsetconstr @ sK2 @ sK3)) = $false) | ~spl0_2),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f432])).
% 1.68/1.39 thf(f144,plain,(
% 1.68/1.39 ((in @ sK4 @ (dsetconstr @ sK2 @ sK3)) = $true)),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f141])).
% 1.68/1.39 thf(f141,plain,(
% 1.68/1.39 (($true => (in @ sK4 @ (dsetconstr @ sK2 @ sK3))) = $true)),
% 1.68/1.39 inference(superposition,[status(thm)],[f138,f124])).
% 1.68/1.39 thf(f138,plain,(
% 1.68/1.39 ( ! [X0 : $i > $o] : ((((X0 @ sK4) => (in @ sK4 @ (dsetconstr @ sK2 @ X0))) = $true)) )),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f132])).
% 1.68/1.39 thf(f132,plain,(
% 1.68/1.39 ( ! [X0 : $i > $o] : ((($true => ((X0 @ sK4) => (in @ sK4 @ (dsetconstr @ sK2 @ X0)))) = $true)) )),
% 1.68/1.39 inference(superposition,[status(thm)],[f62,f127])).
% 1.68/1.39 thf(f62,plain,(
% 1.68/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((in @ X3 @ X2) => ((X1 @ X3) => (in @ X3 @ (dsetconstr @ X2 @ X1)))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.68/1.39 thf(f61,plain,(
% 1.68/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1))))) @ X3) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f60])).
% 1.68/1.39 thf(f60,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1)))))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.68/1.39 thf(f59,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1))))))) @ X2) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f58])).
% 1.68/1.39 thf(f58,plain,(
% 1.68/1.39 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1)))))))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.68/1.39 thf(f57,plain,(
% 1.68/1.39 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))) @ X1) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f41])).
% 1.68/1.39 thf(f363,plain,(
% 1.68/1.39 spl0_1 | spl0_2),
% 1.68/1.39 inference(avatar_split_clause,[status(thm)],[f356,f361,f358])).
% 1.68/1.39 thf(f356,plain,(
% 1.68/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) = $true)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f174])).
% 1.68/1.39 thf(f174,plain,(
% 1.68/1.39 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))))) = $true)),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f170])).
% 1.68/1.39 thf(f170,plain,(
% 1.68/1.39 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))) => $false)) = $true)),
% 1.68/1.39 inference(superposition,[status(thm)],[f95,f166])).
% 1.68/1.39 thf(f166,plain,(
% 1.68/1.39 ($false = ((setadjoin @ sK4 @ emptyset) = (dsetconstr @ sK2 @ sK3)))),
% 1.68/1.39 inference(boolean_simplification,[status(thm)],[f165])).
% 1.68/1.39 thf(f165,plain,(
% 1.68/1.39 ($false = ($true & ((setadjoin @ sK4 @ emptyset) = (dsetconstr @ sK2 @ sK3))))),
% 1.68/1.39 inference(superposition,[status(thm)],[f146,f144])).
% 1.68/1.39 thf(f146,plain,(
% 1.68/1.39 ( ! [X1 : $i] : (($false = ((in @ X1 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK2 @ sK3))))) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f145])).
% 1.68/1.39 thf(f145,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3)))) @ X1) = $false)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f116])).
% 1.68/1.39 thf(f116,plain,(
% 1.68/1.39 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3))))) = $false)),
% 1.68/1.39 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.68/1.39 thf(f95,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.68/1.39 thf(f94,plain,(
% 1.68/1.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))) @ X2) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f82])).
% 1.68/1.39 thf(f82,plain,(
% 1.68/1.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1))))) = $true)) )),
% 1.68/1.39 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.68/1.39 thf(f81,plain,(
% 1.68/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) @ X1) = $true)) )),
% 1.68/1.39 inference(pi_clausification,[status(thm)],[f78])).
% 1.68/1.39 % SZS output end Proof for DTF2THF_1177
% 1.68/1.39 % (1461)------------------------------
% 1.68/1.39 % (1461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (1461)Termination reason: Refutation
% 1.68/1.39
% 1.68/1.39 % (1461)Memory used [KB]: 6268
% 1.68/1.39 % (1461)Time elapsed: 0.054 s
% 1.68/1.39 % (1461)Instructions burned: 142 (million)
% 1.68/1.39 % (1461)------------------------------
% 1.68/1.39 % (1461)------------------------------
% 1.68/1.39 % (1449)Success in time 0.085 s
%------------------------------------------------------------------------------