%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU639^2 : 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 : n022.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 09:35:50 AM UTC 2026
% Result : Theorem 1.84s 1.46s
% Output : Refutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 11
% Syntax : Number of formulae : 151 ( 106 unt; 0 typ; 2 def)
% Number of atoms : 1343 ( 255 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 2391 ( 52 ~; 42 |; 26 &;1644 @)
% ( 2 <=>; 361 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 115 ( 115 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 17 con; 0-2 aty)
% ( 243 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 439 ( 328 ^; 109 !; 2 ?; 439 :)
% 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_12,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_29,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
sK2: $i > $o ).
thf(f625,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f347,f558,f622]) ).
thf(f622,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f621]) ).
thf(f621,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f620]) ).
thf(f620,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f150,f618]) ).
thf(f618,plain,
( ( $false
= ( in @ sK4 @ ( dsetconstr @ sK3 @ sK2 ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f571,f599]) ).
thf(f599,plain,
( ( sK6 = sK4 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f598]) ).
thf(f598,plain,
( ( ( sK4 = sK6 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f588]) ).
thf(f588,plain,
( ( ( $true
=> ( sK4 = sK6 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f103,f572]) ).
thf(f572,plain,
( ( $true
= ( in @ sK6 @ ( setadjoin @ sK4 @ emptyset ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f569]) ).
thf(f569,plain,
( ( ( ( in @ sK6 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ sK6 @ ( dsetconstr @ sK3 @ sK2 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f564]) ).
thf(f564,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) ) )
@ sK6 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f343]) ).
thf(f343,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f342]) ).
thf(f342,definition,
( spl0_1
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f103,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( $false
= ( ( !! @ $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 @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
= ( ( !! @ $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 @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $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 @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $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 @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $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 @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $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 @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
& ( ( setadjoin @ Y6 @ emptyset )
= Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f34,f37,f33,f35,f30,f31,f32,f38]) ).
thf(f38,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f29,f36]) ).
thf(f36,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,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.YHd0are7Zs/DTF2THF_11842.p',singleton) ).
thf(f29,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',ex1) ).
thf(f32,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= eqinunit ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X2: $i,X3: $i] :
( ( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= eqinunit ),
file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',eqinunit) ).
thf(f31,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( uniqinunit
= ( ! [X3: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',uniqinunit) ).
thf(f30,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)],[f23]) ).
thf(f23,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)],[f22]) ).
thf(f22,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.YHd0are7Zs/DTF2THF_11842.p',setext) ).
thf(f35,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)],[f17]) ).
thf(f17,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)],[f16]) ).
thf(f16,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.YHd0are7Zs/DTF2THF_11842.p',dsetconstrER) ).
thf(f33,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( in @ X2 @ X1 ) )
= dsetconstrEL ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',dsetconstrEL) ).
thf(f37,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
( dsetconstrI
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',dsetconstrI) ).
thf(f34,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ex1 @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ex1 @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( X0 = X3 ) ) )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( ex1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f9,conjecture,
( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( ex1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',ex1I) ).
thf(f571,plain,
( ( ( in @ sK6 @ ( dsetconstr @ sK3 @ sK2 ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f569]) ).
thf(f150,plain,
( $true
= ( in @ sK4 @ ( dsetconstr @ sK3 @ sK2 ) ) ),
inference(boolean_simplification,[status(thm)],[f145]) ).
thf(f145,plain,
( $true
= ( $true
=> ( in @ sK4 @ ( dsetconstr @ sK3 @ sK2 ) ) ) ),
inference(superposition,[status(thm)],[f135,f140]) ).
thf(f140,plain,
( ( sK2 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ( sK2 @ sK4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ( sK2 @ Y0 )
=> ( sK4 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ( in @ sK4 @ sK3 )
=> ( ( sK2 @ sK4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ( sK2 @ Y0 )
=> ( sK4 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ( sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( ( sK2 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ sK3 @ sK2 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ( sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( ( sK2 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ sK3 @ sK2 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f118]) ).
thf(f118,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( sK2 @ Y2 )
=> ( Y1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ sK2 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ sK2 ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( sK2 @ Y2 )
=> ( Y1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ sK2 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ sK2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f135,plain,
! [X0: $i > $o] :
( ( ( X0 @ sK4 )
=> ( in @ sK4 @ ( dsetconstr @ sK3 @ X0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f129]) ).
thf(f129,plain,
! [X0: $i > $o] :
( ( $true
=> ( ( X0 @ sK4 )
=> ( in @ sK4 @ ( dsetconstr @ sK3 @ X0 ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f55,f123]) ).
thf(f123,plain,
( $true
= ( in @ sK4 @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f55,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f558,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f557]) ).
thf(f557,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f556]) ).
thf(f556,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f555]) ).
thf(f555,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f477,f548]) ).
thf(f548,plain,
( ( $true
= ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f540]) ).
thf(f540,plain,
( ( ( $true
=> ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f114,f503]) ).
thf(f503,plain,
( ( $true
= ( sK4 = sK5 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f502]) ).
thf(f502,plain,
( ( ( $true
=> ( sK4 = sK5 ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f457,f495]) ).
thf(f495,plain,
( ( $true
= ( in @ sK5 @ sK3 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f485]) ).
thf(f485,plain,
( ( $true
= ( $true
=> ( in @ sK5 @ sK3 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f68,f435]) ).
thf(f435,plain,
( ( ( in @ sK5 @ ( dsetconstr @ sK3 @ sK2 ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f382]) ).
thf(f382,plain,
( ( $false
= ( ( in @ sK5 @ ( dsetconstr @ sK3 @ sK2 ) )
=> ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f376]) ).
thf(f376,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) )
@ sK5 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f353]) ).
thf(f353,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f346]) ).
thf(f346,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f345]) ).
thf(f345,definition,
( spl0_2
<=> ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f68,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
=> ( in @ X1 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( in @ X1 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( in @ X1 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f457,plain,
( ( $true
= ( ( in @ sK5 @ sK3 )
=> ( sK4 = sK5 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f454]) ).
thf(f454,plain,
( ( ( ( in @ sK5 @ sK3 )
=> ( $true
=> ( sK4 = sK5 ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f183,f438]) ).
thf(f438,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f437]) ).
thf(f437,plain,
( ( $false = $true )
| ( $true
= ( sK2 @ sK5 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f436]) ).
thf(f436,plain,
( ( ( $false
=> ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) ) )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f382,f82]) ).
thf(f82,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) )
| ( $true
= ( X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
=> ( X3 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,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)],[f77]) ).
thf(f77,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)],[f76]) ).
thf(f76,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f183,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK3 )
=> ( ( sK2 @ X1 )
=> ( sK4 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f182]) ).
thf(f182,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ( sK2 @ Y0 )
=> ( sK4 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ( sK2 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ( sK2 @ Y0 )
=> ( sK4 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f114,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
=> ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f113]) ).
thf(f113,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f111]) ).
thf(f111,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f477,plain,
( ( $true
= ( ~ ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f465]) ).
thf(f465,plain,
( ( ( ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f103,f460]) ).
thf(f460,plain,
( ( $false
= ( sK5 = sK4 ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f453]) ).
thf(f453,plain,
( ( ( sK5 != sK4 )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f441]) ).
thf(f441,plain,
( ( ( ( sK5 = sK4 )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f114,f440]) ).
thf(f440,plain,
( ( $false
= ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f439]) ).
thf(f439,plain,
( ( ( $true
=> ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f382,f435]) ).
thf(f347,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f340,f345,f342]) ).
thf(f340,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f247]) ).
thf(f247,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) )
=> ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
=> ( in @ Y0 @ ( setadjoin @ sK4 @ emptyset ) ) ) )
=> $false ) )
= $true ),
inference(superposition,[status(thm)],[f92,f242]) ).
thf(f242,plain,
( ( ( setadjoin @ sK4 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f241]) ).
thf(f241,plain,
( $false
= ( $true
& ( ( setadjoin @ sK4 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) ) ) ),
inference(superposition,[status(thm)],[f220,f150]) ).
thf(f220,plain,
! [X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ sK3 @ sK2 ) )
& ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f219]) ).
thf(f219,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK3 @ sK2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK3 @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( $true
= ( !! @ $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(binary_proxy_clausification,[status(thm)],[f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU639^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:29:21 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU639^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : Ordered Pairs - Singletons
% 0.28/0.46 % Version : Especial > Reduced > Especial.
% 0.28/0.46 % English : (! A:i.! phi:i>o.! x:i.in x A -> phi x -> (! y:i.in y A ->
% 0.28/0.46 % phi y -> y = x) -> ex1 A (^ y:i.phi y))
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC141l [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % 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 v5.3.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 21 ( 8 unt; 12 typ; 8 def)
% 0.28/0.46 % Number of atoms : 43 ( 13 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 10 ( 4 avg)
% 0.28/0.46 % Number of connectives : 76 ( 0 ~; 0 |; 1 &; 54 @)
% 0.28/0.46 % ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 17 ( 3 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 13 ( 12 usr; 7 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 30 ( 8 ^; 21 !; 1 ?; 30 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=196
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(in_type,type,
% 0.28/0.46 in: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset_type,type,
% 0.28/0.46 emptyset: $i ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin_type,type,
% 0.28/0.46 setadjoin: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr_type,type,
% 0.28/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI_type,type,
% 0.28/0.46 dsetconstrI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI,definition,
% 0.28/0.46 ( dsetconstrI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL_type,type,
% 0.28/0.46 dsetconstrEL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL,definition,
% 0.28/0.46 ( dsetconstrEL
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER_type,type,
% 0.28/0.46 dsetconstrER: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER,definition,
% 0.28/0.46 ( dsetconstrER
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setext_type,type,
% 0.28/0.46 setext: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setext,definition,
% 0.28/0.46 ( setext
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 => ( A = B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(uniqinunit_type,type,
% 0.28/0.46 uniqinunit: $o ).
% 0.28/0.46
% 0.28/0.46 thf(uniqinunit,definition,
% 0.28/0.46 ( uniqinunit
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(eqinunit_type,type,
% 0.28/0.46 eqinunit: $o ).
% 0.28/0.46
% 0.28/0.46 thf(eqinunit,definition,
% 0.28/0.46 ( eqinunit
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(singleton_type,type,
% 0.28/0.46 singleton: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(singleton,definition,
% 0.28/0.46 ( singleton
% 0.28/0.46 = ( ^ [A: $i] :
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( A
% 0.28/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(ex1_type,type,
% 0.28/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(ex1,definition,
% 0.28/0.46 ( ex1
% 0.28/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( singleton
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(ex1I,conjecture,
% 0.28/0.46 ( dsetconstrI
% 0.28/0.46 => ( dsetconstrEL
% 0.28/0.46 => ( dsetconstrER
% 0.28/0.46 => ( setext
% 0.28/0.46 => ( uniqinunit
% 0.28/0.46 => ( eqinunit
% 0.28/0.46 => ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 => ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xy = Xx ) ) )
% 0.28/0.46 => ( ex1 @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.70/1.36 ---- Embedded in THF ---
% 1.70/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.36 %%% Generated on Tue Feb 24 12:29:22 EST 2026
% 1.70/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.36 %%% Logic specification used:
% 1.70/1.36 %%% thf(spec, logic, $$dhol).
% 1.70/1.36
% 1.70/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2DTF11842.p
% See solution above
% 1.70/1.36 ------------------------
% 1.70/1.37 ---- Cleaned THF ---
% 1.70/1.37 thf(in_type,type,
% 1.70/1.37 in: $i > $i > $o ).
% 1.70/1.37
% 1.70/1.37 thf(emptyset_type,type,
% 1.70/1.37 emptyset: $i ).
% 1.70/1.37
% 1.70/1.37 thf(setadjoin_type,type,
% 1.70/1.37 setadjoin: $i > $i > $i ).
% 1.70/1.37
% 1.70/1.37 thf(dsetconstr_type,type,
% 1.70/1.37 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.70/1.37
% 1.70/1.37 thf(dsetconstrI_type,type,
% 1.70/1.37 dsetconstrI: $o ).
% 1.70/1.37
% 1.70/1.37 thf(dsetconstrI,definition,
% 1.70/1.37 ( dsetconstrI
% 1.70/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.70/1.37 ( ( in @ Xx @ A )
% 1.70/1.37 => ( ( Xphi @ Xx )
% 1.70/1.37 => ( in @ Xx
% 1.70/1.37 @ ( dsetconstr @ A
% 1.70/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.70/1.37
% 1.70/1.37 thf(dsetconstrEL_type,type,
% 1.70/1.37 dsetconstrEL: $o ).
% 1.70/1.37
% 1.70/1.37 thf(dsetconstrEL,definition,
% 1.70/1.37 ( dsetconstrEL
% 1.70/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.70/1.37 ( ( in @ Xx
% 1.70/1.37 @ ( dsetconstr @ A
% 1.70/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.70/1.37 => ( in @ Xx @ A ) ) ) ) ).
% 1.70/1.37
% 1.70/1.37 thf(dsetconstrER_type,type,
% 1.70/1.37 dsetconstrER: $o ).
% 1.70/1.37
% 1.70/1.37 thf(dsetconstrER,definition,
% 1.70/1.37 ( dsetconstrER
% 1.70/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.70/1.37 ( ( in @ Xx
% 1.70/1.37 @ ( dsetconstr @ A
% 1.70/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.70/1.37 => ( Xphi @ Xx ) ) ) ) ).
% 1.70/1.37
% 1.70/1.37 thf(setext_type,type,
% 1.70/1.37 setext: $o ).
% 1.70/1.37
% 1.70/1.37 thf(setext,definition,
% 1.70/1.37 ( setext
% 1.70/1.37 = ( ! [A: $i,B: $i] :
% 1.70/1.37 ( ! [Xx: $i] :
% 1.70/1.37 ( ( in @ Xx @ A )
% 1.70/1.37 => ( in @ Xx @ B ) )
% 1.70/1.37 => ( ! [Xx: $i] :
% 1.70/1.37 ( ( in @ Xx @ B )
% 1.70/1.37 => ( in @ Xx @ A ) )
% 1.70/1.37 => ( A = B ) ) ) ) ) ).
% 1.70/1.37
% 1.70/1.37 thf(uniqinunit_type,type,
% 1.70/1.37 uniqinunit: $o ).
% 1.70/1.37
% 1.70/1.37 thf(uniqinunit,definition,
% 1.70/1.37 ( uniqinunit
% 1.70/1.37 = ( ! [Xx: $i,Xy: $i] :
% 1.70/1.37 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.70/1.37 => ( Xx = Xy ) ) ) ) ).
% 1.70/1.37
% 1.70/1.37 thf(eqinunit_type,type,
% 1.70/1.37 eqinunit: $o ).
% 1.70/1.37
% 1.70/1.37 thf(eqinunit,definition,
% 1.70/1.37 ( eqinunit
% 1.70/1.37 = ( ! [Xx: $i,Xy: $i] :
% 1.70/1.37 ( ( Xx = Xy )
% 1.70/1.37 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.70/1.37
% 1.70/1.37 thf(singleton_type,type,
% 1.70/1.37 singleton: $i > $o ).
% 1.70/1.37
% 1.70/1.37 thf(singleton,definition,
% 1.70/1.37 ( singleton
% 1.70/1.37 = ( ^ [A: $i] :
% 1.70/1.37 ? [Xx: $i] :
% 1.70/1.37 ( ( in @ Xx @ A )
% 1.70/1.37 & ( A
% 1.70/1.37 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.70/1.37
% 1.70/1.37 thf(ex1_type,type,
% 1.70/1.37 ex1: $i > ( $i > $o ) > $o ).
% 1.70/1.37
% 1.70/1.37 thf(ex1,definition,
% 1.70/1.37 ( ex1
% 1.70/1.37 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.70/1.37 ( singleton
% 1.70/1.37 @ ( dsetconstr @ A
% 1.70/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.70/1.37
% 1.70/1.37 thf(ex1I,conjecture,
% 1.70/1.37 ( dsetconstrI
% 1.70/1.37 => ( dsetconstrEL
% 1.70/1.37 => ( dsetconstrER
% 1.70/1.37 => ( setext
% 1.70/1.37 => ( uniqinunit
% 1.70/1.37 => ( eqinunit
% 1.70/1.37 => ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.70/1.37 ( ( in @ Xx @ A )
% 1.70/1.37 => ( ( Xphi @ Xx )
% 1.70/1.37 => ( ! [Xy: $i] :
% 1.70/1.37 ( ( in @ Xy @ A )
% 1.70/1.37 => ( ( Xphi @ Xy )
% 1.70/1.37 => ( Xy = Xx ) ) )
% 1.70/1.37 => ( ex1 @ A
% 1.70/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ) ) ) ) ).
% 1.70/1.37 ------------------------
% 1.70/1.39 % (12119)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_11842 for (2999ds/4Mi)
% 1.70/1.39 % (12120)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_11842 for (2999ds/27Mi)
% 1.70/1.39 % (12119)Instruction limit reached!
% 1.70/1.39 % (12119)------------------------------
% 1.70/1.39 % (12119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (12119)Termination reason: Unknown
% 1.70/1.39 % (12119)Termination phase: Saturation
% 1.70/1.39
% 1.70/1.39 % (12119)Memory used [KB]: 5500
% 1.70/1.39 % (12119)Time elapsed: 0.003 s
% 1.70/1.39 % (12119)Instructions burned: 5 (million)
% 1.70/1.39 % (12119)------------------------------
% 1.70/1.39 % (12119)------------------------------
% 1.70/1.39 % (12118)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/183Mi)
% 1.70/1.39 % (12121)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/2Mi)
% 1.70/1.39 % (12122)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_11842 for (2999ds/2Mi)
% 1.70/1.40 % (12124)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/18Mi)
% 1.70/1.40 % (12123)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_11842 for (2999ds/275Mi)
% 1.70/1.40 % (12121)Instruction limit reached!
% 1.70/1.40 % (12121)------------------------------
% 1.70/1.40 % (12121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.40 % (12121)Termination reason: Unknown
% 1.70/1.40 % (12121)Termination phase: shuffling
% 1.70/1.40
% 1.70/1.40 % (12121)Memory used [KB]: 1023
% 1.70/1.40 % (12121)Time elapsed: 0.003 s
% 1.70/1.40 % (12121)Instructions burned: 2 (million)
% 1.70/1.40 % (12121)------------------------------
% 1.70/1.40 % (12121)------------------------------
% 1.70/1.40 % (12122)Instruction limit reached!
% 1.70/1.40 % (12122)------------------------------
% 1.70/1.40 % (12122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.40 % (12122)Termination reason: Unknown
% 1.70/1.40 % (12122)Termination phase: shuffling
% 1.70/1.40
% 1.70/1.40 % (12122)Memory used [KB]: 1023
% 1.70/1.40 % (12122)Time elapsed: 0.003 s
% 1.70/1.40 % (12122)Instructions burned: 2 (million)
% 1.70/1.40 % (12122)------------------------------
% 1.70/1.40 % (12122)------------------------------
% 1.84/1.40 % (12120)Instruction limit reached!
% 1.84/1.40 % (12120)------------------------------
% 1.84/1.40 % (12120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.40 % (12120)Termination reason: Unknown
% 1.84/1.40 % (12120)Termination phase: Saturation
% 1.84/1.40
% 1.84/1.40 % (12120)Memory used [KB]: 5628
% 1.84/1.40 % (12120)Time elapsed: 0.011 s
% 1.84/1.40 % (12120)Instructions burned: 28 (million)
% 1.84/1.40 % (12120)------------------------------
% 1.84/1.40 % (12120)------------------------------
% 1.84/1.40 % (12125)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/3Mi)
% 1.84/1.40 % (12125)Instruction limit reached!
% 1.84/1.40 % (12125)------------------------------
% 1.84/1.40 % (12125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.40 % (12125)Termination reason: Unknown
% 1.84/1.40 % (12125)Termination phase: Property scanning
% 1.84/1.40
% 1.84/1.40 % (12125)Memory used [KB]: 1023
% 1.84/1.40 % (12125)Time elapsed: 0.003 s
% 1.84/1.40 % (12125)Instructions burned: 4 (million)
% 1.84/1.40 % (12125)------------------------------
% 1.84/1.40 % (12125)------------------------------
% 1.84/1.41 % (12124)Instruction limit reached!
% 1.84/1.41 % (12124)------------------------------
% 1.84/1.41 % (12124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (12124)Termination reason: Unknown
% 1.84/1.41 % (12124)Termination phase: Saturation
% 1.84/1.41
% 1.84/1.41 % (12124)Memory used [KB]: 5628
% 1.84/1.41 % (12124)Time elapsed: 0.014 s
% 1.84/1.41 % (12124)Instructions burned: 19 (million)
% 1.84/1.41 % (12124)------------------------------
% 1.84/1.41 % (12124)------------------------------
% 1.84/1.41 % (12128)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_11842 for (2999ds/3Mi)
% 1.84/1.41 % (12128)Instruction limit reached!
% 1.84/1.41 % (12128)------------------------------
% 1.84/1.41 % (12128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (12128)Termination reason: Unknown
% 1.84/1.41 % (12128)Termination phase: Property scanning
% 1.84/1.41
% 1.84/1.41 % (12128)Memory used [KB]: 1023
% 1.84/1.41 % (12128)Time elapsed: 0.003 s
% 1.84/1.41 % (12128)Instructions burned: 4 (million)
% 1.84/1.41 % (12128)------------------------------
% 1.84/1.41 % (12128)------------------------------
% 1.84/1.41 % (12129)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_11842 for (2999ds/1041Mi)
% 1.84/1.41 % (12126)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_11842 for (2999ds/37Mi)
% 1.84/1.41 % (12127)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_11842 for (2999ds/15Mi)
% 1.84/1.42 % (12131)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/16Mi)
% 1.84/1.42 % (12127)Instruction limit reached!
% 1.84/1.42 % (12127)------------------------------
% 1.84/1.42 % (12127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.42 % (12127)Termination reason: Unknown
% 1.84/1.42 % (12127)Termination phase: Saturation
% 1.84/1.42
% 1.84/1.42 % (12127)Memory used [KB]: 5628
% 1.84/1.42 % (12127)Time elapsed: 0.012 s
% 1.84/1.42 % (12127)Instructions burned: 15 (million)
% 1.84/1.42 % (12127)------------------------------
% 1.84/1.42 % (12127)------------------------------
% 1.84/1.42 % (12130)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/7Mi)
% 1.84/1.43 % (12131)Instruction limit reached!
% 1.84/1.43 % (12131)------------------------------
% 1.84/1.43 % (12131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.43 % (12131)Termination reason: Unknown
% 1.84/1.43 % (12131)Termination phase: Saturation
% 1.84/1.43
% 1.84/1.43 % (12131)Memory used [KB]: 5884
% 1.84/1.43 % (12131)Time elapsed: 0.008 s
% 1.84/1.43 % (12131)Instructions burned: 17 (million)
% 1.84/1.43 % (12131)------------------------------
% 1.84/1.43 % (12131)------------------------------
% 1.84/1.43 % (12130)Instruction limit reached!
% 1.84/1.43 % (12130)------------------------------
% 1.84/1.43 % (12130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.43 % (12130)Termination reason: Unknown
% 1.84/1.43 % (12130)Termination phase: Saturation
% 1.84/1.43
% 1.84/1.43 % (12130)Memory used [KB]: 1023
% 1.84/1.43 % (12130)Time elapsed: 0.006 s
% 1.84/1.43 % (12130)Instructions burned: 8 (million)
% 1.84/1.43 % (12130)------------------------------
% 1.84/1.43 % (12130)------------------------------
% 1.84/1.44 % (12126)Instruction limit reached!
% 1.84/1.44 % (12126)------------------------------
% 1.84/1.44 % (12126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.44 % (12126)Termination reason: Unknown
% 1.84/1.44 % (12126)Termination phase: Saturation
% 1.84/1.44
% 1.84/1.44 % (12126)Memory used [KB]: 5756
% 1.84/1.44 % (12126)Time elapsed: 0.024 s
% 1.84/1.44 % (12126)Instructions burned: 38 (million)
% 1.84/1.44 % (12126)------------------------------
% 1.84/1.44 % (12126)------------------------------
% 1.84/1.44 % (12133)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_11842 for (2999ds/3Mi)
% 1.84/1.44 % (12133)Instruction limit reached!
% 1.84/1.44 % (12133)------------------------------
% 1.84/1.44 % (12133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.44 % (12133)Termination reason: Unknown
% 1.84/1.44 % (12133)Termination phase: Function definition elimination
% 1.84/1.44
% 1.84/1.44 % (12133)Memory used [KB]: 1023
% 1.84/1.44 % (12133)Time elapsed: 0.003 s
% 1.84/1.44 % (12133)Instructions burned: 4 (million)
% 1.84/1.44 % (12133)------------------------------
% 1.84/1.44 % (12133)------------------------------
% 1.84/1.44 % (12132)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_11842 for (2999ds/3Mi)
% 1.84/1.44 % (12132)Instruction limit reached!
% 1.84/1.44 % (12132)------------------------------
% 1.84/1.44 % (12132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.44 % (12132)Termination reason: Unknown
% 1.84/1.44 % (12132)Termination phase: Property scanning
% 1.84/1.44
% 1.84/1.44 % (12132)Memory used [KB]: 1023
% 1.84/1.44 % (12132)Time elapsed: 0.004 s
% 1.84/1.44 % (12132)Instructions burned: 4 (million)
% 1.84/1.44 % (12132)------------------------------
% 1.84/1.44 % (12132)------------------------------
% 1.84/1.45 % (12134)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/7Mi)
% 1.84/1.45 % (12136)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/4Mi)
% 1.84/1.45 % (12136)Instruction limit reached!
% 1.84/1.45 % (12136)------------------------------
% 1.84/1.45 % (12136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.45 % (12136)Termination reason: Unknown
% 1.84/1.45 % (12136)Termination phase: Property scanning
% 1.84/1.45
% 1.84/1.45 % (12136)Memory used [KB]: 1023
% 1.84/1.45 % (12136)Time elapsed: 0.003 s
% 1.84/1.45 % (12136)Instructions burned: 5 (million)
% 1.84/1.45 % (12136)------------------------------
% 1.84/1.45 % (12136)------------------------------
% 1.84/1.45 % (12134)Refutation not found, incomplete strategy
% 1.84/1.45 % (12134)------------------------------
% 1.84/1.45 % (12134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.45 % (12134)Termination reason: Refutation not found, incomplete strategy
% 1.84/1.45
% 1.84/1.45
% 1.84/1.45 % (12134)Memory used [KB]: 5500
% 1.84/1.45 % (12134)Time elapsed: 0.005 s
% 1.84/1.45 % (12134)Instructions burned: 6 (million)
% 1.84/1.45 % (12134)------------------------------
% 1.84/1.45 % (12134)------------------------------
% 1.84/1.45 % (12135)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/3Mi)
% 1.84/1.45 % (12135)Instruction limit reached!
% 1.84/1.45 % (12135)------------------------------
% 1.84/1.45 % (12135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.45 % (12135)Termination reason: Unknown
% 1.84/1.45 % (12135)Termination phase: Property scanning
% 1.84/1.45
% 1.84/1.45 % (12135)Memory used [KB]: 1023
% 1.84/1.45 % (12135)Time elapsed: 0.003 s
% 1.84/1.45 % (12135)Instructions burned: 3 (million)
% 1.84/1.45 % (12135)------------------------------
% 1.84/1.45 % (12135)------------------------------
% 1.84/1.45 % (12137)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/18Mi)
% 1.84/1.46 % (12138)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11842 for (2999ds/710Mi)
% 1.84/1.46 % (12129)First to succeed.
% 1.84/1.46 % (12137)Instruction limit reached!
% 1.84/1.46 % (12137)------------------------------
% 1.84/1.46 % (12137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.46 % (12137)Termination reason: Unknown
% 1.84/1.46 % (12137)Termination phase: Saturation
% 1.84/1.46
% 1.84/1.46 % (12137)Memory used [KB]: 5628
% 1.84/1.46 % (12137)Time elapsed: 0.008 s
% 1.84/1.46 % (12137)Instructions burned: 18 (million)
% 1.84/1.46 % (12137)------------------------------
% 1.84/1.46 % (12137)------------------------------
% 1.84/1.46 % (12129)Refutation found. Thanks to Tanya!
% 1.84/1.46 % SZS status Theorem for DTF2THF_11842
% 1.84/1.46 % SZS output start Proof for DTF2THF_11842
% 1.84/1.46 thf(func_def_0, type, in: $i > $i > $o).
% 1.84/1.46 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.84/1.46 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.84/1.46 thf(func_def_11, type, singleton: $i > $o).
% 1.84/1.46 thf(func_def_12, type, ex1: $i > ($i > $o) > $o).
% 1.84/1.46 thf(func_def_29, type, ph1: !>[X0: $tType]:(X0)).
% 1.84/1.46 thf(func_def_30, type, sK2: $i > $o).
% 1.84/1.46 thf(f625,plain,(
% 1.84/1.46 $false),
% 1.84/1.46 inference(avatar_sat_refutation,[status(thm)],[f347,f558,f622])).
% 1.84/1.46 thf(f622,plain,(
% 1.84/1.46 ~spl0_1),
% 1.84/1.46 inference(avatar_contradiction_clause,[status(thm)],[f621])).
% 1.84/1.46 thf(f621,plain,(
% 1.84/1.46 $false | ~spl0_1),
% 1.84/1.46 inference(trivial_inequality_removal,[status(thm)],[f620])).
% 1.84/1.46 thf(f620,plain,(
% 1.84/1.46 ($false = $true) | ~spl0_1),
% 1.84/1.46 inference(backward_demodulation,[status(thm)],[f150,f618])).
% 1.84/1.46 thf(f618,plain,(
% 1.84/1.46 ($false = (in @ sK4 @ (dsetconstr @ sK3 @ sK2))) | ~spl0_1),
% 1.84/1.46 inference(backward_demodulation,[status(thm)],[f571,f599])).
% 1.84/1.46 thf(f599,plain,(
% 1.84/1.46 (sK6 = sK4) | ~spl0_1),
% 1.84/1.46 inference(equality_proxy_clausification,[status(thm)],[f598])).
% 1.84/1.46 thf(f598,plain,(
% 1.84/1.46 ((sK4 = sK6) = $true) | ~spl0_1),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f588])).
% 1.84/1.46 thf(f588,plain,(
% 1.84/1.46 (($true => (sK4 = sK6)) = $true) | ~spl0_1),
% 1.84/1.46 inference(superposition,[status(thm)],[f103,f572])).
% 1.84/1.46 thf(f572,plain,(
% 1.84/1.46 ($true = (in @ sK6 @ (setadjoin @ sK4 @ emptyset))) | ~spl0_1),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f569])).
% 1.84/1.46 thf(f569,plain,(
% 1.84/1.46 (((in @ sK6 @ (setadjoin @ sK4 @ emptyset)) => (in @ sK6 @ (dsetconstr @ sK3 @ sK2))) = $false) | ~spl0_1),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f564])).
% 1.84/1.46 thf(f564,plain,(
% 1.84/1.46 (((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2)))) @ sK6) = $false) | ~spl0_1),
% 1.84/1.46 inference(sigma_clausification,[status(thm)],[f343])).
% 1.84/1.46 thf(f343,plain,(
% 1.84/1.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) = $false) | ~spl0_1),
% 1.84/1.46 inference(avatar_component_clause,[status(thm)],[f342])).
% 1.84/1.46 thf(f342,definition,(
% 1.84/1.46 spl0_1 <=> ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) = $false)),
% 1.84/1.46 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.84/1.46 thf(f103,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (X2 = X1)))) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.84/1.46 thf(f102,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ emptyset)) => (Y0 = X1))) @ X2) = $true)) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f101])).
% 1.84/1.46 thf(f101,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ emptyset)) => (Y0 = X1)))))) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.84/1.46 thf(f100,plain,(
% 1.84/1.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))) @ X1) = $true)) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f95])).
% 1.84/1.46 thf(f95,plain,(
% 1.84/1.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) = $true)),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.84/1.46 thf(f83,plain,(
% 1.84/1.46 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))))))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.84/1.46 thf(f70,plain,(
% 1.84/1.46 ($false = ((!! @ $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 @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))))))))))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.84/1.46 thf(f57,plain,(
% 1.84/1.46 ($false = ((!! @ $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 @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))))))))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.84/1.46 thf(f44,plain,(
% 1.84/1.46 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $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 @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))))))))))) = $false)),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.84/1.46 thf(f41,plain,(
% 1.84/1.46 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $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 @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))))))))) = $false)),
% 1.84/1.46 inference(not_proxy_clausification,[status(thm)],[f40])).
% 1.84/1.46 thf(f40,plain,(
% 1.84/1.46 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $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 @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))))))))))))) = $true)),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.84/1.46 thf(f39,plain,(
% 1.84/1.46 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y0 @ Y1)))))))) => ((!! @ $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 @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) & ((setadjoin @ Y6 @ emptyset) = Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))))))))))),
% 1.84/1.46 inference(definition_unfolding,[status(thm)],[f34,f37,f33,f35,f30,f31,f32,f38])).
% 1.84/1.46 thf(f38,plain,(
% 1.84/1.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.84/1.46 inference(definition_unfolding,[status(thm)],[f29,f36])).
% 1.84/1.46 thf(f36,plain,(
% 1.84/1.46 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.84/1.46 inference(cnf_transformation,[status(thm)],[f27])).
% 1.84/1.46 thf(f27,plain,(
% 1.84/1.46 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.84/1.46 inference(fool_elimination,[status(thm)],[f26])).
% 1.84/1.46 thf(f26,plain,(
% 1.84/1.46 ((^[X0 : $i] : (? [X1 : $i] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))) = singleton)),
% 1.84/1.46 inference(rectify,[status(thm)],[f7])).
% 1.84/1.46 thf(f7,axiom,(
% 1.84/1.46 ((^[X0 : $i] : (? [X2 : $i] : (((setadjoin @ X2 @ emptyset) = X0) & (in @ X2 @ X0)))) = singleton)),
% 1.84/1.46 file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',singleton)).
% 1.84/1.46 thf(f29,plain,(
% 1.84/1.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.84/1.46 inference(cnf_transformation,[status(thm)],[f28])).
% 1.84/1.46 thf(f28,plain,(
% 1.84/1.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.84/1.46 inference(fool_elimination,[status(thm)],[f8])).
% 1.84/1.46 thf(f8,axiom,(
% 1.84/1.46 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 1.84/1.46 file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',ex1)).
% 1.84/1.46 thf(f32,plain,(
% 1.84/1.46 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 1.84/1.46 inference(cnf_transformation,[status(thm)],[f13])).
% 1.84/1.46 thf(f13,plain,(
% 1.84/1.46 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 1.84/1.46 inference(fool_elimination,[status(thm)],[f12])).
% 1.84/1.46 thf(f12,plain,(
% 1.84/1.46 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))) = eqinunit)),
% 1.84/1.46 inference(rectify,[status(thm)],[f6])).
% 1.84/1.46 thf(f6,axiom,(
% 1.84/1.46 (! [X2 : $i,X3 : $i] : ((X2 = X3) => (in @ X2 @ (setadjoin @ X3 @ emptyset))) = eqinunit)),
% 1.84/1.46 file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',eqinunit)).
% 1.84/1.46 thf(f31,plain,(
% 1.84/1.46 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 1.84/1.46 inference(cnf_transformation,[status(thm)],[f21])).
% 1.84/1.46 thf(f21,plain,(
% 1.84/1.46 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 1.84/1.46 inference(fool_elimination,[status(thm)],[f20])).
% 1.84/1.46 thf(f20,plain,(
% 1.84/1.46 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)))),
% 1.84/1.46 inference(rectify,[status(thm)],[f5])).
% 1.84/1.46 thf(f5,axiom,(
% 1.84/1.46 (uniqinunit = ! [X3 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X3 @ emptyset)) => (X2 = X3)))),
% 1.84/1.46 file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',uniqinunit)).
% 1.84/1.46 thf(f30,plain,(
% 1.84/1.46 (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))))))))),
% 1.84/1.46 inference(cnf_transformation,[status(thm)],[f23])).
% 1.84/1.46 thf(f23,plain,(
% 1.84/1.46 (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))))))))),
% 1.84/1.46 inference(fool_elimination,[status(thm)],[f22])).
% 1.84/1.46 thf(f22,plain,(
% 1.84/1.46 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))) = setext)),
% 1.84/1.46 inference(rectify,[status(thm)],[f4])).
% 1.84/1.46 thf(f4,axiom,(
% 1.84/1.46 (! [X0 : $i,X4 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X4)) => (! [X2 : $i] : ((in @ X2 @ X4) => (in @ X2 @ X0)) => (X0 = X4))) = setext)),
% 1.84/1.46 file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',setext)).
% 1.84/1.46 thf(f35,plain,(
% 1.84/1.46 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 1.84/1.46 inference(cnf_transformation,[status(thm)],[f17])).
% 1.84/1.46 thf(f17,plain,(
% 1.84/1.46 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 1.84/1.46 inference(fool_elimination,[status(thm)],[f16])).
% 1.84/1.46 thf(f16,plain,(
% 1.84/1.46 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 1.84/1.46 inference(rectify,[status(thm)],[f3])).
% 1.84/1.46 thf(f3,axiom,(
% 1.84/1.46 (! [X1 : $i > $o,X0 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.84/1.46 file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',dsetconstrER)).
% 1.84/1.46 thf(f33,plain,(
% 1.84/1.46 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y0 @ Y1)))))))))),
% 1.84/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.46 thf(f19,plain,(
% 1.84/1.46 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y0 @ Y1)))))))))),
% 1.84/1.46 inference(fool_elimination,[status(thm)],[f18])).
% 1.84/1.46 thf(f18,plain,(
% 1.84/1.46 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (in @ X2 @ X1)) = dsetconstrEL)),
% 1.84/1.46 inference(rectify,[status(thm)],[f2])).
% 1.84/1.46 thf(f2,axiom,(
% 1.84/1.46 (! [X1 : $i > $o,X0 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 1.84/1.46 file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',dsetconstrEL)).
% 1.84/1.46 thf(f37,plain,(
% 1.84/1.46 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.84/1.46 inference(cnf_transformation,[status(thm)],[f25])).
% 1.84/1.46 thf(f25,plain,(
% 1.84/1.46 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.84/1.46 inference(fool_elimination,[status(thm)],[f24])).
% 1.84/1.46 thf(f24,plain,(
% 1.84/1.46 (dsetconstrI = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 1.84/1.46 inference(rectify,[status(thm)],[f1])).
% 1.84/1.46 thf(f1,axiom,(
% 1.84/1.46 (dsetconstrI = ! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.84/1.46 file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',dsetconstrI)).
% 1.84/1.46 thf(f34,plain,(
% 1.84/1.46 ((~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))))))))) = $true)),
% 1.84/1.46 inference(cnf_transformation,[status(thm)],[f15])).
% 1.84/1.46 thf(f15,plain,(
% 1.84/1.46 ((~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))))))))) = $true)),
% 1.84/1.46 inference(fool_elimination,[status(thm)],[f14])).
% 1.84/1.46 thf(f14,plain,(
% 1.84/1.46 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (! [X3 : $i] : ((in @ X3 @ X1) => ((X2 @ X3) => (X0 = X3))) => (ex1 @ X1 @ (^[X4 : $i] : (X2 @ X4))))))))))))),
% 1.84/1.46 inference(rectify,[status(thm)],[f10])).
% 1.84/1.46 thf(f10,negated_conjecture,(
% 1.84/1.46 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X3) => (X2 = X3))) => (ex1 @ X0 @ (^[X3 : $i] : (X1 @ X3))))))))))))),
% 1.84/1.46 inference(negated_conjecture,[status(cth)],[f9])).
% 1.84/1.46 thf(f9,conjecture,(
% 1.84/1.46 dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X3) => (X2 = X3))) => (ex1 @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))))))),
% 1.84/1.46 file('/export/starexec/sandbox2/tmp/tmp.YHd0are7Zs/DTF2THF_11842.p',ex1I)).
% 1.84/1.46 thf(f571,plain,(
% 1.84/1.46 ((in @ sK6 @ (dsetconstr @ sK3 @ sK2)) = $false) | ~spl0_1),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f569])).
% 1.84/1.46 thf(f150,plain,(
% 1.84/1.46 ($true = (in @ sK4 @ (dsetconstr @ sK3 @ sK2)))),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f145])).
% 1.84/1.46 thf(f145,plain,(
% 1.84/1.46 ($true = ($true => (in @ sK4 @ (dsetconstr @ sK3 @ sK2))))),
% 1.84/1.46 inference(superposition,[status(thm)],[f135,f140])).
% 1.84/1.46 thf(f140,plain,(
% 1.84/1.46 ((sK2 @ sK4) = $true)),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.84/1.46 thf(f122,plain,(
% 1.84/1.46 (((sK2 @ sK4) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ Y0) => (sK4 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2))))))) = $false)),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.84/1.46 thf(f121,plain,(
% 1.84/1.46 (((in @ sK4 @ sK3) => ((sK2 @ sK4) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ Y0) => (sK4 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2)))))))) = $false)),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.84/1.46 thf(f120,plain,(
% 1.84/1.46 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((sK2 @ Y1) => (Y0 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK3 @ sK2)) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK3 @ sK2))))))))) @ sK4))),
% 1.84/1.46 inference(sigma_clausification,[status(thm)],[f119])).
% 1.84/1.46 thf(f119,plain,(
% 1.84/1.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((sK2 @ Y1) => (Y0 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK3 @ sK2)) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK3 @ sK2)))))))))) = $false)),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f118])).
% 1.84/1.46 thf(f118,plain,(
% 1.84/1.46 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((sK2 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((sK2 @ Y2) => (Y1 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ sK2)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ sK2))))))))))) @ sK3))),
% 1.84/1.46 inference(sigma_clausification,[status(thm)],[f117])).
% 1.84/1.46 thf(f117,plain,(
% 1.84/1.46 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((sK2 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((sK2 @ Y2) => (Y1 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ sK2)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ sK2)))))))))))))),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.84/1.46 thf(f116,plain,(
% 1.84/1.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))))) @ sK2) = $false)),
% 1.84/1.46 inference(sigma_clausification,[status(thm)],[f105])).
% 1.84/1.46 thf(f105,plain,(
% 1.84/1.46 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) = $false)),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.84/1.46 thf(f94,plain,(
% 1.84/1.46 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))))))) = $false)),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.84/1.46 thf(f135,plain,(
% 1.84/1.46 ( ! [X0 : $i > $o] : ((((X0 @ sK4) => (in @ sK4 @ (dsetconstr @ sK3 @ X0))) = $true)) )),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f129])).
% 1.84/1.46 thf(f129,plain,(
% 1.84/1.46 ( ! [X0 : $i > $o] : ((($true => ((X0 @ sK4) => (in @ sK4 @ (dsetconstr @ sK3 @ X0)))) = $true)) )),
% 1.84/1.46 inference(superposition,[status(thm)],[f55,f123])).
% 1.84/1.46 thf(f123,plain,(
% 1.84/1.46 ($true = (in @ sK4 @ sK3))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.84/1.46 thf(f55,plain,(
% 1.84/1.46 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X2 @ X1) => ((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3)))))) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.84/1.46 thf(f54,plain,(
% 1.84/1.46 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0))))) @ X3))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f53])).
% 1.84/1.46 thf(f53,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0)))))))) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.84/1.46 thf(f52,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1))))))) @ X2))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f51])).
% 1.84/1.46 thf(f51,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1)))))))))) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.84/1.46 thf(f50,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2))))))))) @ X1))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f45])).
% 1.84/1.46 thf(f45,plain,(
% 1.84/1.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) = $true)),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.84/1.46 thf(f558,plain,(
% 1.84/1.46 ~spl0_2),
% 1.84/1.46 inference(avatar_contradiction_clause,[status(thm)],[f557])).
% 1.84/1.46 thf(f557,plain,(
% 1.84/1.46 $false | ~spl0_2),
% 1.84/1.46 inference(trivial_inequality_removal,[status(thm)],[f556])).
% 1.84/1.46 thf(f556,plain,(
% 1.84/1.46 ($false = $true) | ~spl0_2),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f555])).
% 1.84/1.46 thf(f555,plain,(
% 1.84/1.46 ($true = (~ $true)) | ~spl0_2),
% 1.84/1.46 inference(backward_demodulation,[status(thm)],[f477,f548])).
% 1.84/1.46 thf(f548,plain,(
% 1.84/1.46 ($true = (in @ sK4 @ (setadjoin @ sK5 @ emptyset))) | ~spl0_2),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f540])).
% 1.84/1.46 thf(f540,plain,(
% 1.84/1.46 (($true => (in @ sK4 @ (setadjoin @ sK5 @ emptyset))) = $true) | ~spl0_2),
% 1.84/1.46 inference(superposition,[status(thm)],[f114,f503])).
% 1.84/1.46 thf(f503,plain,(
% 1.84/1.46 ($true = (sK4 = sK5)) | ~spl0_2),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f502])).
% 1.84/1.46 thf(f502,plain,(
% 1.84/1.46 (($true => (sK4 = sK5)) = $true) | ~spl0_2),
% 1.84/1.46 inference(backward_demodulation,[status(thm)],[f457,f495])).
% 1.84/1.46 thf(f495,plain,(
% 1.84/1.46 ($true = (in @ sK5 @ sK3)) | ~spl0_2),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f485])).
% 1.84/1.46 thf(f485,plain,(
% 1.84/1.46 ($true = ($true => (in @ sK5 @ sK3))) | ~spl0_2),
% 1.84/1.46 inference(superposition,[status(thm)],[f68,f435])).
% 1.84/1.46 thf(f435,plain,(
% 1.84/1.46 ((in @ sK5 @ (dsetconstr @ sK3 @ sK2)) = $true) | ~spl0_2),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f382])).
% 1.84/1.46 thf(f382,plain,(
% 1.84/1.46 ($false = ((in @ sK5 @ (dsetconstr @ sK3 @ sK2)) => (in @ sK5 @ (setadjoin @ sK4 @ emptyset)))) | ~spl0_2),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f376])).
% 1.84/1.46 thf(f376,plain,(
% 1.84/1.46 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))) @ sK5)) | ~spl0_2),
% 1.84/1.46 inference(sigma_clausification,[status(thm)],[f353])).
% 1.84/1.46 thf(f353,plain,(
% 1.84/1.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))) = $false) | ~spl0_2),
% 1.84/1.46 inference(not_proxy_clausification,[status(thm)],[f346])).
% 1.84/1.46 thf(f346,plain,(
% 1.84/1.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))))) | ~spl0_2),
% 1.84/1.46 inference(avatar_component_clause,[status(thm)],[f345])).
% 1.84/1.46 thf(f345,definition,(
% 1.84/1.46 spl0_2 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))))),
% 1.84/1.46 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.84/1.46 thf(f68,plain,(
% 1.84/1.46 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X1 @ (dsetconstr @ X2 @ X3)) => (in @ X1 @ X2)) = $true)) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.84/1.46 thf(f67,plain,(
% 1.84/1.46 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (in @ X1 @ X2))) @ X3) = $true)) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f66])).
% 1.84/1.46 thf(f66,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (in @ X1 @ X2)))) = $true)) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.84/1.46 thf(f65,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (in @ X1 @ Y0))))) @ X2))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f64])).
% 1.84/1.46 thf(f64,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (in @ X1 @ Y0)))))) = $true)) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.84/1.46 thf(f63,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1))))))) @ X1))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f58])).
% 1.84/1.46 thf(f58,plain,(
% 1.84/1.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) = $true)),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.84/1.46 thf(f457,plain,(
% 1.84/1.46 ($true = ((in @ sK5 @ sK3) => (sK4 = sK5))) | ~spl0_2),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f454])).
% 1.84/1.46 thf(f454,plain,(
% 1.84/1.46 (((in @ sK5 @ sK3) => ($true => (sK4 = sK5))) = $true) | ~spl0_2),
% 1.84/1.46 inference(superposition,[status(thm)],[f183,f438])).
% 1.84/1.46 thf(f438,plain,(
% 1.84/1.46 ($true = (sK2 @ sK5)) | ~spl0_2),
% 1.84/1.46 inference(trivial_inequality_removal,[status(thm)],[f437])).
% 1.84/1.46 thf(f437,plain,(
% 1.84/1.46 ($false = $true) | ($true = (sK2 @ sK5)) | ~spl0_2),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f436])).
% 1.84/1.46 thf(f436,plain,(
% 1.84/1.46 (($false => (in @ sK5 @ (setadjoin @ sK4 @ emptyset))) = $false) | ($true = (sK2 @ sK5)) | ~spl0_2),
% 1.84/1.46 inference(superposition,[status(thm)],[f382,f82])).
% 1.84/1.46 thf(f82,plain,(
% 1.84/1.46 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ X2 @ X3))) | ($true = (X3 @ X1))) )),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.84/1.46 thf(f81,plain,(
% 1.84/1.46 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X1 @ (dsetconstr @ X2 @ X3)) => (X3 @ X1)) = $true)) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.84/1.46 thf(f80,plain,(
% 1.84/1.46 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1))) @ X3))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f79])).
% 1.84/1.46 thf(f79,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1)))) = $true)) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.84/1.46 thf(f78,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1))))) @ X2) = $true)) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f77])).
% 1.84/1.46 thf(f77,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1)))))) = $true)) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.84/1.46 thf(f76,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0))))))) @ X1))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f71])).
% 1.84/1.46 thf(f71,plain,(
% 1.84/1.46 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.84/1.46 thf(f183,plain,(
% 1.84/1.46 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => ((sK2 @ X1) => (sK4 = X1))) = $true)) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f182])).
% 1.84/1.46 thf(f182,plain,(
% 1.84/1.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ Y0) => (sK4 = Y0)))) @ X1) = $true)) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f170])).
% 1.84/1.46 thf(f170,plain,(
% 1.84/1.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ Y0) => (sK4 = Y0))))))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 1.84/1.46 thf(f139,plain,(
% 1.84/1.46 ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ Y0) => (sK4 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2)))))))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.84/1.46 thf(f114,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : ((((X2 = X1) => (in @ X2 @ (setadjoin @ X1 @ emptyset))) = $true)) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f113])).
% 1.84/1.46 thf(f113,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((Y0 = X1) => (in @ Y0 @ (setadjoin @ X1 @ emptyset)))) @ X2) = $true)) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f112])).
% 1.84/1.46 thf(f112,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => (in @ Y0 @ (setadjoin @ X1 @ emptyset))))))) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f111])).
% 1.84/1.46 thf(f111,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))) @ X1))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f106])).
% 1.84/1.46 thf(f106,plain,(
% 1.84/1.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) = $true)),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.84/1.46 thf(f477,plain,(
% 1.84/1.46 ($true = (~ (in @ sK4 @ (setadjoin @ sK5 @ emptyset)))) | ~spl0_2),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f465])).
% 1.84/1.46 thf(f465,plain,(
% 1.84/1.46 (((in @ sK4 @ (setadjoin @ sK5 @ emptyset)) => $false) = $true) | ~spl0_2),
% 1.84/1.46 inference(superposition,[status(thm)],[f103,f460])).
% 1.84/1.46 thf(f460,plain,(
% 1.84/1.46 ($false = (sK5 = sK4)) | ~spl0_2),
% 1.84/1.46 inference(not_proxy_clausification,[status(thm)],[f453])).
% 1.84/1.46 thf(f453,plain,(
% 1.84/1.46 ((~ (sK5 = sK4)) = $true) | ~spl0_2),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f441])).
% 1.84/1.46 thf(f441,plain,(
% 1.84/1.46 (((sK5 = sK4) => $false) = $true) | ~spl0_2),
% 1.84/1.46 inference(superposition,[status(thm)],[f114,f440])).
% 1.84/1.46 thf(f440,plain,(
% 1.84/1.46 ($false = (in @ sK5 @ (setadjoin @ sK4 @ emptyset))) | ~spl0_2),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f439])).
% 1.84/1.46 thf(f439,plain,(
% 1.84/1.46 (($true => (in @ sK5 @ (setadjoin @ sK4 @ emptyset))) = $false) | ~spl0_2),
% 1.84/1.46 inference(backward_demodulation,[status(thm)],[f382,f435])).
% 1.84/1.46 thf(f347,plain,(
% 1.84/1.46 spl0_1 | spl0_2),
% 1.84/1.46 inference(avatar_split_clause,[status(thm)],[f340,f345,f342])).
% 1.84/1.46 thf(f340,plain,(
% 1.84/1.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f256])).
% 1.84/1.46 thf(f256,plain,(
% 1.84/1.46 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))))) = $true)),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f247])).
% 1.84/1.46 thf(f247,plain,(
% 1.84/1.46 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))) => $false)) = $true)),
% 1.84/1.46 inference(superposition,[status(thm)],[f92,f242])).
% 1.84/1.46 thf(f242,plain,(
% 1.84/1.46 (((setadjoin @ sK4 @ emptyset) = (dsetconstr @ sK3 @ sK2)) = $false)),
% 1.84/1.46 inference(boolean_simplification,[status(thm)],[f241])).
% 1.84/1.46 thf(f241,plain,(
% 1.84/1.46 ($false = ($true & ((setadjoin @ sK4 @ emptyset) = (dsetconstr @ sK3 @ sK2))))),
% 1.84/1.46 inference(superposition,[status(thm)],[f220,f150])).
% 1.84/1.46 thf(f220,plain,(
% 1.84/1.46 ( ! [X1 : $i] : ((((in @ X1 @ (dsetconstr @ sK3 @ sK2)) & ((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK3 @ sK2))) = $false)) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f219])).
% 1.84/1.46 thf(f219,plain,(
% 1.84/1.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2)))) @ X1) = $false)) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f169])).
% 1.84/1.46 thf(f169,plain,(
% 1.84/1.46 ($false = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2))))))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 1.84/1.46 thf(f92,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.84/1.46 thf(f91,plain,(
% 1.84/1.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))) @ X2))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f90])).
% 1.84/1.46 thf(f90,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1))))))) )),
% 1.84/1.46 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.84/1.46 thf(f89,plain,(
% 1.84/1.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) @ X1))) )),
% 1.84/1.46 inference(pi_clausification,[status(thm)],[f84])).
% 1.84/1.46 thf(f84,plain,(
% 1.84/1.46 ($true = (!! @ $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))))))))),
% 1.84/1.46 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.84/1.46 % SZS output end Proof for DTF2THF_11842
% 1.84/1.46 % (12129)------------------------------
% 1.84/1.46 % (12129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.46 % (12129)Termination reason: Refutation
% 1.84/1.46
% 1.84/1.46 % (12129)Memory used [KB]: 6268
% 1.84/1.46 % (12129)Time elapsed: 0.054 s
% 1.84/1.46 % (12129)Instructions burned: 140 (million)
% 1.84/1.46 % (12129)------------------------------
% 1.84/1.46 % (12129)------------------------------
% 1.84/1.46 % (12117)Success in time 0.079 s
%------------------------------------------------------------------------------